C      ALGORITHM 807, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 26,NO. 4,  December, 2000, P.  602--616.
#! /bin/sh
# This is a shell archive, meaning:
# 1. Remove everything above the #! /bin/sh line.
# 2. Save the resulting text in a file.
# 3. Execute the file with /bin/sh (not csh) to create the files:
#	Doc/
#	Doc/Makefile.Dp
#	Doc/Makefile.Sp
#	Doc/README
#	Doc/install
#	Fortran77/
#	Fortran77/Dp/
#	Fortran77/Dp/Drivers/
#	Fortran77/Dp/Drivers/data1
#	Fortran77/Dp/Drivers/data2
#	Fortran77/Dp/Drivers/data3
#	Fortran77/Dp/Drivers/data4
#	Fortran77/Dp/Drivers/driver.f
#	Fortran77/Dp/Drivers/res1
#	Fortran77/Dp/Drivers/res2
#	Fortran77/Dp/Drivers/res3
#	Fortran77/Dp/Drivers/res4
#	Fortran77/Dp/Src/
#	Fortran77/Dp/Src/src.f
#	Fortran77/Sp/
#	Fortran77/Sp/Drivers/
#	Fortran77/Sp/Drivers/data1
#	Fortran77/Sp/Drivers/data2
#	Fortran77/Sp/Drivers/data3
#	Fortran77/Sp/Drivers/data4
#	Fortran77/Sp/Drivers/driver.f
#	Fortran77/Sp/Src/
#	Fortran77/Sp/Src/src.f
# This archive created: Fri Sep 14 15:00:12 2001
export PATH; PATH=/bin:$PATH
if test ! -d 'Doc'
then
	mkdir 'Doc'
fi
cd 'Doc'
if test -f 'Makefile.Dp'
then
	echo shar: will not over-write existing file "'Makefile.Dp'"
else
cat << "SHAR_EOF" > 'Makefile.Dp'
include makefile.inc
all: res1 res2 res3 res4
SRCLIBS= $(PORT) $(BLAS)
DRIVERLIBS = $(TIMER) $(LAPACK) 
Objs1= driver.o src.o

driver1: $(Objs1)
	$(F77LINK) $(F77LINKOPTS) -o driver1 $(Objs1) $(DRIVERLIBS) $(SRCLIBS)
res1: driver1 data1 
	driver1 <data1 >res1
res2: driver1 data2 
	driver1 <data2 >res2
res3: driver1 data3 
	driver1 <data3 >res3
res4: driver1 data4 
	driver1 <data4 >res4
SHAR_EOF
fi # end of overwriting check
if test -f 'Makefile.Sp'
then
	echo shar: will not over-write existing file "'Makefile.Sp'"
else
cat << "SHAR_EOF" > 'Makefile.Sp'
include makefile.inc
all: res1 res2 res3 res4
SRCLIBS= $(PORT) $(BLAS)
DRIVERLIBS = $(TIMER) $(LAPACK) 
Objs1= driver.o src.o

driver1: $(Objs1)
	$(F77LINK) $(F77LINKOPTS) -o driver1 $(Objs1) $(DRIVERLIBS) $(SRCLIBS)
res1: driver1 data1 
	driver1 <data1 >res1
res2: driver1 data2 
	driver1 <data2 >res2
res3: driver1 data3 
	driver1 <data3 >res3
res4: driver1 data4 
	driver1 <data4 >res4
SHAR_EOF
fi # end of overwriting check
if test -f 'README'
then
	echo shar: will not over-write existing file "'README'"
else
cat << "SHAR_EOF" > 'README'
--------------------------------------------------------------------------------
-                                                                              -
-                      README file for the SBR toolbox                         -
-                                                                              -
--------------------------------------------------------------------------------

Author: Bruno Lang
        Aachen University of Technology
        na.blang@na-net.ornl.gov
Date: May 17, 2000
Version: SBR Toolbox, Rev. 1.4.1

This file provides information for installing, tuning, and testing
the SBR toolbox library on a UNIX system.

Overview:

0.    The installation procedure
1.    Getting and unpacking the SBR toolbox
2.    Building the SBR library
  2.1    Editing the makefile
  2.2    Building
  2.3    Cross-compiling
3.    Performance tuning
4.    Running the testing driver
5.    Running additional timings
6.    Making the SBR toolbox available to other users
7.    Bug reports
8.    Revision history

% ------------------------------------------------------------------------------

0.    The installation procedure
      ==========================

The standard installation procedure is
   1. Get and unpack the SBR toolbox (see Sec. 1).
   2. Build the SBR library
   3. (Optional.) Performance tuning
   4. (Recommended.) Running the testing driver
   5. (Optional.) Running additional timings
   6. (Optional.) Making the SBR toolbox available to other users

If you are adventurous then try the following short cut.
Otherwise, or if anything goes wrong, follow the detailed instructions.

   1.   Get and unpack the SBR toolbox (see Sec. 1).

   2/4. Type

           make checks

        to build the library libSBR.a and to run the quick checks.

   6.   (Optional.) Move the library to a directory searched by the linker.

% ------------------------------------------------------------------------------

1.    Getting and unpacking the SBR toolbox
      =====================================

Get the file sbr.tar.Z and unpack it with the command

   zcat sbr.tar.Z | tar xf -

(Since you are reading this file you probably have already done both.)
This will create a new subdirectory sbr in the current working directory.
Change to this directory. The following files should be present:

   README                           this file

   makefile					a UNIX makefile for building the library
   make.inc					the file containing site-specific settings

   sbr.f                            the SBR toolbox routines
   drun.f                           the double-precision testing program
   srun.f                           the single-precision testing program
   INCHK                            input file for the test runs
   REFCHK                           sample output file from the testing driver
   INTUN1					input file for the first tuning phase
   INTUN2					input file for the second tuning phase
   INTIM 					input file for the additional timings

   la_ori.f					original LAPACK routines needed by the
						testing program
   la_mod.f					modified LAPACK routines needed by the
						testing program
   la_tmg.f					routines from the LAPACK test matrix
						generation suite, needed by the testing
						program
   aux_blas.f                       auxiliary routines for IBM RS machines
   etime.c                          timing routine for IBM RS machines

% ------------------------------------------------------------------------------

2.    Building the SBR library
      ========================

2.1   Editing the file make.inc
      -------------------------

Edit the file make.inc to match your system setup.
In particular, you may want to set:

  * F77           The name of the Fortran compiler (if you don't have a
                  Fortran77 compiler you can't build the library).

  * FF77OPTS      The compile flags for the Fortran compiler with optimization
			turned on.

  * F77LINK		The Fortran linker.

  * F77LINKOPTS	Options for the linker when optimization is on.

  * F77NOOPT      The compile flags for the Fortran compiler with optimization
			turned off.

  * FF77LINKNOOPT Options for the linker when optimization is off.

  * CC		The C compiler.

  * CCOPTS		Compile flags for the C compiler.

  * AR            The command (including flags) for building object archives.

  * RANLIB        The command for converting archives to random libraries.
                  If that's already done with $(AR), set RANLIB = echo.

  * SBR_LIB       The name of the resulting library will be lib$(SBR_LIB).a,
                  e.g., libSBR.a when the default setting SBR_LIB=SBR is used.

  * NEW_LIBS      Additional object files that must be compiled for the
			testing program.
  * OLD_LIBS	Linking options for pre-compiled objects, in particular the
			BLAS.

                  !!! If the BLAS are not already installed then you
                      must install them before installing the SBR toolbox !!!

			The testing program requires some LAPACK routines. There are
			two ways to provide these:

                  - You can compile just the required LAPACK routines; for
                    convenience, they are included in the files la_ori.f and
                    la_tmg.f of the SBR distribution. The makefile is
			  pre-configured to use this option.

                  - Instead you may link to an installed LAPACK library.
                    Then you can include the name of the LAPACK library
                    and the test matrix generation library in OLDLIBS:
                    e.g.,
                    NEW_LIBS  = la_mod.o
                    OLD_LIBS  = -lLAPACK -lTMG -lBLAS

                  Note that the modified LAPACK routines must be recompiled in
			any case.

                  Auxiliary objects: additional objects required for successful
                  linking may be specified in NEW_LIBS:

                  - The ESSL library does not contain the lsame and xerbla
                    functions. Also, etime is provided for timing.

% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

2.2   Building
      --------

Type

   make library

to build the SBR library.

% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

2.3   Cross-compiling
      ---------------

If the compile server is not identical to the target machine for which the
library is built then you must issue a

   make drivers

on the compile server before running the performance tuning and testing driver
on the target machine.
Otherwise, the programs will be compiled on the target machine or be run on
the compile server.
(If you do not intend to run the divers, you may omit this step.)

% ------------------------------------------------------------------------------

3.    Performance tuning
      ==================

The block sizes for the blocked Householder transformations in the SBR toolbox
routines are set in the function NBDFLT, which is the first routine in sbr.f.
The default settings may be adequate to obtain reasonable performance on a
variety of platforms, but for optimal performance this function must be adapted
to the machine.

The toolbox comes with double-precision and single-precision drivers and an
input file for timing the routines DSYRDB (SSYRDB), DSBRDB (SSBRDB), and
DSBRDT (SSBRDT) with matrices of specified size and varying bandwidths and
block sizes. The output of the drivers helps to determine a function that can
compute a (nearly) optimal block size for a given matrix.

* To (build and) run the drivers, have a look at the file INTUN1 (in particular
  you might want to uncomment one of the 'MaxDim' lines at the beginning -
  remember that the time grows cubically with the matrix dimension) and then
  type

     make tuning1

  This command may take a few minutes to complete (about half an hour on a
  400 MHz PentiumII, if the matrix size is not restricted).
  The drivers, 'drun' and 'srun' read the file INTUN1 and produce two output
  files, DOUTTUN1 and SOUTTUN1.

These two files contain the data necessary to determine an optimum block
size: the order and semibandwidth(s) of the matrix, the block size, and the
time required.

In general, the optimum block size will depend on many factors, e.g.,
- the semibandwidth of the matrix before and after the reduction,
- are the transformations accumulated in another matrix U or not ? ,
- the working precision (single or double)
- is the upper or lower triangle of the mattrix worked upon (routines
  DSYRDB and SSYRDB only) ? , and
- the dimension of the matrix.
We have listed the factors with respect to decreasing importance.

In our experience, it is sufficient to consider only the number of diagonals
REMOVED (provided in the variable DELTAB in NBDFLT) for the band reduction
routines, or the matrix size for the reduction of full matrices.
In addition, the working precision (provided in the logical variable SINGLE)
and the accumulation of the transformations (logical variable NEEDU) must
be taken into account.

Therefore, the code for determining a nearly optimal block size for one of
the reduction routines might look like

   IF ( ALGO .EQ. 'SBRDB' ) THEN
*
*       --- blocksize for reduction banded -> banded ---
*
     IF ( NEEDU ) THEN
       IF ( SINGLE ) THEN
         some code
	 ELSE
	   some code
	 ENDIF
     ELSE
       IF ( SINGLE ) THEN
         some code
	 ELSE
	   some code
	 ENDIF
     ENDIF


where each instance of "some code" might be of the form

        IF ( DELTAB .LT. some threshold )
     >  THEN
*
*              --- suppress blocking ---
*
          NBDFLT = 1
        ELSEIF ( DELTAB .GT. some other threshold )
     >  THEN
*
*              --- do not use excessive block sizes ---
*
          NBDFLT = some maximum block size
        ELSE
*
*              --- between these thresholds, increase NBDFLT linearly
*                  with the number of diagonals removed               ---
*
          NBDFLT = nbmin + ( DELTAB / some factor )
        ENDIF

Choosing suitable thresholds and limiting block sizes (which may be obtained
from a close inspection of the xOUTTUN1 files) will give an NBDFLT function
that delivers close to optimum performance for any matrix size.

Note that NBDFLT needs not take care of algorithmic restrictions in the
choice of NB (for example, when reducing banded matrices from semibandwidth
B1 to B2, the block size must not exceed B2). These restrictions are enforced
WITHIN THE REDUCTION ROUTINES. (In the xOUTTUN1 files, NB indicates the
block size proposed by the driver, and INFO returns the block size that was
eventually used in the routine. Thus, you should have a closer look at NB.)
This feature may facilitate obtaining a simple formula for NBDFLT.

!!! You must re-build the library after modifying the routine NBDFLT !!!

If you are cross-compiling, re-make the drivers on the compile server before
proceeding.

The next step is to set the intermediate bandwidths in the reduction drivers
and the cross-over point in the driver xSBRDD from using the LAPACK routine
xSBRDT for tridiagonalizing banded matrices to the SBR routine xSBRDT, which
does the same job.
To this end, have a look at the file INTUN2 (in particular, you might want to
limit the matrix size), and then type

   make tuning2

which will after some minutes (about half an hour on a 400 MHz PentiumII, if
the matrix size was not restricted) produce the files DOUTTUN2 and SOUTTUN2.
These contain timings for the drivers with varying intermediate bandwidths and
comparisons of xSBTRD with xSBRDT for varying bandwidths.

Based on this information, suitable intermediate bandwidths and the crossover
point are coded into NBDFLT.

Now the tuning phase is completed, except ...

!!! You must re-build the library after modifying the routine NBDFLT !!!

If you are cross-compiling, re-make the drivers on the compile server before
proceeding.

% ------------------------------------------------------------------------------

4.    Running the testing drivers
      ===========================

The SBR toolbox comes with double-precision and single-precision testing
drivers and an input file INCHK that tests the following reduction paths:

   - One-step tridiagonalization of a symmetric full matrix (LAPACK)
   - Reduction of a full matrix to banded form (SBR)
   - One-step tridiagonalization of a symmetric banded matrix (LAPACK)
   - Alternative one-step tridiagonalization of a symmetric banded matrix (SBR)
   - Reduction of a full matrix with the SBR driver
   - Reduction of a banded matrix with the SBR driver

To (build and) run the testing drivers, type

   make checks

The testing drivers, 'drun' and 'srun', read the input file INCHK and produce
two output files DOUTCHK and SOUTCHK. This may require a few minutes (about
half a minute on a 400 MHz PentiumII). A sample output file, REFCHK, is
provided with the SBR toolbox.

Note that you can follow the progress of the testing driver through the
input file, as the line numbers are written to the standard output.

By default, INCHK instructs the testing driver to produce only a summary
of all the tests. If the SBR toolbox is installed correctly then
the OUTCHK file should not contain lines starting with '***', and it should
not report any failed or skipped tests.

Note that you may run additional tests or cancel some tests by modifying the
input file INCHK.  The format of the entries is described in that file.

If any of the tests fails, indicating that the residual and/or orthogonality
error exceeded some bound, proceed as follows:

   1. Edit the INCHK file to enable medium or full output (change line 83 to
      '3' or '4'). (Medium output generates output for each reduction path,
      including the problem parameters and timings, full output also includes
      output for each major routine called in the path, with a listing of
      its scalar arguments.)

   2. Re-run the testing driver.

   3. Analyze the output to find the test(s) that failed.
      Usually the ratios will only marginally exceed the thresholds. In this
      case, you may either accept the results or increase the thresholds
      by editing INCHK and re-run the testing driver.
      If the ratios exceed the thresholds by some orders of magnitude there
      is some serious problem.

If the output files contain lines with '*** Error in line ...' then there
was some problem with the input file. Change the INCHK file to enable full
output, re-run the testing driver, and try to localize the problem.

!!! The testing driver may also be used for getting timings: depending on
    the desired level of detail, you should set the output level to "1" or
    "2" by changing line 7 of the INCHK file. Output level 1 will produce
    overall timings for each reduction path, whereas level 2 will also give
    the timings for each subroutine call in the path.                       !!!

% ------------------------------------------------------------------------------

5.    Running additional timings
      ==========================

First have a look at the input file INTIM (in particular you might want to
restrict the matrix size - remember that the execution time grows cubically
with the matrix dimension), then type

   make timing

This will take some minutes (slightly over one hour on a 400 MHz PentiumII)
and produce two output files, DOUTTIM and SOUTTIM for the double and single
precision results, respectively.
These files contain data for the following reduction paths:
  - LAPACK reduction full -> tridiagonal
  - SBR driver full -> tridiagonal
  - LAPACK reduction banded -> tridiagonal
  - SBR one-step reduction banded -> tridiagonal
  - SBR driver banded -> tridiagonal

% ------------------------------------------------------------------------------

6.    Making the SBR toolbox available to other users
      ===============================================

Move the SBR toolbox library (libSBR.a if you did not change the name) into
a directory searched by the linker, e.g., /usr/lib or /usr/local/lib.
This may require superuser privileges.

% ------------------------------------------------------------------------------

7.    Bug reports
      ===========

Please help us to eliminate any remaining bug in the SBR toolbox.
If you discover a bug in one of the SBR toolbox routines, please send a
mail to one of the following addresses

   bischof@sc.rwth-aachen.de        (Christian H. Bischof)
   na.blang@na-net.ornl.gov         (Bruno Lang)
   xiaobai@cs.duke.edu              (Xiaobai Sun)

indicating the version number of the SBR toolbox, the faulty routine and the
conditions under which the error occured (parameters, machine, underlying
BLAS / LAPACK libraries, etc.)

We will try to fix these problems as soon as possible.

% ------------------------------------------------------------------------------

7.    History
      =======

1.0   April 30, 1996.         First public release
1.1   May 09, 1996.           Minor fixes; Fortran standard adherence enhanced;
                              matrix size for the checks reduced.
1.2   June 17, 1996.          Minor changes; number of files reduced;
                              single check driver provided
1.3   July 01, 1996.          Minor fixes; check driver expanded
1.4   December 29, 1999.	Major changes:
					- completely new testing driver
					- added reduction drivers
					- repacking routines have changed
					- reduction routines can now handle tightly
					  packed band.
1.4.1 May 17, 2000.		Minor fixes in the output formats
SHAR_EOF
fi # end of overwriting check
if test -f 'install'
then
	echo shar: will not over-write existing file "'install'"
else
cat << "SHAR_EOF" > 'install'
\section{Installation}
   \label{sec:install}

The SBR toolbox comes with a {\tt UNIX} makefile for easy installation and a
testing program for validation and performance tuning.

In this section we briefly describe the ``standard'' installation procedure.
Detailed information about the installation process may be found in the
\NAME{README} file distributed with the software.

The installation consists of the following steps.
\begin{enumerate}
   \item Get the SBR toolbox from the TOMS repository at \texttt{netlib}
	   and unpack it with
	   \COMMAND{zcat sbr.tar.Z | tar xf -}%
	   This command 
	   puts all the SBR software into a new directory \texttt{sbr}.
   \item Edit the file \NAME{make.inc} to match your system setup (e.g., the
	   location of the LAPACK library, if the latter is installed on your
	   machine).
   \item Type
	   \COMMAND{make library}%
	   This command will build the library (called \NAME{libSBR.a} if you
	   did not change the name).
   \item (Optional.) Fine-tune the performance of the algorithms (cf.\ the
	   \NAME{README} file).
   \item (Recommended.) Run the validation tests by typing
	   \COMMAND{make checks}%
	   and have a look at the output files \NAME{DOUTCHK} and \NAME{SOUTCHK}.
	   They should report no ``skipped'' or ``failed'' tests.
   \item (Optional.) Run the additional timings (cf.\ the \NAME{README} file).
   \item (Optional.) Move the SBR library to a directory searched by
	   the linker.
\end{enumerate}

The testing programs provide the residuals $|| U \tilde A - A U ||_{F}$,
the orthogonality errors $|| U^{T} U - I ||_{F}$, and the timings for the
reduction of a symmetric (full or banded) matrix $A$ to a (narrower) banded
or tridiagonal matrix $\tilde A$ for matrices of different orders $n$ and
different semibandwidths.
If the orthogonal matrix $U$ is not accumulated then the above error
measures are not available.
In this case the deviation of the eigenvalues,
$|| \mbox{spec}( A ) - \mbox{spec}( \tilde A ) ||_{2}$, is computed instead,
where $\mbox{spec}( A )$ and $\mbox{spec}( \tilde A )$ are the eigenvalues
of $A$ and $\tilde A$, respectively, in ascending order.

SHAR_EOF
fi # end of overwriting check
cd ..
if test ! -d 'Fortran77'
then
	mkdir 'Fortran77'
fi
cd 'Fortran77'
if test ! -d 'Dp'
then
	mkdir 'Dp'
fi
cd 'Dp'
if test ! -d 'Drivers'
then
	mkdir 'Drivers'
fi
cd 'Drivers'
if test -f 'data1'
then
	echo shar: will not over-write existing file "'data1'"
else
cat << "SHAR_EOF" > 'data1'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for testing the SBR toolbox               -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  Format of the commands:
C
C  'Comment'     : The remainder of this line is treated as a comment.
C  'FileName'    : The following line contains the name of the output file
C			 (up to 7 characters). For example, if you specify 'OUTHCK'
C			 and run the double-precision test driver 'drun', then the
C			 output is directed to the file 'DOUTCHK', whereas the
C			 output of the single-precision driver 'srun' would be
C			 directed to 'SOUTCHK'.
C  'MaxDim'      : The following line determines a maximum matrix size for
C			 the runs. All runs with larger matrices will be skipped.
C			 This feature can be used to limit the execution time of
C			 the timing/tuning runs without much file editing.
C  'NoChecks'    : Switch off all numerical checks, even if they are
C			 requested in the following runs. This feature can be used
C			 to reduce the execution time of the timing/tuning runs
C			 without much file editing.
C  'OutputLevel' : The value in the following line determines how much output
C			 is produced.
C			 1 : Generate only the overall summary.
C			 2 : Generate also condensed summaries for selected
C			     computational routines (this mode should be used to
C			     obtain tuning information).
C			 3 : Generate a more detailed summary for each test run.
C			 4 : Generate summaries for each routine called.
C  'Print'       : The following line (up to 78 characters) is printed to
C			 the output file.
C  'Quit'        : Quit the test driver, ignore the remainder of the input
C			 file.
C
C  For the above commands, only the first character is relevant (see the
C  current comment lines), case is ignored.
C  The following commands trigger tests for computational routines. These
C  commands must be specified with all 5 characters (case is ignored), and
C  each requires at least two additional lines (see below).
C
C  'SYTRD' (cf. lines   86ff): Test run for the one-step reduction
C					 full -> tridiagonal (LAPACK) and, optionally,
C					 for the backward accumulation of the
C					 transformations (ORGTR from LAPACK)
C  'SBTRD' (cf. lines  138ff): Test run for the one-step reduction
C					 banded -> tridiagonal (LAPACK)
C  'SYRDB' (cf. lines  182ff): Test run for the one-step reduction
C					 full -> banded (SBR) and, optionally, for the
C					 backward accumulation of the transformations
C					 (SYGTR from SBR)
C  'SBRDB' (cf. lines  387ff): Test run for the one-step reduction
C					 banded -> banded (SBR)
C  'SBRDT' (cf. lines  591ff): Test run for the one-step reduction
C					 banded -> tridiagonal (SBR)
C  'SY2BC' (cf. lines  773ff): Test run for the copy full -> banded (SBR)
C  'SY2BI' (cf. lines  897ff): Test run for the in-place repacking
C					 full -> banded (SBR)
C  'SB2BC' (cf. lines 1021ff): Test run for the copy banded -> banded (SBR)
C  'SB2BI' (cf. lines 1123ff): Test run for the in-place repacking
C					 banded -> banded (SBR)
C  'SYRDD' (cf. lines 1225ff): Test run for the multi-step reduction driver
C					 full -> banded/tridiagonal (SBR)
C  'SBRDD' (cf. lines 1463ff): Test run for the multi-step reduction driver
C					 banded -> banded/tridiagonal (SBR)
C			
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTCHK'
C  --- set output level ---
'OutputLevel'
 1
C ------------------------------------------------------------------------------
C
C  SYTRD : one-step reduction full -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : nb1 = blocking factor for the reduction (nb1=0 : use default)
C     7 : nx1 = cross-over point to non-blocked algorithm for the reduction
C               (nx1=0 : use default)
C     8 : lwork1 = length of the workspace for the reduction
C     9 : xinfo1 = expected info value for the routine sytrd
C                  (xinfo1 <> 0 may be used for checking error exits)
C    10 : jobu = accumulate the transformations in a matrix U with the
C                routine orgtr (jobu='U') or not (jobu='N') ?
C    11 : nb2 = blocking factor for the accumulation (nb2=0 : use default)
C    12 : nx2 = cross-over point to non-blocked algorithm for the accumulation
C               (nb2=0 : use default)
C    13 : lwork2 = length of workspace for the accumulation
C    14 : xinfo2 = expected info value for the routine orgtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'SYTRD'
   'Rand'   0.0 'Upper'   30   30   8   8   10000   0 'Upd'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'   30   30   8   8   10000   0 'Upd'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Upper'   30   30   8   8   10000   0 'NoU'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'   30   30   8   8   10000   0 'NoU'   8   8   10000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'SBTRD'
   'Rand'   0.0 'Upper'   30    7    8 'Upd'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'   30    7    8 'Upd'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Upper'   30    7    8 'NoU'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'   30    7    8 'NoU'   50   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDB : one-step reduction full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : lwork1 = length of the workspace for the reduction
C    10 : xinfo1 = expected info value for the routine syrdb
C                  (xinfo1 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : jobu = accumulate the transformations in a matrix U or not ?
C                jobu = 'O' : do the accumulation 'on the fly' in syrdb
C		          = 'U' : do the accumulation after the reduction with
C					sygtr
C		     jobu = 'N' : no accumulation
C     2 : ldu = leading dimension of the array u
C     3 : lwork2 = length of workspace for the accumulation with sygtr
C     4 : xinfo2 = expected info value for the routine sygtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the fourth line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U' or 'O'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U' or 'O'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- nonblocked reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'Onf'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- autopilot, non-exact dimensions ---
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'OnF'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'OnF'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'Upd'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'Upd'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
C --- small workspace forcing blocksize reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    8    0.0   6     300   4
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    8    0.0   0     300   4
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SYRDB'
   'ISDA' 1.0E3 'Upper'   30   30    8  1.0E4   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0  1.0E4   10.0
'SYRDB'
   'ISDA' 1.0E3 'Upper'   30   30    8  1.0E4   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0  1.0E4
C --- checks for quick return ---
'SYRDB'
   'Rand'   0.0 'Upper'    1   30    0    0.0   1     600   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30   29    0.0   1     600   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits : ---
C --- uplo is neither 'U' nor 'L' ---
'SYRDB'
   'Rand'   0.0 'Error'   10   10    4    0.0   4   10000  -1
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- jobu is neither 'U' nor 'N' ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4   10000  -2
   'Err'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SYRDB'
   'Rand'   0.0 'Lower'  -10   10    4    0.0   4   10000  -3
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SYRDB'
   'Rand'   0.0 'Lower'    1   10    4    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    0    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   10   10   10    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10    8    4    0.0   4   10000  -6
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4   -1.0   4   10000  -7
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4   10000  -9
   'Upd'    7   10000   1
   'Check'   10.0   10.0   10.0
C --- nb negative ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0  -4   10000 -10
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- lwork is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4      21 -13
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- this should be just enough ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4      22   1
   'NoU'   10   10000   1
   'Check'     10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDB : one-step reduction banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    10 : ldu = leading dimension of the array u
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine sbrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- nonblocked reduction ---
'SBRDB'
   'Rand'   0.0   30    8   13    4    0.0   1 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    8   13    4    0.0   1 'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction ---
'SBRDB'
   'Rand'   0.0   31    8   15    4    0.0   3 'Upd'   31   10000   3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   31    8   15    4    0.0   3 'NoU'   31   10000   3
   'Check'   10.0   10.0   10.0
C --- autopilot, nonexact dimensions ---
'SBRDB'
   'Rand'   0.0   29    8   23    4    0.0   0 'Upd'   32   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   29    8   23    4    0.0   0 'NoU'   32   10000   4
   'Check'   10.0   10.0   10.0
C --- force blocksize reduction by insufficient workspace ---
'SBRDB'
   'Rand'   0.0   30    8   20    5    0.0   5 'Upd'   30     200   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    8   20    5    0.0   5 'NoU'   30     100   3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   29   59    5    0.0   0 'Upd'   30     400   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   29   59    5    0.0   0 'NoU'   30     300   3
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SBRDB'
   'ISDA' 1.0E3   30   12   24    8  1.0E4   8 'Upd'   30   10000   8
   'Check'   10.0  1.0E4   10.0
'SBRDB'
   'ISDA' 1.0E3   30   12   24    8  1.0E4   8 'NoU'   30   10000   8
   'Check'   10.0   10.0  1.0E4
C --- now the workspace should fit exactly ---
'SBRDB'
   'Rand'   0.0   30   10   20    6    0.0   6 'Upd'   30     306   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   10   20    6    0.0   6 'NoU'   30     216   6
   'Check'   10.0   10.0   10.0
C --- force buffering by providing very tight lda ---
'SBRDB'
   'Rand'   0.0   30    9   16    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   16    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   15    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   15    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   14    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   14    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   13    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   13    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   12    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   12    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   11    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   11    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   10    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   10    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   20    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   20    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   13    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   13    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   19   20    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   19   20    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
C --- checks for quick return ---
'SBRDB'
   'Rand'   0.0   10    6   10    6    0.0   1 'Upd'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits : ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Err'   10   10000  -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDB'
   'Rand'   0.0  -10    6   10    3    0.0   1 'Upd'   10   10000  -2
   'Check'   10.0   10.0   10.0
C --- b1 is out of range ---
'SBRDB'
   'Rand'   0.0   10   -6   10    3    0.0   1 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10   10   10    3    0.0   1 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SBRDB'
   'Rand'   0.0   10    6   10   -3    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    0    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    7    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDB'
   'Rand'   0.0   10    6    6    3    0.0   1 'Upd'   10   10000  -6
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SBRDB'
   'Rand'   0.0   10    6   10    3   -1.0   1 'Upd'   10   10000  -7
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'    8   10000  -9
   'Check'   10.0   10.0   10.0
C --- nb is negative ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0  -1 'Upd'   10   10000 -10
   'Check'   10.0   10.0   10.0
C --- lwork is too small ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'   10      22 -12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'NoU'   10      20 -12
   'Check'   10.0   10.0   10.0
C --- for these, workspace should be just sufficient ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'   10      23   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'NoU'   10      21   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- non-blocked reduction/update ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   1 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   1 'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction/update ---
'SBRDT'
   'Rand'   0.0   31    8   16    0.0   8 'Upd'   31   10000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   31    8   16    0.0   8 'NoU'   31   10000   1
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SBRDT'
   'Rand'   0.0   29    4    5    0.0   0 'Upd'   32   10000   3
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    4    5    0.0   0 'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    8   18    0.0   0 'Upd'   32   10000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    8   18    0.0   0 'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SBRDT'
   'ISDA' 1.0E3   30    8   16  1.0E4   8 'Upd'   30   10000   8
   'Check'   10.0  1.0E4   10.0
'SBRDT'
   'ISDA' 1.0E3   30    8   16  1.0E4   8 'NoU'   30   10000   1
   'Check'   10.0   10.0  1.0E4
C --- force repacking by providing rather tight lda ---
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'Upd'   30     517   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'NoU'   30      17   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'Upd'   30     522   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'NoU'   30      23   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   13    0.0   6 'Upd'   30     531   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   13    0.0   6 'NoU'   30      31   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   12    0.0   6 'Upd'   30     544   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   12    0.0   6 'NoU'   30      44   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   11    0.0   6 'Upd'   30     561   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   11    0.0   6 'NoU'   30      61   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   10    0.0   6 'Upd'   30     582   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   10    0.0   6 'NoU'   30      82   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'Upd'   30     607   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'NoU'   30     107   1
   'Check'   10.0   10.0   10.0
C --- force blocksize reduction by providing too small workspace ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'Upd'   30     350   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30   13   26    0.0   0 'Upd'   30     370   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'Upd'   30     250   3
   'Check'   10.0   10.0   10.0
C --- checks for quick return ---
'SBRDT'
   'Rand'   0.0    0    0    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    0    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    1    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0   6 'Err'   10   10000  -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDT'
   'Rand'   0.0  -10    6   12    0.0   6 'Upd'   10   10000  -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SBRDT'
   'Rand'   0.0   10   -6   12    0.0   6 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   10   10   12    0.0   6 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDT'
   'Rand'   0.0   10    6    6    0.0   6 'Upd'   10   10000  -5
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SBRDT'
   'Rand'   0.0   10    6   12   -1.0   6 'Upd'   10   10000  -6
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0   6 'Upd'    8   10000 -10
   'Check'   10.0   10.0   10.0
C --- nb is negative ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0  -6 'Upd'   10   10000 -11
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'Upd'   50      37 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'NoU'   50      15 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'Upd'   50      38 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'NoU'   50      16 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'Upd'   50     128 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'NoU'   50     106 -13
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SY2BC : copy full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the array a in full storage
C     7 : lda2 = leading dimension of the array holding A in packed storage
C     8 : xinfo = expected info value for the routine sy2bc
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack to a tightly fitting band ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with leading dimension larger by 1 ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
C --- and now the same tests again, with inexact lda ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SY2BC'
   'Rand'   0.0 'Lower'    0    8   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SY2BC'
   'Rand'   0.0 'Error'   25    8   30    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SY2BC'
   'Rand'   0.0 'Lower'  -25    8   30    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SY2BC'
   'Rand'   0.0 'Lower'   25   -8   30    9   -3
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25   25   30    9   -3
   'Check'   10.0   10.0   10.0
C --- ldfull is too small ---
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   23    9   -5
   'Check'   10.0   10.0   10.0
C --- ldband is too small ---
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30    8   -7
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SY2BI : in-place copy full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the array a in full storage
C     7 : lda2 = leading dimension of the array holding A in packed storage
C     8 : xinfo = expected info value for the routine sy2bi
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack to a tightly fitting band ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with leading dimension larger by 1 ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
C --- and now the same tests again, with inexact lda ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SY2BI'
   'Rand'   0.0 'Lower'    0    8   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SY2BI'
   'Rand'   0.0 'Error'   25    8   30    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SY2BI'
   'Rand'   0.0 'Lower'  -25    8   30    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SY2BI'
   'Rand'   0.0 'Lower'   25   -8   30    9   -3
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25   25   30    9   -3
   'Check'   10.0   10.0   10.0
C --- ldfull is too small ---
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   23    9   -5
   'Check'   10.0   10.0   10.0
C --- ldband is too small ---
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30    8   -6
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SB2BC : copy banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the source array a
C     7 : lda2 = leading dimension of the destination array
C     8 : xinfo = expected info value for the routine sb2bc
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack a tightly fitting band ---
C --- repack to a tightly fitting band ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
C --- and now repack a band with diagonals to spare ---
C --- repack to tight fit ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SB2BC'
   'Rand'   0.0 'Lower'    0    0   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SB2BC'
   'Rand'   0.0 'Error'   25    8   12    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SB2BC'
   'Rand'   0.0 'Lower'  -25    8   12    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SB2BC'
   'Rand'   0.0 'Lower'   25   -8   12    9   -3
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25   25   25    9   -3
   'Check'   10.0   10.0   10.0
C --- ldsrc is too small ---
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    6    9   -5
   'Check'   10.0   10.0   10.0
C --- lddst is too small ---
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   11    7   -7
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SB2BI : in-place copy banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the source array a
C     7 : lda2 = leading dimension of the destination array
C     8 : xinfo = expected info value for the routine sb2bi
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack a tightly fitting band ---
C --- repack to a tightly fitting band ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
C --- and now repack a band with diagonals to spare ---
C --- repack to tight fit ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SB2BI'
   'Rand'   0.0 'Lower'    0    0   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SB2BI'
   'Rand'   0.0 'Error'   25    8   12    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SB2BI'
   'Rand'   0.0 'Lower'  -25    8   12    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SB2BI'
   'Rand'   0.0 'Lower'   25   -8   12    9   -3
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25   25   25    9   -3
   'Check'   10.0   10.0   10.0
C --- ldsrc is too small ---
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    6    9   -5
   'Check'   10.0   10.0   10.0
C --- lddst is too small ---
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   11    7   -6
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- one-step reduction ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8    9    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8    9    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8    9    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8    9    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
C --- two-step reduction ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1   16    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1   16    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1   16    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1   16    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8   14    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8   14    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8   14    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8   14    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    5    6    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    5    6    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    5    6    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    5    6    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  300  300    1   64    0    0.0 'Upd'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  300  300    1   64    0    0.0 'NoU'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'  300  300    1   64    0    0.0 'Upd'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'  300  300    1   64    0    0.0 'NoU'   20000    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SYRDD'
   'Rand'   0.0 'Lower'    0    4    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
C --- check for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Err'   10000   -1
       5
   'Check'   10.0   10.0   10.0
C --- uplo is neither 'U' nor 'L' ---
'SYRDD'
   'Rand'   0.0 'Error'   10   10    4    8    1    0.0 'Upd'   10000   -2
       5
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SYRDD'
   'Rand'   0.0 'Lower'  -10   10    4    8    1    0.0 'Upd'   10000   -3
       5
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10   -1    8    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    0    8    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10   10   20    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SYRDD'
   'Rand'   0.0 'Lower'   10    8    4    8    1    0.0 'Upd'   10000   -6
       5
   'Check'   10.0   10.0   10.0
C --- drptol is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1   -1.0 'Upd'   10000   -7
       5
   'Check'   10.0   10.0   10.0
C --- ldband is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    4    1    0.0 'Upd'   10000   -9
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    6    2    0.0 'Upd'   10000   -9
       6
       5    3
   'Check'   10.0   10.0   10.0
C --- nsteps is negative ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8   -1    0.0 'Upd'   10000  -12
   'Check'   10.0   10.0   10.0
C --- sequence of bandwidths is non-decreasing ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    1   20    3    0.0 'Upd'   10000  -13
      10    3
       5    5    5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    3    8    3    0.0 'Upd'   10000  -13
       6    2
       5    5    5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    1    8    3    0.0 'Upd'   10000  -13
       4    5
       5    5    5
   'Check'   10.0   10.0   10.0
C --- sequence of blocking factors contains negative entries ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Upd'   10000  -14
      -5
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Upd'      38  -16
       5
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- one-step reduction ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30    4    8    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30    4    8    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30    4    8    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30    4    8    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
C --- two-step reduction ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    3    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    3    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    3    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    3    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'Upd'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'NoU'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'NoU'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
C --- doubling sequence ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   16    1    4    0.0 'Upd'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   16    1    4    0.0 'NoU'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   16    1    4    0.0 'Upd'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   16    1    4    0.0 'NoU'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SBRDD'
   'Rand'   0.0 'Upper'   80   70   80    1    0    0.0 'Upd'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   80   70   80    1    0    0.0 'NoU'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   80   70   80    1    0    0.0 'Upd'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   80   70   80    1    0    0.0 'NoU'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   12   30    1    0    0.0 'Upd'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   12   30    1    0    0.0 'NoU'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   12   30    1    0    0.0 'Upd'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   12   30    1    0    0.0 'NoU'   30   10000    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SBRDD'
   'Rand'   0.0 'Lower'    0    4    8    1    0    0.0 'Upd'   10   10000    1
   'Check'   10.0   10.0   10.0
C --- check for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Err'   10   10000   -1
       5
   'Check'   10.0   10.0   10.0
C --- uplo is neither 'U' nor 'L' ---
'SBRDD'
   'Rand'   0.0 'Error'   10    4    8    1    1    0.0 'Upd'   10   10000   -2
       5
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDD'
   'Rand'   0.0 'Lower'  -10    4    8    1    1    0.0 'Upd'   10   10000   -3
       5
   'Check'   10.0   10.0   10.0
C --- b1 is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10   -4    8    1    1    0.0 'Upd'   10   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10   10   18    1    1    0.0 'Upd'   10   10000   -4
       5
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    0    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'    0    0    8    1    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    5    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    4    1    1    0.0 'Upd'   10   10000   -7
       5
   'Check'   10.0   10.0   10.0
C --- drptol is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1   -1.0 'Upd'   10   10000   -8
       5
   'Check'   10.0   10.0   10.0
C --- ldu is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Upd'    8   10000  -12
       5
   'Check'   10.0   10.0   10.0
C --- nsteps is negative ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1   -1    0.0 'Upd'   10   10000  -13
   'Check'   10.0   10.0   10.0
C --- sequence of bandwidths is non-decreasing ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       5    3    2
       5    5    5    5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       3    5    2
       5    5    5    5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       3    2    5
       5    5    5    5
   'Check'   10.0   10.0   10.0
C --- negative blocking factors ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    3    0.0 'Upd'   10   10000  -15
       3    2
       5   -5    5
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'Upd'   30      42  -17
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Upd'   10       8  -17
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30      55  -17
       8
       5    5
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data2'
then
	echo shar: will not over-write existing file "'data2'"
else
cat << "SHAR_EOF" > 'data2'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for timing the SBR toolbox               -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C800
C  --- if you are in a real hurry, uncomment the following two lines ---
C'MaxDim'
C400
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTIM'
C  --- set output level ---
'OutputLevel'
 3
C  -----------------------------------------------------------------------------
C
C  SYTRD : one-step reduction full -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : nb1 = blocking factor for the reduction (nb1=0 : use default)
C     7 : nx1 = cross-over point to non-blocked algorithm for the reduction
C               (nx1=0 : use default)
C     8 : lwork1 = length of the workspace for the reduction
C     9 : xinfo1 = expected info value for the routine sytrd
C                  (xinfo1 <> 0 may be used for checking error exits)
C    10 : jobu = accumulate the transformations in a matrix U with the
C                routine orgtr (jobu='U') or not (jobu='N') ?
C    11 : nb2 = blocking factor for the accumulation (nb2=0 : use default)
C    12 : nx2 = cross-over point to non-blocked algorithm for the accumulation
C               (nb2=0 : use default)
C    13 : lwork2 = length of workspace for the accumulation
C    14 : xinfo2 = expected info value for the routine orgtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Timing the LAPACK reduction full -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SYTRD'
   'Rand'   0.0 'Lower'  200  200   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  400  400   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  600  600   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  800  800   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower' 1000 1000   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SYTRD'
   'Rand'   0.0 'Lower'  200  200   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  400  400   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  600  600   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  800  800   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower' 1000 1000   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR driver full -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SYRDD'
   'Rand'   0.0 'Upper'  200  200    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  400  400    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  600  600    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  800  800    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper' 1000 1000    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SYRDD'
   'Rand'   0.0 'Upper'  200  200    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  400  400    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  600  600    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  800  800    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper' 1000 1000    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the LAPACK reduction banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  800    4    5 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800    8    9 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   12   13 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   16   17 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   24   25 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   32   33 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   48   49 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   64   65 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower' 1000    4    5 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000    8    9 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   12   13 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   16   17 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   24   25 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   32   33 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   48   49 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   64   65 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  800    4    5 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800    8    9 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   12   13 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   16   17 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   24   25 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   32   33 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   48   49 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   64   65 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower' 1000    4    5 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000    8    9 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   12   13 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   16   17 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   24   25 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   32   33 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   48   49 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   64   65 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR reduction banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  800    4    8    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800    8   16    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   12   24    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   16   32    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   24   48    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   32   64    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   48   96    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   64  128    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0 1000    4    8    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000    8   16    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   12   24    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   16   32    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   24   48    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   32   64    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   48   96    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   64  128    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
'      *** ignore messages about tests failing because ***'
'Print'
'      *** SBRDT returned a wrong (but positive) info  ***'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  800    4    8    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800    8   16    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   12   24    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   16   32    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   24   48    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   32   64    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   48   96    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   64  128    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0 1000    4    8    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000    8   16    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   12   24    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   16   32    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   24   48    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   32   64    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   48   96    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   64  128    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR driver banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  200    4    8    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200    8   16    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   12   24    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   16   32    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   24   48    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   48   96    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  400    4    8    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400    8   16    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   12   24    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   16   32    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   24   48    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   48   96    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  600    4    8    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600    8   16    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   12   24    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   16   32    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   24   48    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   48   96    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  800    4    8    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800    8   16    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   12   24    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   16   32    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   24   48    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   32   64    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   48   96    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   64  128    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower' 1000    4    8    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000    8   16    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   12   24    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   16   32    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   24   48    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   32   64    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   48   96    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   64  128    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  200    4    8    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200    8   16    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   12   24    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   16   32    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   24   48    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   48   96    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  400    4    8    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400    8   16    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   12   24    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   16   32    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   24   48    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   48   96    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  600    4    8    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600    8   16    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   12   24    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   16   32    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   24   48    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   48   96    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  800    4    8    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800    8   16    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   12   24    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   16   32    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   24   48    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   32   64    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   48   96    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   64  128    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower' 1000    4    8    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000    8   16    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   12   24    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   16   32    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   24   48    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   32   64    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   48   96    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   64  128    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data3'
then
	echo shar: will not over-write existing file "'data3'"
else
cat << "SHAR_EOF" > 'data3'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for tuning the SBR toolbox                -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C400
C  --- if you are in a real hurry, uncomment the following two lines ---
C'MaxDim'
C200
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTUN1'
C  --- set output level ---
'OutputLevel'
 2
C ------------------------------------------------------------------------------
C
C  SYRDB : one-step reduction full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : lwork1 = length of the workspace for the reduction
C    10 : xinfo1 = expected info value for the routine syrdb
C                  (xinfo1 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : jobu = accumulate the transformations in a matrix U or not ?
C                jobu = 'O' : do the accumulation 'on the fly' in syrdb
C		          = 'U' : do the accumulation after the reduction with
C					sygtr
C		     jobu = 'N' : no accumulation
C     2 : ldu = leading dimension of the array u
C     3 : lwork2 = length of workspace for the accumulation with sygtr
C     4 : xinfo2 = expected info value for the routine sygtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the fourth line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U' or 'O'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U' or 'O'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Setting nb for SYRDB ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   1 1000000   1
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   4 1000000   4
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   6 1000000   6
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   8 1000000   8
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  12 1000000  12
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  16 1000000  16
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  20 1000000  20
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  24 1000000  24
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  32 1000000  32
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  40 1000000  40
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  48 1000000  48
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  64 1000000  64
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   1 1000000   1
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   4 1000000   4
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   6 1000000   6
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   8 1000000   8
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  12 1000000  12
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  16 1000000  16
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  20 1000000  20
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  24 1000000  24
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  32 1000000  32
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  40 1000000  40
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  48 1000000  48
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  64 1000000  64
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   1 1000000   1
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   4 1000000   4
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   6 1000000   6
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   8 1000000   8
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  12 1000000  12
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  16 1000000  16
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  20 1000000  20
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  24 1000000  24
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  32 1000000  32
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  40 1000000  40
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  48 1000000  48
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  64 1000000  64
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   1 1000000   1
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   4 1000000   4
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   6 1000000   6
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   8 1000000   8
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  12 1000000  12
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  16 1000000  16
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  20 1000000  20
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  24 1000000  24
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  32 1000000  32
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  40 1000000  40
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  48 1000000  48
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  64 1000000  64
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   1 1000000   1
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   4 1000000   4
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   6 1000000   6
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   8 1000000   8
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  12 1000000  12
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  16 1000000  16
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  20 1000000  20
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  24 1000000  24
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  32 1000000  32
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  40 1000000  40
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  48 1000000  48
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  64 1000000  64
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   1 1000000   1
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   4 1000000   4
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   6 1000000   6
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   8 1000000   8
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  12 1000000  12
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  16 1000000  16
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  20 1000000  20
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  24 1000000  24
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  32 1000000  32
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  40 1000000  40
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  48 1000000  48
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  64 1000000  64
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDB : one-step reduction banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    10 : ldu = leading dimension of the array u
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine sbrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting nb for SBRDB ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  10 'NoU'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  12 'NoU'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  16 'NoU'  200 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  10 'NoU'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  12 'NoU'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  16 'NoU'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  20 'NoU'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  24 'NoU'  200 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  32 'NoU'  200 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  10 'NoU'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  12 'NoU'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  16 'NoU'  400 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  10 'NoU'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  12 'NoU'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  16 'NoU'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  20 'NoU'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  24 'NoU'  400 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  32 'NoU'  400 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  10 'NoU'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  12 'NoU'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  16 'NoU'  600 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  10 'NoU'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  12 'NoU'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  16 'NoU'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  20 'NoU'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  24 'NoU'  600 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  32 'NoU'  600 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  24 'Upd'  200 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  32 'Upd'  200 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  24 'Upd'  400 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  32 'Upd'  400 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  24 'Upd'  600 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  32 'Upd'  600 1000000  32
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting nb for SBRDT ***'
'Print'
''
'Print'
'    with update'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  24 'Upd'  200 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  32 'Upd'  200 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  40 'Upd'  200 1000000  40
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  24 'Upd'  400 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  32 'Upd'  400 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  40 'Upd'  400 1000000  40
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  24 'Upd'  600 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  32 'Upd'  600 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  40 'Upd'  600 1000000  40
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data4'
then
	echo shar: will not over-write existing file "'data4'"
else
cat << "SHAR_EOF" > 'data4'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for tuning the SBR toolbox                -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C400
C  --- if you are in a real hurry, uncomment the following two lines ---
C'MaxDim'
C200
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTUN2'
C  --- set output level ---
'OutputLevel'
 2
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Setting intermediate bandwidth for SYRDD ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting intermediate bandwidth for SBRDD ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Where to switch from SYTRD to SYRDT ? ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  200    6    7 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    6   12    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  200   10   11 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   10   20    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  200   20   21 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   20   40    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  200   40   41 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   40   80    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  400    6    7 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    6   12    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  400   10   11 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   10   20    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  400   20   21 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   20   40    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  400   40   41 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   40   80    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  600    6    7 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    6   12    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  600   10   11 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   10   20    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  600   20   21 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   20   40    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  600   40   41 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   40   80    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
'      *** ignore messages about tests failing because ***'
'Print'
'      *** SBRDT returned a wrong (but positive) info  ***'
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  200    6    7 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    6   12    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  200   10   11 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   10   20    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  200   20   21 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   20   40    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  200   40   41 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   40   80    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  400    6    7 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    6   12    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  400   10   11 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   10   20    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  400   20   21 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   20   40    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  400   40   41 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   40   80    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  600    6    7 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    6   12    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  600   10   11 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   10   20    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  600   20   21 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   20   40    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  600   40   41 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   40   80    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'driver.f'
then
	echo shar: will not over-write existing file "'driver.f'"
else
cat << "SHAR_EOF" > 'driver.f'
      SUBROUTINE DORQLX( NB0, NX0,
     >                   M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            NB0, NX0, INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  dORQLx generates an M-by-N real matrix Q with orthonormal columns,
C*  DORGQL generates an M-by-N real matrix Q with orthonormal columns,
*  which is defined as the last N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by DGEQLF.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the nonblocked algorithm.
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) double precision array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the (n-k+i)-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by DGEQLF in the last k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) double precision array, dimension (K)
C*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DGEQLF.
*
*  WORK    (workspace/output) double precision array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
C      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
C      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
     $                   NB, NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLARFB, DLARFT, DORG2L, XERBLA
C      EXTERNAL           DLARFB, DLARFT, DORG2L, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF ( NB0 .GT. 0 ) THEN
        NB = NB0
      ELSE
        NB = ILAENV( 1, 'dORGQL', ' ', M, N, K, -1 )
      ENDIF
C      NB = ILAENV( 1, 'DORGQL', ' ', M, N, K, -1 )
      LWKOPT = MAX( 1, N )*NB
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'dORGQL', -INFO )
C         CALL XERBLA( 'DORGQL', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      NX = 0
      IWS = N
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         IF ( NX0 .GT. 0 ) THEN
           NX = NX0
         ELSE
           NX = MAX( 0, ILAENV( 3, 'dORGQL', ' ', M, N, K, -1 ) )
         ENDIF
C         NX = MAX( 0, ILAENV( 3, 'DORGQL', ' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = 2
C               NBMIN = MAX( 2, ILAENV( 2, 'DORGQL', ' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
*
*        Use blocked code after the first block.
*        The last kk columns are handled by the block method.
*
         KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
*
*        Set A(m-kk+1:m,1:n-kk) to zero.
*
         DO 20 J = 1, N - KK
            DO 10 I = M - KK + 1, M
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the first or only block.
*
      CALL DORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
C      CALL DORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = K - KK + 1, K, NB
            IB = MIN( NB, K-I+1 )
            IF( N-K+I.GT.1 ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i+ib-1) . . . H(i+1) H(i)
*
               CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
     $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
C               CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
C     $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
*
               CALL DLARFB( 'Left', 'No transpose', 'Backward',
     $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
     $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
     $                      WORK( IB+1 ), LDWORK )
C               CALL DLARFB( 'Left', 'No transpose', 'Backward',
C     $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
C     $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
C     $                      WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H to rows 1:m-k+i+ib-1 of current block
*
            CALL DORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
     $                   TAU( I ), WORK, IINFO )
C            CALL DORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
C     $                   TAU( I ), WORK, IINFO )
*
*           Set rows m-k+i+ib:m of current block to zero
*
            DO 40 J = N - K + I, N - K + I + IB - 1
               DO 30 L = M - K + I + IB, M
                  A( L, J ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of dORQLx
C*     End of DORGQL
*
      END
      SUBROUTINE DORQRX( NB0, NX0,
     >                   M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            NB0, NX0, INFO, K, LDA, LWORK, M, N
C      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  dORQRx generates an M-by-N real matrix Q with orthonormal columns,
C*  DORGQR generates an M-by-N real matrix Q with orthonormal columns,
*  which is defined as the first N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(1) H(2) . . . H(k)
*
*  as returned by dGEQRF.
C*  as returned by DGEQRF.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the non-blocked algorithm.
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) double precision array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the i-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by dGEQRF in the first k columns of its array
C*          returned by DGEQRF in the first k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) double precision array, dimension (K)
C*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by dGEQRF.
C*          reflector H(i), as returned by DGEQRF.
*
*  WORK    (workspace/output) double precision array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
C      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
C      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
     $                   LWKOPT, NB, NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLARFB, DLARFT, DORG2R, XERBLA
C      EXTERNAL           DLARFB, DLARFT, DORG2R, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF ( NB0 .GT. 0 ) THEN
        NB = NB0
      ELSE
        NB = ILAENV( 1, 'dORGQR', ' ', M, N, K, -1 )
      ENDIF
C      NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
      LWKOPT = MAX( 1, N )*NB
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'dORGQR', -INFO )
C         CALL XERBLA( 'DORGQR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      NX = 0
      IWS = N
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         IF ( NX0 .GT. 0 ) THEN
           NX = NX0
         ELSE
           NX = MAX( 0, ILAENV( 3, 'dORGQR', ' ', M, N, K, -1 ) )
         ENDIF
C         NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = 2
C               NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
*
*        Use blocked code after the last block.
*        The first kk columns are handled by the block method.
*
         KI = ( ( K-NX-1 ) / NB )*NB
         KK = MIN( K, KI+NB )
*
*        Set A(1:kk,kk+1:n) to zero.
*
         DO 20 J = KK + 1, N
            DO 10 I = 1, KK
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the last or only block.
*
      IF( KK.LT.N )
     $   CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
     $                TAU( KK+1 ), WORK, IINFO )
C     $   CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
C     $                TAU( KK+1 ), WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = KI + 1, 1, -NB
            IB = MIN( NB, K-I+1 )
            IF( I+IB.LE.N ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i) H(i+1) . . . H(i+ib-1)
*
               CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
     $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
C               CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
C     $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H to A(i:m,i+ib:n) from the left
*
               CALL DLARFB( 'Left', 'No transpose', 'Forward',
     $                      'Columnwise', M-I+1, N-I-IB+1, IB,
     $                      A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
     $                      LDA, WORK( IB+1 ), LDWORK )
C               CALL DLARFB( 'Left', 'No transpose', 'Forward',
C     $                      'Columnwise', M-I+1, N-I-IB+1, IB,
C     $                      A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
C     $                      LDA, WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H to rows i:m of current block
*
            CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
     $                   IINFO )
C            CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
C     $                   IINFO )
*
*           Set rows 1:i-1 of current block to zero
*
            DO 40 J = I, I + IB - 1
               DO 30 L = 1, I - 1
                  A( L, J ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of dORQRx
C*     End of DORGQR
*
      END
      SUBROUTINE DORGTX( NB0, NX0,
     >                   UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            NB0, NX0, INFO, LDA, LWORK, N
C      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  dORGTx generates a real orthogonal matrix Q which is defined as the
C*  DORGTR generates a real orthogonal matrix Q which is defined as the
*  product of n-1 elementary reflectors of order N, as returned by
*  dSYTRD:
C*  DSYTRD:
*
*  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the nonblocked algorithm.
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangle of A contains elementary reflectors
*                 from dSYTRD;
C*                 from DSYTRD;
*          = 'L': Lower triangle of A contains elementary reflectors
*                 from dSYTRD.
C*                 from DSYTRD.
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  A       (input/output) dPreicision array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by dSYTRD.
C*          as returned by DSYTRD.
*          On exit, the N-by-N orthogonal matrix Q.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,N).
*
*  TAU     (input) dPreicision array, dimension (N-1)
C*  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by dSYTRD.
C*          reflector H(i), as returned by DSYTRD.
*
*  WORK    (workspace/output) double precision array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N-1).
*          For optimum performance LWORK >= (N-1)*NB, where NB is
*          the optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
C      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
C      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, J, LWKOPT, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           DORQLX, DORQRX, XERBLA
C      EXTERNAL           DORGQL, DORGQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
         INFO = -7
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( UPPER ) THEN
            IF ( NB0 .GT. 0 ) THEN
              NB = NB0
            ELSE
              NB = ILAENV( 1, 'dORGQL', ' ', N-1, N-1, N-1, -1 )
            ENDIF
C            NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
         ELSE
            IF ( NB0 .GT. 0 ) THEN
              NB = NB0
            ELSE
              NB = ILAENV( 1, 'dORGQR', ' ', N-1, N-1, N-1, -1 )
            ENDIF
C            NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
         END IF
         LWKOPT = MAX( 1, N-1 )*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'dORGTR', -INFO )
C         CALL XERBLA( 'DORGTR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      IF( UPPER ) THEN
*
*        Q was determined by a call to dSYTRD with UPLO = 'U'
C*        Q was determined by a call to DSYTRD with UPLO = 'U'
*
*        Shift the vectors which define the elementary reflectors one
*        column to the left, and set the last row and column of Q to
*        those of the unit matrix
*
         DO 20 J = 1, N - 1
            DO 10 I = 1, J - 1
               A( I, J ) = A( I, J+1 )
   10       CONTINUE
            A( N, J ) = ZERO
   20    CONTINUE
         DO 30 I = 1, N - 1
            A( I, N ) = ZERO
   30    CONTINUE
         A( N, N ) = ONE
*
*        Generate Q(1:n-1,1:n-1)
*
         CALL DORQLX( NB0, NX0,
     >                N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
C         CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
*
      ELSE
*
*        Q was determined by a call to dSYTRD with UPLO = 'L'.
C*        Q was determined by a call to DSYTRD with UPLO = 'L'.
*
*        Shift the vectors which define the elementary reflectors one
*        column to the right, and set the first row and column of Q to
*        those of the unit matrix
*
         DO 50 J = N, 2, -1
            A( 1, J ) = ZERO
            DO 40 I = J + 1, N
               A( I, J ) = A( I, J-1 )
   40       CONTINUE
   50    CONTINUE
         A( 1, 1 ) = ONE
         DO 60 I = 2, N
            A( I, 1 ) = ZERO
   60    CONTINUE
         IF( N.GT.1 ) THEN
*
*           Generate Q(2:n,2:n)
*
            CALL DORQRX( NB0, NX0,
     >                   N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
     $                   LWORK, IINFO )
C            CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
C     $                   LWORK, IINFO )
         END IF
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of dORGTR
C*     End of DORGTR
*
      END
C      SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
      SUBROUTINE DSBTRX( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
     $                   WORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO, VECT
      INTEGER            INFO, KD, LDAB, LDQ, N
*     ..
*     .. Array Arguments ..
C      DOUBLE PRECISION   AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ),
      DOUBLE PRECISION   AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ),
     $                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
C*  DSBTRD reduces a real symmetric band matrix A to symmetric
*  dSBTRD reduces a real symmetric band matrix A to symmetric
*  tridiagonal form T by an orthogonal similarity transformation:
*  Q**T * A * Q = T.
*
*  Arguments
*  =========
*
*  VECT    (input) CHARACTER*1
*          = 'N':  do not form Q;
*          = 'V':  form Q;
*          = 'U':  update a matrix X, by forming X*Q.
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
C*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*  AB      (input/output) double precision array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*          On exit, the diagonal elements of AB are overwritten by the
*          diagonal elements of the tridiagonal matrix T; if KD > 0, the
*          elements on the first superdiagonal (if UPLO = 'U') or the
*          first subdiagonal (if UPLO = 'L') are overwritten by the
*          off-diagonal elements of T; the rest of AB is overwritten by
*          values generated during the reduction.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
C*  D       (output) DOUBLE PRECISION array, dimension (N)
*  D       (output) double precision array, dimension (N)
*          The diagonal elements of the tridiagonal matrix T.
*
C*  E       (output) DOUBLE PRECISION array, dimension (N-1)
*  E       (output) double precision array, dimension (N-1)
*          The off-diagonal elements of the tridiagonal matrix T:
*          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
*
C*  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
*  Q       (input/output) double precision array, dimension (LDQ,N)
*          On entry, if VECT = 'U', then Q must contain an N-by-N
*          matrix X; if VECT = 'N' or 'V', then Q need not be set.
*
*          On exit:
*          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
*          if VECT = 'U', Q contains the product X*Q;
*          if VECT = 'N', the array Q is not referenced.
*
*  LDQ     (input) INTEGER
*          The leading dimension of the array Q.
*          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
*
C*  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
*  WORK    (workspace) double precision array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  Further Details
*  ===============
*
*  Modified by Linda Kaufman, Bell Labs.
*
*  =====================================================================
*
*     .. Parameters ..
C      DOUBLE PRECISION   ZERO, ONE
      DOUBLE PRECISION   ZERO, ONE
C      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            INITQ, UPPER, WANTQ
      INTEGER            I, I2, IBL, INCA, INCX, IQAEND, IQB, IQEND, J,
     $                   J1, J1END, J1INC, J2, JEND, JIN, JINC, K, KD1,
     $                   KDM1, KDN, L, LAST, LEND, NQ, NR, NRT
C      DOUBLE PRECISION   TEMP
      DOUBLE PRECISION   TEMP
*     ..
*     .. External Subroutines ..
C      EXTERNAL           DLAR2V, DLARGV, DLARTG, DLARTV, DLASET, DROT,
      EXTERNAL           DLAR2V, DLARGV, DLARTG, DLARTV, DLASET, DROT,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INITQ = LSAME( VECT, 'V' )
      WANTQ = INITQ .OR. LSAME( VECT, 'U' )
      UPPER = LSAME( UPLO, 'U' )
      KD1 = KD + 1
      KDM1 = KD - 1
      INCX = LDAB - 1
      IQEND = 1
*
      INFO = 0
      IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'N' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( KD.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD1 ) THEN
         INFO = -6
      ELSE IF( LDQ.LT.MAX( 1, N ) .AND. WANTQ ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
C         CALL XERBLA( 'DSBTRD', -INFO )
         CALL XERBLA( 'dSBTRD', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Initialize Q to the unit matrix, if needed
*
      IF( INITQ )
C     $   CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
     $   CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
*
*     Wherever possible, plane rotations are generated and applied in
*     vector operations of length NR over the index set J1:J2:KD1.
*
*     The cosines and sines of the plane rotations are stored in the
*     arrays D and WORK.
*
      INCA = KD1*LDAB
      KDN = MIN( N-1, KD )
      IF( UPPER ) THEN
*
         IF( KD.GT.1 ) THEN
*
*           Reduce to tridiagonal form, working with upper triangle
*
            NR = 0
            J1 = KDN + 2
            J2 = 1
*
            DO 90 I = 1, N - 2
*
*              Reduce i-th row of matrix to tridiagonal form
*
               DO 80 K = KDN + 1, 2, -1
                  J1 = J1 + KDN
                  J2 = J2 + KDN
*
                  IF( NR.GT.0 ) THEN
*
*                    generate plane rotations to annihilate nonzero
*                    elements which have been created outside the band
*
C                     CALL DLARGV( NR, AB( 1, J1-1 ), INCA, WORK( J1 ),
                     CALL DLARGV( NR, AB( 1, J1-1 ), INCA, WORK( J1 ),
     $                            KD1, D( J1 ), KD1 )
*
*                    apply rotations from the right
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    dLARTV or dROT is used
*
                     IF( NR.GE.2*KD-1 ) THEN
                        DO 10 L = 1, KD - 1
C                           CALL DLARTV( NR, AB( L+1, J1-1 ), INCA,
                           CALL DLARTV( NR, AB( L+1, J1-1 ), INCA,
     $                                  AB( L, J1 ), INCA, D( J1 ),
     $                                  WORK( J1 ), KD1 )
   10                   CONTINUE
*
                     ELSE
                        JEND = J1 + ( NR-1 )*KD1
                        DO 20 JINC = J1, JEND, KD1
C                           CALL DROT( KDM1, AB( 2, JINC-1 ), 1,
                           CALL DROT( KDM1, AB( 2, JINC-1 ), 1,
     $                                AB( 1, JINC ), 1, D( JINC ),
     $                                WORK( JINC ) )
   20                   CONTINUE
                     END IF
                  END IF
*
*
                  IF( K.GT.2 ) THEN
                     IF( K.LE.N-I+1 ) THEN
*
*                       generate plane rotation to annihilate a(i,i+k-1)
*                       within the band
*
C                        CALL DLARTG( AB( KD-K+3, I+K-2 ),
                        CALL DLARTG( AB( KD-K+3, I+K-2 ),
     $                               AB( KD-K+2, I+K-1 ), D( I+K-1 ),
     $                               WORK( I+K-1 ), TEMP )
                        AB( KD-K+3, I+K-2 ) = TEMP
*
*                       apply rotation from the right
*
C                        CALL DROT( K-3, AB( KD-K+4, I+K-2 ), 1,
                        CALL DROT( K-3, AB( KD-K+4, I+K-2 ), 1,
     $                             AB( KD-K+3, I+K-1 ), 1, D( I+K-1 ),
     $                             WORK( I+K-1 ) )
                     END IF
                     NR = NR + 1
                     J1 = J1 - KDN - 1
                  END IF
*
*                 apply plane rotations from both sides to diagonal
*                 blocks
*
                  IF( NR.GT.0 )
C     $               CALL DLAR2V( NR, AB( KD1, J1-1 ), AB( KD1, J1 ),
     $               CALL DLAR2V( NR, AB( KD1, J1-1 ), AB( KD1, J1 ),
     $                            AB( KD, J1 ), INCA, D( J1 ),
     $                            WORK( J1 ), KD1 )
*
*                 apply plane rotations from the left
*
                  IF( NR.GT.0 ) THEN
                     IF( 2*KD-1.LT.NR ) THEN
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    dLARTV or dROT is used
*
                        DO 30 L = 1, KD - 1
                           IF( J2+L.GT.N ) THEN
                              NRT = NR - 1
                           ELSE
                              NRT = NR
                           END IF
                           IF( NRT.GT.0 )
C     $                        CALL DLARTV( NRT, AB( KD-L, J1+L ), INCA,
     $                        CALL DLARTV( NRT, AB( KD-L, J1+L ), INCA,
     $                                     AB( KD-L+1, J1+L ), INCA,
     $                                     D( J1 ), WORK( J1 ), KD1 )
   30                   CONTINUE
                     ELSE
                        J1END = J1 + KD1*( NR-2 )
                        IF( J1END.GE.J1 ) THEN
                           DO 40 JIN = J1, J1END, KD1
C                              CALL DROT( KD-1, AB( KD-1, JIN+1 ), INCX,
                              CALL DROT( KD-1, AB( KD-1, JIN+1 ), INCX,
     $                                   AB( KD, JIN+1 ), INCX,
     $                                   D( JIN ), WORK( JIN ) )
   40                      CONTINUE
                        END IF
                        LEND = MIN( KDM1, N-J2 )
                        LAST = J1END + KD1
                        IF( LEND.GT.0 )
C     $                     CALL DROT( LEND, AB( KD-1, LAST+1 ), INCX,
     $                     CALL DROT( LEND, AB( KD-1, LAST+1 ), INCX,
     $                                AB( KD, LAST+1 ), INCX, D( LAST ),
     $                                WORK( LAST ) )
                     END IF
                  END IF
*
                  IF( WANTQ ) THEN
*
*                    accumulate product of plane rotations in Q
*
                     IF( INITQ ) THEN
*
*                 take advantage of the fact that Q was
*                 initially the Identity matrix
*
                        IQEND = MAX( IQEND, J2 )
                        I2 = MAX( 0, K-3 )
                        IQAEND = 1 + I*KD
                        IF( K.EQ.2 )
     $                     IQAEND = IQAEND + KD
                        IQAEND = MIN( IQAEND, IQEND )
                        DO 50 J = J1, J2, KD1
                           IBL = I - I2 / KDM1
                           I2 = I2 + 1
                           IQB = MAX( 1, J-IBL )
                           NQ = 1 + IQAEND - IQB
                           IQAEND = MIN( IQAEND+KD, IQEND )
C                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
     $                                1, D( J ), WORK( J ) )
   50                   CONTINUE
                     ELSE
*
                        DO 60 J = J1, J2, KD1
C                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
     $                                D( J ), WORK( J ) )
   60                   CONTINUE
                     END IF
*
                  END IF
*
                  IF( J2+KDN.GT.N ) THEN
*
*                    adjust J2 to keep within the bounds of the matrix
*
                     NR = NR - 1
                     J2 = J2 - KDN - 1
                  END IF
*
                  DO 70 J = J1, J2, KD1
*
*                    create nonzero element a(j-1,j+kd) outside the band
*                    and store it in WORK
*
                     WORK( J+KD ) = WORK( J )*AB( 1, J+KD )
                     AB( 1, J+KD ) = D( J )*AB( 1, J+KD )
   70             CONTINUE
   80          CONTINUE
   90       CONTINUE
         END IF
*
         IF( KD.GT.0 ) THEN
*
*           copy off-diagonal elements to E
*
            DO 100 I = 1, N - 1
               E( I ) = AB( KD, I+1 )
  100       CONTINUE
         ELSE
*
*           set E to zero if original matrix was diagonal
*
            DO 110 I = 1, N - 1
               E( I ) = ZERO
  110       CONTINUE
         END IF
*
*        copy diagonal elements to D
*
         DO 120 I = 1, N
            D( I ) = AB( KD1, I )
  120    CONTINUE
*
      ELSE
*
         IF( KD.GT.1 ) THEN
*
*           Reduce to tridiagonal form, working with lower triangle
*
            NR = 0
            J1 = KDN + 2
            J2 = 1
*
            DO 210 I = 1, N - 2
*
*              Reduce i-th column of matrix to tridiagonal form
*
               DO 200 K = KDN + 1, 2, -1
                  J1 = J1 + KDN
                  J2 = J2 + KDN
*
                  IF( NR.GT.0 ) THEN
*
*                    generate plane rotations to annihilate nonzero
*                    elements which have been created outside the band
*
C                     CALL DLARGV( NR, AB( KD1, J1-KD1 ), INCA,
                     CALL DLARGV( NR, AB( KD1, J1-KD1 ), INCA,
     $                            WORK( J1 ), KD1, D( J1 ), KD1 )
*
*                    apply plane rotations from one side
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    dLARTV or dROT is used
*
                     IF( NR.GT.2*KD-1 ) THEN
                        DO 130 L = 1, KD - 1
C                           CALL DLARTV( NR, AB( KD1-L, J1-KD1+L ), INCA,
                           CALL DLARTV( NR, AB( KD1-L, J1-KD1+L ), INCA,
     $                                  AB( KD1-L+1, J1-KD1+L ), INCA,
     $                                  D( J1 ), WORK( J1 ), KD1 )
  130                   CONTINUE
                     ELSE
                        JEND = J1 + KD1*( NR-1 )
                        DO 140 JINC = J1, JEND, KD1
C                           CALL DROT( KDM1, AB( KD, JINC-KD ), INCX,
                           CALL DROT( KDM1, AB( KD, JINC-KD ), INCX,
     $                                AB( KD1, JINC-KD ), INCX,
     $                                D( JINC ), WORK( JINC ) )
  140                   CONTINUE
                     END IF
*
                  END IF
*
                  IF( K.GT.2 ) THEN
                     IF( K.LE.N-I+1 ) THEN
*
*                       generate plane rotation to annihilate a(i+k-1,i)
*                       within the band
*
C                        CALL DLARTG( AB( K-1, I ), AB( K, I ),
                        CALL DLARTG( AB( K-1, I ), AB( K, I ),
     $                               D( I+K-1 ), WORK( I+K-1 ), TEMP )
                        AB( K-1, I ) = TEMP
*
*                       apply rotation from the left
*
C                        CALL DROT( K-3, AB( K-2, I+1 ), LDAB-1,
                        CALL DROT( K-3, AB( K-2, I+1 ), LDAB-1,
     $                             AB( K-1, I+1 ), LDAB-1, D( I+K-1 ),
     $                             WORK( I+K-1 ) )
                     END IF
                     NR = NR + 1
                     J1 = J1 - KDN - 1
                  END IF
*
*                 apply plane rotations from both sides to diagonal
*                 blocks
*
                  IF( NR.GT.0 )
C     $               CALL DLAR2V( NR, AB( 1, J1-1 ), AB( 1, J1 ),
     $               CALL DLAR2V( NR, AB( 1, J1-1 ), AB( 1, J1 ),
     $                            AB( 2, J1-1 ), INCA, D( J1 ),
     $                            WORK( J1 ), KD1 )
*
*                 apply plane rotations from the right
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    dLARTV or dROT is used
*
                  IF( NR.GT.0 ) THEN
                     IF( NR.GT.2*KD-1 ) THEN
                        DO 150 L = 1, KD - 1
                           IF( J2+L.GT.N ) THEN
                              NRT = NR - 1
                           ELSE
                              NRT = NR
                           END IF
                           IF( NRT.GT.0 )
C     $                        CALL DLARTV( NRT, AB( L+2, J1-1 ), INCA,
     $                        CALL DLARTV( NRT, AB( L+2, J1-1 ), INCA,
     $                                     AB( L+1, J1 ), INCA, D( J1 ),
     $                                     WORK( J1 ), KD1 )
  150                   CONTINUE
                     ELSE
                        J1END = J1 + KD1*( NR-2 )
                        IF( J1END.GE.J1 ) THEN
                           DO 160 J1INC = J1, J1END, KD1
C                              CALL DROT( KDM1, AB( 3, J1INC-1 ), 1,
                              CALL DROT( KDM1, AB( 3, J1INC-1 ), 1,
     $                                   AB( 2, J1INC ), 1, D( J1INC ),
     $                                   WORK( J1INC ) )
  160                      CONTINUE
                        END IF
                        LEND = MIN( KDM1, N-J2 )
                        LAST = J1END + KD1
                        IF( LEND.GT.0 )
C     $                     CALL DROT( LEND, AB( 3, LAST-1 ), 1,
     $                     CALL DROT( LEND, AB( 3, LAST-1 ), 1,
     $                                AB( 2, LAST ), 1, D( LAST ),
     $                                WORK( LAST ) )
                     END IF
                  END IF
*
*
*
                  IF( WANTQ ) THEN
*
*                    accumulate product of plane rotations in Q
*
                     IF( INITQ ) THEN
*
*                 take advantage of the fact that Q was
*                 initially the Identity matrix
*
                        IQEND = MAX( IQEND, J2 )
                        I2 = MAX( 0, K-3 )
                        IQAEND = 1 + I*KD
                        IF( K.EQ.2 )
     $                     IQAEND = IQAEND + KD
                        IQAEND = MIN( IQAEND, IQEND )
                        DO 170 J = J1, J2, KD1
                           IBL = I - I2 / KDM1
                           I2 = I2 + 1
                           IQB = MAX( 1, J-IBL )
                           NQ = 1 + IQAEND - IQB
                           IQAEND = MIN( IQAEND+KD, IQEND )
C                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
     $                                1, D( J ), WORK( J ) )
  170                   CONTINUE
                     ELSE
*
                        DO 180 J = J1, J2, KD1
C                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
     $                                D( J ), WORK( J ) )
  180                   CONTINUE
                     END IF
                  END IF
*
                  IF( J2+KDN.GT.N ) THEN
*
*                    adjust J2 to keep within the bounds of the matrix
*
                     NR = NR - 1
                     J2 = J2 - KDN - 1
                  END IF
*
                  DO 190 J = J1, J2, KD1
*
*                    create nonzero element a(j+kd,j-1) outside the
*                    band and store it in WORK
*
                     WORK( J+KD ) = WORK( J )*AB( KD1, J )
                     AB( KD1, J ) = D( J )*AB( KD1, J )
  190             CONTINUE
  200          CONTINUE
  210       CONTINUE
         END IF
*
         IF( KD.GT.0 ) THEN
*
*           copy off-diagonal elements to E
*
            DO 220 I = 1, N - 1
               E( I ) = AB( 2, I )
  220       CONTINUE
         ELSE
*
*           set E to zero if original matrix was diagonal
*
            DO 230 I = 1, N - 1
               E( I ) = ZERO
  230       CONTINUE
         END IF
*
*        copy diagonal elements to D
*
         DO 240 I = 1, N
            D( I ) = AB( 1, I )
  240    CONTINUE
      END IF
*
      RETURN
*
C*     End of DSBTRD
*     End of dSBTRD
*
      END
      SUBROUTINE DSYTRX( NB0, NX0,
     >                   UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            NB0, NX0, INFO, LDA, LWORK, N
C      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAU( * ),
     $                   WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAU( * ),
C     $                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  dSYTRx reduces a real symmetric matrix A to real symmetric
C*  DSYTRD reduces a real symmetric matrix A to real symmetric
*  tridiagonal form T by an orthogonal similarity transformation:
*  Q**T * A * Q = T.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point to the nonblocked algorithm.
C
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) double precision array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
*          N-by-N upper triangular part of A contains the upper
*          triangular part of the matrix A, and the strictly lower
*          triangular part of A is not referenced.  If UPLO = 'L', the
*          leading N-by-N lower triangular part of A contains the lower
*          triangular part of the matrix A, and the strictly upper
*          triangular part of A is not referenced.
*          On exit, if UPLO = 'U', the diagonal and first superdiagonal
*          of A are overwritten by the corresponding elements of the
*          tridiagonal matrix T, and the elements above the first
*          superdiagonal, with the array TAU, represent the orthogonal
*          matrix Q as a product of elementary reflectors; if UPLO
*          = 'L', the diagonal and first subdiagonal of A are over-
*          written by the corresponding elements of the tridiagonal
*          matrix T, and the elements below the first subdiagonal, with
*          the array TAU, represent the orthogonal matrix Q as a product
*          of elementary reflectors. See Further Details.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  D       (output) double precision array, dimension (N)
C*  D       (output) DOUBLE PRECISION array, dimension (N)
*          The diagonal elements of the tridiagonal matrix T:
*          D(i) = A(i,i).
*
*  E       (output) double precision array, dimension (N-1)
C*  E       (output) DOUBLE PRECISION array, dimension (N-1)
*          The off-diagonal elements of the tridiagonal matrix T:
*          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
*
*  TAU     (output) double precision array, dimension (N-1)
C*  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
*          The scalar factors of the elementary reflectors (see Further
*          Details).
*
*  WORK    (workspace/output) double precision array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.  LWORK >= 1.
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  Further Details
*  ===============
*
*  If UPLO = 'U', the matrix Q is represented as a product of elementary
*  reflectors
*
*     Q = H(n-1) . . . H(2) H(1).
*
*  Each H(i) has the form
*
*     H(i) = I - tau * v * v'
*
*  where tau is a real scalar, and v is a real vector with
*  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
*  A(1:i-1,i+1), and tau in TAU(i).
*
*  If UPLO = 'L', the matrix Q is represented as a product of elementary
*  reflectors
*
*     Q = H(1) H(2) . . . H(n-1).
*
*  Each H(i) has the form
*
*     H(i) = I - tau * v * v'
*
*  where tau is a real scalar, and v is a real vector with
*  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
*  and tau in TAU(i).
*
*  The contents of A on exit are illustrated by the following examples
*  with n = 5:
*
*  if UPLO = 'U':                       if UPLO = 'L':
*
*    (  d   e   v2  v3  v4 )              (  d                  )
*    (      d   e   v3  v4 )              (  e   d              )
*    (          d   e   v4 )              (  v1  e   d          )
*    (              d   e  )              (  v1  v2  e   d      )
*    (                  d  )              (  v1  v2  v3  e   d  )
*
*  where d and e denote diagonal and off-diagonal elements of T, and vi
*  denotes an element of the vector defining H(i).
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION    ONE
C      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
C      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB,
     $                   NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLATRD, DSYR2K, DSYTD2, XERBLA
C      EXTERNAL           DLATRD, DSYR2K, DSYTD2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      LQUERY = ( LWORK.EQ.-1 )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
         INFO = -9
      END IF
*
      IF( INFO.EQ.0 ) THEN
*
*        Determine the block size.
*
         IF ( NB0 .GT. 0 ) THEN
           NB = NB0
         ELSE
           NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         ENDIF
C         NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         LWKOPT = N*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'dSYTRD', -INFO )
C         CALL XERBLA( 'DSYTRD', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NX = N
      IWS = 1
      IF( NB.GT.1 .AND. NB.LT.N ) THEN
*
*        Determine when to cross over from blocked to unblocked code
*        (last block is always handled by unblocked code).
*
         IF ( NX0 .GT. 0 ) THEN
           NX = MAX( NB, NX0 )
         ELSE
           NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
         ENDIF
C         NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
         IF( NX.LT.N ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  determine the
*              minimum value of NB, and reduce NB or force use of
*              unblocked code by setting NX = N.
*
               NB = MAX( LWORK / LDWORK, 1 )
               NBMIN = 2
C               NBMIN = ILAENV( 2, 'DSYTRD', UPLO, N, -1, -1, -1 )
               IF( NB.LT.NBMIN )
     $            NX = N
            END IF
         ELSE
            NX = N
         END IF
      ELSE
         NB = 1
      END IF
*
      IF( UPPER ) THEN
*
*        Reduce the upper triangle of A.
*        Columns 1:kk are handled by the unblocked method.
*
         KK = N - ( ( N-NX+NB-1 ) / NB )*NB
         DO 20 I = N - NB + 1, KK + 1, -NB
*
*           Reduce columns i:i+nb-1 to tridiagonal form and form the
*           matrix W which is needed to update the unreduced part of
*           the matrix
*
            CALL DLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK,
     $                   LDWORK )
C            CALL DLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK,
C     $                   LDWORK )
*
*           Update the unreduced submatrix A(1:i-1,1:i-1), using an
*           update of the form:  A := A - V*W' - W*V'
*
            CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
     $                   LDA, WORK, LDWORK, ONE, A, LDA )
C            CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
C     $                   LDA, WORK, LDWORK, ONE, A, LDA )
*
*           Copy superdiagonal elements back into A, and diagonal
*           elements into D
*
            DO 10 J = I, I + NB - 1
               A( J-1, J ) = E( J-1 )
               D( J ) = A( J, J )
   10       CONTINUE
   20    CONTINUE
*
*        Use unblocked code to reduce the last or only block
*
         CALL DSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO )
C         CALL DSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO )
      ELSE
*
*        Reduce the lower triangle of A
*
         DO 40 I = 1, N - NX, NB
*
*           Reduce columns i:i+nb-1 to tridiagonal form and form the
*           matrix W which is needed to update the unreduced part of
*           the matrix
*
            CALL DLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ),
     $                   TAU( I ), WORK, LDWORK )
C            CALL DLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ),
C     $                   TAU( I ), WORK, LDWORK )
*
*           Update the unreduced submatrix A(i+ib:n,i+ib:n), using
*           an update of the form:  A := A - V*W' - W*V'
*
            CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
     $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
     $                   A( I+NB, I+NB ), LDA )
C            CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
C     $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
C     $                   A( I+NB, I+NB ), LDA )
*
*           Copy subdiagonal elements back into A, and diagonal
*           elements into D
*
            DO 30 J = I, I + NB - 1
               A( J+1, J ) = E( J )
               D( J ) = A( J, J )
   30       CONTINUE
   40    CONTINUE
*
*        Use unblocked code to reduce the last or only block
*
         CALL DSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ),
     $                TAU( I ), IINFO )
C         CALL DSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ),
C     $                TAU( I ), IINFO )
      END IF
*
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of dSYTRD
C*     End of DSYTRD
*
      END
      SUBROUTINE DLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
*  -- LAPACK auxiliary test routine (version 3.0)
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      DOUBLE PRECISION   A( LDA, * ), D( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DLAGSY generates a real symmetric matrix A, by pre- and post-
*  multiplying a real diagonal matrix D with a random orthogonal matrix:
*  A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*  orthogonal transformations.
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  K       (input) INTEGER
*          The number of nonzero subdiagonals within the band of A.
*          0 <= K <= N-1.
*
*  D       (input) DOUBLE PRECISION array, dimension (N)
*          The diagonal elements of the diagonal matrix D.
*
*  A       (output) DOUBLE PRECISION array, dimension (LDA,N)
*          The generated n by n symmetric matrix A (the full matrix is
*          stored).
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= N.
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry, the seed of the random number generator; the array
*          elements must be between 0 and 4095, and ISEED(4) must be
*          odd.
*          On exit, the seed is updated.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, HALF
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   ALPHA, TAU, WA, WB, WN
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DGEMV, DGER, DLARNV, DSCAL, DSYMV,
     $                   DSYR2, XERBLA
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DDOT, DNRM2
      EXTERNAL           DDOT, DNRM2
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SIGN
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      END IF
      IF( INFO.LT.0 ) THEN
         CALL XERBLA( 'DLAGSY', -INFO )
         RETURN
      END IF
*
*     initialize lower triangle of A to diagonal matrix
*
      DO 20 J = 1, N
         DO 10 I = J + 1, N
            A( I, J ) = ZERO
   10    CONTINUE
   20 CONTINUE
      DO 30 I = 1, N
         A( I, I ) = D( I )
   30 CONTINUE
*
*     Generate lower triangle of symmetric matrix
*
      DO 40 I = N - 1, 1, -1
*
*        generate random reflection
*
         CALL DLARNV( 3, ISEED, N-I+1, WORK )
         WN = DNRM2( N-I+1, WORK, 1 )
         WA = SIGN( WN, WORK( 1 ) )
         IF( WN.EQ.ZERO ) THEN
            TAU = ZERO
         ELSE
            WB = WORK( 1 ) + WA
            CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
            WORK( 1 ) = ONE
            TAU = WB / WA
         END IF
*
*        apply random reflection to A(i:n,i:n) from the left
*        and the right
*
*        compute  y := tau * A * u
*
         CALL DSYMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO,
     $               WORK( N+1 ), 1 )
*
*        compute  v := y - 1/2 * tau * ( y, u ) * u
*
         ALPHA = -HALF*TAU*DDOT( N-I+1, WORK( N+1 ), 1, WORK, 1 )
         CALL DAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 )
*
*        apply the transformation as a rank-2 update to A(i:n,i:n)
*
         CALL DSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
     $               A( I, I ), LDA )
   40 CONTINUE
*
*     Reduce number of subdiagonals to K
*
      DO 60 I = 1, N - 1 - K
*
*        generate reflection to annihilate A(k+i+1:n,i)
*
         WN = DNRM2( N-K-I+1, A( K+I, I ), 1 )
         WA = SIGN( WN, A( K+I, I ) )
         IF( WN.EQ.ZERO ) THEN
            TAU = ZERO
         ELSE
            WB = A( K+I, I ) + WA
            CALL DSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 )
            A( K+I, I ) = ONE
            TAU = WB / WA
         END IF
*
*        apply reflection to A(k+i:n,i+1:k+i-1) from the left
*
         CALL DGEMV( 'Transpose', N-K-I+1, K-1, ONE, A( K+I, I+1 ), LDA,
     $               A( K+I, I ), 1, ZERO, WORK, 1 )
         CALL DGER( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1,
     $              A( K+I, I+1 ), LDA )
*
*        apply reflection to A(k+i:n,k+i:n) from the left and the right
*
*        compute  y := tau * A * u
*
         CALL DSYMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA,
     $               A( K+I, I ), 1, ZERO, WORK, 1 )
*
*        compute  v := y - 1/2 * tau * ( y, u ) * u
*
         ALPHA = -HALF*TAU*DDOT( N-K-I+1, WORK, 1, A( K+I, I ), 1 )
         CALL DAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 )
*
*        apply symmetric rank-2 update to A(k+i:n,k+i:n)
*
         CALL DSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
     $               A( K+I, K+I ), LDA )
*
         A( K+I, I ) = -WA
         DO 50 J = K + I + 1, N
            A( J, I ) = ZERO
   50    CONTINUE
   60 CONTINUE
*
*     Store full symmetric matrix
*
      DO 80 J = 1, N
         DO 70 I = J + 1, N
            A( J, I ) = A( I, J )
   70    CONTINUE
   80 CONTINUE
      RETURN
*
*     End of DLAGSY
*
      END
      DOUBLE PRECISION FUNCTION DLARAN( ISEED )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
*     ..
*
*  Purpose
*  =======
*
*  DLARAN returns a random real number from a uniform (0,1)
*  distribution.
*
*  Arguments
*  =========
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry, the seed of the random number generator; the array
*          elements must be between 0 and 4095, and ISEED(4) must be
*          odd.
*          On exit, the seed is updated.
*
*  Further Details
*  ===============
*
*  This routine uses a multiplicative congruential method with modulus
*  2**48 and multiplier 33952834046453 (see G.S.Fishman,
*  'Multiplicative congruential random number generators with modulus
*  2**b: an exhaustive analysis for b = 32 and a partial analysis for
*  b = 48', Math. Comp. 189, pp 331-344, 1990).
*
*  48-bit integers are stored in 4 integer array elements with 12 bits
*  per element. Hence the routine is portable across machines with
*  integers of 32 bits or more.
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            M1, M2, M3, M4
      PARAMETER          ( M1 = 494, M2 = 322, M3 = 2508, M4 = 2549 )
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
      INTEGER            IPW2
      DOUBLE PRECISION   R
      PARAMETER          ( IPW2 = 4096, R = ONE / IPW2 )
*     ..
*     .. Local Scalars ..
      INTEGER            IT1, IT2, IT3, IT4
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE, MOD
*     ..
*     .. Executable Statements ..
*
*     multiply the seed by the multiplier modulo 2**48
*
      IT4 = ISEED( 4 )*M4
      IT3 = IT4 / IPW2
      IT4 = IT4 - IPW2*IT3
      IT3 = IT3 + ISEED( 3 )*M4 + ISEED( 4 )*M3
      IT2 = IT3 / IPW2
      IT3 = IT3 - IPW2*IT2
      IT2 = IT2 + ISEED( 2 )*M4 + ISEED( 3 )*M3 + ISEED( 4 )*M2
      IT1 = IT2 / IPW2
      IT2 = IT2 - IPW2*IT1
      IT1 = IT1 + ISEED( 1 )*M4 + ISEED( 2 )*M3 + ISEED( 3 )*M2 +
     $      ISEED( 4 )*M1
      IT1 = MOD( IT1, IPW2 )
*
*     return updated seed
*
      ISEED( 1 ) = IT1
      ISEED( 2 ) = IT2
      ISEED( 3 ) = IT3
      ISEED( 4 ) = IT4
*
*     convert 48-bit integer to a real number in the interval (0,1)
*
      DLARAN = R*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R*
     $         ( DBLE( IT4 ) ) ) ) )
      RETURN
*
*     End of DLARAN
*
      END
* **********************************************************************
*
        PROGRAM DRUN
*
* Description:
*
*   This is the testing and timing driver for the SBR toolbox.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Local constants and variables:
*
        DOUBLE PRECISION      ONE
        PARAMETER             ( ONE = 1.0D0 )
*
*          --- array dimensions ---
*
        INTEGER               NMAX, SZA, SZACPY, SZU, SZWORK
        PARAMETER             ( NMAX = 1400 ,
     >                          SZA = NMAX * NMAX ,
     >                          SZACPY = 500 * NMAX ,
     >                          SZU = NMAX * NMAX ,
     >                          SZWORK = NMAX * NMAX  )
        DOUBLE PRECISION      A( SZA ), ACPY( SZACPY ), U( SZU ),
     >                        EVLS( NMAX ), D( NMAX ), E( NMAX ),
     >                        TAU( NMAX ), WORK( SZWORK )
        COMMON    /ARRAYS/    A, ACPY, U, EVLS, D, E, TAU, WORK
*
*   nmax    maximum matrix size
*   a       holds the matrix A to be reduced (full or banded)
*   sza     size of the array a.
*           sza >= nmax * nmax,       if full matrices are handled
*               >= ( bmax+1 ) * nmax, if only banded matrices with
*                                     semibandwidth <= bmax are handled
*   acpy    holds the reduced matrix (banded)
*   szacpy  size of the array acpy.
*           szacpy >= ( bmax+1 ) * nmax, where bmax is the maximum
*                                        semibandwith
*   u       holds the accumulated transformation matrix U, if required
*   szu     size of the array u.
*           szu >= nmax * nmax, if U is accumulated
*               >= 0,           otherwise
*   evls    the eigenvalues of the matrix A (accessed during
*           initialization)
*   d       main diagonal of the reduced tridiagonal matrix
*   e       sub(super)diagonal of the reduced tridiagonal matrix
*   tau     scaling factors in the reduction full -> banded/tridiagonal
*   work    workspace
*   szwork  size of the array work.
*           szwork depends on the reduction algorithms that are run, on
*           the matrix sizes, on the blocking factors, and on the
*           leading dimensions of the matrices.
*           Recomended: szwork >= 100 * nmax.
*   arrays  common block is used only because some machines cannot
*           handle large arrays on the stack
*
*          --- I/O control ---
*
        INTEGER               IUNIT, OUNIT, OUNITF, I1MACH
*       PARAMETER             ( IUNIT = 5, OUNITF = 8 )
*       CHARACTER*8           IFILE
        CHARACTER*8           OFILE
*       PARAMETER             ( IFILE = 'INFILE' )
        INTEGER               OLEVEL, OUTSUM, OUTTUN, OUTRUN, OUTDET,
     >                        LINENO, LINE0
        PARAMETER             ( OUTSUM = 1, OUTTUN = 2, OUTRUN = 3,
     >                          OUTDET = 4 )
        CHARACTER*78          MBUF
*
*   iunit   unit number for input file
*   ounit   unit number for output
*   ounitf  unit number for output file
*   ifile   name of input file
*   ofile   name of output file
*   olevel  level of output
*           olevel = outsum : only summary for all the runs
*                  = outtun : short summaries for tuning
*                  = outrun : summary for each run
*                  = outdet : detailed output for each run
*   lineno  number of current input line
*   line0   first input line corresponding to the current run
*   mbuf    buffer for messages
*
*          --- for statistics ---
*
        INTEGER               SYTRD, ORGTR, SBTRD, SYRDB, SYGTR, SBRDB,
     >                        SBRDT, SY2BC, SY2BI, SB2BC, SB2BI, SYRDD,
     >                        SBRDD, TOTAL
        PARAMETER             ( SYTRD = 1, ORGTR = 2, SBTRD = 3,
     >                          SYRDB = 4, SYGTR = 5, SBRDB = 6,
     >                          SBRDT = 7, SY2BC = 8, SY2BI = 9,
     >                          SB2BC = 10, SB2BI = 11, SYRDD = 12,
     >                          SBRDD = 13, TOTAL = 14 )
        INTEGER               TRY( TOTAL ), SKIP( TOTAL ), FAIL( TOTAL )
        CHARACTER*6           PRBLMN( TOTAL )
        CHARACTER*40          COMMNT( TOTAL )
*
*   sytrd   tests for dsytrd (full -> tridiagonal, LAPACK)
*   orgtr   tests for dorgtr (backward accumulation, LAPACK)
*   sbtrd   tests for dsbtrd (banded -> tridiagonal, LAPACK)
*   syrdb   tests for dsyrdb (full -> banded, SBR)
*   sygtr   tests for dsygtr (backward accumulation, SBR)
*   sbrdb   tests for dsbrdb (banded -> banded, SBR)
*   sbrdt   tests for dsbrdt (banded -> tridiagonal, SBR)
*   sy2bc   tests for dsy2bc (full -> banded copy, SBR)
*   sy2bi   tests for dsy2bi (full -> banded repacking, SBR)
*   sb2bc   tests for dsb2bc (banded -> banded copy, SBR)
*   sb2bi   tests for dsb2bi (banded -> banded repacking, SBR)
*   syrdd   tests for dsyrdd (reduction driver for full matrices, SBR)
*   sbrdd   tests for dsbrdd (reduction driver for banded matrices, SBR)
*   total   all tests
*   count   counters for all tests
*   fail    counters for failed tests
*   skip    counters for skipped tests
*   prblmn  names of the reduction paths (for output)
*   commnt  comments to the reduction paths (for output)
*
        REAL      STIME, BTIME, CTIME, RTIME
*
*   stime   time before all the tests
*   btime   time before the procedure call
*   ctime   time for the procedure call
*   rtime   time for a full reduction/accumulation path
*
*        --- controlling the test runs ---
*
        DOUBLE PRECISION      EPS, NOTUSD
*
*   eps     machine epsilon
*   notusd  (large) value for marking memory that should not be accessed
*
        CHARACTER*5           PNAME
        INTEGER               MAXDIM, PRBLM, N, B1, LDA1, B2, LDA2, LDU,
     >                        NSTEPS, STEP, LWORK1, LWORK2, NX1, NX2,
     >                        XINFO1, XINFO2, INFO
        CHARACTER             MTYPE, UPLO, FRMT1, FRMT2, JOBU, JOBU0
        DOUBLE PRECISION      DIAM, DRPTOL
        INTEGER               B( 100 ), NB( 100 )
*
*   pname   name of the routine to test (without precision specifier)
*   maxdim  maximum matrix size for the runs (runs with larger matrices
*           are skipped)
*   prblm   number of the routine to test (numbering sytrd=1, etc. as
*           above)
*   mtype   matrix type
*           mtype = 'R' : Eigenvalues are uniformly random in [ -1, 1 ).
*                 = 'I' : ISDA-type matrix: eigenvalues are clustered
*                         around 0 and 1.
*   diam    diameter of the eigenvalue clusters in multiples of the
*           machine precision (used only for ISDA-type matrices)
*   uplo    use upper or lower triangle of the matrix ?
*   n       matrix dimension
*   frmt1   format of the matrix before the reduction ('F'ull/'B'anded)
*   b1      semibandwidth before the reduction
*   lda1    leading dimension before the reductino
*   frmt2   format after the reduction ('B'anded/'T'ridiagonal)
*   b2      semibandwidth after the reduction
*   lda2    leading dimension after the reduction
*   jobu0   accumulate the transformations in an orthogonal matrix ?
*   jobu    accumulate in the current routine ?
*   ldu     leading dimension of the array u
*   nsteps  number of reduction steps (used only in the driver routines)
*   step    number of the last step performed or tried
*   b       intermediate bandwidths for multi-step reduction
*   nb      blocking factors for the reduction/accumulation steps
*   drptol  threshold for skipping ransformations
*   lwork1  length of workspace for the reduction
*   lwork2  length of workspace for backward accumulation
*   nx1     cross-over point for LAPACK tridiagonalization dsytrd
*   nx2     cross-over point for LAPACK backward accumulation dorgtr
*   xinfo1  error code expected from the reduction routine
*   xinfo2  error code expected from backward accumulation
*   info    actual error code returned from the routines
*
        CHARACTER             CHECK
        DOUBLE PRECISION      ORTHU, SORTHU, TORTHU, RES, SRES, TRES,
     >                        DEVLS, SDEVLS, TDEVLS
        LOGICAL               CHECKS, ERRCHK, OK
        INTEGER               NUSED
*
*   check   is result checking required ? ('C'check/'N'oCheck)
*   checks  are checks enabled ?
*   orthu   ortogonality error, i.e., (Frobenius) norm of U' * U - I
*   sorthu  = orthu / ( n * eps ), the scaled orthogonality error
*   torthu  threshold on sorthu for accepting the run
*   res     residual, i.e., (Frobenius) norm of U * B - A * U, where
*           A is the original matrix and B is the reduced matrix
*   sres    = res / ( n * eps * norm( A ) ), the scaled residual
*   tres    threshold on sres
*   devls   deviation of the eigenvalues, i.e., (Frobenius) norm of
*           spec( A ) - spec( B ), where spec( A ) and spec( B ) are
*           the (ascendingly sorted) eigenvalues of the original matrix
*           and the reduced matrix, respectively
*   sdevls  = devls / ( n * eps * norm( A ) ), the scaled deviation
*   tdevls  threshold on devls
*   errchk  was it a check for error exit ?
*   ok      did the numerical checks meet the thresholds ?
*   nused   number of workspace elements that were modified
*
      INTEGER                 I
*
* Routines called:
*
        REAL                  SECOND
        DOUBLE PRECISION      D1MACH
        LOGICAL               LSAME, LXSAME
        EXTERNAL              SECOND, D1MACH, LSAME, LXSAME
*
*   dsecnd  timer (LAPACK)
*   dlamch  determine machine parameters (LAPACK)
*   lsame   case-insensitive character-matching (BLAS)
*   lxsame  case-insensitive string matching (this file)
*
        EXTERNAL              DLACPY, DORGTX, DSB2BC, DSB2BI, DSBRDB,
     >                        DSBRDD, DSBRDT, DSBTRX, DSY2BC, DSY2BI,
     >                        DSYGTR, DSYINI, DSYNCK, DSYRDB, DSYRDD,
     >                        DSYTRX
*
*   dlacpy  copy matrix (LAPACK)
*   dorgtx  backward accumulation of transformations (LAPACK, modified)
*   dsb2bc  banded -> banded copy (SBR)
*   dsb2bi  banded -> banded repacking (SBR)
*   dsbrdb  banded -> banded reduction (SBR)
*   dsbrdd  reduction driver for banded matrices (SBR)
*   dsbrdt  banded -> tridiagonal reduction (SBR)
*   dsbtrx  banded -> tridiagonal reduction (LAPACK, modified)
*   dsy2bc  full -> banded copy (SBR)
*   dsy2bi  full -> banded repacking (SBR)
*   dsygtr  backward accumulation of transformations (SBR)
*   dsyini  initialize symmetric (full or banded) matrix
*   dsynck  numerical checks for the reduction
*   dsyrdb  full -> banded reduction (SBR)
*   dsyrdd  reduction driver for full matrices (SBR)
*   dsytrx  full -> tridiagonal reduction (LAPACK, modified)
*
        INTRINSIC             MAX, MIN
*
*          --- names and explanations for the test paths ---
*
        DATA
     >      PRBLMN( SYTRD )/'dsytrd'/,
     >      COMMNT( SYTRD )/'full -> tridiagonal, one-step (LAPACK)'/,
     >      PRBLMN( ORGTR )/'dorgtr'/,
     >      COMMNT( ORGTR )/'accumulation of transformations (LAPACK)'/,
     >      PRBLMN( SBTRD )/'dsbtrd'/,
     >      COMMNT( SBTRD )/'banded -> tridiagonal, one-step (LAPACK)'/
        DATA
     >      PRBLMN( SYRDB )/'dsyrdb'/,
     >      COMMNT( SYRDB )/'full -> banded, one-step (SBR)'/,
     >      PRBLMN( SYGTR )/'dsygtr'/,
     >      COMMNT( SYGTR )/'accumulation of transformations (SBR)'/,
     >      PRBLMN( SBRDB )/'dsbrdb'/,
     >      COMMNT( SBRDB )/'banded -> banded, one-step (SBR)'/,
     >      PRBLMN( SBRDT )/'dsbrdt'/,
     >      COMMNT( SBRDT )/'banded -> tridiagonal, one-step (SBR)'/
        DATA
     >      PRBLMN( SY2BC )/'dsy2bc'/,
     >      COMMNT( SY2BC )/'copy full -> banded (SBR)'/,
     >      PRBLMN( SY2BI )/'dsy2bi'/,
     >      COMMNT( SY2BI )/'in-place copy full -> banded (SBR)'/,
     >      PRBLMN( SB2BC )/'dsb2bc'/,
     >      COMMNT( SB2BC )/'copy banded -> banded (SBR)'/,
     >      PRBLMN( SB2BI )/'dsb2bi'/,
     >      COMMNT( SB2BI )/'in-place copy banded -> banded (SBR)'/
        DATA
     >      PRBLMN( SYRDD )/'dsyrdd'/,
     >      COMMNT( SYRDD )/'reduction driver for full matrices (SBR)'/,
     >      PRBLMN( SBRDD )/'dsbrdd'/,
     >      COMMNT( SBRDD )/'reduction driver for banded matrcs (SBR)'/,
     >      PRBLMN( TOTAL )/'Total '/,
     >      COMMNT( TOTAL )/' '/
*
* ----------------------------------------------------------------------
*
        STIME = SECOND()
*
*          --- initialize ---
*
        DO 1000 I = 1, TOTAL
          TRY( I ) = 0
          SKIP( I ) = 0
          FAIL( I ) = 0
 1000   CONTINUE
*
*       EPS = DLAMCH( 'Epsilon' )
*       NOTUSD = ONE / DLAMCH( 'SafeMinimum' )
        EPS = D1MACH(4)
	NOTUSD = ONE /(D1MACH(1)*(ONE+EPS))
*
*          --- open input and output files ---
*
*       OPEN( UNIT=IUNIT, FILE=IFILE )
        LINENO = 0
*
	IUNIT = I1MACH(1)
        OUNIT = I1MACH(2)
        OLEVEL = OUTSUM
        MAXDIM = NMAX
        CHECKS = .TRUE.
*
 2000   CONTINUE
*
*            --- read next line from input file ---
*
          LINENO = LINENO + 1
          LINE0 = LINENO
          READ( IUNIT, * ) PNAME
*         WRITE( *, * ) LINE0
*
*            --- if comment line then just skip it ---
*
          IF ( LSAME( PNAME( 1:1 ), 'Comment' ) ) THEN
            GOTO 2000
*
*            --- filename for output file ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'FileName' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) OFILE( 2:8 )
            OFILE( 1:1 ) = 'DoublePrec'
            OUNIT = OUNITF
            OPEN( UNIT=OUNIT, FILE=OFILE )
            GOTO 2000
*
*            --- set output level ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'OutputLevel' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) I
            IF ( ( I .LT. OUTSUM ) .OR. ( I .GT. OUTDET ) ) THEN
              WRITE( OUNIT, 9300 ) LINENO, 'Output level out of range'
            ELSE
              OLEVEL = I
            ENDIF
            GOTO 2000
*
*            --- message to print ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'Print' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) MBUF
            WRITE( OUNIT, 9100 ) MBUF
            GOTO 2000
*
*            --- maximum matrix size ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'MaxDim' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) MAXDIM
            GOTO 2000
*
*            --- disable checks ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'NoChecks' ) ) THEN
            CHECKS = .FALSE.
            GOTO 2000
*
*            --- test run ?
*                If so then read and set parameters for the run ---
*
          ELSEIF ( LXSAME( PNAME, 'SYTRD' ) ) THEN
*
*              --- LAPACK reduction full -> tridiagonal ---
*
            PRBLM = SYTRD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, NB( 1 ), NX1,
     >                       LWORK1, XINFO1, JOBU, NB( 2 ), NX2, LWORK2,
     >                       XINFO2
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SBTRD' ) ) THEN
*
*              --- LAPACK reduction banded -> tridiagonal ---
*
            PRBLM = SBTRD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, JOBU, LDU,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
            LWORK1 = N
          ELSEIF ( LXSAME( PNAME, 'SYRDB' ) ) THEN
*
*              --- SBR reduction full -> banded ---
*
            PRBLM = SYRDB
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, B2, DRPTOL,
     >                       NB( 1 ), LWORK1, XINFO1
            LINENO = LINENO + 1
            READ( IUNIT, * ) JOBU0, LDU, LWORK2, XINFO2
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Banded'
            LDA2 = B2 + 1
            IF ( LSAME( JOBU0, 'OnFly' ) ) THEN
              JOBU = 'Update'
            ELSEIF ( LSAME( JOBU0, 'Update' ) ) THEN
              JOBU = 'NoU'
            ELSE
              JOBU = JOBU0
            ENDIF
          ELSEIF ( LXSAME( PNAME, 'SBRDB' ) ) THEN
*
*              --- SBR reduction banded -> banded ---
*
            PRBLM = SBRDB
            READ( IUNIT, * ) MTYPE, DIAM, N, B1, LDA1, B2, DRPTOL,
     >                       NB( 1 ), JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            UPLO = 'Lower'
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Banded'
            LDA2 = B2 + 1
          ELSEIF ( LXSAME( PNAME, 'SBRDT' ) ) THEN
*
*              --- SBR reduction banded -> tridiagonal ---
*
            PRBLM = SBRDT
            READ( IUNIT, * ) MTYPE, DIAM, N, B1, LDA1, DRPTOL, NB( 1 ),
     >                       JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            UPLO = 'Lower'
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
          ELSEIF ( LXSAME( PNAME, 'SY2BC' ) ) THEN
*
*              --- SBR copy full -> banded ---
*
            PRBLM = SY2BC
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Full'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SY2BI' ) ) THEN
*
*              --- SBR in-place copy full -> banded ---
*
            PRBLM = SY2BI
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Full'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SB2BC' ) ) THEN
*
*              --- SBR copy banded -> banded ---
*
            PRBLM = SB2BC
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SB2BI' ) ) THEN
*
*              --- SBR in-place copy full -> banded ---
*
            PRBLM = SB2BI
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SYRDD' ) ) THEN
*
*              --- SBR driver for full matrices ---
*
            PRBLM = SYRDD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, B2, LDA2,
     >                       NSTEPS, DRPTOL, JOBU, LWORK1, XINFO1
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            DRPTOL = DRPTOL * EPS
            IF ( B2 .EQ. 1 ) THEN
              FRMT2 = 'Tridiagonal'
            ELSE
              FRMT2 = 'Banded'
            ENDIF
            LDU = N
            IF ( NSTEPS .GT. 1 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( B( I ), I = 1, NSTEPS-1 )
            ENDIF
            IF ( NSTEPS .GT. 0 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( NB( I ), I = 1, NSTEPS )
            ENDIF
          ELSEIF ( LXSAME( PNAME, 'SBRDD' ) ) THEN
*
*              --- SBR driver for banded matrices ---
*
            PRBLM = SBRDD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, B2, NSTEPS,
     >                       DRPTOL, JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            DRPTOL = DRPTOL * EPS
            IF ( B2 .EQ. 1 ) THEN
              FRMT2 = 'Tridiagonal'
            ELSE
              FRMT2 = 'Banded'
            ENDIF
            LDA2 = B2 + 1
            IF ( NSTEPS .GT. 1 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( B( I ), I = 1, NSTEPS-1 )
            ENDIF
            IF ( NSTEPS .GT. 0 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( NB( I ), I = 1, NSTEPS )
            ENDIF
*
*            --- done ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'Quit' ) ) THEN
            GOTO 8000
          ELSE
            WRITE( OUNIT, 9300 ) LINENO, 'Command not recognized'
            GOTO 2000
          ENDIF
*
*  - - - - - - - - if we get here then a test run is required - - - - -
*
          LINENO = LINENO + 2
          READ ( IUNIT, * ) CHECK, TORTHU, TRES, TDEVLS
          ERRCHK = .FALSE.
*
          TRY( PRBLM ) = TRY( PRBLM ) + 1
*
*            --- is the problem too large ? ---
*
          IF ( N .GT. MAXDIM ) THEN
            SKIP( PRBLM ) = SKIP( PRBLM ) + 1
            WRITE( OUNIT, 9310 ) LINE0
            GOTO 2000
          ENDIF
*
*            ---  initialize matrices ---
*
          INFO = 0
          BTIME = SECOND()
          CALL DSYINI( MTYPE, EVLS, NMAX, DIAM,
     >                 FRMT1, UPLO, N, B1, A, LDA1, SZA,
     >                 JOBU, U, LDU, SZU,
     >                 NOTUSD, WORK, SZWORK, INFO )
          CTIME = SECOND() - BTIME
*
*            --- protocol output, if required ---
*
          IF ( OLEVEL .GE. OUTDET ) THEN
            WRITE( OUNIT, 9500 ) MTYPE, NMAX, DIAM, FRMT1, UPLO, N
            WRITE( OUNIT, 9501 ) B1, LDA1, SZA, JOBU, LDU, SZU
            WRITE( OUNIT, 9502 ) NOTUSD, SZWORK
            WRITE( OUNIT, 9400 ) INFO, CTIME
          ENDIF
*
          IF ( ( INFO .EQ. -3 ) .OR. ( INFO .EQ. -11 ) .OR.
     >         ( INFO .EQ. -15 ) .OR. ( INFO .EQ. -18 ) ) THEN
*
*              --- test problem is too large : skip ---
*
            SKIP( PRBLM ) = SKIP( PRBLM ) + 1
            WRITE( OUNIT, 9310 ) LINE0
            GOTO 3000
          ENDIF
*
*            --- mark workspace "unused" ---
*
          DO 2100 I = 1, MIN( MAX( 2*LWORK1, 10000 ), SZWORK )
            WORK( I ) = NOTUSD
 2100     CONTINUE
*
*  - - - - - - - - do the reduction / repacking - - - - - - - - - - - -
*
          INFO = 0
          BTIME = SECOND()
          IF ( PRBLM .EQ. SYTRD ) THEN
            CALL DSYTRX( NB( 1 ), NX1, UPLO, N, A, LDA1, D, E,
     >                   TAU, WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBTRD ) THEN
            CALL DSBTRX( JOBU, UPLO, N, B1, A, LDA1, D, E,
     >                   U, LDU, WORK, INFO )
          ELSEIF ( PRBLM .EQ. SYRDB ) THEN
            CALL DSYRDB( UPLO, JOBU, N, B2, A, LDA1, DRPTOL,
     >                   U, LDU, NB( 1 ), TAU, WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBRDB ) THEN
            CALL DSBRDB( JOBU, N, B1, B2, A, LDA1, DRPTOL,
     >                   U, LDU, NB( 1 ), WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBRDT ) THEN
            CALL DSBRDT( JOBU, N, B1, A, LDA1, DRPTOL, D, E,
     >                   U, LDU, NB( 1 ), WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SY2BC ) THEN
            CALL DSY2BC( UPLO, N, B1, A, LDA1, ACPY, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SY2BI ) THEN
            CALL DSY2BI( UPLO, N, B1, A, LDA1, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SB2BC ) THEN
            CALL DSB2BC( UPLO, N, B1, A, LDA1, ACPY, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SB2BI ) THEN
            CALL DSB2BI( UPLO, N, B1, A, LDA1, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SYRDD ) THEN
            CALL DSYRDD( JOBU, UPLO, N, B2, A, LDA1, DRPTOL,
     >                   ACPY, LDA2, D, E, NSTEPS, B, NB,
     >                   WORK, LWORK1, STEP, INFO )
          ELSEIF ( PRBLM .EQ. SBRDD ) THEN
            CALL DSBRDD( JOBU, UPLO, N, B1, B2, A, LDA1, DRPTOL,
     >                   D, E, U, LDU, NSTEPS, B, NB,
     >                   WORK, LWORK1, STEP, INFO )
          ENDIF
          CTIME = SECOND() - BTIME
          RTIME = CTIME
*
*            --- protocol output, if required ---
*
          IF ( OLEVEL .GE. OUTDET ) THEN
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9510 ) UPLO, N, LDA1, NB( 1 ), NX1, LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9520 ) JOBU, UPLO, N, B1, LDA1, LDU
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9530 ) UPLO, JOBU, N, B2, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9540 ) JOBU, N, B1, B2, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9550 ) JOBU, N, B1, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SY2BC ) THEN
              WRITE( OUNIT, 9560 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SY2BI ) THEN
              WRITE( OUNIT, 9570 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SB2BC ) THEN
              WRITE( OUNIT, 9580 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SB2BI ) THEN
              WRITE( OUNIT, 9590 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9600 ) JOBU, UPLO, N, B2, LDA1
              WRITE( OUNIT, 9601 ) DRPTOL, LDA2, NSTEPS, LWORK1
              WRITE( OUNIT, 9401 ) STEP, INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9610 ) JOBU, UPLO, N, B1, B2, LDA1
              WRITE( OUNIT, 9611 ) DRPTOL, LDU, NSTEPS, LWORK1
              WRITE( OUNIT, 9401 ) STEP, INFO, CTIME
            ENDIF
          ELSEIF ( OLEVEL .EQ. OUTTUN ) THEN
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9515 ) UPLO, N, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9525 ) UPLO, JOBU, N, B1, INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9535 ) UPLO, JOBU, N, B2, NB( 1 ), INFO,
     >                             CTIME
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9545 ) JOBU, N, B1, B2, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9555 ) JOBU, N, B1, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9605 ) UPLO, JOBU, N, B2, NSTEPS, STEP,
     >                             INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9615 ) UPLO, JOBU, N, B1, B2, NSTEPS, STEP,
     >                             INFO, CTIME
            ENDIF
          ENDIF
*
*  - - - - - - - - check if the error code is as expected - - - - - - -
*
          IF ( INFO .NE. XINFO1 ) THEN
*
*              --- wrong error code ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            IF ( ( PRBLM .EQ. SYRDD ) .OR. ( PRBLM .EQ. SBRDD ) ) THEN
              WRITE( OUNIT, 9900 ) LINE0, PRBLMN( PRBLM ), INFO, STEP,
     >                             XINFO1
            ELSE
              WRITE( OUNIT, 9901 ) LINE0, PRBLMN( PRBLM ), INFO, XINFO1
            ENDIF
            GOTO 3000
          ELSEIF ( ( ( PRBLM .EQ. SYRDD ) .OR. ( PRBLM .EQ. SBRDD ) )
     >             .AND. ( INFO .EQ. 1 ) .AND. ( NSTEPS .GT. 0 )
     >             .AND. ( STEP .NE. NSTEPS ) ) THEN
*
*              --- error code was ok, but the driver took a wrong
*                  number of steps                                ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            WRITE( OUNIT, 9910 ) LINE0, PRBLMN( PRBLM ), STEP,
     >                           NSTEPS
            GOTO 3000
          ELSEIF ( INFO .LT. 0 ) THEN
*
*              --- successful error exit ---
*
            ERRCHK = .TRUE.
            GOTO 3000
          ENDIF
*
*  - - - - - - - - check workspace usage - - - - - - - - - - - - - - - -
*
          NUSED = 0
          DO 2200 I = 1, MIN( MAX( 2*LWORK1, 10000 ), SZWORK )
            IF ( .NOT. ( WORK( I ) .EQ. NOTUSD ) )     NUSED = I
 2200     CONTINUE
*
          IF ( NUSED .GT. LWORK1 ) THEN
*
*              --- ran over the workspace bounds ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            WRITE( OUNIT, 9920 ) LINE0, PRBLMN( PRBLM ), NUSED, LWORK1
            GOTO 3000
          ELSEIF ( OLEVEL .GE. OUTDET ) THEN
*
*            --- write protocol ---
*
            WRITE( OUNIT, 9410 ) NUSED, LWORK1
          ENDIF
*
*  - - - - - - - - accumulate transformations, if required - - - - - - -
*
          IF ( ( PRBLM .EQ. SYTRD ) .AND. LSAME( JOBU, 'Update' ) ) THEN
*
*              --- copy the Householder vectors into the array u ---
*
            CALL DLACPY( UPLO, N, N, A, LDA1, U, LDU )
*
*              --- backward accumulation ---
*
            TRY( ORGTR ) = TRY( ORGTR ) + 1
            INFO = 0
            BTIME = SECOND()
            CALL DORGTX( NB( 2 ), NX2, UPLO, N, U, LDU, TAU,
     >                   WORK, LWORK2, INFO )
            CTIME = SECOND() - BTIME
            RTIME = RTIME + CTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9620 ) UPLO, N, LDU, NB( 2 ), NX2, LWORK2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- is the error code as expected ? ---
*
            IF ( INFO .NE. XINFO2 ) THEN
              FAIL( ORGTR ) = FAIL( ORGTR ) + 1
              WRITE( OUNIT, 9901 ) LINE0, 'dorgtr', INFO, XINFO2
              GOTO 3000
            ELSEIF ( INFO .NE. 0 ) THEN
              ERRCHK = .TRUE.
              GOTO 3000
            ENDIF
*
          ELSEIF ( ( PRBLM .EQ. SYRDB ) .AND. LSAME( JOBU0, 'Update' ) )
     >    THEN
*
*              --- copy the Householder vectors into the array u ---
*
            CALL DLACPY( UPLO, N, N, A, LDA1, U, LDU )
*
*              --- backward accumulation ---
*
            TRY( SYGTR ) = TRY( SYGTR ) + 1
            INFO = 0
            BTIME = SECOND()
            CALL DSYGTR( UPLO, N, B2, U, LDU, TAU, WORK, LWORK2, INFO )
            CTIME = SECOND() - BTIME
            RTIME = RTIME + CTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9630 ) UPLO, N, B2, LDU, LWORK2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- is the error code as expected ? ---
*
            IF ( INFO .NE. XINFO2 ) THEN
              FAIL( SYGTR ) = FAIL( SYGTR ) + 1
              WRITE( OUNIT, 9901 ) LINE0, 'dsygtr', INFO, XINFO2
              GOTO 3000
            ELSEIF ( INFO .NE. 1 ) THEN
              GOTO 3000
            ENDIF
          ENDIF
*
*  - - - - - - - - check results - - - - - - - - - - - - - - - - - - - -
*
          ORTHU = -ONE
          SORTHU = -ONE
          RES = -ONE
          SRES = -ONE
          DEVLS = -ONE
          SDEVLS = -ONE
*
          IF ( ( .NOT. ERRCHK ) .AND.
     >         CHECKS .AND. LSAME( CHECK, 'Check' ) ) THEN
            OK = .TRUE.
*
*              --- if the reduced matrix is banded then copy it
*                  into the array acpy                          ---
*
            IF ( PRBLM .EQ. SYRDB ) THEN
              INFO = 0
              BTIME = SECOND()
              CALL DSY2BC( UPLO, N, B2, A, LDA1, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9560 ) UPLO, N, B2, LDA1, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
              IF ( LSAME( JOBU0, 'Update' ) )      JOBU = 'Update'
            ELSEIF ( ( PRBLM .EQ. SBRDB ) .OR.
     >               ( ( PRBLM .EQ. SBRDD ) .AND. ( B2 .GT. 1 ) ) ) THEN
              INFO = 0
              BTIME = SECOND()
              CALL DSB2BC( 'Lower', N, B2, A, LDA1, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9580 ) 'Lower', N, B2, LDA1, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
            ELSEIF ( ( PRBLM .EQ. SY2BI ) .OR. ( PRBLM .EQ. SB2BI ) )
     >      THEN
              INFO = 0
              BTIME = SECOND()
              CALL DSB2BC( 'Lower', N, B2, A, LDA2, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9580 ) UPLO, N, B2, LDA2, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
*
*                --- copy orthogonal matrix into u ---
*
              CALL DLACPY( 'Full', N, N, A, LDA1, U, LDU )
            ENDIF
*
*              --- perform numerical checks ---
*
            INFO = 0
            BTIME = SECOND()
            CALL DSYNCK( EVLS, FRMT1, UPLO, N, B1, A, LDA1, SZA,
     >                   FRMT2, B2, ACPY, LDA2, D, E, JOBU, U, LDU,
     >                   ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                   NOTUSD, WORK, SZWORK, INFO )
            CTIME = SECOND() - BTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9640 ) FRMT1, UPLO, N, B1, LDA1, SZA
              WRITE( OUNIT, 9641 ) FRMT2, B2, LDA2, JOBU, LDU
              WRITE( OUNIT, 9642 ) ORTHU, SORTHU
              WRITE( OUNIT, 9643 ) RES, SRES
              WRITE( OUNIT, 9644 ) DEVLS, SDEVLS
              WRITE( OUNIT, 9645 ) NOTUSD, SZWORK
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- failed any computational check ? ---
*
            IF ( .NOT. ( SORTHU .LE. TORTHU ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'orhogonality', SORTHU, TORTHU
              OK = .FALSE.
            ENDIF
            IF ( .NOT. ( SRES .LE. TRES ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'residual', SRES, TRES
              OK = .FALSE.
            ENDIF
            IF ( .NOT. ( SDEVLS .LE. TDEVLS ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'eigenvalues', SDEVLS, TDEVLS
              OK = .FALSE.
            ENDIF
            IF ( .NOT. OK )     FAIL( PRBLM ) = FAIL( PRBLM ) + 1
          ENDIF
*
*  - - - - - - - - print summary for this run - - - - - - - - - - - - -
*
 3000     IF ( OLEVEL .GE. OUTRUN ) THEN
            WRITE( OUNIT, 9700 ) LINE0, PRBLMN( PRBLM ), COMMNT( PRBLM )
*
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9710 ) MTYPE, DIAM, UPLO, N, LDA1
              WRITE( OUNIT, 9711 ) NB( 1 ), NX1, LWORK1, XINFO1
              WRITE( OUNIT, 9712 ) JOBU, NB( 2 ), NX2, LWORK2, XINFO2
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9720 ) MTYPE, DIAM, UPLO, N, B1, LDA1
              WRITE( OUNIT, 9721 ) JOBU, LDU, XINFO1
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9730 ) MTYPE, DIAM, UPLO, N, LDA1, B2
              WRITE( OUNIT, 9731 ) DRPTOL, NB( 1 ), LWORK1, XINFO1
              WRITE( OUNIT, 9732 ) JOBU, LDU, LWORK2, XINFO2
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9740 ) MTYPE, DIAM, N, B1, LDA1, B2
              WRITE( OUNIT, 9741 ) DRPTOL, NB( 1 ), JOBU, LDU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9750 ) MTYPE, DIAM, N, B1, LDA1
              WRITE( OUNIT, 9741 ) DRPTOL, NB( 1 ), JOBU, LDU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
            ELSEIF ( ( PRBLM .EQ. SY2BC )
     >               .OR. ( PRBLM .EQ. SY2BI )
     >               .OR. ( PRBLM .EQ. SB2BC )
     >               .OR. ( PRBLM .EQ. SB2BI ) ) THEN
              WRITE( OUNIT, 9760 ) MTYPE, DIAM, UPLO, N, B1, LDA1
              WRITE( OUNIT, 9761 ) LDA2, XINFO1
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9770 ) MTYPE, DIAM, UPLO, N, LDA1, B2
              WRITE( OUNIT, 9771 ) LDA2, NSTEPS, DRPTOL, JOBU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
              IF ( NSTEPS .GT. 1 ) THEN
                WRITE( OUNIT, 9772 ) ( B( I ), I = 1, NSTEPS-1 )
              ENDIF
              IF ( NSTEPS .GT. 0 ) THEN
                WRITE( OUNIT, 9773 ) ( NB( I ), I = 1, NSTEPS )
              ENDIF
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9780 ) MTYPE, DIAM, UPLO, N, B1, LDA1, B2
              WRITE( OUNIT, 9781 ) NSTEPS, DRPTOL, JOBU, LDU
              WRITE( OUNIT, 9782 ) LWORK1, XINFO1
              IF ( NSTEPS .GT. 1 ) THEN
                WRITE( OUNIT, 9772 ) ( B( I ), I = 1, NSTEPS-1 )
              ENDIF
              IF ( NSTEPS .GT. 0 ) THEN
                WRITE( OUNIT, 9773 ) ( NB( I ), I = 1, NSTEPS )
              ENDIF
            ENDIF
*
*              --- print available information on numerical checks ---
*
            IF ( ERRCHK ) THEN
              WRITE( OUNIT, 9420 )
            ELSE
              IF ( .NOT. ( SORTHU .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9430 ) ORTHU, SORTHU, TORTHU
              ENDIF
              IF ( .NOT. ( SRES .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9431 ) RES, SRES, TRES
              ENDIF
              IF ( .NOT. ( SDEVLS .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9432 ) DEVLS, SDEVLS, TDEVLS
              ENDIF
            ENDIF
*
            WRITE( OUNIT, 9440 ) RTIME
          ENDIF
*
          IF ( OLEVEL .GE. OUTDET )     WRITE( OUNIT, 9000 )
*
*            --- end of the main loop ---
*
        GOTO 2000
*
*  - - - - - - - - print "global" summary - - - - - - - - - - - - - - -
*
 8000   WRITE( OUNIT, * )
        WRITE( OUNIT, 9010 )
        WRITE( OUNIT, 9020 )
        WRITE( OUNIT, 9000 )
        DO 8100 PRBLM = SYTRD, TOTAL-1
          WRITE( OUNIT, 9030 ) PRBLMN( PRBLM ), COMMNT( PRBLM ),
     >                         TRY( PRBLM ), SKIP( PRBLM ),
     >                         FAIL( PRBLM )
          TRY( TOTAL ) = TRY( TOTAL ) + TRY( PRBLM )
          SKIP( TOTAL ) = SKIP( TOTAL ) + SKIP( PRBLM )
          FAIL( TOTAL ) = FAIL( TOTAL ) + FAIL( PRBLM )
 8100   CONTINUE
        WRITE( OUNIT, 9000 )
        WRITE( OUNIT, 9030 ) PRBLMN( TOTAL ), COMMNT( TOTAL ),
     >                       TRY( TOTAL ), SKIP( TOTAL ), FAIL( TOTAL )
        WRITE( OUNIT, 9000 )
        WRITE( OUNIT, 9040 ) SECOND() - STIME
*
*  - - - - - - - - formats - - - - - - - - - - - - - - - - - - - - - - -
*
*          --- "global" summary" ---
*
 9000   FORMAT( 1X, '----------------------------------------',
     >          '---------------------------------------' )
 9010   FORMAT( 1X, '========================================',
     >          '=======================================' )
*
 9020   FORMAT( 1X, 'Tests for                               ',
     >          '              Total Skipped  Failed' )
 9030   FORMAT( 1X, A6, ' : ', A40, ' :', I8, I8, I8 )
*
 9040   FORMAT( 1X, 'Total time : ', F8.2, ' seconds' )
*
*          --- messages ---
*
 9100   FORMAT( 1X, A )
*
*          --- problems with the input file ---
*
 9300   FORMAT( 1X, '*** Error in line ', I5, ' : ', A40 )
 9310   FORMAT( 1X, '+++ Line ', I5, ' : Test too large - skipped' )
*
*          --- general status reporting ---
*
 9400   FORMAT( 1X, '          info=', I5, ', time=', F12.6 )
 9401   FORMAT( 1X, '          step=', I5, ', info=', I5,
     >          ', time=', F12.6 )
*
 9410   FORMAT( 1X, '          used ', I8, ' out of ',
     >          I8, ' workspace' )
*
 9420   FORMAT( 1X, '    ((( check for error exit ))),' )
*
 9430   FORMAT( 1X, '    Norm(U''*U-I) =', E10.3, '=',
     >          E10.3, '*n*macheps         (thresh=', E10.3, '),' )
 9431   FORMAT( 1X, '    Norm(U*B-A*U)=', E10.3, '=',
     >          E10.3, '*n*macheps*Norm(A) (thresh=', E10.3, '),' )
 9432   FORMAT( 1X, '    Norm(Dlambda)=', E10.3, '=',
     >          E10.3, '*n*macheps*Norm(A) (thresh=', E10.3, '),' )
*
 9440   FORMAT( 1X, '    reduction time=', F12.6 )
*
*          --- formats for tracing single routine calls ---
*
 9500   FORMAT( 1X, '  dsyini: mtype=', A1, ', szevls=', I5,
     >          ', diam=', E11.4, ', frmt=', A1, ', uplo=', A1,
     >          ', n=', I5, ',' )
 9501   FORMAT( 1X, '          b=', I5, ', lda=', I5, ', sza=', I8,
     >          ', jobu=', A1, ', ldu=', I5, ', szu=', I8, ',' )
 9502   FORMAT( 1X, '          notusd=', E11.4, ', szwork=', I8, ',' )
*
 9510   FORMAT( 1X, '  dsytrd: uplo=', A1, ', n=', I5, ', lda=', I5,
     >          ', nb0=', I5, ', nx0=', I5, ', lwork=', I8, ',' )
 9515   FORMAT( 1X, 'dsytrd: uplo=', A1, ', n=', I5, ', nb=', I3,
     >          ', info=', I3, ', time=', F9.3 )
*
 9520   FORMAT( 1X, '  dsbtrd: vect=', A1, ', uplo=', A1, ', n=', I5,
     >          ', kd=', I5, ', ldab=', I5, ', ldu=', I5, ',' )
 9525   FORMAT( 1X, 'dsbtrd: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b1=', I3, ', info=', I3, ', time=', F9.3 )
*
 9530   FORMAT( 1X, '  dsyrdb: uplo=', A1, ', job=', A1, ', n=', I5,
     >          ', b=', I5, ', lda=', I5, ', drptol=', E11.4, ',' )
 9531   FORMAT( 1X, '          ldu=', I5, ', nb=', I5, ', lwork=', I8,
     >          ',' )
 9535   FORMAT( 1X, 'dsyrdb: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b2=', I3, ', nb=', I3, ', info=', I3,
     >          ', time=', F9.3 )
*
 9540   FORMAT( 1X, '  dsbrdb: job=', A1, ', n=', I5, ', b1=', I5,
     >          ', b2=', I5, ', lda=', I5, ', drptol=', E11.4, ',' )
 9545   FORMAT( 1X, 'dsbrdb: jobu=', A1, ', n=', I5, ', b1=', I3,
     >          ', b2=', I3, ', nb=',I3, ', info=', I3,
     >          ', time=', F9.3 )
*
 9550   FORMAT( 1X, '  dsbrdt: job=', A1, ', n=', I5, ', b=', I5,
     >          ', lda=', I5, ', drptol=', E11.4, ',' )
 9555   FORMAT( 1X, 'dsbrdt: jobu=', A1, ', n=', I5, ', b1=', I3,
     >          ', nb=', I3, ', info=', I3, ', time=', F9.3 )
*
 9560   FORMAT( 1X, '  dsy2bc: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldfull=', I5, ', ldband=', I5, ',' )
*
 9570   FORMAT( 1X, '  dsy2bi: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldfull=', I5, ', ldband=', I5, ',' )
*
 9580   FORMAT( 1X, '  dsb2bc: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldsrc=', I5, ', lddst=', I5, ',' )
*
 9590   FORMAT( 1X, '  dsb2bi: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldsrc=', I5, ', lddst=', I5, ',' )
*
 9600   FORMAT( 1X, '  dsyrdd: job=', A1, ', uplo=', A1, ', n=', I5,
     >          ', b2=', I5, ', lda=', I5, ',' )
 9601   FORMAT( 1X, '          drptol=', E11.4, ', ldband=', I5,
     >          ', nsteps=', I5, ', lwork=', I8, ',' )
 9605   FORMAT( 1X, 'dsyrdd: uplo=', A1, ', job=', A1, ', n=', I5,
     >          ', b2=', I3, ', nsteps=', I2, ', step=', I2,
     >          ', info=', I3, ', time=', F9.3 )
*
 9610   FORMAT( 1X, '  dsbrdd: jobu=', A1, ', uplo=', A1, ', n=', I5,
     >          ', b1=', I5, ', b2=', I5, ', lda=', I5, ',' )
 9611   FORMAT( 1X, '          drptol=', E11.4, ', ldu=', I5,
     >          ', nsteps=', I5, ', lwork=', I8, ',' )
 9615   FORMAT( 1X, 'dsbrdd: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b1=', I3, ', b2=', I3, ', nsteps=', I2,
     >          ', step=', I2, ', info=', I3, ', time=', F9.3 )
*
 9620   FORMAT( 1X, '  dorgtr: uplo=', A1, ', n=', I5, ', lda=', I5,
     >          ', nb=', I5, ', nx=', I5, ', lwork=', I8, ',' )
*
 9630   FORMAT( 1X, '  dsygtr: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', lda=', I5, ', lwork=', I8, ',' )
*
 9640   FORMAT( 1X, '  dsynck: frmt1=', A1, ', uplo1=', A1, ', n=', I5,
     >          ', b1=', I5, ', lda1=', I5, ', sza1=', I8, ',' )
 9641   FORMAT( 1X, '          frmt2=', A1, ', b2=', I5, ', lda2=', I5,
     >          ', jobu=', A1, ', ldu=', I5, ',' )
 9642   FORMAT( 1X, '          Norm( U''*U - I ) =', E11.4,
     >          ' = ', E11.4, '*n*macheps,' )
 9643   FORMAT( 1X, '          Norm( U*B - A*U )=', E11.4,
     >          ' = ', E11.4, '*n*macheps*Norm( A ),' )
 9644   FORMAT( 1X, '          Norm( Dlambda )  =', E11.4,
     >          ' = ', E11.4, '*n*macheps*Norm( A ),' )
 9645   FORMAT( 1X, '          notusd=', E11.4, ', szwork=', I8, ',' )
*
*          --- formats for tracing single runs ---
*
 9700   FORMAT( 1X, 'Line ', I5, ' / ', A, ' : ', A, ',' )
*
 9710   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4,
     >          ', uplo=', A1, ', n=', I5, ', lda=', I5, ',' )
 9711   FORMAT( 1X, '    nb1=', I5, ', nx1=', I5, ', lwork1=', I8,
     >          ', xinfo1=', I5, ',' )
 9712   FORMAT( 1X, '    jobu=', A1, ', nb2=', I5, ', nx2=', I5,
     >          ', lwork2=', I8, ', xinfo2=', I5, ',' )
*
 9720   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ',' )
 9721   FORMAT( 1X, '    jobu=', A1, ', ldu=', I5, ', xinfo=', I5, ',' )
*
 9730   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', lda=', I5, ', b2=', I5, ',' )
 9731   FORMAT( 1X, '    drptol=', E11.4, ', nb=', I5, ', lwork1=', I8,
     >          ', xinfo1=', I5, ',' )
 9732   FORMAT( 1X, '    jobu=', A1, ', ldu=', I5, ', lwork2=', I8,
     >          ', xinfo2=', I5, ',' )
*
 9740   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', n=', I5,
     >          ', b1=', I5, ', lda=', I5, ', b2=', I5, ',' )
 9741   FORMAT( 1X, '    drptol=', E11.4, ', nb=', I5, ', jobu=', A1,
     >          ', ldu=', I5, ', lwork=', I8, ',' )
 9742   FORMAT( 1X, '    xinfo=', I5, ',' )
*
 9750   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ',' )
*
 9760   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda1=', I5, ',' )
 9761   FORMAT( 1X, '    lda2=', I5, ', xinfo=', I5, ',' )
*
 9770   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', lda1=', I5, ', b2=', I5, ',' )
 9771   FORMAT( 1X, '    lda2=', I5, ', nsteps=', I5,
     >          ', drptol=', E11.4, ', jobu=', A1, ', lwork=', I8, ',' )
 9772   FORMAT( 1X, '    b ( 2: )=', 100(I5, ',') )
 9773   FORMAT( 1X, '    nb( 1: )=', 100(I5, ',') )
*
 9780   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ', b2=', I5,
     >          ',' )
 9781   FORMAT( 1X, '    nsteps=', I5, ', drptol=', E11.4,
     >          ', jobu=', A1, ', ldu=', I5, ',' )
 9782   FORMAT( 1X, '    lwork=', I8, ', xinfo=', I5, ',' )
*
*          --- unexpected behaviour of the routines ---
*
 9900   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned info=', I5, ' in step ', I5,
     >          ' (expected ', I5, ')' )
 9901   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned info=', I5, ' (expected ', I5, ')' )
*
 9910   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned step=', I5, ' (expected ', I5, ')' )
*
 9920   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' used ', I8, ' workspace (allowed ', I8, ')' )
*
 9930   FORMAT( 1X, '*** Test in line ', I5, ' failed ', A,
     >          ' test: ', E10.3, ' (thresh=', E10.3, ')' )
*
*  - - - - - - - - done - - - - - - - - - - - - - - - - - - - - - - - -
*
        STOP
        END
*
* **********************************************************************
*
        SUBROUTINE DSYINI( MTYPE, EVLS, SZEVLS, DIAM,
     >                     FRMT, UPLO, N, B, A, LDA, SZA,
     >                     JOBU, U, LDU, SZU,
     >                     NOTUSD, WORK, SZWORK, INFO )
*
* Description:
*
*   Generates a symmetric (full or banded) matrix A with either
*   prescribed eigenvalues, random eigenvalues, or two clusters of
*   eigenvalues. The matrix is returned either in (upper or lower)
*   symmetric full storage or in (upper or lower) symmetric banded
*   storage. In addition, U can be set to the identity matrix.
*
*   Note: In contrast to the LAPACK routine dlagsy, this routine
*         generates the banded matrix within an n-by-(b+1) array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           MTYPE, FRMT, UPLO, JOBU
        INTEGER               N, B, LDA, SZA, LDU, SZU, SZWORK, SZEVLS,
     >                        INFO
        DOUBLE PRECISION      DIAM, NOTUSD
        DOUBLE PRECISION      A( LDA, * ), U( LDU, * ), EVLS( * ),
     >                        WORK( * )
*
*   mtype   (in) character*1
*           The matrix type.
*           mtype = 'S' : Generate a matrix with prescribed eigenvalues.
*                 = 'R' : Eigenvalues are uniformly random in [ -1, 1 ).
*                 = 'I' : ISDA-type matrix: eigenvalues are clustered
*                         around 0 and 1.
*
*   evls    (in OR out) double precision array, dimension ( szevls )
*           The eigenvalues of the matrix A.
*           If mtype = 'S' then evls is an input parameter, and the
*           first n elements of evls are taken as eigenvalues for the
*           matrix A.
*           If mtype = 'R' or 'I', then evls is an output parameter and
*           contains the eigenvalues of the matrix A.
*
*   szevls  (in) integer
*           The size of the array evls.
*           szevls >= n.
*
*   diam    (in) double precision
*           The diameter of the eigenvalue clusters (in multiples of
*           machine_epsilon).
*           Accessed only if mtype = 'I'.
*
*   frmt    (in) character*1
*           The storage format for the matrix A.
*           frmt = 'F' : (Symmetric upper or lower) full storage.
*                = 'B' : (Symmetric upper or lower) banded storage.
*
*   uplo    (in) character*1
*           Which triangle of the matrix is used?
*           uplo = 'U' : Initialize the upper triangle.
*                = 'L' : Initialize the lower triangle.
*           In banded storage (frmt = 'B'), uplo also determines
*           whether the upper or lower banded storage scheme is used.
*
*   n       (in) integer
*           The dimension of the matrix.
*           n >= 0.
*
*   b       (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           matrix A.
*           0 <= b <= max( n-1, 0 ).
*
*   a       (out) double precision array, dimension ( lda, n )
*           The n-by-n symmetric matrix with semibandwidth b.
*           If frmt = 'F' then A is returned in the leading n-by-n
*           subarray - that is, matrix element A( i, j ) is stored at
*           array position a( i, j ) -, with the strict lower
*           (uplo = 'U') or the strictly upper (uplo = 'L') triangle set
*           to some large value (NOT_USED).
*           If frmt = 'B' then A is returned in banded format in the
*           leading (b+1)-times-n subarray - that is, matrix element
*           A( i, j ) is stored at array position a( b+1+i-j, j ) if
*           uplo = 'U', and at position a( 1+i-j, j ) if uplo = 'L'.
*           In any case, the remainder of the first n columns is set
*           to the same large value mentioned above.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= n,   if frmt = 'F'
*               >= b+1, if frmt = 'B'.
*
*   sza     (in) integer
*           The total size (in elements) of the array (not matrix!) a.
*           sza >= lda * n.
*
*   jobu    (in) character*1
*           Set the matrix U to identity?
*           jobu = 'U' : Yes.
*                = 'N' : No.
*
*   u       (out) double precision array, dimension ( ldu, n )
*           If jobu = 'U' then the leading n-by-n subarray is set to
*           an n-by-n identity matrix.
*           If jobu = 'N' then u is not accessed.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= n.
*
*   szu     (in) integer
*           The total size (in elements) of the array (not matrix!) u.
*           szu >= ldu * n, if jobu = 'U'
*               >= 0      , if jobu = 'N'.
*
*   notusd  (in) double precision
*           Value for marking elements that should not be used.
*           Typically a rather large number.
*
*   work    (workspace) double precision array, dimension ( szwork )
*
*   szwork  (in) integer
*           The size of the array work.
*           szwork >= 2 * n.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           =   0 : All arguments are OK.
*           =  -1 : mtype is none of 'S', 'R', 'I' (upper/lower case).
*           =  -3 : szevls is too small ( < n ).
*           =  -4 : diam is out of range (negative).
*           =  -5 : frmt is none of 'F', 'B' (upper or lower case).
*           =  -6 : uplo is none of 'U', 'L' (upper or lower case).
*           =  -7 : n is out of range ( < 0 ).
*           =  -8 : b is out of range ( < 0 or > max( n-1, 0 ) ).
*           = -10 : lda is too small ( < n, if full, < b+1, if banded).
*           = -11 : sza is too small ( < n*lda ).
*           = -12 : jobu is none of 'U', 'N' (upper or lower case).
*           = -14 : ldu is too small ( < n ).
*           = -15 : szu is too small ( < n*ldu, if U is required).
*           = -18 : szwork is too small (see above).
*
* ----------------------------------------------------------------------
*
* Local constants and variables:
*
        DOUBLE PRECISION      ZERO, HALF, ONE, TWO
        PARAMETER             ( ZERO = 0.0D0, HALF = 0.5D0,
     >                          ONE = 1.0D0, TWO = 2.0D0 )
*
        LOGICAL               SPEC, ISDA, FULL, UPPER, NEEDU
        INTEGER               ISEED( 4 )
        DOUBLE PRECISION      SDIAM
*
*   spec    matrix with prescribed spectrum ?
*   isda    ISDA-type matrix or random matrix ?
*   full    store the matrix in full or banded format ?
*   upper   use upper or lower triangle ?
*   needu   update I or not ?
*   iseed   seed for the random number generator
*   sdiam   scaled diameter
*
        INTEGER               D, I, J, K, Q
        DOUBLE PRECISION      C, S, FILL, A11, A12, A21, A22, TMP
*
*   d       the number of the new diagonal
*   c       cosine of the rotation angle
*   s       sine of the rotation angle
*   fill    new fill-in element
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        DOUBLE PRECISION      D1MACH, DLARAN
        EXTERNAL              DCOPY, DLAGSY, D1MACH, DLARAN, DLARTG,
     >                        DLASET
*
*   dcopy   vector copy (BLAS)
*   dlagsy  generate symmetric matrix (LAPACK TMG)
*   dlamch  inquire machine parameters (LAPACK)
*   dlaran  random number generator (LAPACK TMG)
*   dlartg  generate rotation (LAPACK)
*   dlaset  initialize diagonal matrix (LAPACK)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- sanity check for the arguments ---
*
        SPEC = LSAME( MTYPE, 'Spectrum' )
        ISDA = LSAME( MTYPE, 'Isda' )
        FULL = LSAME( FRMT, 'Full' )
        UPPER = LSAME( UPLO, 'Upper' )
        NEEDU = LSAME( JOBU, 'Update' )
*
        IF ( .NOT. ( ISDA .OR. SPEC .OR. LSAME( MTYPE, 'Random' ) ) )
     >  THEN
          INFO = -1
        ELSEIF ( SZEVLS .LT. N ) THEN
          INFO = -3
        ELSEIF ( DIAM .LT. ZERO ) THEN
          INFO = -4
        ELSEIF ( .NOT. ( FULL .OR. LSAME( FRMT, 'Banded' ) ) ) THEN
          INFO = -5
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -6
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -7
        ELSEIF ( ( B .LT. 0 ) .OR. ( B .GT. MAX( N-1, 0 ) ) ) THEN
          INFO = -8
        ELSEIF ( ( FULL .AND. ( LDA .LT. N ) )
     >           .OR. ( LDA .LT. B+1 ) ) THEN
          INFO = -10
        ELSEIF ( SZA .LT. N*LDA ) THEN
          INFO = -11
        ELSEIF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'NoUpdate' ) ) ) THEN
          INFO = -12
        ELSEIF ( LDU .LT. N ) THEN
          INFO = -14
        ELSEIF ( NEEDU .AND. ( SZU .LT. N*LDU ) ) THEN
          INFO = -15
        ELSEIF ( SZWORK .LT. 2*N ) THEN
          INFO = -18
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .NE. 0 )     GOTO 9999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 9999
*
        IF ( .NOT. SPEC ) THEN
*
*            --- set up eigenvalue distribution ---
*
          ISEED( 1 ) = 4001
          ISEED( 2 ) = 3001
          ISEED( 3 ) = 2001
          ISEED( 4 ) = 1001
*
          SDIAM = TWO * DIAM * D1MACH(4)
          DO 1000 I = 1, N
            IF ( ISDA ) THEN
              EVLS( I ) = SDIAM * ( DLARAN( ISEED ) - HALF )
              IF ( DLARAN( ISEED ) .LT. HALF ) THEN
                EVLS( I ) = EVLS( I ) + ONE
              ENDIF
            ELSE
              EVLS( I ) = TWO * ( DLARAN( ISEED ) - HALF )
            ENDIF
 1000     CONTINUE
        ENDIF
*
*          --- initialize random number generator ---
*
        ISEED( 1 ) = 1001
        ISEED( 2 ) = 2001
        ISEED( 3 ) = 3001
        ISEED( 4 ) = 4001
*
        IF ( FULL ) THEN
*
*  - - - - - - - initialize matrix in full storage - - - - - - - - - - -
*
          CALL DLAGSY( N, B, EVLS, A, LDA, ISEED, WORK, INFO )
*
          IF ( UPPER ) THEN
*
*              --- mark lower triangle "not used" ---
*
            DO 2100 J = 1, N-1
              DO 2010 I = J+1, N
                A( I, J ) = NOTUSD
 2010         CONTINUE
 2100       CONTINUE
          ELSE
*
*              --- mark upper triangle "not used" ---
*
            DO 2300 J = 2, N
              DO 2210 I = 1, J-1
                A( I, J ) = NOTUSD
 2210         CONTINUE
 2300       CONTINUE
          ENDIF
*
        ELSE
*
* - - - - - - - - initialize matrix in banded storage - - - - - - - - -
*
* - - - - - - - - first initialize in lower packed storage - - - - - - -
*
          CALL DCOPY( N, EVLS, 1, A( 1, 1 ), LDA )
*
          DO 3500 D = 1, B
*
*              --- add d-th diagonal ---
*
            DO 3300 I = N-1, 1, -1
*
*                --- to generate an new element at position
*                    ( i+1, i-d ), ...                      ---
*
*                --- ... first determine a random rotation, ... ---
*
              A11 = DLARAN( ISEED )
              A12 = DLARAN( ISEED )
              CALL DLARTG( A11, A12, C, S, TMP )
*
*                --- ... apply it to rows i and i+1, ... ---
*
              DO 3010 Q = MAX( I-D+1, 1 ), I-1
                IF ( Q .EQ. ( I-D+1 ) ) THEN
                  A( D+1, Q ) = -S * A( D, Q )
                  A( D, Q ) = C * A( D, Q )
                ELSE
                  TMP = C * A( I-Q+2, Q ) - S * A( I-Q+1, Q )
                  A( I-Q+1, Q ) = C * A( I-Q+1, Q ) + S * A( I-Q+2, Q )
                  A( I-Q+2, Q ) = TMP
                ENDIF
 3010         CONTINUE
*
*                --- ... apply it to A( i:i+1, i:i+1 ), ... ---
*
              IF ( D .EQ. 1 ) THEN
                A11 = C * A( 1, I )
                A21 = -S * A( 1, I )
                A12 = S * A( 1, I+1 )
                A22 = C * A( 1, I+1 )
              ELSE
                A11 = C * A( 1, I ) + S * A( 2, I )
                A21 = C * A( 2, I ) - S * A( 1, I )
                A12 = C * A( 2, I ) + S * A( 1, I+1 )
                A22 = C * A( 1, I+1 ) - S * A( 2, I )
              ENDIF
              A( 1, I ) = C * A11 + S * A12
              A( 2, I ) = C * A21 + S * A22
              A( 1, I+1 ) = C * A22 - S * A21
*
*                --- ... apply it to columns i and i+1, ... ---
*
              DO 3020 Q = I+2, MIN( I+D, N )
                TMP = C * A( Q-I, I+1 ) - S * A( Q-I+1, I )
                A( Q-I+1, I ) = C * A( Q-I+1, I ) + S * A( Q-I, I+1 )
                A( Q-I, I+1 ) = TMP
 3020         CONTINUE
              IF ( ( I+D+1 ) .LE. N ) THEN
                FILL = S * A( D+1, I+1 )
                A( D+1, I+1 ) = C * A( D+1, I+1 )
              ENDIF
*
*                --- ... and chase the fill-in element down the band ---
*
              DO 3200 K = I+D, N-1, D
*
                CALL DLARTG( A( D+1, K-D ), FILL, C, S, TMP )
                A( D+1, K-D ) = TMP
*
                DO 3110 Q = K-D+1, K-1
                  TMP = C * A( K-Q+2, Q ) - S * A( K-Q+1, Q )
                  A( K-Q+1, Q ) = C * A( K-Q+1, Q ) + S * A( K-Q+2, Q )
                  A( K-Q+2, Q ) = TMP
 3110           CONTINUE
*
                A11 = C * A( 1, K ) + S * A( 2, K )
                A21 = C * A( 2, K ) - S * A( 1, K )
                A12 = C * A( 2, K ) + S * A( 1, K+1 )
                A22 = C * A( 1, K+1 ) - S * A( 2, K )
                A( 1, K ) = C * A11 + S * A12
                A( 2, K ) = C * A21 + S * A22
                A( 1, K+1 ) = C * A22 - S * A21
*
                DO 3120 Q = K+2, MIN( K+D, N )
                  TMP = C * A( Q-K, K+1 ) - S * A( Q-K+1, K )
                  A( Q-K+1, K ) = C * A( Q-K+1, K ) + S * A( Q-K, K+1 )
                  A( Q-K, K+1 ) = TMP
 3120           CONTINUE
                IF ( ( K+D+1 ) .LE. N ) THEN
                  FILL = S * A( D+1, K+1 )
                  A( D+1, K+1 ) = C * A( D+1, K+1 )
                ENDIF
 3200         CONTINUE
*
 3300       CONTINUE
*
*              --- mark the last d entries of the row "not used" ---
*
            DO 3410 I = N-D+1, N
              A( D+1, I ) = NOTUSD
 3410       CONTINUE
*
 3500     CONTINUE
*
* - - - - - - - - end : first initialize in lower packed storage - - - -
*
          IF ( UPPER ) THEN
*
*              --- convert from lower to upper banded storage ---
*
            DO 3700 I = 0, B/2
              CALL DCOPY( N-B+I, A( B+1-I, 1 ), LDA, WORK, 1 )
              DO 3610 J = 1, N-I
                A( B+1-I, I+J ) = A( I+1, J )
 3610         CONTINUE
              DO 3620 K = 1, I
                A( B+1-I, K ) = NOTUSD
 3620         CONTINUE
              CALL DCOPY( N-B+I, WORK, 1, A( I+1, B+1-I ), LDA )
              DO 3630 K = 1, B-I
                A( I+1, K ) = NOTUSD
 3630         CONTINUE
 3700       CONTINUE
          ENDIF
*
* - - - - - - - - end : initialize matrix in banded storage - - - - - -
*
        ENDIF
*
*          --- generate identity matrix in U ---
*
        IF ( NEEDU ) THEN
          CALL DLASET( 'All', N, N, ZERO, ONE, U, LDU )
        ENDIF
*
 9999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYNCK( EVLS, FRMT1, UPLO1, N, B1, A1, LDA1, SZA1,
     >                     FRMT2, B2, A2, LDA2, D, E,
     >                     JOBU, U, LDU,
     >                     ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                     NOTUSD, WORK, SZWORK, INFO )
*
* Description:
*
*   This routine performs numerical tests after an orthogonal
*   transformation
*                 T
*      A --> B = U  * A * U.
*   A is rebuilt by calling dsyini, B may be given in banded or
*   tridiagonal format.
*   Depending on whether U was build explicitly during the reduction,
*   either
*                           T
*      the orthogonality   U  * U - I      of U
*      and the residual    U * B - A * U
*   or
*      the difference between A's and B's eigenvalues
*   is checked.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           FRMT1, UPLO1, FRMT2, JOBU
        INTEGER               N, B1, LDA1, SZA1, B2, LDA2, LDU,
     >                        SZWORK, INFO
        DOUBLE PRECISION      ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                        NOTUSD
        DOUBLE PRECISION      EVLS( * ), A1( LDA1, * ), A2( LDA2, * ),
     >                        D( * ), E( * ), U( LDU, * ), WORK( * )
*
*   evls    (in) double precision array, dimension ( n )
*           The eigenvalues of the matrix A, as returned from dsyini.
*
*   frmt1   (in) character*1
*           The storage format of the original matrix A.
*           frmt1 = 'F' : (Symmetric) full storage.
*                 = 'B' : (Symmetric) banded storage.
*
*   uplo1   (in) character*1
*           Which triangle of the matrix A (and B) is used?
*           uplo1 = 'U' : Use the upper triangle.
*                 = 'L' : Use the lower triangle.
*           In banded storage (frmt1 = 'B'), uplo1 also determines
*           whether the upper or lower banded storage scheme is used.
*
*   n       (in) integer
*           The dimension of the matrix.
*           n >= 0.
*
*   b1      (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           original matrix A.
*           0 <= b1 <= max( n-1, 0 ).
*
*   a1      (out) double precision array, dimension ( lda1, n )
*           a1 is used to build a copy of the original n-by-n symmetric
*           matrix A with semibandwidth b1.
*           If frmt = 'F' then A is returned in the leading n-by-n
*           subarray - that is, matrix element A( i, j ) is stored at
*           array position a1( i, j ) -, with the strict lower
*           (uplo = 'U') or the strictly upper (uplo = 'L') triangle set
*           to some large value (NOT_USED).
*           If frmt = 'B' then A is returned in banded format in the
*           leading (b1+1)-times-n subarray - that is, matrix element
*           A( i, j ) is stored at array position a1( b1+1+i-j, j ) if
*           uplo = 'U', and at position a1( 1+i-j, j ) if uplo = 'L'.
*
*   lda1    (in) integer
*           The leading dimension of the array a1.
*           lda >= n,    if frmt1 = 'F'
*               >= b1+1, if frmt1 = 'B'.
*
*   sza1    (in) integer
*           The total size (in elements) of the array (not matrix!) a1.
*           sza1 >= lda1 * n.
*
*   frmt2   (in) character*1
*           The storage format of the reduced matrix B.
*           frmt1 = 'B' : (Symmetric) banded storage.
*                 = 'T' : (Symmetric) tridiagonal in arrays d and e.
*
*   b2      (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           reduced matrix B.
*           0 <= b2 <= max( n-1, 0 ).
*
*   a2      (in) double precision array, dimension ( lda2, n )
*           If frmt2 = 'B' then the leading (b2+1)-times-n subarray of
*           a2 holds the reduced symmetric matrix B with semibandwidth
*           b2 in banded format - that is, matrix element A( i, j ) is
*           stored at array position a2( b2+1+i-j, j ) if uplo = 'U',
*           and at position a2( 1+i-j, j ) if uplo = 'L'.
*           If frmt2 = 'T' then a2 is not referenced.
*
*   lda2    (in) integer
*           The leading dimension of the array a2.
*           lda2 >= b2+1.
*
*   d       (in) double precision array, dimension ( n )
*           If frmt2 = 'T' then the first n elements of d hold the
*           main diagonal of the tridiagonal matrix B.
*           If frmt2 = 'B' then d is not referenced.
*
*   e       (in) double precision array, dimension ( n-1 )
*           If frmt2 = 'T' then the first n-1 elements of e hold the
*           subdiagonal (superdiagonal) of the tridiagonal matrix B.
*           If frmt2 = 'B' then e is not referenced.
*
*   jobu    (in) character*1
*           Does U contain the accumulated transformations ?
*           jobu = 'U' : Yes.
*                = 'N' : No.
*
*   u       (in) double precision array, dimension ( ldu, n )
*           If jobu = 'U' then the leading n-by-n subarray contains
*           the accumulated transformations from the reduction (an
*           orthogonal matrix).
*           If jobu = 'N' then u is not accessed.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= n.
*
*   orthu   (out) double precision
*           The orthogonality error : F-norm( U''*U - I ).
*           If jobu = 'N' then orthu is set to 0.
*
*   sorthu  (out) double precision
*           The scaled orthogonality error : orthu / ( n * macheps).
*           If jobu = 'N' then sorthu is set to 0.
*
*   res     (out) double precision
*           The residual : F-norm( U*B - A*U ).
*           If jobu = 'N' then res is set to 0.
*
*   sres    (out) double precision
*           The scaled residual : res / ( n * macheps * F-norm( A ) ).
*           If jobu = 'N' then sres is set to 0.
*
*   devls   (out) double precision
*           The change of the eigenvalues :
*              2-norm( sort(evls) - sort(spec(B)) ).
*           If jobu = 'U' then devls is set to 0.
*
*   sdevls  (out) double precision
*           The scaled eigenvalue changes :
*              devls / ( n * macheps * F-norm( A ) ).
*           If jobu = 'U' then sdevls is set to 0.
*
*   notusd  (in) double precision
*           Value for marking elements that should not be used.
*           Typically a rather large number.
*
*   work    (workspace) double precision array, dimension ( szwork )
*
*   szwork  (in) integer
*           The length of the array work.
*           szwork >= max( 3*n-2, 2*n ).
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           =   0 : All arguments are OK.
*           =  -2 : frmt1 is none of 'F', 'B' (upper/lower case).
*           =  -3 : uplo1 is none of 'U', 'L' (upper/lower case).
*           =  -4 : n is out of range ( < 0 ).
*           =  -5 : b1 is out of range ( < 0 or > max( n-1, 0 ) ).
*           =  -7 : lda1 too small ( < n, if full, < b1+1, if banded).
*           =  -8 : sza1 is too small ( < n * lda1 ).
*           =  -9 : frmt2 is none of 'B', 'T' (upper/lower case).
*           = -10 : b2 is out of range ( < 0 or > max( n-1, 0 ),
*                   or > 1 if frmt2 = 'T' ).
*           = -12 : lda2 is too small ( < b2+1 ).
*           = -15 : jobu is none of 'U', 'N' (upper/lower case).
*           = -17 : ldu is too small ( < n ).
*           = -26 : szwork is too small (see above).
*
* ----------------------------------------------------------------------
*
* Local constants and variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        LOGICAL               FULL1, UPPER, TRI2, HAVEU
        DOUBLE PRECISION      EPS, NORMA
        INTEGER               NCOLS, COLS, J0, J, IX
*
*   full1   build A in full storage ?
*   upper   use upper triangle ?
*   tri2    is B given in tridiagonal storage ?
*   haveu   is the accumulated matrix U available ?
*   eps     machine epsilon
*   norma   the Frobenius norm of the matrix A
*   ncols   maximum width of a block column that fits into workspace
*   cols    width of current block column
*   j0      first column of the current block column
*   j       current column
*   ix      points to the position of the current column in workspace
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        DOUBLE PRECISION      D1MACH, DLANGE, DNRM2
        EXTERNAL              DAXPY, DCOPY, DGEMM, DGEMV, D1MACH,
     >                        DLANGE, DLASRT, DNRM2, DSBEV, DSBMV,
     >                        DSCAL, DSTEV, DSYINI, DSYMM
*
*   daxpy   add multiple of a vector to another one (BLAS)
*   dcopy   vector copy (BLAS)
*   dgemm   matrix-matrix product (BLAS)
*   dgemv   matrix-vector product (BLAS)
*   dlamch  determine machine parameters (LAPACK)
*   dlange  matrix norm (LAPACK)
*   dlasrt  sort a vector (LAPACK)
*   dnrm2   2-norm of a vector (BLAS)
*   dsbev   compute eigensystem of symmetric banded matrix (LAPACK)
*   dsbmv   banded symmetri matrix-vector product (BLAS)
*   dscal   scale a vector (BLAS)
*   dstev   compute eigensystem of symmetric tridiagonal matrix (LAPACK)
*   dsyini  initialize symmetric matrix (this file)
*   dsymm   symmetric matrix-matrix product (BLAS)
*
        INTRINSIC             MAX, MIN, SQRT
*
* ----------------------------------------------------------------------
*
*          --- sanity check for the arguments ---
*
        FULL1 = LSAME( FRMT1, 'Full' )
        UPPER = LSAME( UPLO1, 'Upper' )
        TRI2 = LSAME( FRMT2, 'Tridiagonal' )
        HAVEU = LSAME( JOBU, 'U' )
*
        IF ( .NOT. ( FULL1 .OR. LSAME( FRMT1, 'Banded' ) ) ) THEN
          INFO = -2
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO1, 'Lower' ) ) ) THEN
          INFO = -3
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -4
        ELSEIF ( ( B1 .LT. 0 ) .OR. ( B1 .GT. MAX( N-1, 0 ) ) ) THEN
          INFO = -5
        ELSEIF ( ( FULL1 .AND. ( LDA1 .LT. N ) ) .OR.
     >           ( LDA1 .LT. B1+1 ) ) THEN
          INFO = -7
        ELSEIF ( SZA1 .LT. N*LDA1 ) THEN
          INFO = -8
        ELSEIF ( .NOT. ( TRI2 .OR. LSAME( FRMT2, 'Banded' ) ) ) THEN
          INFO = -9
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND.
     >             ( ( B2 .GT. N-1 ) .OR.
     >               ( TRI2 .AND. ( B2 .GT. 1 ) ) ) ) ) THEN
          INFO = -10
        ELSEIF ( LDA2 .LT. B2+1 ) THEN
          INFO = -12
        ELSEIF ( .NOT. ( HAVEU .OR. LSAME( JOBU, 'NoU' ) ) ) THEN
          INFO = -15
        ELSEIF ( LDU .LT. N ) THEN
          INFO = -17
        ELSEIF ( SZWORK .LT. MAX( 3*N-2, 2*N ) ) THEN
          INFO = -26
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .NE. 0 )     GOTO 9999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 9999
*
*          --- determine machine precision ---
*
        EPS = D1MACH(4)
*                                                     T
*  - - - - - - compute orthogonality error = F-Norm( U  * U - I ) - - -
*
        IF ( LSAME( JOBU, 'Update' ) ) THEN
          ORTHU = ZERO
*                                     T
*            --- how many columns of U  * U - I fit into workspace ? ---
*
          NCOLS = SZWORK / N
          DO 1100 J0 = 1, N, NCOLS
            COLS = MIN( NCOLS, N-J0+1 )
*                                                     T
*              --- compute n-by-cols block column of U  * U ---
*
            CALL DGEMM( 'Transpose', 'NoTranspose', N, COLS, N,
     >                  ONE, U, LDU, U( 1, J0 ), LDU, ZERO, WORK, N )
*
*              --- subtract corresponding parts of I ---
*
            DO 1010 J = J0, J0+COLS-1
              WORK( (J-J0)*N+J ) = WORK( (J-J0)*N+J ) - ONE
 1010       CONTINUE
            ORTHU = ORTHU + DLANGE( 'Frobenius', N, COLS, WORK, N,
     >                              WORK )**2
 1100     CONTINUE
          ORTHU = SQRT( ORTHU )
          SORTHU = ORTHU / ( N * EPS )
        ELSE
*
*            --- no orthogonality information available ---
*
          ORTHU = - ONE
          SORTHU = - ONE
        ENDIF
*                                                           T
*  - - - - - - end : compute orthogonality error = F-Norm( U  * U - I )
*
        NORMA = DNRM2( N, EVLS, 1 )
*
        IF ( LSAME( JOBU, 'Update' ) ) THEN
*
*            --- do not compute changes in eigenvalues ---
*
          DEVLS = - ONE
          SDEVLS = - ONE
*
*  - - - - - - - compute residual error = F-Norm( U * B - A * U ) - - -
*
*            --- build another copy of the original matrix A ---
*
          CALL DSYINI( 'Spectrum', EVLS, N, ZERO,
     >                 FRMT1, UPLO1, N, B1, A1, LDA1, SZA1,
     >                 'NoU', WORK, N, 0,
     >                 NOTUSD, WORK, SZWORK, INFO )
*
          RES = ZERO
*
*            --- how many cols of U * B - A * U fit into workspace ? ---
*
          NCOLS = SZWORK / N
*
          DO 2000 J0 = 1, N, NCOLS
            COLS = MIN( NCOLS, N-J0+1 )
*
*              --- build the next cols columns of U * B ---
*
            IF ( LSAME( FRMT2, 'Tridiagonal' ) ) THEN
              DO 2010 J = J0, J0+COLS-1
                IX = ( J - J0 ) * N + 1
                CALL DCOPY( N, U( 1, J ), 1, WORK( IX ), 1 )
                CALL DSCAL( N, D( J ), WORK( IX ), 1 )
                IF ( J .GT. 1 ) THEN
                  CALL DAXPY( N, E( J-1 ), U( 1, J-1 ), 1,
     >                        WORK( IX ), 1 )
                ENDIF
                IF ( J .LT. N ) THEN
                  CALL DAXPY( N, E( J ), U( 1, J+1 ), 1, WORK( IX ), 1 )
                ENDIF
 2010         CONTINUE
            ELSE
              DO 2020 J = J0, J0+COLS-1
                IX = ( J - J0 ) * N + 1
                CALL DGEMV( 'NoTranspose', N, MIN( B2+1, N-J+1 ),
     >                      ONE, U( 1, J ), LDU, A2( 1, J ), 1,
     >                      ZERO, WORK( IX ), 1 )
                IF ( B2 .GT. 0 ) THEN
                  IF ( J .GT. B2 ) THEN
                    CALL DGEMV( 'NoTranspose', N, B2,
     >                          ONE, U( 1, J-B2 ), LDU,
     >                          A2( B2+1, J-B2 ), LDA2 - 1,
     >                          ONE, WORK( IX ), 1 )
                  ELSEIF ( J .GT. 1 ) THEN
                    CALL DGEMV( 'NoTranspose', N, J - 1,
     >                          ONE, U( 1, 1 ), LDU,
     >                          A2( J, 1 ), LDA2 - 1,
     >                          ONE, WORK( IX ), 1 )
                  ENDIF
                ENDIF
 2020         CONTINUE
            ENDIF
*
*              --- subtract corresponding columns of A * U ---
*
            IF ( LSAME( FRMT1, 'Full' ) ) THEN
              CALL DSYMM( 'Left', UPLO1, N, COLS,
     >                   -ONE, A1, LDA1, U( 1, J0 ), LDU,
     >                   ONE, WORK, N )
            ELSE
              DO 2110 J = J0, J0+COLS-1
                CALL DSBMV( UPLO1, N, B1, -ONE, A1, LDA1, U( 1, J ), 1,
     >                      ONE, WORK( (J-J0)*N+1 ), 1 )
 2110         CONTINUE
            ENDIF
*
            RES = RES + DLANGE( 'Frobenius', N, COLS, WORK, N, WORK )**2
 2000     CONTINUE
*
          RES = SQRT( RES )
          SRES = RES / ( N * NORMA * EPS )
*
*  - - - - - - - end : compute residual error = F-Norm( U * B - A * U )
*
        ELSE
*
*            --- no residual information available ---
*
          RES = - ONE
          SRES = - ONE
*
*  - - - - - - - check if eigenvalues have changed - - - - - - - - - - -
*
*            --- compute eigenvalues of the tridiagonal or banded
*                matrix                                           ---
*
          IF ( LSAME( FRMT2, 'Tridiagonal' ) ) THEN
            CALL DSTEV( 'NoEigenvectors', N, D, E, WORK, N, WORK, INFO )
          ELSE
            CALL DSBEV( 'NoEigenvectors', 'Lower', N, B2, A2, LDA2,
     >                  D, WORK, N, WORK, INFO )
          ENDIF
*
*            --- compare with (sorted) original eigenvalues ---
*
          IF ( INFO .EQ. 0 ) THEN
            CALL DLASRT( 'Increasing', N, EVLS, INFO )
            CALL DAXPY( N, -ONE, EVLS, 1, D, 1 )
            DEVLS = DNRM2( N, D, 1 )
            SDEVLS = DEVLS / ( N * NORMA * EPS )
          ELSE
            DEVLS = - ONE
            SDEVLS = - ONE
          ENDIF
*
*  - - - - - - - end : check if eigenvalues have changed - - - - - - - -
*
        ENDIF
*
 9999   RETURN
        END
*
* **********************************************************************
*
        LOGICAL FUNCTION LXSAME( S1, S2 )
*
* Description:
*
*   Checks if two strings agree (ignoring case).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*( * )       S1, S2
*
*   s1      (in) character*( * )
*           The first string.
*
*   s2      (in) character*( * )
*           The second string.
*
* Local constants and variables:
*
        INTEGER               I
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             LEN
*
* ----------------------------------------------------------------------
*
        LXSAME = ( LEN( S1 ) .EQ. LEN( S2 ) )
        IF ( LXSAME ) THEN
          DO 100 I = 1, LEN( S1 )
            LXSAME = LXSAME .AND. LSAME( S1( I:I ), S2( I:I ) )
  100     CONTINUE
        ENDIF
*
        RETURN
        END
*
SHAR_EOF
fi # end of overwriting check
if test -f 'res1'
then
	echo shar: will not over-write existing file "'res1'"
else
cat << "SHAR_EOF" > 'res1'
 
 ===============================================================================
 Tests for                                             Total Skipped  Failed
 -------------------------------------------------------------------------------
 dsytrd : full -> tridiagonal, one-step (LAPACK)   :       4       0       0
 dorgtr : accumulation of transformations (LAPACK) :       2       0       0
 dsbtrd : banded -> tridiagonal, one-step (LAPACK) :       4       0       0
 dsyrdb : full -> banded, one-step (SBR)           :      36       0       0
 dsygtr : accumulation of transformations (SBR)    :      11       0       0
 dsbrdb : banded -> banded, one-step (SBR)         :      50       0       0
 dsbrdt : banded -> tridiagonal, one-step (SBR)    :      44       0       0
 dsy2bc : copy full -> banded (SBR)                :      27       0       0
 dsy2bi : in-place copy full -> banded (SBR)       :      27       0       0
 dsb2bc : copy banded -> banded (SBR)              :      19       0       0
 dsb2bi : in-place copy banded -> banded (SBR)     :      19       0       0
 dsyrdd : reduction driver for full matrices (SBR) :      45       0       0
 dsbrdd : reduction driver for banded matrcs (SBR) :      52       0       0
 -------------------------------------------------------------------------------
 Total  :                                          :     340       0       0
 -------------------------------------------------------------------------------
 Total time :   129.96 seconds
SHAR_EOF
fi # end of overwriting check
if test -f 'res2'
then
	echo shar: will not over-write existing file "'res2'"
else
cat << "SHAR_EOF" > 'res2'
 *** Timing the LAPACK reduction full -> tridiagonal ***                       
                                                                               
    no update                                                                  
                                                                               
 Line    81 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, lda=  200,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=N, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=    1.400000
 Line    84 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, lda=  400,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=N, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=   10.709999
 Line    87 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, lda=  600,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=N, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=   37.089996
 Line    90 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, lda=  800,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=N, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=   89.190002
 Line    93 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, lda= 1000,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=N, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=  175.879974
                                                                               
    with update                                                                
                                                                               
 Line   102 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, lda=  200,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=U, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=    3.750061
 Line   105 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, lda=  400,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=U, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=   30.540039
 Line   108 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, lda=  600,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=U, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=  103.380005
 Line   111 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, lda=  800,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=U, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=  247.030090
 Line   114 / dsytrd : full -> tridiagonal, one-step (LAPACK)  ,
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, lda= 1000,
     nb1=    0, nx1=    0, lwork1= 1000000, xinfo1=    0,
     jobu=U, nb2=    0, nx2=    0, lwork2= 1000000, xinfo2=    0,
     reduction time=  482.520020
                                                                               
 *** Timing the SBR driver full -> tridiagonal ***                             
                                                                               
    no update                                                                  
                                                                               
 Line   171 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  200, lda1=  200, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=N, lwork= 1000000,
     xinfo=    1,
     reduction time=    1.260010
 Line   174 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  400, lda1=  400, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=N, lwork= 1000000,
     xinfo=    1,
     reduction time=   10.060059
 Line   177 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  600, lda1=  600, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=N, lwork= 1000000,
     xinfo=    1,
     reduction time=   34.719971
 Line   180 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  800, lda1=  800, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=N, lwork= 1000000,
     xinfo=    1,
     reduction time=   84.540161
 Line   183 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n= 1000, lda1= 1000, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=N, lwork= 1000000,
     xinfo=    1,
     reduction time=  167.760010
                                                                               
    with update                                                                
                                                                               
 Line   192 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  200, lda1=  200, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=U, lwork= 1000000,
     xinfo=    1,
     reduction time=    3.699951
 Line   195 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  400, lda1=  400, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=U, lwork= 1000000,
     xinfo=    1,
     reduction time=   29.310059
 Line   198 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  600, lda1=  600, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=U, lwork= 1000000,
     xinfo=    1,
     reduction time=  100.560059
 Line   201 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n=  800, lda1=  800, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=U, lwork= 1000000,
     xinfo=    1,
     reduction time=  241.930176
 Line   204 / dsyrdd : reduction driver for full matrices (SBR),
     mtype=R, diam= 0.0000E+00, uplo=U, n= 1000, lda1= 1000, b2=    1,
     lda2=    2, nsteps=    0, drptol= 0.0000E+00, jobu=U, lwork= 1000000,
     xinfo=    1,
     reduction time=  473.800049
                                                                               
 *** Timing the LAPACK reduction banded -> tridiagonal ***                     
                                                                               
    no update                                                                  
                                                                               
 Line   249 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    4, lda=    5,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.110107
 Line   252 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    8, lda=    9,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.280029
 Line   255 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   12, lda=   13,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.389893
 Line   258 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   16, lda=   17,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.460205
 Line   261 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   24, lda=   25,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.580078
 Line   264 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   32, lda=   33,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.700195
 Line   267 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   48, lda=   49,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    0.889893
 Line   270 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   64, lda=   65,
     jobu=N, ldu=  200, xinfo=    0,
     reduction time=    1.060059
                                                                               
 Line   275 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    4, lda=    5,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    0.390137
 Line   278 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    8, lda=    9,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    0.899902
 Line   281 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   12, lda=   13,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    1.469971
 Line   284 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   16, lda=   17,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    1.820068
 Line   287 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   24, lda=   25,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    2.319824
 Line   290 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   32, lda=   33,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    2.810059
 Line   293 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   48, lda=   49,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    3.719971
 Line   296 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   64, lda=   65,
     jobu=N, ldu=  400, xinfo=    0,
     reduction time=    4.600098
                                                                               
 Line   301 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    4, lda=    5,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    0.850098
 Line   304 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    8, lda=    9,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    1.859863
 Line   307 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   12, lda=   13,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    3.110107
 Line   310 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   16, lda=   17,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    4.020020
 Line   313 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   24, lda=   25,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    5.189941
 Line   316 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   32, lda=   33,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    6.340088
 Line   319 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   48, lda=   49,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=    8.659912
 Line   322 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   64, lda=   65,
     jobu=N, ldu=  600, xinfo=    0,
     reduction time=   10.760010
                                                                               
 Line   327 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    4, lda=    5,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=    1.459961
 Line   330 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    8, lda=    9,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=    3.220215
 Line   333 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   12, lda=   13,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=    5.169922
 Line   336 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   16, lda=   17,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=    6.910156
 Line   339 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   24, lda=   25,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=    9.379883
 Line   342 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   32, lda=   33,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=   11.469971
 Line   345 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   48, lda=   49,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=   15.540039
 Line   348 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   64, lda=   65,
     jobu=N, ldu=  800, xinfo=    0,
     reduction time=   19.250000
                                                                               
 Line   353 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    4, lda=    5,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=    2.270020
 Line   356 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    8, lda=    9,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=    4.869873
 Line   359 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   12, lda=   13,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=    7.830078
 Line   362 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   16, lda=   17,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=   10.510010
 Line   365 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   24, lda=   25,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=   14.540039
 Line   368 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   32, lda=   33,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=   17.910156
 Line   371 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   48, lda=   49,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=   24.200195
 Line   374 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   64, lda=   65,
     jobu=N, ldu= 1000, xinfo=    0,
     reduction time=   30.220215
                                                                               
    with update                                                                
                                                                               
 Line   383 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    4, lda=    5,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    1.259766
 Line   386 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    8, lda=    9,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    1.589844
 Line   389 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   12, lda=   13,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    1.779785
 Line   392 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   16, lda=   17,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    1.889648
 Line   395 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   24, lda=   25,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    2.030273
 Line   398 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   32, lda=   33,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    2.160156
 Line   401 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   48, lda=   49,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    2.350098
 Line   404 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   64, lda=   65,
     jobu=U, ldu=  200, xinfo=    0,
     reduction time=    2.500000
                                                                               
 Line   409 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    4, lda=    5,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=    9.290039
 Line   412 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    8, lda=    9,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   11.290039
 Line   415 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   12, lda=   13,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   12.409668
 Line   418 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   16, lda=   17,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   12.990234
 Line   421 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   24, lda=   25,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   13.759766
 Line   424 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   32, lda=   33,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   14.400391
 Line   427 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   48, lda=   49,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   15.609863
 Line   430 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   64, lda=   65,
     jobu=U, ldu=  400, xinfo=    0,
     reduction time=   16.390137
                                                                               
 Line   435 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    4, lda=    5,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   32.070313
 Line   438 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    8, lda=    9,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   37.889648
 Line   441 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   12, lda=   13,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   41.080078
 Line   444 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   16, lda=   17,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   42.890137
 Line   447 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   24, lda=   25,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   45.090332
 Line   450 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   32, lda=   33,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   46.979980
 Line   453 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   48, lda=   49,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   49.069824
 Line   456 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   64, lda=   65,
     jobu=U, ldu=  600, xinfo=    0,
     reduction time=   52.009766
                                                                               
 Line   461 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    4, lda=    5,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=   79.229980
 Line   464 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    8, lda=    9,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=   93.649902
 Line   467 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   12, lda=   13,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  100.850098
 Line   470 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   16, lda=   17,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  100.650391
 Line   473 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   24, lda=   25,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  109.579590
 Line   476 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   32, lda=   33,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  107.930176
 Line   479 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   48, lda=   49,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  113.150391
 Line   482 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   64, lda=   65,
     jobu=U, ldu=  800, xinfo=    0,
     reduction time=  122.680176
                                                                               
 Line   487 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    4, lda=    5,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  154.910156
 Line   490 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    8, lda=    9,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  176.100098
 Line   493 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   12, lda=   13,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  193.929688
 Line   496 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   16, lda=   17,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  192.419922
 Line   499 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   24, lda=   25,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  200.620117
 Line   502 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   32, lda=   33,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  206.000000
 Line   505 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   48, lda=   49,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  213.649902
 Line   508 / dsbtrd : banded -> tridiagonal, one-step (LAPACK),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   64, lda=   65,
     jobu=U, ldu= 1000, xinfo=    0,
     reduction time=  229.709961
                                                                               
 *** Timing the SBR reduction banded -> tridiagonal ***                        
                                                                               
    no update                                                                  
                                                                               
 Line   555 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.370117
 Line   558 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.329590
 Line   561 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.540039
 Line   564 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.620117
 Line   567 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.800293
 Line   570 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    0.939941
 Line   573 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    1.169922
 Line   576 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    1.380371
                                                                               
 Line   581 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    1.520020
 Line   584 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    1.390137
 Line   587 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    2.239746
 Line   590 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    2.610352
 Line   593 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    3.490234
 Line   596 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    4.299805
 Line   599 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.899902
 Line   602 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=    7.330078
                                                                               
 Line   607 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=    3.399902
 Line   610 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=    3.160156
 Line   613 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.120117
 Line   616 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=    6.000000
 Line   619 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=    8.060059
 Line   622 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=   10.120117
 Line   625 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=   14.099609
 Line   628 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=   18.010254
                                                                               
 Line   633 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=    6.079590
 Line   636 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.600098
 Line   639 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=    9.179688
 Line   642 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=   10.760742
 Line   645 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=   14.620117
 Line   648 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=   18.359375
 Line   651 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=   25.959961
 Line   654 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=   33.459961
                                                                               
 Line   659 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=    9.459961
 Line   662 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=    8.769531
 Line   665 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   14.440430
 Line   668 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   16.919922
 Line   671 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   22.909180
 Line   674 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   28.959961
 Line   677 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   41.360352
 Line   680 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=N, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=   53.570313
                                                                               
    with update                                                                
       *** ignore messages about tests failing because ***                     
       *** SBRDT returned a wrong (but positive) info  ***                     
                                                                               
 *** Test in line   693 failed : dsbrdt returned info=    3 (expected     1)
 Line   693 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.169922
 *** Test in line   696 failed : dsbrdt returned info=    4 (expected     1)
 Line   696 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    4.809570
 *** Test in line   699 failed : dsbrdt returned info=    4 (expected     1)
 Line   699 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    4.870117
 *** Test in line   702 failed : dsbrdt returned info=    6 (expected     1)
 Line   702 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.160156
 *** Test in line   705 failed : dsbrdt returned info=    8 (expected     1)
 Line   705 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.140625
 *** Test in line   708 failed : dsbrdt returned info=   12 (expected     1)
 Line   708 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.389648
 *** Test in line   711 failed : dsbrdt returned info=   16 (expected     1)
 Line   711 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.629883
 *** Test in line   714 failed : dsbrdt returned info=   22 (expected     1)
 Line   714 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  200, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  200, lwork= 1000000,
     xinfo=    1,
     reduction time=    5.889648
                                                                               
 *** Test in line   719 failed : dsbrdt returned info=    3 (expected     1)
 Line   719 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   40.810547
 *** Test in line   722 failed : dsbrdt returned info=    4 (expected     1)
 Line   722 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   38.150391
 *** Test in line   725 failed : dsbrdt returned info=    4 (expected     1)
 Line   725 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   37.580078
 *** Test in line   728 failed : dsbrdt returned info=    6 (expected     1)
 Line   728 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   37.529297
 *** Test in line   731 failed : dsbrdt returned info=    8 (expected     1)
 Line   731 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   38.089844
 *** Test in line   734 failed : dsbrdt returned info=   12 (expected     1)
 Line   734 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   39.389648
 *** Test in line   737 failed : dsbrdt returned info=   16 (expected     1)
 Line   737 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   41.040039
 *** Test in line   740 failed : dsbrdt returned info=   22 (expected     1)
 Line   740 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  400, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  400, lwork= 1000000,
     xinfo=    1,
     reduction time=   42.830078
                                                                               
 *** Test in line   745 failed : dsbrdt returned info=    3 (expected     1)
 Line   745 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  135.049805
 *** Test in line   748 failed : dsbrdt returned info=    4 (expected     1)
 Line   748 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  126.279297
 *** Test in line   751 failed : dsbrdt returned info=    4 (expected     1)
 Line   751 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  123.990234
 *** Test in line   754 failed : dsbrdt returned info=    6 (expected     1)
 Line   754 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  126.099609
 *** Test in line   757 failed : dsbrdt returned info=    8 (expected     1)
 Line   757 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  127.290039
 *** Test in line   760 failed : dsbrdt returned info=   12 (expected     1)
 Line   760 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  131.120117
 *** Test in line   763 failed : dsbrdt returned info=   16 (expected     1)
 Line   763 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  134.370117
 *** Test in line   766 failed : dsbrdt returned info=   22 (expected     1)
 Line   766 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  600, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  600, lwork= 1000000,
     xinfo=    1,
     reduction time=  139.489258
                                                                               
 *** Test in line   771 failed : dsbrdt returned info=    3 (expected     1)
 Line   771 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  314.759766
 *** Test in line   774 failed : dsbrdt returned info=    4 (expected     1)
 Line   774 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  298.330078
 *** Test in line   777 failed : dsbrdt returned info=    4 (expected     1)
 Line   777 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  291.160156
 *** Test in line   780 failed : dsbrdt returned info=    6 (expected     1)
 Line   780 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  296.000000
 *** Test in line   783 failed : dsbrdt returned info=    8 (expected     1)
 Line   783 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  297.229492
 *** Test in line   786 failed : dsbrdt returned info=   12 (expected     1)
 Line   786 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  304.639648
 *** Test in line   789 failed : dsbrdt returned info=   16 (expected     1)
 Line   789 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  310.850586
 *** Test in line   792 failed : dsbrdt returned info=   22 (expected     1)
 Line   792 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n=  800, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu=  800, lwork= 1000000,
     xinfo=    1,
     reduction time=  320.259766
                                                                               
 *** Test in line   797 failed : dsbrdt returned info=    3 (expected     1)
 Line   797 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=    4, lda=    8,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  612.699219
 *** Test in line   800 failed : dsbrdt returned info=    4 (expected     1)
 Line   800 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=    8, lda=   16,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  582.500000
 *** Test in line   803 failed : dsbrdt returned info=    4 (expected     1)
 Line   803 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   12, lda=   24,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  567.380859
 *** Test in line   806 failed : dsbrdt returned info=    6 (expected     1)
 Line   806 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   16, lda=   32,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  574.790039
 *** Test in line   809 failed : dsbrdt returned info=    8 (expected     1)
 Line   809 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   24, lda=   48,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  576.379883
 *** Test in line   812 failed : dsbrdt returned info=   12 (expected     1)
 Line   812 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   32, lda=   64,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  589.299805
 *** Test in line   815 failed : dsbrdt returned info=   16 (expected     1)
 Line   815 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   48, lda=   96,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  597.101563
 *** Test in line   818 failed : dsbrdt returned info=   22 (expected     1)
 Line   818 / dsbrdt : banded -> tridiagonal, one-step (SBR)   ,
     mtype=R, diam= 0.0000E+00, n= 1000, b1=   64, lda=  128,
     drptol= 0.0000E+00, nb=    0, jobu=U, ldu= 1000, lwork= 1000000,
     xinfo=    1,
     reduction time=  612.800781
                                                                               
 *** Timing the SBR driver banded -> tridiagonal ***                           
                                                                               
    no update                                                                  
                                                                               
 Line   876 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.109375
 Line   879 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.291016
 Line   882 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.509766
 Line   885 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.599609
 Line   888 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.769531
 Line   891 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.919922
 Line   894 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.509766
 Line   897 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.990234
                                                                               
 Line   902 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.390625
 Line   905 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.900391
 Line   908 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.560547
 Line   911 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    2.560547
 Line   914 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.400391
 Line   917 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    4.191406
 Line   920 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    7.160156
 Line   923 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    9.830078
                                                                               
 Line   928 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.839844
 Line   931 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.869141
 Line   934 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.179688
 Line   937 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    5.871094
 Line   940 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    7.880859
 Line   943 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    9.880859
 Line   946 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=   16.980469
 Line   949 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=   23.710938
                                                                               
 Line   954 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.451172
 Line   957 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.210938
 Line   960 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    5.300781
 Line   963 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   10.570313
 Line   966 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   14.279297
 Line   969 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   17.919922
 Line   972 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   30.880859
 Line   975 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   43.470703
                                                                               
 Line   980 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    2.250000
 Line   983 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    4.849609
 Line   986 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    7.990234
 Line   989 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   16.589844
 Line   992 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   22.480469
 Line   995 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   28.359375
 Line   998 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   48.900391
 Line  1001 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   69.310547
                                                                               
    with update                                                                
                                                                               
 Line  1010 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.109375
 Line  1013 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.289063
 Line  1016 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.509766
 Line  1019 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.611328
 Line  1022 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.781250
 Line  1025 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.919922
 Line  1028 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.529297
 Line  1031 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  200, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  200,
     lwork= 1000000, xinfo=    1,
     reduction time=    2.000000
                                                                               
 Line  1036 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.390625
 Line  1039 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.898438
 Line  1042 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.558594
 Line  1045 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    2.560547
 Line  1048 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.410156
 Line  1051 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    4.199219
 Line  1054 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    7.160156
 Line  1057 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  400, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  400,
     lwork= 1000000, xinfo=    1,
     reduction time=    9.859375
                                                                               
 Line  1062 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    0.841797
 Line  1065 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.880859
 Line  1068 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.179688
 Line  1071 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    5.878906
 Line  1074 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    7.900391
 Line  1077 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=    9.900391
 Line  1080 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=   17.089844
 Line  1083 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  600, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  600,
     lwork= 1000000, xinfo=    1,
     reduction time=   23.699219
                                                                               
 Line  1088 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    1.449219
 Line  1091 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    3.189453
 Line  1094 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=    5.320313
 Line  1097 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   10.560547
 Line  1100 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   14.240234
 Line  1103 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   17.900391
 Line  1106 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   30.910156
 Line  1109 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n=  800, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu=  800,
     lwork= 1000000, xinfo=    1,
     reduction time=   43.628906
                                                                               
 Line  1114 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    4, lda=    8, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    2.259766
 Line  1117 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=    8, lda=   16, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    4.949219
 Line  1120 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   12, lda=   24, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=    8.111328
 Line  1123 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   16, lda=   32, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   16.529297
 Line  1126 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   24, lda=   48, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   22.419922
 Line  1129 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   32, lda=   64, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   28.361328
 Line  1132 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   48, lda=   96, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   49.230469
 Line  1135 / dsbrdd : reduction driver for banded matrcs (SBR),
     mtype=R, diam= 0.0000E+00, uplo=L, n= 1000, b1=   64, lda=  128, b2=    1,
     nsteps=    0, drptol= 0.0000E+00, jobu=N, ldu= 1000,
     lwork= 1000000, xinfo=    1,
     reduction time=   69.419922
 
 ===============================================================================
 Tests for                                             Total Skipped  Failed
 -------------------------------------------------------------------------------
 dsytrd : full -> tridiagonal, one-step (LAPACK)   :      10       0       0
 dorgtr : accumulation of transformations (LAPACK) :       5       0       0
 dsbtrd : banded -> tridiagonal, one-step (LAPACK) :      80       0       0
 dsyrdb : full -> banded, one-step (SBR)           :       0       0       0
 dsygtr : accumulation of transformations (SBR)    :       0       0       0
 dsbrdb : banded -> banded, one-step (SBR)         :       0       0       0
 dsbrdt : banded -> tridiagonal, one-step (SBR)    :      80       0      40
 dsy2bc : copy full -> banded (SBR)                :       0       0       0
 dsy2bi : in-place copy full -> banded (SBR)       :       0       0       0
 dsb2bc : copy banded -> banded (SBR)              :       0       0       0
 dsb2bi : in-place copy banded -> banded (SBR)     :       0       0       0
 dsyrdd : reduction driver for full matrices (SBR) :      10       0       0
 dsbrdd : reduction driver for banded matrcs (SBR) :      80       0       0
 -------------------------------------------------------------------------------
 Total  :                                          :     265       0      40
 -------------------------------------------------------------------------------
 Total time : 20163.49 seconds
SHAR_EOF
fi # end of overwriting check
if test -f 'res3'
then
	echo shar: will not over-write existing file "'res3'"
else
cat << "SHAR_EOF" > 'res3'
 *** Setting nb for SYRDB ***                                                  
                                                                               
     no update                                                                 
                                                                               
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb=  1, info=  1, time=    1.270
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb=  4, info=  4, time=    1.240
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb=  6, info=  6, time=    1.320
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb=  8, info=  8, time=    1.290
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 12, info= 12, time=    1.420
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 16, info= 16, time=    1.450
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 20, info= 20, time=    1.510
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 24, info= 24, time=    1.580
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 32, info= 32, time=    1.730
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 40, info= 40, time=    1.880
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 48, info= 48, time=    2.040
 dsyrdb: uplo=L, jobu=N, n=  200, b2= 64, nb= 64, info= 64, time=    2.430
                                                                               
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb=  1, info=  1, time=   13.390
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb=  4, info=  4, time=   13.300
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb=  6, info=  6, time=   13.450
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb=  8, info=  8, time=   13.800
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 12, info= 12, time=   14.120
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 16, info= 16, time=   14.760
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 20, info= 20, time=   14.640
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 24, info= 24, time=   14.980
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 32, info= 32, time=   15.730
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 40, info= 40, time=   16.440
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 48, info= 48, time=   17.400
 dsyrdb: uplo=L, jobu=N, n=  400, b2= 64, nb= 64, info= 64, time=   19.230
                                                                               
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb=  1, info=  1, time=   48.980
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb=  4, info=  4, time=   49.430
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb=  6, info=  6, time=   49.630
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb=  8, info=  8, time=   49.520
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 12, info= 12, time=   50.610
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 16, info= 16, time=   51.060
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 20, info= 20, time=   52.040
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 24, info= 24, time=   53.560
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 32, info= 32, time=   55.650
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 40, info= 40, time=   56.910
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 48, info= 48, time=   58.370
 dsyrdb: uplo=L, jobu=N, n=  600, b2= 64, nb= 64, info= 64, time=   62.150
                                                                               
     with update                                                               
                                                                               
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb=  1, info=  1, time=    3.070
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb=  4, info=  4, time=    3.120
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb=  6, info=  6, time=    3.140
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb=  8, info=  8, time=    3.170
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 12, info= 12, time=    3.250
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 16, info= 16, time=    3.470
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 20, info= 20, time=    3.550
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 24, info= 24, time=    3.620
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 32, info= 32, time=    3.810
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 40, info= 40, time=    4.030
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 48, info= 48, time=    4.140
 dsyrdb: uplo=L, jobu=U, n=  200, b2= 64, nb= 64, info= 64, time=    4.610
                                                                               
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb=  1, info=  1, time=   36.240
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb=  4, info=  4, time=   35.970
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb=  6, info=  6, time=   36.550
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb=  8, info=  8, time=   36.880
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 12, info= 12, time=   37.120
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 16, info= 16, time=   37.410
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 20, info= 20, time=   37.980
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 24, info= 24, time=   38.480
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 32, info= 32, time=   39.160
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 40, info= 40, time=   40.440
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 48, info= 48, time=   41.380
 dsyrdb: uplo=L, jobu=U, n=  400, b2= 64, nb= 64, info= 64, time=   44.110
                                                                               
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb=  1, info=  1, time=  138.830
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb=  4, info=  4, time=  138.800
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb=  6, info=  6, time=  139.300
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb=  8, info=  8, time=  139.740
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 12, info= 12, time=  141.290
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 16, info= 16, time=  142.420
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 20, info= 20, time=  143.170
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 24, info= 24, time=  144.470
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 32, info= 32, time=  146.940
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 40, info= 40, time=  150.100
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 48, info= 48, time=  153.050
 dsyrdb: uplo=L, jobu=U, n=  600, b2= 64, nb= 64, info= 64, time=  156.950
                                                                               
 *** Setting nb for SBRDB ***                                                  
                                                                               
     no update                                                                 
                                                                               
 dsbrdb: jobu=N, n=  200, b1= 16, b2=  8, nb=  1, info=  1, time=    0.630
 dsbrdb: jobu=N, n=  200, b1= 16, b2=  8, nb=  4, info=  4, time=    0.640
 dsbrdb: jobu=N, n=  200, b1= 16, b2=  8, nb=  6, info=  6, time=    0.700
 dsbrdb: jobu=N, n=  200, b1= 16, b2=  8, nb=  8, info=  8, time=    0.820
                                                                               
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb=  1, info=  1, time=    0.750
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb=  4, info=  4, time=    0.780
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb=  6, info=  6, time=    0.870
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb=  8, info=  8, time=    0.950
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb= 10, info= 10, time=    1.060
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb= 12, info= 12, time=    1.070
 dsbrdb: jobu=N, n=  200, b1= 32, b2= 16, nb= 16, info= 16, time=    1.260
                                                                               
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb=  1, info=  1, time=    0.960
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb=  4, info=  4, time=    1.000
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb=  6, info=  6, time=    1.070
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb=  8, info=  8, time=    1.120
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 10, info= 10, time=    1.120
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 12, info= 12, time=    1.250
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 16, info= 16, time=    1.320
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 20, info= 20, time=    1.480
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 24, info= 24, time=    1.670
 dsbrdb: jobu=N, n=  200, b1= 64, b2= 32, nb= 32, info= 32, time=    1.940
                                                                               
 dsbrdb: jobu=N, n=  400, b1= 16, b2=  8, nb=  1, info=  1, time=    2.620
 dsbrdb: jobu=N, n=  400, b1= 16, b2=  8, nb=  4, info=  4, time=    2.700
 dsbrdb: jobu=N, n=  400, b1= 16, b2=  8, nb=  6, info=  6, time=    3.010
 dsbrdb: jobu=N, n=  400, b1= 16, b2=  8, nb=  8, info=  8, time=    3.410
                                                                               
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb=  1, info=  1, time=    3.330
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb=  4, info=  4, time=    3.500
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb=  6, info=  6, time=    3.880
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb=  8, info=  8, time=    4.270
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb= 10, info= 10, time=    4.780
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb= 12, info= 12, time=    4.960
 dsbrdb: jobu=N, n=  400, b1= 32, b2= 16, nb= 16, info= 16, time=    5.790
                                                                               
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb=  1, info=  1, time=    5.000
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb=  4, info=  4, time=    5.250
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb=  6, info=  6, time=    5.610
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb=  8, info=  8, time=    5.650
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 10, info= 10, time=    5.920
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 12, info= 12, time=    6.240
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 16, info= 16, time=    7.160
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 20, info= 20, time=    7.660
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 24, info= 24, time=    8.450
 dsbrdb: jobu=N, n=  400, b1= 64, b2= 32, nb= 32, info= 32, time=   10.080
                                                                               
 dsbrdb: jobu=N, n=  600, b1= 16, b2=  8, nb=  1, info=  1, time=    5.970
 dsbrdb: jobu=N, n=  600, b1= 16, b2=  8, nb=  4, info=  4, time=    6.120
 dsbrdb: jobu=N, n=  600, b1= 16, b2=  8, nb=  6, info=  6, time=    6.840
 dsbrdb: jobu=N, n=  600, b1= 16, b2=  8, nb=  8, info=  8, time=    7.870
                                                                               
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb=  1, info=  1, time=    7.790
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb=  4, info=  4, time=    8.280
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb=  6, info=  6, time=    9.020
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb=  8, info=  8, time=   10.090
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb= 10, info= 10, time=   10.990
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb= 12, info= 12, time=   11.510
 dsbrdb: jobu=N, n=  600, b1= 32, b2= 16, nb= 16, info= 16, time=   13.560
                                                                               
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb=  1, info=  1, time=   12.380
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb=  4, info=  4, time=   12.830
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb=  6, info=  6, time=   13.780
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb=  8, info=  8, time=   14.010
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 10, info= 10, time=   14.709
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 12, info= 12, time=   15.780
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 16, info= 16, time=   17.170
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 20, info= 20, time=   18.850
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 24, info= 24, time=   20.540
 dsbrdb: jobu=N, n=  600, b1= 64, b2= 32, nb= 32, info= 32, time=   24.650
                                                                               
     with update                                                               
                                                                               
 dsbrdb: jobu=U, n=  200, b1= 16, b2=  8, nb=  1, info=  1, time=    2.930
 dsbrdb: jobu=U, n=  200, b1= 16, b2=  8, nb=  4, info=  4, time=    3.060
 dsbrdb: jobu=U, n=  200, b1= 16, b2=  8, nb=  6, info=  6, time=    3.210
 dsbrdb: jobu=U, n=  200, b1= 16, b2=  8, nb=  8, info=  8, time=    3.480
                                                                               
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb=  1, info=  1, time=    2.780
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb=  4, info=  4, time=    2.920
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb=  6, info=  6, time=    3.000
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb=  8, info=  8, time=    3.180
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb= 10, info= 10, time=    3.310
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb= 12, info= 12, time=    3.460
 dsbrdb: jobu=U, n=  200, b1= 32, b2= 16, nb= 16, info= 16, time=    3.750
                                                                               
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb=  1, info=  1, time=    2.740
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb=  4, info=  4, time=    2.790
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb=  6, info=  6, time=    2.940
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb=  8, info=  8, time=    2.980
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 10, info= 10, time=    3.040
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 12, info= 12, time=    3.130
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 16, info= 16, time=    3.330
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 20, info= 20, time=    3.510
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 24, info= 24, time=    3.660
 dsbrdb: jobu=U, n=  200, b1= 64, b2= 32, nb= 32, info= 32, time=    4.140
                                                                               
 dsbrdb: jobu=U, n=  400, b1= 16, b2=  8, nb=  1, info=  1, time=   20.950
 dsbrdb: jobu=U, n=  400, b1= 16, b2=  8, nb=  4, info=  4, time=   22.300
 dsbrdb: jobu=U, n=  400, b1= 16, b2=  8, nb=  6, info=  6, time=   23.640
 dsbrdb: jobu=U, n=  400, b1= 16, b2=  8, nb=  8, info=  8, time=   24.880
                                                                               
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb=  1, info=  1, time=   20.020
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb=  4, info=  4, time=   21.020
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb=  6, info=  6, time=   21.940
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb=  8, info=  8, time=   22.590
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb= 10, info= 10, time=   23.700
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb= 12, info= 12, time=   23.920
 dsbrdb: jobu=U, n=  400, b1= 32, b2= 16, nb= 16, info= 16, time=   26.150
                                                                               
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb=  1, info=  1, time=   20.490
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb=  4, info=  4, time=   20.790
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb=  6, info=  6, time=   21.900
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb=  8, info=  8, time=   22.290
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 10, info= 10, time=   22.880
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 12, info= 12, time=   23.110
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 16, info= 16, time=   24.390
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 20, info= 20, time=   25.380
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 24, info= 24, time=   27.070
 dsbrdb: jobu=U, n=  400, b1= 64, b2= 32, nb= 32, info= 32, time=   29.140
                                                                               
 dsbrdb: jobu=U, n=  600, b1= 16, b2=  8, nb=  1, info=  1, time=   70.370
 dsbrdb: jobu=U, n=  600, b1= 16, b2=  8, nb=  4, info=  4, time=   74.440
 dsbrdb: jobu=U, n=  600, b1= 16, b2=  8, nb=  6, info=  6, time=   79.360
 dsbrdb: jobu=U, n=  600, b1= 16, b2=  8, nb=  8, info=  8, time=   82.550
                                                                               
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb=  1, info=  1, time=   66.310
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb=  4, info=  4, time=   68.650
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb=  6, info=  6, time=   71.141
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb=  8, info=  8, time=   74.350
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb= 10, info= 10, time=   76.760
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb= 12, info= 12, time=   78.660
 dsbrdb: jobu=U, n=  600, b1= 32, b2= 16, nb= 16, info= 16, time=   84.010
                                                                               
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb=  1, info=  1, time=   67.820
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb=  4, info=  4, time=   68.250
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb=  6, info=  6, time=   70.200
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb=  8, info=  8, time=   71.410
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 10, info= 10, time=   73.390
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 12, info= 12, time=   74.640
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 16, info= 16, time=   77.880
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 20, info= 20, time=   80.810
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 24, info= 24, time=   84.390
 dsbrdb: jobu=U, n=  600, b1= 64, b2= 32, nb= 32, info= 32, time=   91.760
                                                                               
 *** Setting nb for SBRDT ***                                                  
                                                                               
     with update                                                               
                                                                               
 dsbrdt: jobu=U, n=  200, b1=  8, nb=  1, info=  1, time=    1.061
 dsbrdt: jobu=U, n=  200, b1=  8, nb=  4, info=  4, time=    4.899
 dsbrdt: jobu=U, n=  200, b1=  8, nb=  6, info=  6, time=    5.300
 dsbrdt: jobu=U, n=  200, b1=  8, nb=  8, info=  8, time=    5.400
 dsbrdt: jobu=U, n=  200, b1=  8, nb= 10, info= 10, time=    5.650
 dsbrdt: jobu=U, n=  200, b1=  8, nb= 12, info= 12, time=    5.931
                                                                               
 dsbrdt: jobu=U, n=  200, b1= 16, nb=  1, info=  1, time=    3.279
 dsbrdt: jobu=U, n=  200, b1= 16, nb=  4, info=  4, time=    4.890
 dsbrdt: jobu=U, n=  200, b1= 16, nb=  6, info=  6, time=    5.021
 dsbrdt: jobu=U, n=  200, b1= 16, nb=  8, info=  8, time=    5.210
 dsbrdt: jobu=U, n=  200, b1= 16, nb= 10, info= 10, time=    5.320
 dsbrdt: jobu=U, n=  200, b1= 16, nb= 12, info= 12, time=    5.510
 dsbrdt: jobu=U, n=  200, b1= 16, nb= 16, info= 16, time=    5.790
 dsbrdt: jobu=U, n=  200, b1= 16, nb= 20, info= 20, time=    6.120
 dsbrdt: jobu=U, n=  200, b1= 16, nb= 24, info= 24, time=    6.330
                                                                               
 dsbrdt: jobu=U, n=  200, b1= 32, nb=  1, info=  1, time=    3.630
 dsbrdt: jobu=U, n=  200, b1= 32, nb=  4, info=  4, time=    5.060
 dsbrdt: jobu=U, n=  200, b1= 32, nb=  6, info=  6, time=    5.190
 dsbrdt: jobu=U, n=  200, b1= 32, nb=  8, info=  8, time=    5.280
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 10, info= 10, time=    5.431
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 12, info= 12, time=    5.390
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 16, info= 16, time=    5.640
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 20, info= 20, time=    5.840
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 32, info= 32, time=    6.351
 dsbrdt: jobu=U, n=  200, b1= 32, nb= 40, info= 40, time=    6.750
                                                                               
 dsbrdt: jobu=U, n=  400, b1=  8, nb=  1, info=  1, time=    7.909
 dsbrdt: jobu=U, n=  400, b1=  8, nb=  4, info=  4, time=   37.670
 dsbrdt: jobu=U, n=  400, b1=  8, nb=  6, info=  6, time=   39.450
 dsbrdt: jobu=U, n=  400, b1=  8, nb=  8, info=  8, time=   41.660
 dsbrdt: jobu=U, n=  400, b1=  8, nb= 10, info= 10, time=   43.540
 dsbrdt: jobu=U, n=  400, b1=  8, nb= 12, info= 12, time=   45.710
                                                                               
 dsbrdt: jobu=U, n=  400, b1= 16, nb=  1, info=  1, time=   24.511
 dsbrdt: jobu=U, n=  400, b1= 16, nb=  4, info=  4, time=   36.641
 dsbrdt: jobu=U, n=  400, b1= 16, nb=  6, info=  6, time=   37.859
 dsbrdt: jobu=U, n=  400, b1= 16, nb=  8, info=  8, time=   38.819
 dsbrdt: jobu=U, n=  400, b1= 16, nb= 10, info= 10, time=   39.811
 dsbrdt: jobu=U, n=  400, b1= 16, nb= 12, info= 12, time=   41.170
 dsbrdt: jobu=U, n=  400, b1= 16, nb= 16, info= 16, time=   43.399
 dsbrdt: jobu=U, n=  400, b1= 16, nb= 20, info= 20, time=   45.570
 dsbrdt: jobu=U, n=  400, b1= 16, nb= 24, info= 24, time=   47.580
                                                                               
 dsbrdt: jobu=U, n=  400, b1= 32, nb=  1, info=  1, time=   25.990
 dsbrdt: jobu=U, n=  400, b1= 32, nb=  4, info=  4, time=   37.250
 dsbrdt: jobu=U, n=  400, b1= 32, nb=  6, info=  6, time=   38.069
 dsbrdt: jobu=U, n=  400, b1= 32, nb=  8, info=  8, time=   38.739
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 10, info= 10, time=   39.380
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 12, info= 12, time=   40.000
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 16, info= 16, time=   40.950
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 20, info= 20, time=   42.250
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 32, info= 32, time=   46.030
 dsbrdt: jobu=U, n=  400, b1= 32, nb= 40, info= 40, time=   48.239
                                                                               
 dsbrdt: jobu=U, n=  600, b1=  8, nb=  1, info=  1, time=   25.600
 dsbrdt: jobu=U, n=  600, b1=  8, nb=  4, info=  4, time=  127.690
 dsbrdt: jobu=U, n=  600, b1=  8, nb=  6, info=  6, time=  134.300
 dsbrdt: jobu=U, n=  600, b1=  8, nb=  8, info=  8, time=  141.820
 dsbrdt: jobu=U, n=  600, b1=  8, nb= 10, info= 10, time=  148.960
 dsbrdt: jobu=U, n=  600, b1=  8, nb= 12, info= 12, time=  155.729
                                                                               
 dsbrdt: jobu=U, n=  600, b1= 16, nb=  1, info=  1, time=   81.830
 dsbrdt: jobu=U, n=  600, b1= 16, nb=  4, info=  4, time=  123.700
 dsbrdt: jobu=U, n=  600, b1= 16, nb=  6, info=  6, time=  127.140
 dsbrdt: jobu=U, n=  600, b1= 16, nb=  8, info=  8, time=  131.060
 dsbrdt: jobu=U, n=  600, b1= 16, nb= 10, info= 10, time=  134.700
 dsbrdt: jobu=U, n=  600, b1= 16, nb= 12, info= 12, time=  137.830
 dsbrdt: jobu=U, n=  600, b1= 16, nb= 16, info= 16, time=  145.110
 dsbrdt: jobu=U, n=  600, b1= 16, nb= 20, info= 20, time=  154.210
 dsbrdt: jobu=U, n=  600, b1= 16, nb= 24, info= 24, time=  161.670
                                                                               
 dsbrdt: jobu=U, n=  600, b1= 32, nb=  1, info=  1, time=   86.070
 dsbrdt: jobu=U, n=  600, b1= 32, nb=  4, info=  4, time=  125.300
 dsbrdt: jobu=U, n=  600, b1= 32, nb=  6, info=  6, time=  127.330
 dsbrdt: jobu=U, n=  600, b1= 32, nb=  8, info=  8, time=  128.700
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 10, info= 10, time=  131.110
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 12, info= 12, time=  132.750
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 16, info= 16, time=  136.310
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 20, info= 20, time=  140.510
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 32, info= 32, time=  152.310
 dsbrdt: jobu=U, n=  600, b1= 32, nb= 40, info= 40, time=  160.960
 
 ===============================================================================
 Tests for                                             Total Skipped  Failed
 -------------------------------------------------------------------------------
 dsytrd : full -> tridiagonal, one-step (LAPACK)   :       0       0       0
 dorgtr : accumulation of transformations (LAPACK) :       0       0       0
 dsbtrd : banded -> tridiagonal, one-step (LAPACK) :       0       0       0
 dsyrdb : full -> banded, one-step (SBR)           :      72       0       0
 dsygtr : accumulation of transformations (SBR)    :       0       0       0
 dsbrdb : banded -> banded, one-step (SBR)         :     126       0       0
 dsbrdt : banded -> tridiagonal, one-step (SBR)    :      75       0       0
 dsy2bc : copy full -> banded (SBR)                :       0       0       0
 dsy2bi : in-place copy full -> banded (SBR)       :       0       0       0
 dsb2bc : copy banded -> banded (SBR)              :       0       0       0
 dsb2bi : in-place copy banded -> banded (SBR)     :       0       0       0
 dsyrdd : reduction driver for full matrices (SBR) :       0       0       0
 dsbrdd : reduction driver for banded matrcs (SBR) :       0       0       0
 -------------------------------------------------------------------------------
 Total  :                                          :     273       0       0
 -------------------------------------------------------------------------------
 Total time : 13000.97 seconds
SHAR_EOF
fi # end of overwriting check
if test -f 'res4'
then
	echo shar: will not over-write existing file "'res4'"
else
cat << "SHAR_EOF" > 'res4'
 *** Setting intermediate bandwidth for SYRDD ***                              
                                                                               
     no update                                                                 
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 1, step= 1, info=  1, time=    1.320
 b=12:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.690
 b=16:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.860
 b=20:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.010
 b=24:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.100
 b=32:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.350
 b=40:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.400
 b=48:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.230
 b=64:                                                                         
 dsyrdd: uplo=L, job=N, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    3.090
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 1, step= 1, info=  1, time=   10.130
 b=12:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   18.920
 b=16:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   20.190
 b=20:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   20.610
 b=24:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   20.900
 b=32:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   21.980
 b=40:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   22.510
 b=48:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   23.210
 b=64:                                                                         
 dsyrdd: uplo=L, job=N, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   23.240
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 1, step= 1, info=  1, time=   35.030
 b=12:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   60.340
 b=16:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   63.460
 b=20:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   64.890
 b=24:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   66.460
 b=32:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   69.220
 b=40:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   71.170
 b=48:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   71.720
 b=64:                                                                         
 dsyrdd: uplo=L, job=N, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=   73.120
                                                                               
     with update                                                               
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 1, step= 1, info=  1, time=    3.620
 b=12:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.020
 b=16:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.090
 b=20:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.200
 b=24:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.130
 b=32:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.230
 b=40:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.070
 b=48:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.750
 b=64:                                                                         
 dsyrdd: uplo=L, job=U, n=  200, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.460
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 1, step= 1, info=  1, time=   29.590
 b=12:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   71.840
 b=16:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   72.500
 b=20:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   73.100
 b=24:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   72.620
 b=32:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   72.770
 b=40:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   71.920
 b=48:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   71.840
 b=64:                                                                         
 dsyrdd: uplo=L, job=U, n=  400, b2=  1, nsteps= 2, step= 2, info=  1, time=   70.300
                                                                               
 one-step (b=1):                                                               
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 1, step= 1, info=  1, time=  101.170
 b=12:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  245.990
 b=16:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  247.640
 b=20:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  249.290
 b=24:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  246.640
 b=32:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  248.040
 b=40:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  246.080
 b=48:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  244.880
 b=64:                                                                         
 dsyrdd: uplo=L, job=U, n=  600, b2=  1, nsteps= 2, step= 2, info=  1, time=  243.220
                                                                               
 *** Setting intermediate bandwidth for SBRDD ***                              
                                                                               
     no update                                                                 
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=    0.950
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    1.540
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    1.600
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    1.410
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    1.240
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=    1.380
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.310
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.490
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.490
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.280
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.000
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    1.700
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=    1.490
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.530
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.790
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.860
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.850
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.670
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.410
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    2.110
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=    4.310
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    6.540
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    6.260
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    6.290
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    5.600
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=    7.260
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   11.350
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   11.820
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   12.070
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.910
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.000
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.500
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=    9.570
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   14.540
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   15.230
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   16.330
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   16.020
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   14.850
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   13.220
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   11.840
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=   10.090
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   15.160
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   14.300
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   14.500
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   12.890
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=   17.790
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   27.650
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   28.510
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   29.250
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   26.330
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   24.000
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   20.440
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=   24.290
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   36.580
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   38.040
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   41.210
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   43.010
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   37.120
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   33.150
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=N, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   29.580
                                                                               
     with update                                                               
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=    5.420
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.370
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.580
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    7.960
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=    6.720
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=    6.030
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.530
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.340
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.020
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.290
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.440
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=    7.200
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=    6.160
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.710
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.630
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.600
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   10.130
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    9.560
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    8.730
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  200, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=    7.720
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=   39.940
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   69.140
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   63.600
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   58.660
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=   50.510
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=   43.370
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   77.150
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   75.050
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   72.570
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   67.130
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   61.830
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=   52.180
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=   45.500
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   80.890
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   80.150
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   79.350
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   76.190
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   72.450
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   63.960
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  400, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=   57.730
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 32, b2=  1, nsteps= 1, step= 1, info=  1, time=  132.370
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=  230.830
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=  211.480
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=  197.271
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 32, b2=  1, nsteps= 2, step= 2, info=  1, time=  165.730
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 1, step= 1, info=  1, time=  140.061
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  253.980
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  245.500
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  240.290
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  219.939
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  204.771
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 64, b2=  1, nsteps= 2, step= 2, info=  1, time=  170.040
                                                                               
 one-step (b=1):                                                               
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 1, step= 1, info=  1, time=  146.820
 b=8:                                                                          
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  267.130
 b=12:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  261.311
 b=16:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  261.090
 b=24:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  248.360
 b=32:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  237.181
 b=48:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  210.290
 b=64:                                                                         
 dsbrdd: uplo=L, jobu=U, n=  600, b1= 96, b2=  1, nsteps= 2, step= 2, info=  1, time=  189.641
                                                                               
 *** Where to switch from SYTRD to SYRDT ? ***                                 
                                                                               
     no update                                                                 
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=N, n=  200, b1=  4, info=  0, time=    0.110
 dsbrdt: jobu=N, n=  200, b1=  4, nb=  0, info=  1, time=    0.410
 b=6                                                                           
 dsbtrd: uplo=L, jobu=N, n=  200, b1=  6, info=  0, time=    0.200
 dsbrdt: jobu=N, n=  200, b1=  6, nb=  0, info=  1, time=    0.370
 b=8                                                                           
 dsbtrd: uplo=L, jobu=N, n=  200, b1=  8, info=  0, time=    0.280
 dsbrdt: jobu=N, n=  200, b1=  8, nb=  0, info=  1, time=    0.359
 b=10                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 10, info=  0, time=    0.360
 dsbrdt: jobu=N, n=  200, b1= 10, nb=  0, info=  1, time=    0.369
 b=12                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 12, info=  0, time=    0.380
 dsbrdt: jobu=N, n=  200, b1= 12, nb=  0, info=  1, time=    0.550
 b=16                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 16, info=  0, time=    0.449
 dsbrdt: jobu=N, n=  200, b1= 16, nb=  0, info=  1, time=    0.630
 b=20                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 20, info=  0, time=    0.530
 dsbrdt: jobu=N, n=  200, b1= 20, nb=  0, info=  1, time=    0.710
 b=24                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 24, info=  0, time=    0.590
 dsbrdt: jobu=N, n=  200, b1= 24, nb=  0, info=  1, time=    0.801
 b=32                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 32, info=  0, time=    0.689
 dsbrdt: jobu=N, n=  200, b1= 32, nb=  0, info=  1, time=    0.960
 b=40                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 40, info=  0, time=    0.811
 dsbrdt: jobu=N, n=  200, b1= 40, nb=  0, info=  1, time=    1.100
 b=48                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 48, info=  0, time=    0.880
 dsbrdt: jobu=N, n=  200, b1= 48, nb=  0, info=  1, time=    1.220
 b=64                                                                          
 dsbtrd: uplo=L, jobu=N, n=  200, b1= 64, info=  0, time=    1.060
 dsbrdt: jobu=N, n=  200, b1= 64, nb=  0, info=  1, time=    1.420
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=N, n=  400, b1=  4, info=  0, time=    0.400
 dsbrdt: jobu=N, n=  400, b1=  4, nb=  0, info=  1, time=    1.609
 b=6                                                                           
 dsbtrd: uplo=L, jobu=N, n=  400, b1=  6, info=  0, time=    0.641
 dsbrdt: jobu=N, n=  400, b1=  6, nb=  0, info=  1, time=    1.470
 b=8                                                                           
 dsbtrd: uplo=L, jobu=N, n=  400, b1=  8, info=  0, time=    0.891
 dsbrdt: jobu=N, n=  400, b1=  8, nb=  0, info=  1, time=    1.431
 b=10                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 10, info=  0, time=    1.130
 dsbrdt: jobu=N, n=  400, b1= 10, nb=  0, info=  1, time=    1.490
 b=12                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 12, info=  0, time=    1.439
 dsbrdt: jobu=N, n=  400, b1= 12, nb=  0, info=  1, time=    2.300
 b=16                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 16, info=  0, time=    1.800
 dsbrdt: jobu=N, n=  400, b1= 16, nb=  0, info=  1, time=    2.670
 b=20                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 20, info=  0, time=    2.060
 dsbrdt: jobu=N, n=  400, b1= 20, nb=  0, info=  1, time=    3.100
 b=24                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 24, info=  0, time=    2.300
 dsbrdt: jobu=N, n=  400, b1= 24, nb=  0, info=  1, time=    3.520
 b=32                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 32, info=  0, time=    2.850
 dsbrdt: jobu=N, n=  400, b1= 32, nb=  0, info=  1, time=    4.340
 b=40                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 40, info=  0, time=    3.280
 dsbrdt: jobu=N, n=  400, b1= 40, nb=  0, info=  1, time=    5.189
 b=48                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 48, info=  0, time=    3.779
 dsbrdt: jobu=N, n=  400, b1= 48, nb=  0, info=  1, time=    5.910
 b=64                                                                          
 dsbtrd: uplo=L, jobu=N, n=  400, b1= 64, info=  0, time=    4.580
 dsbrdt: jobu=N, n=  400, b1= 64, nb=  0, info=  1, time=    7.380
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=N, n=  600, b1=  4, info=  0, time=    0.840
 dsbrdt: jobu=N, n=  600, b1=  4, nb=  0, info=  1, time=    3.620
 b=6                                                                           
 dsbtrd: uplo=L, jobu=N, n=  600, b1=  6, info=  0, time=    1.350
 dsbrdt: jobu=N, n=  600, b1=  6, nb=  0, info=  1, time=    3.311
 b=8                                                                           
 dsbtrd: uplo=L, jobu=N, n=  600, b1=  8, info=  0, time=    1.840
 dsbrdt: jobu=N, n=  600, b1=  8, nb=  0, info=  1, time=    3.280
 b=10                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 10, info=  0, time=    2.410
 dsbrdt: jobu=N, n=  600, b1= 10, nb=  0, info=  1, time=    3.410
 b=12                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 12, info=  0, time=    3.040
 dsbrdt: jobu=N, n=  600, b1= 12, nb=  0, info=  1, time=    5.240
 b=16                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 16, info=  0, time=    4.040
 dsbrdt: jobu=N, n=  600, b1= 16, nb=  0, info=  1, time=    6.149
 b=20                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 20, info=  0, time=    4.630
 dsbrdt: jobu=N, n=  600, b1= 20, nb=  0, info=  1, time=    7.150
 b=24                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 24, info=  0, time=    5.199
 dsbrdt: jobu=N, n=  600, b1= 24, nb=  0, info=  1, time=    8.190
 b=32                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 32, info=  0, time=    6.400
 dsbrdt: jobu=N, n=  600, b1= 32, nb=  0, info=  1, time=   10.170
 b=40                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 40, info=  0, time=    7.460
 dsbrdt: jobu=N, n=  600, b1= 40, nb=  0, info=  1, time=   12.320
 b=48                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 48, info=  0, time=    8.479
 dsbrdt: jobu=N, n=  600, b1= 48, nb=  0, info=  1, time=   14.260
 b=64                                                                          
 dsbtrd: uplo=L, jobu=N, n=  600, b1= 64, info=  0, time=   10.659
 dsbrdt: jobu=N, n=  600, b1= 64, nb=  0, info=  1, time=   18.220
                                                                               
     with update                                                               
       *** ignore messages about tests failing because ***                     
       *** SBRDT returned a wrong (but positive) info  ***                     
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=U, n=  200, b1=  4, info=  0, time=    1.270
 dsbrdt: jobu=U, n=  200, b1=  4, nb=  0, info=  3, time=    5.180
 *** Test in line  1768 failed : dsbrdt returned info=    3 (expected     1)
 b=6                                                                           
 dsbtrd: uplo=L, jobu=U, n=  200, b1=  6, info=  0, time=    1.460
 dsbrdt: jobu=U, n=  200, b1=  6, nb=  0, info=  4, time=    5.050
 *** Test in line  1776 failed : dsbrdt returned info=    4 (expected     1)
 b=8                                                                           
 dsbtrd: uplo=L, jobu=U, n=  200, b1=  8, info=  0, time=    1.610
 dsbrdt: jobu=U, n=  200, b1=  8, nb=  0, info=  4, time=    4.870
 *** Test in line  1784 failed : dsbrdt returned info=    4 (expected     1)
 b=10                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 10, info=  0, time=    1.710
 dsbrdt: jobu=U, n=  200, b1= 10, nb=  0, info=  4, time=    4.790
 *** Test in line  1792 failed : dsbrdt returned info=    4 (expected     1)
 b=12                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 12, info=  0, time=    1.760
 dsbrdt: jobu=U, n=  200, b1= 12, nb=  0, info=  4, time=    4.891
 *** Test in line  1800 failed : dsbrdt returned info=    4 (expected     1)
 b=16                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 16, info=  0, time=    1.869
 dsbrdt: jobu=U, n=  200, b1= 16, nb=  0, info=  6, time=    5.070
 *** Test in line  1808 failed : dsbrdt returned info=    6 (expected     1)
 b=20                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 20, info=  0, time=    1.970
 dsbrdt: jobu=U, n=  200, b1= 20, nb=  0, info=  8, time=    5.160
 *** Test in line  1816 failed : dsbrdt returned info=    8 (expected     1)
 b=24                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 24, info=  0, time=    2.040
 dsbrdt: jobu=U, n=  200, b1= 24, nb=  0, info=  8, time=    5.180
 *** Test in line  1824 failed : dsbrdt returned info=    8 (expected     1)
 b=32                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 32, info=  0, time=    2.170
 dsbrdt: jobu=U, n=  200, b1= 32, nb=  0, info= 12, time=    5.400
 *** Test in line  1832 failed : dsbrdt returned info=   12 (expected     1)
 b=40                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 40, info=  0, time=    2.270
 dsbrdt: jobu=U, n=  200, b1= 40, nb=  0, info= 14, time=    5.630
 *** Test in line  1840 failed : dsbrdt returned info=   14 (expected     1)
 b=48                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 48, info=  0, time=    2.350
 dsbrdt: jobu=U, n=  200, b1= 48, nb=  0, info= 16, time=    5.660
 *** Test in line  1848 failed : dsbrdt returned info=   16 (expected     1)
 b=64                                                                          
 dsbtrd: uplo=L, jobu=U, n=  200, b1= 64, info=  0, time=    2.490
 dsbrdt: jobu=U, n=  200, b1= 64, nb=  0, info= 22, time=    6.000
 *** Test in line  1856 failed : dsbrdt returned info=   22 (expected     1)
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=U, n=  400, b1=  4, info=  0, time=    9.490
 dsbrdt: jobu=U, n=  400, b1=  4, nb=  0, info=  3, time=   39.631
 *** Test in line  1866 failed : dsbrdt returned info=    3 (expected     1)
 b=6                                                                           
 dsbtrd: uplo=L, jobu=U, n=  400, b1=  6, info=  0, time=   10.620
 dsbrdt: jobu=U, n=  400, b1=  6, nb=  0, info=  4, time=   38.910
 *** Test in line  1874 failed : dsbrdt returned info=    4 (expected     1)
 b=8                                                                           
 dsbtrd: uplo=L, jobu=U, n=  400, b1=  8, info=  0, time=   11.380
 dsbrdt: jobu=U, n=  400, b1=  8, nb=  0, info=  4, time=   37.540
 *** Test in line  1882 failed : dsbrdt returned info=    4 (expected     1)
 b=10                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 10, info=  0, time=   11.980
 dsbrdt: jobu=U, n=  400, b1= 10, nb=  0, info=  4, time=   36.870
 *** Test in line  1890 failed : dsbrdt returned info=    4 (expected     1)
 b=12                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 12, info=  0, time=   12.480
 dsbrdt: jobu=U, n=  400, b1= 12, nb=  0, info=  4, time=   37.170
 *** Test in line  1898 failed : dsbrdt returned info=    4 (expected     1)
 b=16                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 16, info=  0, time=   13.120
 dsbrdt: jobu=U, n=  400, b1= 16, nb=  0, info=  6, time=   37.710
 *** Test in line  1906 failed : dsbrdt returned info=    6 (expected     1)
 b=20                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 20, info=  0, time=   13.529
 dsbrdt: jobu=U, n=  400, b1= 20, nb=  0, info=  8, time=   38.771
 *** Test in line  1914 failed : dsbrdt returned info=    8 (expected     1)
 b=24                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 24, info=  0, time=   13.900
 dsbrdt: jobu=U, n=  400, b1= 24, nb=  0, info=  8, time=   38.681
 *** Test in line  1922 failed : dsbrdt returned info=    8 (expected     1)
 b=32                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 32, info=  0, time=   14.430
 dsbrdt: jobu=U, n=  400, b1= 32, nb=  0, info= 12, time=   39.950
 *** Test in line  1930 failed : dsbrdt returned info=   12 (expected     1)
 b=40                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 40, info=  0, time=   15.021
 dsbrdt: jobu=U, n=  400, b1= 40, nb=  0, info= 14, time=   40.830
 *** Test in line  1938 failed : dsbrdt returned info=   14 (expected     1)
 b=48                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 48, info=  0, time=   15.529
 dsbrdt: jobu=U, n=  400, b1= 48, nb=  0, info= 16, time=   41.530
 *** Test in line  1946 failed : dsbrdt returned info=   16 (expected     1)
 b=64                                                                          
 dsbtrd: uplo=L, jobu=U, n=  400, b1= 64, info=  0, time=   16.470
 dsbrdt: jobu=U, n=  400, b1= 64, nb=  0, info= 22, time=   43.271
 *** Test in line  1954 failed : dsbrdt returned info=   22 (expected     1)
                                                                               
 b=4                                                                           
 dsbtrd: uplo=L, jobu=U, n=  600, b1=  4, info=  0, time=   31.620
 dsbrdt: jobu=U, n=  600, b1=  4, nb=  0, info=  3, time=  134.631
 *** Test in line  1964 failed : dsbrdt returned info=    3 (expected     1)
 b=6                                                                           
 dsbtrd: uplo=L, jobu=U, n=  600, b1=  6, info=  0, time=   35.880
 dsbrdt: jobu=U, n=  600, b1=  6, nb=  0, info=  4, time=  132.239
 *** Test in line  1972 failed : dsbrdt returned info=    4 (expected     1)
 b=8                                                                           
 dsbtrd: uplo=L, jobu=U, n=  600, b1=  8, info=  0, time=   38.141
 dsbrdt: jobu=U, n=  600, b1=  8, nb=  0, info=  4, time=  127.700
 *** Test in line  1980 failed : dsbrdt returned info=    4 (expected     1)
 b=10                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 10, info=  0, time=   40.050
 dsbrdt: jobu=U, n=  600, b1= 10, nb=  0, info=  4, time=  126.499
 *** Test in line  1988 failed : dsbrdt returned info=    4 (expected     1)
 b=12                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 12, info=  0, time=   41.290
 dsbrdt: jobu=U, n=  600, b1= 12, nb=  0, info=  4, time=  126.221
 *** Test in line  1996 failed : dsbrdt returned info=    4 (expected     1)
 b=16                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 16, info=  0, time=   44.010
 dsbrdt: jobu=U, n=  600, b1= 16, nb=  0, info=  6, time=  131.989
 *** Test in line  2004 failed : dsbrdt returned info=    6 (expected     1)
 b=20                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 20, info=  0, time=   44.570
 dsbrdt: jobu=U, n=  600, b1= 20, nb=  0, info=  8, time=  132.899
 *** Test in line  2012 failed : dsbrdt returned info=    8 (expected     1)
 b=24                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 24, info=  0, time=   45.700
 dsbrdt: jobu=U, n=  600, b1= 24, nb=  0, info=  8, time=  129.671
 *** Test in line  2020 failed : dsbrdt returned info=    8 (expected     1)
 b=32                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 32, info=  0, time=   46.770
 dsbrdt: jobu=U, n=  600, b1= 32, nb=  0, info= 12, time=  133.810
 *** Test in line  2028 failed : dsbrdt returned info=   12 (expected     1)
 b=40                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 40, info=  0, time=   47.640
 dsbrdt: jobu=U, n=  600, b1= 40, nb=  0, info= 14, time=  135.030
 *** Test in line  2036 failed : dsbrdt returned info=   14 (expected     1)
 b=48                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 48, info=  0, time=   49.592
 dsbrdt: jobu=U, n=  600, b1= 48, nb=  0, info= 16, time=  135.590
 *** Test in line  2044 failed : dsbrdt returned info=   16 (expected     1)
 b=64                                                                          
 dsbtrd: uplo=L, jobu=U, n=  600, b1= 64, info=  0, time=   51.391
 dsbrdt: jobu=U, n=  600, b1= 64, nb=  0, info= 22, time=  140.850
 *** Test in line  2052 failed : dsbrdt returned info=   22 (expected     1)
 
 ===============================================================================
 Tests for                                             Total Skipped  Failed
 -------------------------------------------------------------------------------
 dsytrd : full -> tridiagonal, one-step (LAPACK)   :       0       0       0
 dorgtr : accumulation of transformations (LAPACK) :       0       0       0
 dsbtrd : banded -> tridiagonal, one-step (LAPACK) :      72       0       0
 dsyrdb : full -> banded, one-step (SBR)           :       0       0       0
 dsygtr : accumulation of transformations (SBR)    :       0       0       0
 dsbrdb : banded -> banded, one-step (SBR)         :       0       0       0
 dsbrdt : banded -> tridiagonal, one-step (SBR)    :      72       0      36
 dsy2bc : copy full -> banded (SBR)                :       0       0       0
 dsy2bi : in-place copy full -> banded (SBR)       :       0       0       0
 dsb2bc : copy banded -> banded (SBR)              :       0       0       0
 dsb2bi : in-place copy banded -> banded (SBR)     :       0       0       0
 dsyrdd : reduction driver for full matrices (SBR) :      54       0       0
 dsbrdd : reduction driver for banded matrcs (SBR) :     120       0       0
 -------------------------------------------------------------------------------
 Total  :                                          :     318       0      36
 -------------------------------------------------------------------------------
 Total time : 16797.73 seconds
SHAR_EOF
fi # end of overwriting check
cd ..
if test ! -d 'Src'
then
	mkdir 'Src'
fi
cd 'Src'
if test -f 'src.f'
then
	echo shar: will not over-write existing file "'src.f'"
else
cat << "SHAR_EOF" > 'src.f'
* **********************************************************************
*
        INTEGER FUNCTION NBDFLT( ALGO, PREC, REQEST, N, B1, B2, NEEDU )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Determine an appropriate default blocking factor or crossover point
*   or intermediate bandwidth for the reduction routine specified in
*   algo.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*5           ALGO
        CHARACTER*1           PREC, REQEST
        INTEGER               N, B1, B2
        LOGICAL               NEEDU
*
*   algo    (in) character*5
*           For which SBR routine do we need a control parameter ?
*           algo = 'SYRDB' : Reduction full -> banded.
*                = 'SBRDB' : Reduction banded -> banded.
*                = 'SBRDT' : Reduction banded -> tridiagonal.
*                = 'SYRDD' : Driver for reducing full matrices.
*                = 'SBRDD' : Driver for reducing banded matrices.
*
*   prec    (in) character*1
*           Is it the single or double precision routine ?
*           prec = 'D' : Double precision.
*                = 'S' : Single precision.
*
*   reqest  (in) character*1
*           Which control parameter is required ?
*           reqest = 'B' : Blocking factor or intermediate bandwidth.
*                  = 'C' : Crossover point to LAPACK code.
*
*   n       (in) integer
*           The size of the matrix to reduce.
*           n >= 0.
*
*   b1      (in) integer
*           The bandwidth of the matrix before the reduction.
*           0 <= b1 < n.
*
*   b2      (in) integer
*           The bandwidth of the matrix after the reduction.
*           1 <= b2 <= b1 or b1 = b2 = 0.
*
*   needu   (in) logical
*           Do we update the transformation matrix ?
*           needu = .true.  : Yes.
*                 = .false. : No.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               SINGLE
        INTEGER               DELTAB
*
*   single  single or double precision routine ?
*   deltab  number of diagonals to reduce
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
* ----------------------------------------------------------------------
*
        SINGLE = LSAME( PREC, 'SinglePrecision' )
        DELTAB = B1 - B2
*
        IF ( ( ALGO .EQ. 'SYRDB' ) .AND.
     >       ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for reduction from full to banded ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDB' ) .AND.
     >           ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for bandwidth reduction ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ELSE
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ELSE
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ENDIF
          IF ( NBDFLT .LT. 1 )     NBDFLT = 1
*
        ELSEIF ( ( ALGO .EQ. 'SBRDT' ) .AND.
     >           ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for reduction to tridiagonal form ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = ( ( B1 + 5 ) / 6 ) * 2
            ELSE
              NBDFLT = ( ( B1 + 5 ) / 6 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ELSE
            NBDFLT = 1
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SYRDD' ) .AND.
     >           ( LSAME( REQEST, 'Bandwidth' ) ) ) THEN
*
*            --- intermediate bandwidth in the reduction driver ---
*
          IF ( NEEDU ) THEN
            NBDFLT = 1
          ELSE
            IF ( ( N .GE. 300 ) .OR. ( B2 .GT. 1 ) ) THEN
              IF ( SINGLE ) THEN
                NBDFLT = 32
              ELSE
                NBDFLT = 32
              ENDIF
            ELSE
              NBDFLT = 1
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDD' ) .AND.
     >           ( LSAME( REQEST, 'Bandwidth' ) ) ) THEN
*
*            --- intermediate bandwidth in the reduction driver ---
*
          IF ( NEEDU ) THEN
            NBDFLT = 1
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDD' ) .AND.
     >           ( LSAME( REQEST, 'CrossoverPoint' ) ) ) THEN
*
*            --- crossover point from SBRDT to SBTRD ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = 8
            ELSE
              NBDFLT = 8
            ENDIF
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 16
            ELSE
              NBDFLT = 16
            ENDIF
          ENDIF
*
        ELSE
          NBDFLT = 1
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYRDB( UPLO, JOB, N, B, A, LDA, DRPTOL,
     >                     U, LDU, NB, TAU,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-times-n matrix A with either its lower or upper
*   triangle explicitly stored, dsyrdb reduces A to a symmetric banded
*   matrix B with b sub(super)diagonals by using a sequence of
*   orthogonal similarity transformations. If desired, the same
*   transformations are also applied from the right to the matrix U.
*   That is, if initially U was the identity, then the resulting banded
*   matrix B and the updated U fulfill the equation
*
*       T
*      U  * A * U   =   B  .
*
*   A must be given in full storage (with either its lower or upper
*   triangle explicitly stored) and will be overwritten with B and
*   the "mantissae" of the Householder vectors used for the reduction.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO, JOB
        INTEGER               N, B, LDA, LDU, NB, LWORK, INFO
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), U( LDU, * ), TAU( * ),
     >                        WORK( * )
*
*   uplo    (in) character*1
*           Reduce the upper or lower triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   job     (in) character*1
*           Specifies if U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of the reduced matrix B.
*           1 <= b < n, if n > 1.
*           b = 0     , if n <= 1.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A with
*           either its lower (uplo = 'L') or upper (uplo = 'U') triangle
*           stored.
*           On exit, the main diagonal and the first b sub-(super-)
*           diagonals contain the banded matrix B, and the Householder
*           vectors that were used in the reduction are stored in the
*           remaining parts of the lower (upper) triangle.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   drptol  (in) double precision
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   u       (in/out) double precision array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce A to banded form.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor, as suggested by the user, for the
*           reduction and the update of U.
*           0 <= nb <= b.
*           nb = 0 : User does not know how many Householder transforms
*                    should be blocked for reasonable performance.
*                    Let the routine figure it out (depending on the
*                    workspace available).
*           nb = 1 : Do not block.
*           nb > 1 : Try to block nb Housholder transforms
*                    (if the workspace is not sufficient then a smaller
*                    blocking factor will be used).
*
*   tau     (out) double precision array, dimension ( n )
*           The scaling factors for the Householder transforms used in
*           the reduction.
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= 3 * n - 2 * b.
*
*           Workspace that small prevents blocking and may degrade
*           performance. For using nb-blocked transformations, provide
*           lwork >= nb * ( 3 * n - 2 * b ).
*           As a rule, lwork >= 50 * n should be fine.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : uplo is none of 'U', 'L' (upper/lower case).
*                = - 2 : job is none of 'U', 'N' (upper/lower case).
*                = - 3 : n is out of range (negative).
*                = - 4 : b is out of range ( < 0, or = 0 while n > 1,
*                        or >= n ).
*                = - 6 : lda is out of range ( < n or < 1 ).
*                = - 7 : drptol is out of range (negative).
*                = - 9 : ldu is out of range ( < n or < 1 ).
*                = -10 : nb is out of range (negative).
*                = -13 : lwork is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the reduction and in the
*                        update of U.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO
        PARAMETER             ( ZERO = 0.0D0 )
*
        LOGICAL               UPPER, NEEDU
        INTEGER               NB0, NB1, NB2, J, J0,
     >                        LEN, IW, IY, IWORK
*
*   upper   reduce the upper triangle of A ?
*   needu   update U ?
*   nb0     the final blocking factor for "full" block columns
*   nb1     width of the current block column to reduce (= nb0, except
*           for the last block column)
*   nb2     number of nonzero Householder vectors in the current
*           WY transform
*   j       first column of the current block column
*   j0      last column of the current block column
*   len     length of the current block column
*   iw      points to the portion of the workspace where the block
*           transform W is stored
*   iy      points to the location of Y in the workspace
*   iwork   points to the portion of work that is used as workspace for
*           other routines
*
* The workspace is used as follows:
*
*   - The first nb1 * len <= nb0 * ( n - b ) elements hold the block W
*     of the current block WY transform.
*     Here, nb1 <= nb0 denotes the width of the current block column and
*     len <= n - b denotes its height; nb0 is the final blocking factor.
*   - The next nb1 * len elements hold the block Y.
*   - Another ( len + nb1 ) * nb1 <= n * nb0 elements are used as
*     workspace in the routines dgeqrl, dgewyg, dgewy, and dsywy.
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor (SBR)
*
        EXTERNAL              DGEQRL, DGEWY, DGEWYG, DSYWY
*
*   dgeqrl  QR or QL factorization (SBR)
*   dgewy   apply WY transform from one side (SBR)
*   dgewyg  generate WY factors (SBRtoolbox)
*   dsywy   apply two-sided WY transform to a symmetric matrix (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        UPPER = LSAME( UPLO, 'U' )
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
          INFO = - 1
        ELSEIF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = - 2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 3
        ELSEIF ( ( ( N .LE. 1 ) .AND. ( B .NE. 0 ) ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B .LT. 1 ) .OR. ( B .GE. N ) ) ) ) THEN
          INFO = - 4
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = - 6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = - 7
        ELSEIF ( LDU .LT. MAX( N, 1 ) ) THEN
          INFO = - 9
        ELSEIF ( NB .LT. 0 ) THEN
          INFO = -10
        ELSEIF ( LWORK .LT. ( 3*N-2*B ) ) THEN
          INFO = -13
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( ( N .LE. 1 ) .OR. ( B .EQ. ( N-1 ) ) )      GOTO 999
*
*          --- compute the maximum blocking factor for the
*                given workspace                             ---
*
        NB0 = LWORK / ( 3 * N - 2 * B )
*
*          --- adjust to the user-supplied or default value ---
*
        IF ( NB .GT. 0 ) THEN
          NB0 = MIN( NB, B, NB0 )
        ELSE
          NB0 = MIN( NBDFLT( 'SYRDB', 'DoublePrec', 'BlockingFactor',
     >                       N, N-1, B, NEEDU ),
     >               B, NB0 )
        ENDIF
*
* ......................................................................
*
        IW = 1
*
        IF ( UPPER ) THEN
*
*            --- reduce the upper triangle ---
*
          DO 100 J0 = N, B+2, - NB0
*
            LEN = J0 - B
            NB1 = MIN( NB0, LEN-1 )
            J = J0 - NB1 + 1
            IY = IW + NB1 * LEN
            IWORK = IY + NB1 * LEN
*
            CALL DGEQRL( 'L', LEN, NB1, A( 1, J ), LDA, DRPTOL,
     >                   TAU( J ), WORK( IWORK ) )
            CALL DGEWYG( 'Upper', LEN, NB1, A( 1, J ), LDA, TAU( J ),
     >                   WORK( IW ), LEN, WORK( IY ), LEN, NB2,
     >                   WORK( IWORK ) )
            CALL DGEWY( 'Left', LEN, B - NB1, NB2, A( 1, LEN+1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
            CALL DSYWY( 'Upper', LEN, NB2, A( 1, 1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
*
            IF ( NEEDU ) THEN
              CALL DGEWY( 'Right', N, LEN, NB2, U( 1, 1 ), LDU,
     >                    WORK( IW ), LEN, WORK( IY ), LEN,
     >                    WORK( IWORK ) )
            ENDIF
*
  100     CONTINUE
*
          TAU( B+1 ) = ZERO
*
        ELSE
*
*            --- reduce the lower triangle ---
*
          DO 200 J = 1, N-B-1, NB0
*
            LEN = N - ( J + B ) + 1
            NB1 = MIN( NB0, LEN - 1 )
            IY = IW + NB1 * LEN
            IWORK = IY + NB1 * LEN
*
            CALL DGEQRL( 'R', LEN, NB1, A( J+B, J ), LDA, DRPTOL,
     >                   TAU( J ), WORK( IWORK ) )
            CALL DGEWYG( 'Lower', LEN, NB1, A( J+B, J ), LDA, TAU( J ),
     >                   WORK( IW ), LEN, WORK( IY ), LEN, NB2,
     >                   WORK( IWORK ) )
            CALL DGEWY( 'Left', LEN, B - NB1, NB2, A( J+B, J+NB1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
            CALL DSYWY( 'Lower', LEN, NB2, A( J+B, J+B ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
*
            IF ( NEEDU ) THEN
              CALL DGEWY( 'Right', N, LEN, NB2, U( 1, J+B ), LDU,
     >                    WORK( IW ), LEN, WORK( IY ), LEN,
     >                    WORK( IWORK ) )
            ENDIF
     >
  200     CONTINUE
*
          TAU( N-B ) = ZERO
*
        ENDIF
*
*          --- return the blocking factor ---
*
        INFO = NB0
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYGTR( UPLO, N, B, A, LDA, TAU, WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dsygtr generates a real orthogonal matrix U of size n, defined as
*   the product of n - b Householder transformations, as returned by
*   dsyrdb.
*
*   If uplo = 'U' then
*
*      U  =  H( n ) * ... * H( b + 2 ),
*
*   where the "mantissa" of the length-( k - b ) Householder
*   transformation H( k ) is stored in a( 1:k-b-1, k ) and its scaling
*   factor is stored in tau( k ),
*
*   if uplo = 'L' then
*
*      U  =  H( 1 ) * ... * H( n - b - 1 ),
*
*   where the "mantiassa" of the length-(n - b - k - 1) Householder
*   transformation H( k ) is stored in a( b+k+1:n, k ) and its scaling
*   factor is stored in tau( k ).
*
*   On exit, a is overwritten with the orthogonal matrix U.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDA, LWORK, INFO
        DOUBLE PRECISION      A( LDA, * ), TAU( * ), WORK( * )
*
*   uplo    (in) character*1
*           Are the Householder vectors stored in the upper or lower
*           triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The dimension of the reduced matrix A (and of the requested
*           orthogonal matrix).
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of the reduced matrix.
*           1 <= b < n, if n > 1.
*           b = 0     , if n <= 1.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the columns of a hold the "mantissae" of the
*           Householder transformations, as returned from dsyrdb.
*           On exit, a is overwritten with the orthogonal matrix U.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   tau     (in) double precision array, dimension ( n ).
*           The scaling factors for the Householder transformations, as
*           returned by dsyrdb.
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= n - b.
*
*           Workspace that small prevents blocking and may degrade
*           performance. For using nb-blocked transformations, provide
*           lwork >= nb * ( n - b ).
*           As a rule, lwork >= 20 * n should be fine.
*
*   info    (out) integer
*           On exit, info indocates the consistence of the arguments.
*           info =  1 : All arguments were OK.
*           info = -1 : uplo is none of 'U', 'L' (upper/lower case).
*                = -2 : n is out of range (negative).
*                = -3 : b is out of range ( < 0, or = 0 while n > 1,
*                       or >= n ).
*                = -5 : lda is out of range ( < n or < 1 ).
*                = -8 : lwork is out of range ( < n - b ).
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        LOGICAL               UPPER
        INTEGER               B1, J
*
*   upper   are the Householder vectors stored in the upper triangle ?
*   b1      = b + 1
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              DCOPY, DLASET, DORGQL, DORGQR
*
*   dcopy   vector copy (BLAS)
*   dlaset  initialize matrix (LAPACK)
*   dorgql  build orthogonal matrix after QL factorization (LAPACK)
*   dorgqr  build orthogonal matrix after QR factorization (LAPACK)
*
        INTRINSIC             MAX
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the input ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( ( N .LE. 1 ) .AND. ( B .NE. 0 ) ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B .LT. 1 ) .OR. ( B .GE. N ) ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LWORK .LT. ( N-B ) ) THEN
          INFO = - 8
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( B1 .GE. N ) THEN
          CALL DLASET( 'All', N, N, ZERO, ONE, A, LDA )
          GOTO 999
        ENDIF
*
* ......................................................................
*
        IF ( UPPER ) THEN
*
*            --- move the Householder vectors by b columns to
*                the left                                     ---
*
          DO 100 J = B+2, N
            CALL DCOPY( J-B1, A( 1, J ), 1, A( 1, J-B ), 1 )
  100     CONTINUE
*
*            --- set the last b columns and rows to identity ---
*
          CALL DLASET( 'All', B, N-B, ZERO, ZERO, A( N-B+1, 1 ), LDA )
          CALL DLASET( 'All', N-B, B, ZERO, ZERO, A( 1, N-B+1 ), LDA )
          CALL DLASET( 'All', B, B, ZERO, ONE, A( N-B+1, N-B+1 ), LDA )
*
*            --- generate the leading ( n-b )-by-( n-b )
*                orthogonal matrix                       ---
*
          CALL DORGQL( N-B, N-B, N-B, A, LDA, TAU( B+1 ),
     >                 WORK, LWORK, INFO )
*
        ELSE
*
*            --- move the Householder vectors by b columns to
*                the right                                    ---
*
          DO 200 J = N-1, B1, -1
            CALL DCOPY( N-J, A( J+1, J-B ), 1, A( J+1, J ), 1 )
  200     CONTINUE
*
*            --- set the first b columns and rows to identity ---
*
          CALL DLASET( 'All', N, B, ZERO, ONE, A, LDA )
          CALL DLASET( 'All', B, N-B, ZERO, ZERO, A( 1, B1 ), LDA )
*
*            --- generate the trailing ( n-b )-by-( n-b )
*                orthogonal matrix                        ---
*
          CALL DORGQR( N-B, N-B, N-B, A( B1, B1 ), LDA, TAU,
     >                 WORK, LWORK, INFO )
*
        ENDIF
*
        IF ( INFO .EQ. 0 )     INFO = 1
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSBRDB( JOB, N, B1, B2, A, LDA, DRPTOL,
     >                     U, LDU, NB,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-times-n matrix A with b1 sub(or super-)
*   diagonals, dsbrdb reduces A to a narrower band with b2 sub(super)
*   diagonals by using a sequence of orthogonal similarity
*   transformations. If desired, the same transformations are also
*   applied from the right to the matrix U. That is, if initially U was
*   the identity, then the resulting banded matrix B and the updated U
*   fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK packed storage scheme for lower
*   triangular banded matrices and will be overwritten with B.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOB
        INTEGER               N, B1, B2, LDA, LDU, NB, LWORK, INFO
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), U( LDU, * ), WORK( * )
*
*   job     (in) character*1
*           Specifies whether U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix.
*           n >= 0.
*
*   b1      (in) integer
*           The number of sub(super-)diagonals of A.
*           b1 >= 0 and b1 < n (if n > 0).
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 <= b1 or b2 = b1 = 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A. The
*           leading ( b1+1 )-by-n part of a contains the lower triangle
*           of A with A( i, j ) stored in a( 1+i-j, j ), and the
*           strictly upper triangle is not referenced.
*           On exit, for i = 1, ..., b2+1, the first n - i + 1 elements
*           in the i-th row of a contain the reduced matrix B,
*           for i = b2 + 2, ..., b1+1, the first n - i + 1 elements in
*           the i-th row of a are zeroed, and
*           for i = b1 + 2, ..., min( b1+(b1-b2)+nb, n, lda ), the first
*           n - i + 1 elements in the i-th row of a are destroyed.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( b1 + 1, n ).
*
*           To avoid unnecessary copying and therefore improve the
*           performance in the blocked case, we recommend
*           lda >= nb + b1 + ( b1 - b2 ).
*
*   drptol  (in) double precision
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   u       (in/out) double precision array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied by all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor nb, as suggested by the user, for the
*           reduction of A and the update of U.
*           0 <= nb <= b2.
*           nb = 0 : User does not know how many Householder transforms
*                    should be blocked for reasonable performance. Let
*                    the routine figure it out (depending on the
*                    workspace available).
*              = 1 : Do not block
*              > 1 : Try to block nb Householder transforms (if the
*                    workspace is not sufficient then a smaller blocking
*                    factor will be used).
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= 3 * b1 + b2,    if U is not required, and
*                 >= n + 2 * b1 + 1, if U is required.
*
*           Workspace that small enforces non-blocked transforms.
*           For using nb-blocked transforms, we need
*           lwork >= ( 3 * b1 + b2 ) * nb,    if U is not required, and
*                 >= ( n + 2 * b1 + 1 ) * nb, if U is required.
*
*           If lda < b1 + ( b1 - b2 ) + nb, then ADDITIONAL workspace
*           is needed to buffer some of the intermediate fill-in during
*           the reduction. More precisely, we need
*           another ndiag * ( ndiag+1 ) / 2 elements to buffer one
*              ndiag-by-ndiag triangle of each diagonal block, where
*              ndiag = min( b1+(b1-b2)+nb, n ) - lda, and
*           another ( n / b1 ) * nsub * ( nsub+1 ) / 2  elements to
*              buffer an nsub-by-nsub triangle from each of the n / b1
*              subdiagonal blocks, where
*              nsub = min( b1+(b1-b2), n ) - lda
*           Note that roughly n * ( b1 + (b1-b2) - lda ) / 2 elements
*           are sufficient, and that no buffer space is required if
*           lda >= b1 + ( b1 - b2 ) + nb.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : job is none of 'U', 'N' (upper/lower case).
*                = - 2 : n is out of range (negative).
*                = - 3 : b1 is out of range (negative or >= n ).
*                = - 4 : b2 is out of range ( < 0, or = 0 while b1 >= 1,
*                        or > b1 ).
*                = - 6 : lda is out of range ( < b1 + ( b1 - b2 ) + 1
*                        and < n ).
*                = - 7 : drptol is out of range ( < 0.0 ).
*                = - 9 : ldu is out of range ( < n ).
*                = -10 : nb is out of range (negative).
*                = -12 : lwork is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the reduction and in the
*                        update of U.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
*            --- constants ---
*
        DOUBLE PRECISION      ZERO
        PARAMETER             ( ZERO = 0.0D0 )
*
*            --- for the reduction part ---
*
        LOGICAL               NEEDU
        INTEGER               DELTAB, NB0, LDH, PREW, K,
     >                        L, NBLK, NB1, LDWY
*
*   needu   is U required ?
*   deltab  = b1 - b2, the number of diagonals to remove
*   nb0     blocking factor that is ultimately used in the reduction
*           and in the update
*   ldh     = min( deltab + nb0, n - b2 ), the size of the blocks
*           affected by each block transform
*   prew    = b2 - nb0, the width of the block to be premultiplied
*   k       numbers the "elimination steps"
*   l       numbers the bulge chasing operations associated with each
*           elimination step
*   nblk    number of the current block column
*   nb1     number of nonzero Householder vectors in the current block
*           transform
*   ldwy    leading dimension of the arrays containing W and Y
*
*          --- workspace management ---
*
        INTEGER               NSUB, SZSUB, LSUB, NSUB1, NDIAG, LDIAG,
     >                        NDIAG1, ISUB, IDIAG, IC, ID, ID1, IX,
     >                        IW, IY, IWORK, J
*
*   nsub    the dimension of the triangles from the subdiagonal blocks
*           that must be buffered in the workspace
*           (nsub <= b1 + ( b1 - b2 ) - lda)
*   szsub   = nsub * ( nsub+1 ) / 2, the size of each such triangle
*   lsub    = ( n / b ) * szsub, the total size of all these triangles
*   nsub1   the dimension of the current triangle, plus 1
*   ndiag   the dimension of the triangle from the main diagonal block
*           that must be buffered in the workspace
*           (ndiag <= b1 + ( b1 - b2 ) + nb0 - lda )
*   ldiag   = ndiag * ( ndiag+1 ) / 2, the size of this triangle
*   ndiag1  the dimension of the current triangle, plus 1
*   isub    points to the portion of the workspace that will hold the
*           triangles from all the subdiagonal blocks
*   idiag   points to the portion of the workspace that will hold the
*           triangle from the current diagonal block
*   ic      column position of the next element to be buffered
*   id      diagonal position of the next element to be buffered
*   id1     = id + 1
*   ix      position in the workspace for this element
*   iw      points to the portion of work that will hold the block
*           W of the WY tranform
*   iy      points to the portion of work that will hold Y
*   iwork   points to the portion of work that is used as workspace
*           in the routines dqrupd, dsywy, and dgewy
*
* The workspace is used as follows:
*
*   - The first ( n / b1 ) * nsub * ( nsub+1 ) / 2 elements are used to
*     buffer nsub-by-nsub triangles of fill-in from the subdiagonal
*     blocks (see the discussion on lwork).
*     Here, nsub = min( b1+(b1-b2), n ) - lda <= b1 - b2 - 1.
*     These elements are needed only if nsub > 0.
*   - The next ndiag * ( ndiag+1 ) / 2 elements are used to buffer one
*     ndiag-by-ndiag triangle from the current diagonal block.
*     Here, ndiag = min( b1+(b1-b2)+nb0, n ) - lda <= b1 - 1.
*     These elements are needed only if ndiag > 0.
*   - The following ldh * nb0 elements hold the block W of the block WY
*     transform.
*     Here, ldh = min( b1-b2+nb0, n-b2 ) <= b1 - b2 + nb0 <= b1.
*   - The following ldh * nb0 elements hold the block Y.
*   - The remaining workspace is alternatively used by the routines
*     dqrupd (which needs ( n+1 )*nb0 elements if U is required and
*     ( ldh+1 )*nb0 elements otherwise), dsywy (( b1+1 )*nb0 elements),
*     and dgewy (b1*nb0 elements).
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor
*
        EXTERNAL              DGEWY, DQRUPD, DSYWY
*
*   dgewy   apply WY block transform (SBR)
*   dqrupd  QR decomposition of a block of A, update of U, and premulti-
*           plication of another block of A (SBR)
*   dsywy   apply two-sided block transform to a symmetric matrix (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B1 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B1 .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( B1 .GE. 1 ) .AND. ( B2 .EQ. 0 ) ) .OR.
     >           ( B2 .GT. B1 ) ) THEN
          INFO = - 4
        ELSEIF ( LDA .LT. MIN( B1+1, N ) ) THEN
          INFO = - 6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = - 7
        ELSEIF ( NEEDU .AND. ( LDU .LT. MAX( N, 1 ) ) ) THEN
          INFO = - 9
        ELSEIF ( NB .LT. 0 ) THEN
          INFO = - 10
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( ( N .EQ. 0 ) .OR. ( B2 .EQ. B1 ) )     GOTO 999
*
*          --- determine blocking factor ---
*
        IF ( NB .GT. 0 ) THEN
          NB0 = NB
        ELSE
          NB0 = NBDFLT( 'SBRDB', 'PrecString', 'BlockingFactor',
     >                  N, B1, B2, NEEDU )
        ENDIF
        NB0 = MIN( NB0, B2 )
*
*          --- how many diagonals are eliminated, and how many must
*              be buffered ?                                        ---
*
        DELTAB = B1 - B2
        NSUB = MAX( MIN( B1+DELTAB, N ) - LDA, 0 )
        SZSUB = ( NSUB * ( NSUB + 1 ) ) / 2
        LSUB = ( N / B1 ) * SZSUB
*
*          --- reduce nb0 until workspace is sufficient ---
*
   10   CONTINUE
*
*            --- how much of the diagonal blocks must be buffered ? ---
*
          NDIAG = MAX( MIN( B1+DELTAB+NB0, N ) - LDA, 0 )
          LDIAG = ( NDIAG * ( NDIAG + 1 ) ) / 2
          IF ( NEEDU ) THEN
            IWORK = ( N + 2 * B1 + 1 ) * NB0
          ELSE
            IWORK = ( 3 * B1 + B2 ) * NB0
          ENDIF
          IF ( LWORK .LT. ( LSUB+LDIAG+IWORK ) ) THEN
            IF ( NB0 .GT. 1 ) THEN
              NB0 = NB0 - 1
              GOTO 10
            ELSE
              INFO = -12
              GOTO 999
            ENDIF
          ENDIF
*
*          --- OK, now that we have nb0, set other constants ---
*
        LDH = MIN( DELTAB+NB0, N-B2 )
        PREW = MAX( B2-NB0, 0 )
*
*          --- set up pointers to the submatrices stored in work
*              (the data layout is pointed out above)            ---
*
        ISUB = 1
        IDIAG = ISUB + LSUB
        IW = IDIAG + LDIAG
        IY = IW + LDH * NB0
        IWORK = IY + LDH * NB0
*
*          --- make sure that the "bulge buffer" is empty ---
*
        DO 30 K = B1+2, MIN( B1+NB0+DELTAB, LDA, N )
          DO 20 J = 1, N-K+1
            A( K, J ) = ZERO
   20     CONTINUE
   30   CONTINUE
*
        DO 40 K = ISUB, IDIAG+LDIAG-1
          WORK( K ) = ZERO
   40   CONTINUE
*
* ......................................................................
*
        DO 400 K = 1, N - B2 - 1, NB0
*
*            --- QR decomposition to eliminate the leading nb0
*                columns of the band                           ---
*
          CALL DQRUPD( MIN( LDH, N-K-B2+1 ), NB0, DELTAB,
     >                 A( B2+1, K ), LDA - 1, DRPTOL,
     >                 NEEDU, N, U( 1, K+B2 ), LDU,
     >                 PREW, A( PREW+1, K+NB0 ),
     >                 NB1, WORK( IY ), WORK( IW ), LDWY,
     >                 WORK( IWORK ) )
*
*              --- bulge chasing ---
*
          DO 300 L = K + B2, N - 1, B1
*
            NBLK = 1 + ( L - K - B2 ) / B1
            IF ( NB1 .GT. 0 ) THEN
*
*                --- symmetric update of diagonal block ---
*
              CALL DSYWY( 'Lower', MIN( LDH, N-L+1 ), NB1,
     >                    A( 1, L ), LDA - 1,
     >                    WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                    WORK( IWORK ) )
            ENDIF
*
*              --- if lda < b1 + ( b1 - b2 ) + nb0, then before
*                  transforming the subdiagonal block, an
*                  ndiag-by-ndiag triangle of the diagonal block
*                  must be copied into the workspace ...         ---
*
            NDIAG = MIN( B1+LDH, N-L+1 ) - LDA
            NDIAG1 = NDIAG + 1
            IX = IDIAG
            DO 120 J = 1, NDIAG
              IC = L + J
              DO 110 ID = 1, NDIAG1-J
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  110         CONTINUE
  120       CONTINUE
*
*              --- ... the bottommost rows of the subdiagonal block
*                  must be set to zero                              ---
*
            NSUB = MIN( MAX( N-L+1-LDA, 0 ), B1+(B1-B2)-LDA )
            NSUB1 = NSUB + 1
            DO 140 ID = NSUB1, NDIAG
              ID1 = ID + 1
              DO 130 J = 1, ID
                A( ID1-J, L+J ) = ZERO
  130         CONTINUE
  140       CONTINUE
*
*              --- ... and an nsub-by-nsub triangle of the
*                  subdiagonal block must be restored from workspace ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 160 J = 1, NSUB
              IC = L + J
              DO 150 ID = 1, NSUB1-J
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  150         CONTINUE
  160       CONTINUE
*
            IF ( NB1 .GT. 0 ) THEN
*
*                  --- postmultiply ---
*
              IF ( N .GE. ( L+LDH ) ) THEN
                CALL DGEWY( 'Right', MIN( B1, N-L-LDH+1 ),
     >                      LDH, NB1, A( LDH+1, L ), LDA - 1,
     >                      WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                      WORK( IWORK ) )
              ENDIF
            ENDIF
*
            IF ( N .GT. ( L+B1 ) ) THEN
*
*                --- QR decomposition to eliminate the leading
*                    nb0 columns of the bulge                  ---
*
              CALL DQRUPD( MIN( LDH, N-L-B1+1 ), NB0, DELTAB,
     >                     A( B1+1, L ), LDA - 1, DRPTOL,
     >                     NEEDU, N, U( 1, L+B1 ), LDU,
     >                     B1 - NB0, A( B1-NB0+1, L+NB0 ),
     >                     NB1, WORK( IY ), WORK( IW ), LDWY,
     >                     WORK( IWORK ) )
            ENDIF
*
*              --- if lda < b1 + ( b1 - b2 ) + nb0, then an
*                  nsub-by-nsub triangle of the subdiagonal block
*                  must be copied into the workspace ...          ---
*
            NSUB = MIN( MAX( N-L-NB0+1-LDA, 0 ), B1+(B1-B2)-LDA )
            NSUB1 = NSUB + 1
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 220 J = 1, NSUB
              IC = L + J + NB0
              DO 210 ID = 1, NSUB1-J
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  210         CONTINUE
  220       CONTINUE
*
*              --- ... and the ndiag-by-ndiag triangle of the
*                  diagonal block must be restored from workspace ---
*
            IX = IDIAG
            DO 240 J = 1, NDIAG
              IC = L + J
              DO 230 ID = 1, NDIAG1-J
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  230         CONTINUE
  240       CONTINUE
*
  300     CONTINUE
*
  400   CONTINUE
*
        INFO = NB0
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSBRDT( JOB, N, B, A, LDA, DRPTOL,
     >                     D, E,
     >                     U, LDU, NB,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-by-n matrix A with b sub(or super-) diagonals,
*   dsbrdt reduces A to tridiagonal form using a sequence of orthogonal
*   similarity transformations. If desired, the same transformations are
*   also applied from the right to the matrix U. That is, if initially U
*   was the identity, then the resulting tridiagonal matrix T and the
*   updated U fulfill the equation
*
*       T
*      U  * A * U = T  .
*
*   A must be given in the LAPACK packed storage scheme for lower
*   triangular banded matrices.
*
* Author: Bruno Lang
*         Aachen University of technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOB
        INTEGER               N, B, LDA, LDU, NB, LWORK, INFO
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), D( * ), E( * ), U( LDU, * ),
     >                        WORK( * )
*
*   job     (in) character*1
*           Specifies whether U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A. The
*           leading ( b+1 )-by-n part of a contains the lower triangle
*           of A with A( i, j ) stored in a( 1+i-j, j ), and the
*           strictly upper triangle is not referenced.
*           On exit, for i = 1, ..., min( 2*b, n, lda ), the first
*           n - i + 1 elements in the i-th row of a are destroyed.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= b+1.
*           For optimum performance, we recommend lda >= 2*b.
*
*   drptol  (in) double precision
*           The threshold for dropping Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   d       (out) double precision array, dimension ( n )
*           On exit, d( 1 .. n ) contains the main diagonal of the
*           reduced tridiagonal matrix.
*
*   e       (out) double precision array, dimension ( n-1 )
*           On exit, e( 1 .. n-1 ) contains the sub(super-)diagonal of
*           the reduced tridiagonal matrix.
*
*   u       (in/out) double precision array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor nb, as suggested by the user, for the
*           update of U (nb is accessed only if U is required).
*           nb >= 0.
*               = 0 : User does not know how many Householder transforms
*                     should be blocked for reasonable performance. Let
*                     the routine figure it out (depending on the
*                     workspace available).
*               = 1 : Do not block the update of U.
*               > 1 : Try to block nb Householder transforms (if the
*                     workspace is not sufficient then a smaller
*                     blocking factor will be used).
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           If lda >= 2*b, then
*             lwork >= 2 * b, if U is not required.
*             lwork >= b + n, if U is required and is updated with
*                             non-blocked Householder transforms.
*             lwork >= 2 * nb * ( n + b + nb - 1 ), if U is updated
*                             with nb-blocked transforms.
*           If lda < 2*b, then ADDITIONAL ( n/b + 1 )*szsub + nsave
*                         elements of workspace are needed to buffer
*                         intermediate elements. Here, nsave = 2*b-lda,
*                         and szsub = (nsave*(nsave-1))/2.
*                         Note that this is roughly n*(2*b-lda)/2
*                         elements.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : job is none of 'U', 'N' (upper/lower case).
*                = - 2 : n is out of range (negative).
*                = - 3 : b is out of range (negative or
*                        >= n, while n > 0 ).
*                = - 5 : lda is too small ( < min( b+1, n ) ).
*                = - 6 : drptol is out of range (negative).
*                = -10 : ldu is too small ( < n or < 1 ).
*                = -11 : nb is out of range (negative).
*                = -13 : workspace is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the update of U (if job='U'),
*                        or info = 1 (if job='N').
*
* ----------------------------------------------------------------------
*
* Local variables:
*
*          --- constants ---
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
*          --- for the reduction part ---
*
        INTEGER               NSAVE, NSAVE1, IDIAG, ISUB, SZSUB, ID, IC,
     >                        IX, NBLK, HEIGHT, WIDTH, K, J, I, J0
        DOUBLE PRECISION      TAU
*
*   nsave   the number of diagonals that must be saved
*   nsave1  = nsave + 1
*   idiag   points to the portion of the workspace that holds the part
*           of the current diagonal block of the band
*   isub    points to the portion of the workspace that holds the part
*           of the subdiagonal blocks of the band
*   szsub   number of elements that must be saved from each subdiagonal
*           block
*   id      diagonal position of the element to save
*   ic      column position of the element to save
*   ix      position in the workspace for saving the element
*   nblk    number of the block to process next
*   height  height of the block to process next
*   width   width of the subdiagonal block
*   k       numbers the columns to be eliminated
*   j       counter for the "progress" of the bulge chasing
*   tau     scaling factor of the current Householder transform
*
*          --- for updating U ---
*
        LOGICAL               NEEDU, BLOCK, ONFLY
        INTEGER               NB0, IV, IY, IW, ITAU, IWORK, LDWY0,
     >                        K0, IFIRST, NB1, LDWY, NB2, V
        DOUBLE PRECISION      BETA
*
*   needu   is U needed ?
*   block   is U needed, and is there enough workspace for blocking the
*           updates ?
*   onfly   is U needed, and is blocking prohibited by small workspace ?
*   nb0     blocking factor that is ultimately used in the update
*   iv      points to the portion of work that will hold the Householder
*           vectors for nb consecutive "eliminate & chase" sweeps
*           (required size for this buffer : n * nb0)
*   iy      points to the portion of work that will hold the block
*           transform Y in the WY representation (required size for this
*           buffer : ( b + nb0 - 1 ) * nb0)
*   iw      points to the portion of work that will hold the block
*           transform W in the WY representation (required size for this
*           buffer : ( b + nb0 - 1 ) * nb0)
*   itau    points to the portion of work that will hold the scaling
*           factors (required size for this buffer: nb0)
*   iwork   points to the protion of work that may be used as working
*           space by the routines dlarfx, dsyrf, and dgewy.
*           (required size for this buffer : n * nb0, if U is needed,
*           b otherwise)
*   ldwy0   = b + nb0 - 1, the leading dimension of "full" block
*           Householder reflectors W and Y, resp.
*   k0      number of the first sweep that contributed to the the
*           current block transform
*   ifirst  first row affected by the current block transform
*   nb1     number of transforms in the current block update (usually
*           = nb0, except for the one at the bottom or the last sweeps)
*   ldwy    size of the current block transform (usually = ldwy0,
*           except for the last block transform of the sweep)
*   nb2     number of nonzero transforms in the current block update
*           (usually = nb1, except for special matrices)
*   v       points to the portion of work that holds the current
*           Householder vector
*   beta    coefficient in the quadratic equation for determining the
*           maximum possible blocking factor
*
* The workspace is used as follows:
*
*   If lda < 2 * b then some of the intermediate fill-in is held in the
*   workspace. More precisely, nsave = 2 * b - lda is the size of the
*   (triangular) blocks that extend beyond the array a. Then
*   nsave-by-nsave blocks of the band must be swapped between the array
*   a and the workspace. Note that actually only (nsave-1)-by-(nsave-1)
*   blocks of size szsub = ( ( nsave - 1 ) * nsave ) / 2 must be saved
*   as the remaining nsave elements are made zero by the algorithm.
*   - The first szsub + nsave elements of the workspace are used to
*     buffer a triangular portion of the current diagonal block, and
*   - the next ( n / b ) * szsub elements hold n / b triangular
*     (nsave-1)-by-(nsave-1) portions of the subdiagonal blocks.
*   If lda >= 2 * b then the whole fill-in fits into the array a, and
*   the above-mentioned buffers are not needed.
*
*   If U is not needed (or U is needed, but its update is non-blocked)
*   then the next b places of work hold the current Householder vector
*   and the following b (or n, resp.) places are used as workspace for
*   applying the transformation.
*
*   If U is updated via blocked Householder transforms (comprising nb0
*   Householder transforms)
*                                                  T
*      (affected part of)   U  =  U  *  ( I + W * Y  )
*   then in the current implementation
*   - the next n * nb0 places hold the Householder vectors for
*     nb0 successive "eliminate & chase" sweeps down the band,
*   - the next ( b + nb0 - 1 ) * nb0 places hold the block Y,
*   - the next ( b + nb0 - 1 ) * nb0 places hold W,
*   - the next n * nb0 places are alternatively used as workspace for
*     the routines dsyrf (b elements), dlarfx (b elements), and dgewyr
*     (n * nb0 elements), and
*   - the buffer for nb0 scaling factors is overlapped with the first
*     nb0 elements of the "multiuse" workspace.
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor
*
        EXTERNAL              DCOPY, DGBWYG, DGEWY, DLARFX, DLBRFG,
     >                        DSYRF
*
*   dcopy   vector copy (BLAS)
*   dgbwyg  generate WY block reflector (SBR)
*   dgewy   apply WY block reflector (SBR)
*   dlbrfg  determine Householder vector (SBR)
*   dsyrf   apply two-sided transform to a symmetric matrix (SBR)
*   dlarfx  apply Householder transform (LAPACK)
*
        INTRINSIC             DBLE, INT, MAX, MIN, MOD, SQRT
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -2
        ELSEIF ( ( B .LT. 0 ) .OR. ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) )
     >  THEN
          INFO = -3
        ELSEIF ( LDA .LT. ( B+1 ) ) THEN
          INFO = -5
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -6
        ELSEIF ( LDU .LT. MAX( N, 1 ) ) THEN
          INFO = -10
        ELSEIF ( NEEDU .AND. ( NB .LT. 0 ) ) THEN
          INFO = -11
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 ) THEN
          GOTO 999
        ELSEIF ( B .EQ. 0 ) THEN
          CALL DCOPY( N, A( 1, 1 ), LDA, D, 1 )
          DO 10 J = 1, N-1
            E( J ) = ZERO
   10     CONTINUE
          GOTO 999
        ELSEIF ( B .EQ. 1 ) THEN
          CALL DCOPY( N, A( 1, 1 ), LDA, D, 1 )
          CALL DCOPY( N-1, A( 2, 1 ), LDA, E, 1 )
          GOTO 999
        ENDIF
*
*          --- check if workspace is sufficient ---
*
        NSAVE = 2 * B - LDA
        IF ( NSAVE .GT. 0 ) THEN
          SZSUB = ( ( NSAVE - 1 ) * NSAVE ) / 2
          IX = SZSUB + NSAVE + ( N / B ) * SZSUB
        ELSE
          SZSUB = 0
          IX = 0
        ENDIF
        IF ( ( LWORK .LT. ( IX+2*B ) ) .OR.
     >       ( NEEDU .AND. ( LWORK .LT. ( IX+B+N ) ) ) ) THEN
          INFO = -13
          GOTO 999
        ENDIF
*
*          --- compute the final blocking factor for updating U ---
*
        IF ( NEEDU ) THEN
*
*            --- first determine the maximum possible value nb0
*                (for blocking nb0 updates, we need
*                2 * nb0 * ( n + b + nb0 - 1 ) workspace).      ---
*
          BETA = DBLE( N + B - 1 )
          NB0 = INT( ( SQRT( BETA**2 + 2.0D0*( LWORK-IX ) ) - BETA )
     >               / 2.0D0 )
*
*            --- adjust to the user-supplied or default value ---
*
          IF ( NB .GT. 0 ) THEN
            NB0 = MIN( NB, NB0, N-2 )
          ELSE
            NB0 = MIN( NBDFLT( 'SBRDT', 'DoublePrec', 'BlockingFactor',
     >                         N, B, 1, .TRUE. ),
     >                 NB0 )
          ENDIF
*
          IF ( NB0 .LT. 1 )     NB0 = 1
*
*            --- OK, now we are done ---
*
          BLOCK = ( NB0 .GT. 1 )
          ONFLY = ( .NOT. BLOCK )
          INFO = NB0
        ELSE
          NB0 = 1
          BLOCK = .FALSE.
          ONFLY = .FALSE.
        ENDIF
*
*          --- set up pointers to the submatrices stored in work
*              (the data layout is pointed out above)            ---
*
        IF ( NSAVE .GT. 0 ) THEN
          IDIAG = 1
          ISUB = IDIAG + ( SZSUB + NSAVE )
          IV = ISUB + ( N / B ) * SZSUB
        ELSE
          IDIAG = -1
          ISUB = -1
          IV = 1
        ENDIF
*
        LDWY0 = B + NB0 - 1
        IF ( BLOCK ) THEN
          IY = IV + N * NB0
          IW = IY + LDWY0 * NB0
          IWORK = IW + LDWY0 * NB0
          ITAU = IWORK
        ELSE
          IY = -1
          IW = -1
          IWORK = IV + B
          ITAU = -1
        ENDIF
        V = IV
*
*          --- make sure that the "bulge buffer" is empty ---
*
        DO 30 J = 2, N-B
          DO 20 K = B+2, MIN( 2*B, LDA, N-J+1 )
            A( K, J ) = ZERO
   20     CONTINUE
   30   CONTINUE
*
        DO 40 IX = 1, IV-1
          WORK( IX ) = ZERO
   40   CONTINUE
*
* ......................................................................
*
        K0 = 1
*
*          --- in the k-th pass of the following main loop,
*              the k-th column of the band is zeroed and the
*              resulting bulge is chased down the band       ---
*
        DO 700 K = 1, N-2
*
*            --- determine the length of the column and the
*                Householder vector                         ---
*
          HEIGHT = MIN( B, N-K )
          CALL DLBRFG( HEIGHT, A( 2, K ), A( 3, K ), 1, TAU, DRPTOL )
*
*            --- save the vector and zero column of A ---
*
          IF ( BLOCK ) THEN
            V = IV + ( K - K0 ) * ( N - K0 + 1 )
          ENDIF
          WORK( V ) = ONE
          CALL DCOPY( HEIGHT-1, A( 3, K ), 1, WORK( V+1 ), 1 )
          DO 110 I = 3, HEIGHT+1
            A( I, K ) = ZERO
  110     CONTINUE
*
*            --- save the new tridiagonal elements ---
*
          D( K ) = A( 1, K )
          E( K ) = A( 2, K )
*
          IF ( TAU .NE. ZERO ) THEN
*
*              --- apply the Householder transform to both sides
*                  of the first diagonal block                   ---
*
            CALL DSYRF( 'Lower', HEIGHT, WORK( V ), 1, TAU,
     >                  A( 1, K+1 ), LDA - 1, WORK( IWORK ) )
*
*              --- if the transformations of U are not blocked
*                  then apply them as they are generated       ---
*
            IF ( ONFLY ) THEN
              CALL DLARFX( 'Right', N, HEIGHT, WORK( V ), TAU,
     >                     U( 1, K+1 ), LDU, WORK( IWORK ) )
            ENDIF
          ENDIF
*
*            --- start the bulge chasing ---
*
          DO 500 J = K+1, N-B, B
            NBLK = 1 + ( J - K - 1 ) / B
*
*              --- determine the size of the subdiagonal block ---
*
            WIDTH = HEIGHT
            HEIGHT = MIN( B, N-J-(B-1) )
*
*              --- if lda is too small then parts of the diagonal
*                  block must be saved ...                        ---
*
            NSAVE = B + HEIGHT - LDA
            NSAVE1 = NSAVE + 1
            IX = IDIAG
            DO 220 J0 = 1, NSAVE
              IC = J + J0
              DO 210 ID = 1, NSAVE1-J0
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  210         CONTINUE
  220       CONTINUE
*
*              --- ... and the subdiagonal block must be restored ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            IF ( HEIGHT .EQ. B ) THEN
              DO 230 J0 = 1, NSAVE
                A( NSAVE1-J0, J+J0 ) = ZERO
  230         CONTINUE
              DO 250 J0 = 2, NSAVE
                IC = J + J0 - 1
                DO 240 ID = 1, NSAVE1-J0
                  A( ID, IC ) = WORK( IX )
                  IX = IX + 1
  240           CONTINUE
  250         CONTINUE
            ELSE
              DO 270 J0 = 1, NSAVE
                IC = J + J0
                DO 260 ID = 1, NSAVE1-J0
                  A( ID, IC ) = WORK( IX )
                  IX = IX + 1
  260           CONTINUE
  270         CONTINUE
            ENDIF
*
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the previous Householder transform
*                    to the subdiagonal block (from the right) ---
*
              CALL DLARFX( 'Right', HEIGHT, WIDTH, WORK( V ), TAU,
     >                     A( B+1, J ), LDA-1, WORK( IWORK ) )
            ENDIF
*
*              --- save the previous scaling factor ---
*
            WORK( V ) = TAU
*
*              --- generate a new Householder transform to
*                  zero the first column of the subdiagonal block ---
*
            CALL DLBRFG( HEIGHT, A( B+1, J ), A( B+2, J ), 1,
     >                   TAU, DRPTOL )
*
            IF ( BLOCK ) THEN
              V = IV + ( K - K0 ) * ( N - K0 + 1 ) + NBLK * B
            ENDIF
            WORK( V ) = ONE
            CALL DCOPY( HEIGHT-1, A( B+2, J ), 1, WORK( V+1 ), 1 )
            DO 310 I = B+2, B+HEIGHT
              A( I, J ) = ZERO
  310       CONTINUE
*
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the transform to the subdiagonal block
*                    (from the left)                              ---
*
              CALL DLARFX( 'Left', HEIGHT, WIDTH-1, WORK( V ), TAU,
     >                     A( B, J+1 ), LDA-1, WORK( IWORK ) )
            ENDIF
*
*              --- if lda is too small then the subdiagonal block
*                  must be saved ...                              ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 420 J0 = 2, NSAVE
              IC = J + J0
              DO 410 ID = 1, NSAVE1-J0
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  410         CONTINUE
  420       CONTINUE
*
*              --- ... and the diagonal block must be restored ---
*
            IX = IDIAG
            DO 440 J0 = 1, NSAVE
              IC = J + J0
              DO 430 ID = 1, NSAVE1-J0
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  430         CONTINUE
  440       CONTINUE
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the transform to the diagonal block
*                    (two-sided)                               ---
*
              CALL DSYRF( 'Lower', HEIGHT, WORK( V ), 1, TAU,
     >                    A( 1, J+B ), LDA-1, WORK( IWORK ) )
*
*                --- if the transformations of U are not blocked
*                    then apply them as they are generated       ---
*
              IF ( ONFLY ) THEN
                CALL DLARFX( 'Right', N, HEIGHT, WORK( V ), TAU,
     >                      U( 1, J+B ), LDU, WORK( IWORK ) )
              ENDIF
            ENDIF
*
  500     CONTINUE
*
*            --- save the last scaling factor ---
*
          WORK( V ) = TAU
*
* ......................................................................
*
          IF ( BLOCK ) THEN
*
*              --- (delayed) update of the transformation matrix U.
*                  To allow blocked operations, the update is only
*                  done in every nb0-th pass through the k loop     ---
*
            IF ( ( MOD( K, NB0 ) .EQ. 0 ) .OR. ( K .EQ. ( N-2 ) ) )
     >      THEN
*
*                --- the following loop applies block transforms
*                    reversely to their generation, e.g., starting
*                    at the bottom and working up.
*                      First, determine which columns ifirst ...
*                    are affected by the block transform and
*                    how many (nb1) transforms it contains         ---
*
              DO 600 IFIRST = N-MOD( N-K0-1, B ), K0+1, -B
*
*                  --- how many Householder transforms contribute
*                      to the current block transform ?           ---
*
                NB1 = MIN( K-K0+1, N-IFIRST+1 )
                LDWY = MIN( LDWY0, N-IFIRST+1 )
*
*                  --- determine the block Householder reflector
*                      corresponding to these nb1 vectors        ---
*
                V = IFIRST - K0 - 1 + IV
                CALL DCOPY( NB1, WORK( V ), N-K0+1, WORK( ITAU ), 1 )
                CALL DGBWYG( LDWY, NB1, B-1,
     >                       WORK( V ), N-K0, WORK( ITAU ),
     >                       WORK( IW ), LDWY, WORK( IY ), LDWY, NB2 )
*
*                  --- update U by postmultiplying ---
*
                CALL DGEWY( 'Right', N, LDWY, NB2,
     >                      U( 1, IFIRST ), LDU,
     >                      WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                      WORK( IWORK ) )
*
  600         CONTINUE
*
              K0 = K0 + NB0
*
            ENDIF
          ENDIF
*
* ......................................................................
*
  700   CONTINUE
*
*          --- end of the main loop: cleanup for the very tail
*              of the band                                     ---
*
        D( N-1 ) = A( 1, N-1 )
        E( N-1 ) = A( 2, N-1 )
*
        D( N ) = A( 1, N )
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSY2BC( UPLO, N, B, AFULL, LDFULL, ABAND, LDBAND,
     >                     INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dsy2bc copies a symmetric banded A matrix from (upper or lower)
*   symmetric (full) storage to lower banded storage.
*
*   Note that afull and aband must refer to different memory locations,
*   i.e., A may NOT be repacked within the same array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDFULL, LDBAND, INFO
        DOUBLE PRECISION      AFULL( LDFULL, * ), ABAND( LDBAND, * )
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of the
*           array afull ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   afull   (in) double precision array, dimension ( ldfull, n )
*           The symmetric banded matrix A in upper or lower symmetric
*           storage.
*
*   ldfull  (in) integer
*           The leading dimension of the array afull.
*           ldfull >= max( n, 1 ).
*
*   aband   (out) double precision array, dimension ( ldband, n )
*           The symmetric banded matrix A in lower banded storage (upper
*           banded storage is not supported).
*
*   ldband  (in)
*           The leading dimension of the array aband.
*           ldband >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldfull was out of range ( < n or < 1 ).
*                = -7 : ldband was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               J, I
*
*   upper   is A given in upper symmetric storage ?
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDFULL .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LDBAND .LT. ( B+1 ) ) THEN
          INFO = - 7
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower" ---
*
          DO 110 J = 1, N
            DO 100 I = MAX( J-B, 1 ), J
              ABAND( 1+J-I, I ) = AFULL( I, J )
  100       CONTINUE
  110     CONTINUE
        ELSE
*
*            --- "lower to lower" ---
*
          DO 210 J = 1, N
            DO 200 I = J, MIN( J+B, N )
              ABAND( 1+I-J, J ) = AFULL( I, J )
  200       CONTINUE
  210     CONTINUE
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSY2BI( UPLO, N, B, A, LDFULL, LDBAND, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dsy2bi copies a symmetric banded A matrix from (upper or lower)
*   symmetric (full) storage to lower banded storage within the same
*   array a (i.e., in-place).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDFULL, LDBAND, INFO
        DOUBLE PRECISION      A( * )
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of the
*           array a ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   a       (in/out) double precision array,
*           dimension ( max( ldfull, ldband), n )
*           On entry, the symmetric banded matrix A in upper or lower
*           symmetric storage.
*           On exit, the symmetric banded matrix A in lower banded
*           storage (upper banded storage is not supported).
*           Note that this routine treats a as a one-dimensional array.
*
*   ldfull  (in) integer
*           The leading dimension of the array a (in full storage).
*           ldfull >= max( n, 1 ).
*
*   ldband  (in)
*           The leading dimension of the array a (in banded storage).
*           ldband >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldfull was out of range ( < n or < 1 ).
*                = -6 : ldband was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, IBAND, IFULL, J, I
*
*   upper   is A given in upper symmetric storage ?
*   b1      = b + 1
*   iband   iband + i points to the next entry in a (banded storage)
*   ifull   ifull + i points to the next entry in a (full storage)
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              DSB2BI
*
*   dsb2bi  in-place repacking from banded to banded storage (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDFULL .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LDBAND .LT. B1 ) THEN
          INFO = - 6
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower"; avoid overwriting by first
*                packing the band as tight as possible (i.e.,
*                leading dimension b + 1) and then "stretching"
*                to leading dimension ldband                    ---
*
          DO 110 J = 1, N
              IBAND = ( J - 1 ) * B1 + 1 - J
              DO 100 I = J, MIN( J+B, N )
                A( IBAND+I ) = A( (I-1)*LDFULL+J )
  100         CONTINUE
  110     CONTINUE
*
          IF ( LDBAND .GT. B1 ) THEN
            CALL DSB2BI( 'Lower', N, B, A, B1, LDBAND, INFO )
          ENDIF
*
        ELSE
*
*            --- "lower to lower"; avoid overwriting by
*                 copying the columns in the "safe" order ---
*
          IF ( LDBAND .LE. ( LDFULL+1 ) ) THEN
            DO 210 J = 1, N
              IBAND = ( J - 1 ) * LDBAND + 1 - J
              IFULL = ( J - 1 ) * LDFULL
              DO 200 I = J, MIN( J+B, N )
                A( IBAND+I ) = A( IFULL+I )
  200         CONTINUE
  210       CONTINUE
          ELSE
            DO 310 J = N, 1, -1
              IBAND = ( J - 1 ) * LDBAND + 1 - J
              IFULL = ( J - 1 ) * LDFULL
              DO 300 I = MIN( J+B, N ), J, -1
                A( IBAND+I ) = A( IFULL+I )
  300         CONTINUE
  310       CONTINUE
          ENDIF
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSB2BC( UPLO, N, B, ASRC, LDSRC, ADST, LDDST, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dsb2bc copies a symmetric banded A matrix from upper or lower
*   banded storage to lower banded storage. It may be used to pack the
*   matrix tightly by setting lddst accordingly.
*
*   Note that asrc and adst must refer to different memory locations,
*   i.e., A may NOT be repacked within the same array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDSRC, LDDST, INFO
        DOUBLE PRECISION      ASRC( LDSRC, * ), ADST( LDDST, * )
*
*   uplo    (in) character*1
*           Is the matrix A given in upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   asrc    (in) double precision array, dimension ( ldsrc, n )
*           The symmetric banded matrix A in upper or lower banded
*           storage.
*
*   ldsrc   (in) integer
*           The leading dimension of the array asrc.
*           ldsrc >= b + 1.
*
*   adst    (out) double precision array, dimension ( lddst, n )
*           The symmetric banded matrix A in lower banded storage.
*
*   lddst   (in) integer
*           The leading dimension of the array adst.
*           lddst >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldsrc was out of range ( < b + 1 ).
*                = -7 : lddst was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, J, I
*
*   upper   is A given in upper banded storage ?
*   b1      = b + 1
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDSRC .LT. B1 ) THEN
          INFO = - 5
        ELSEIF ( LDDST .LT. B1 ) THEN
          INFO = - 7
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*              --- "upper to lower" ---
*
          DO 110 J = 1, N
            DO 100 I = 1, MIN( B1, N-J+1 )
              ADST( I, J ) = ASRC( B+2-I, J+I-1 )
  100       CONTINUE
  110     CONTINUE
        ELSE
*
*            --- "lower to lower" ---
*
          DO 210 J = 1, N
            DO 200 I = 1, MIN( B1, N-J+1 )
              ADST( I, J ) = ASRC( I, J )
  200       CONTINUE
  210     CONTINUE
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSB2BI( UPLO, N, B, A, LDSRC, LDDST, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dsb2bi copies a symmetric banded A matrix from upper or lower banded
*   storage to lower banded storage within the same array a (i.e.,
*   in-place). It may be used to pack the matrix tightly by setting
*   lddst accordingly.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDSRC, LDDST, INFO
        DOUBLE PRECISION      A( * )
*
*   uplo    (in) character*1
*           Is the matrix A given in the upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n.
*
*   a       (in/out) double precision array,
*           dimension ( max( ldsrc, lddst ), n )
*           On entry, the symmetric banded matrix A in upper or lower
*           banded storage.
*           On exit, the symmetric banded matrix A in lower banded
*           storage (upper banded storage is not supported).
*           Note that this routine treats a as a one-dimensional array.
*
*   ldsrc   (in) integer
*           The leading dimension of the array a (input storage scheme).
*           ldsrc >= b + 1.
*
*   lddst   (in) integer
*           The leading dimension of the array a (output storage
*           scheme).
*           lddst >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldsrc was out of range ( < b + 1 ).
*                = -6 : lddst was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, LDSRC1, ISRC, IDST, J, I
*
*   upper   is A given in upper banded storage ?
*   b1      = b + 1
*   ldsrc1  leading dimension of the current source, minus 1
*   isrc    isrc + i points to the next source element in a
*   idst    idst + something points to the next destination element in a
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDSRC .LT. B1 ) THEN
          INFO = - 5
        ELSEIF ( LDDST .LT. B1 ) THEN
          INFO = - 6
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower" ---
*
          IF ( LDDST .LE. LDSRC ) THEN
*
*              --- no danger of overwriting ---
*
            LDSRC1 = LDSRC - 1
            DO 110 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 2 ) * LDSRC + B + 2
              DO 100 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I*LDSRC1 )
  100         CONTINUE
  110       CONTINUE
          ELSE
*
*              --- first copy to upper storage, then transpose ---
*
            DO 210 J = N, 1, -1
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 200 I = B1, MAX( B1-J+1, 1 ), -1
                A( IDST+I ) = A( ISRC+I )
  200         CONTINUE
  210       CONTINUE
*
            LDSRC1 = LDDST - 1
            DO 230 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 2 ) * LDDST + B + 2
              DO 220 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I*LDSRC1 )
  220         CONTINUE
  230       CONTINUE
          ENDIF
*
        ELSE
*
*            --- "lower to lower"; avoid overwriting by
*                 copying the columns in the "safe" order ---
*
          IF ( LDDST .LE. LDSRC )
     >    THEN
            DO 310 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 300 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I )
  300         CONTINUE
  310       CONTINUE
          ELSE
            DO 410 J = N, 1, -1
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 400 I = MIN( B1, N-J+1 ), 1, -1
                A( IDST+I ) = A( ISRC+I )
  400         CONTINUE
  410       CONTINUE
          ENDIF
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSBRDD( JOBU, UPLO, N, B1, B2, A, LDA, DRPTOL, D, E,
     >                     U, LDU, NSTEPS, B, NB,
     >                     WORK, LWORK, STEP, INFO )
*
* Description:
*
*   Driver routine for the multi-step reduction of symmetric banded
*   matrices to narrower banded form.
*   Given a symmetric n-by-n matrix A with b1 sub(or super-) diagonals,
*   dsbrdd reduces A to a symmetric banded matrix B with b2 sub(or
*   super-) diagonals using a sequence of orthogonal transformations.
*   If desired, the same transformations are also applied from the right
*   to the matrix U. That is, if initially U was the identity, then the
*   resulting banded matrix B and the updated U fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK packed storage scheme for upper or
*   lower banded matrices and is returned in lower banded storage (upper
*   banded is not supported for output).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOBU, UPLO
        INTEGER               N, B1, B2, LDA, LDU, NSTEPS, LWORK, STEP,
     >                        INFO
        INTEGER               B( * ), NB( * )
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), D( * ), E( * ), U( LDU, * ),
     >                        WORK( * )
*
*   jobu    (in) character*1
*           Specifies whether U is required or not.
*           jobu = 'U' : Update U.
*                = 'N' : Do not update U.
*
*   uplo    (in) character*1
*           Is the matrix A given in the upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b1      (in) integer
*           The number of sub(super-)diagonals of A.
*           0 <= b1 < n, if n > 0.
*           b1 = 0,      if n = 0.
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 <= b1 or b2 = b1 = 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the leading (b1+1)-by-n portion of a contains the
*           symmetric banded matrix A in upper or lower banded storage.
*           If uplo='U' then for i = 1, ..., n, the matrix elements
*           A( i, j ), j = i, ..., min( i+b1, n ), are stored at
*           position a( b1+1+i-j, j ), whereas for uplo='L', the matrix
*           elements A( i, j ), j = max( i-b, 1 ), ..., i, are stored at
*           position a( 1+i-j, j ).
*           On exit, the leading (b2+1)-by-n portion of a contains the
*           reduced matrix B in lower (!) banded storage.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( b1+1, n ) and lda > 0.
*
*   drptol  (in) double precision
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   d       (out) double precision array, dimension ( n )
*           If b2 = 1 then, on exit, d( 1 .. n ) contains the main
*           diagonal of the resulting tridiagonal matrix B.
*
*   e       (out) double precision array, dimension ( n-1 )
*           If b2 = 1 then, on exit, e( 1 .. n-1 ) contains the
*           subdiagonal of the resulting tridiagonal matrix B.
*
*   u       (in/out) double precision array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nsteps  (in) integer
*           The number of reduction steps.
*           nsteps >= 0.
*
*           If nsteps > 0 then the reduction from b1 to b2 is done in
*           exactly nsteps steps with user-specified intermediate
*           bandwidths and blocking factors (see paramaters b and nb,
*           below).
*           If nsteps = 0 then the routine tries to determine these
*           parameters on its own.
*           If you do not know or if you do not care, use 0.
*
*   b       (in) integer array, dimension ( nsteps-1 )
*           The sequence of intermediate bandwidths. The nsteps
*           bandwidth reduction steps are
*              b1 --> b( 1 ),
*              b( 1 ) --> b( 2 ),
*              ...
*              b( nsteps-1 ) --> b2.
*           This array is accessed only if nsteps > 1.
*
*   nb      (in) integer array, dimension ( nsteps )
*           The blocking factors nb, as suggested by the user, for the
*           reduction and/or the accumulation of the transformations
*           in each of the nb reduction steps.
*           Note that the automatic selection of suitable blocking
*           factors is enabled by setting nb( i ) = 0 for some steps i.
*           This array is accessed only if nsteps > 0.
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The length of the workspace array.
*           The exact amount of workspace required depends on the
*           sequence of intermediate bandwidths (i.e., b), on the
*           leading dimension of the array a (i.e., lda), and on the
*           blocking factors for the reduction steps (i.e., nb).
*           lwork >= maximum workspace requirement for any of the
*                    reduction steps.
*           As a rule, lwork >= b1 * n should work fine.
*
*   step    (out) integer
*           On exit, step returns the number of the last reduction step
*           that was performed (or tried).
*
*   info    (out) integer
*           On exit, info indicates the status of the reduction.
*           info =   1 : All arguments were OK, and the reduction went
*                        without problems.
*                =  -1 : jobu is none of 'U', 'N' (upper/lower case).
*                =  -2 : uplo is none of 'U', 'L' (upper/lower case).
*                =  -3 : n is out of range (negative).
*                =  -4 : b1 is out of range ( < 0 or >= n ).
*                =  -5 : b2 is out of range ( < 0, or = 0 while b1 >= 1,
*                        or > b1 ).
*                =  -7 : lda is too small (see above).
*                =  -8 : drptol is out of range (negative).
*                = -12 : ldu is out of range ( < n ).
*                = -13 : nsteps is out of range (negative).
*                = -14 : the sequence of bandwidths b1, b( 1 ), b( 2 ),
*                        ..., b( nsteps-1 ), b2 is not monotonically
*                        decreasing
*                = -15 : nb contains negative entries
*                = -17 : lwork is too small (see above).
*           If info < 0 and step > 0 then the parameter for the step-th
*           reduction step was not OK.
*
* Local constants and variables:
*
        DOUBLE PRECISION      ZERO
        PARAMETER             ( ZERO = 0.0D0 )
*
        LOGICAL               NEEDU, UPPER
        INTEGER               BCURR, LDCURR, NBCURR, BNEXT, LDNEXT, NX
        CHARACTER*1           ULCURR
*
*   needu   is U needed ?
*   upper   is A given in upper or lower banded storage ?
*   bcurr   current bandwidth
*   ldcurr  current leading dimension of the band
*   nbcurr  blocking factor for the current step
*   bnext   bandwidth after the next reduction step
*   ldnext  leading dimension of the band after repacking
*   nx      cross-over point from LAPACK to SBR code, and block size
*   ulcurr  is the current band in upper or lower storage ?
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default crossover point from LAPACK to SBR code
*           or default intermediate bandwidth (SBR)
*
        EXTERNAL              DSB2BI, DSBRDB, DSBRDT, DSBTRD
*
*   dsb2bi  in-place repacking of banded matrices (SBR)
*   dsbrdb  one-step reduction banded -> banded (SBR)
*   dsbrdt  one-step reduction banded -> tridiagonal (SBR)
*   dsbtrd  one-step reduction banded -> tridiagonal (LAPACK)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOBU, 'U' )
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -3
        ELSEIF ( ( B1 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B1 .GE. N ) ) ) THEN
          INFO = -4
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( B2 .EQ. 0 ) .AND. ( B1 .GE. 1 ) ) .OR.
     >           ( B2 .GT. B1 ) ) THEN
          INFO = -5
        ELSEIF ( LDA .LT. ( B1+1 ) ) THEN
          INFO = -7
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -8
        ELSEIF ( NEEDU .AND. ( LDU .LT. MAX( N, 1 ) ) ) THEN
          INFO = -12
        ELSEIF ( NSTEPS .LT. 0 ) THEN
          INFO = -13
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 1 ) THEN
          IF ( ( B( 1 ) .GT. B1 ) .OR. ( B2 .GT. B( NSTEPS-1 ) ) ) THEN
            INFO = -14
          ELSE
            DO 10 STEP = 1, NSTEPS-2
              IF ( B( STEP+1 ) .GT. B( STEP ) )     INFO = -14
   10       CONTINUE
          ENDIF
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 0 ) THEN
          DO 20 STEP = 1, NSTEPS
            IF ( NB( STEP ) .LT. 0 )     INFO = -15
   20     CONTINUE
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
*          --- set current bandwidth, leading dimension, etc. ---
*
        ULCURR = UPLO
        BCURR = B1
        LDCURR = LDA
        STEP = 0
*
*          --- while bandwidth is too large do next reduction step ---
*
  100   IF ( BCURR .GT. B2 ) THEN
          STEP = STEP + 1
*
*            --- determine target bandwidth and blocking factor
*                for the next reduction step                    ---
*
          IF ( STEP .LT. NSTEPS ) THEN
            BNEXT = B( STEP )
            NBCURR = NB( STEP )
          ELSEIF ( STEP .EQ. NSTEPS ) THEN
            BNEXT = B2
            NBCURR = NB( STEP )
          ELSE
*
*              --- automatic bandwidth selection ---
*
            BNEXT = NBDFLT( 'SBRDD', 'DoublePrec', 'Bandwidth',
     >                      N, BCURR, B2, NEEDU )
*
*              --- if the proposed intermediate bandwidth is out
*                  of range then do a one-step reduction         ---
*
            IF ( ( BNEXT .GE. BCURR ) .OR. ( BNEXT .LT. B2 ) ) THEN
              BNEXT = B2
            ENDIF
            NBCURR = 0
          ENDIF
*
          IF ( BNEXT .EQ. 1 ) THEN
*
*              --- reduction to tridiagonal form;
*                  use SBR or LAPACK code ?       ---
*
            NX = NBDFLT( 'SBRDD', 'DoublePrec', 'CrossoverPoint',
     >                   N, BCURR, B2, NEEDU )
            IF ( BCURR .LT. NX ) THEN
*
*                --- LAPACK tridiagonalization; first repack the
*                    band to improve performance                 ---
*
              LDNEXT = BCURR + 1
              IF ( LDCURR .NE. LDNEXT ) THEN
                CALL DSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
                LDCURR = LDNEXT
                ULCURR = 'Lower'
              ENDIF
*
              IF ( LWORK .LT. N ) THEN
                INFO = -17
              ELSE
                CALL DSBTRD( JOBU, ULCURR, N, BCURR, A, LDCURR, D, E,
     >                       U, LDU, WORK, INFO )
              ENDIF
            ELSE
*
*                --- SBR tridiagonalization; first repack the band
*                    to improve performance                        ---
*
              LDNEXT = MIN( 2*BCURR, LDA )
              IF ( ( LDCURR .NE. LDNEXT ) .OR.
     >             LSAME( ULCURR, 'Upper' ) ) THEN
                CALL DSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
                LDCURR = LDNEXT
                ULCURR = 'Lower'
              ENDIF
*
              CALL DSBRDT( JOBU, N, BCURR, A, LDCURR, DRPTOL, D, E,
     >                     U, LDU, NBCURR, WORK, LWORK, INFO )
              IF ( INFO .EQ. -13 )     INFO = -17
            ENDIF
*
          ELSE
*
*              --- SBR reduction to narrower banded form; first
*                  repack the band to improve performance (optimum
*                  leading dimension depends on the blocking
*                  factor - so determine that one first)           ---
*
            IF ( NBCURR .EQ. 0 ) THEN
              NX = NBDFLT( 'SBRDB', 'DoublePrec', 'BlockingFactor',
     >                     N, BCURR, BNEXT, NEEDU )
            ELSE
              NX = NBCURR
            ENDIF
            IF ( NX .GT. BNEXT )     NX = BNEXT
            IF ( NX .LT. 1 )     NX = 1
            LDNEXT = MIN( BCURR+(BCURR-BNEXT)+NX, LDA )
            IF ( ( LDCURR .NE. LDNEXT ) .OR.
     >           LSAME( ULCURR, 'Upper' ) ) THEN
              CALL DSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
              LDCURR = LDNEXT
              ULCURR = 'Lower'
            ENDIF
*
            CALL DSBRDB( JOBU, N, BCURR, BNEXT, A, LDCURR, DRPTOL,
     >                   U, LDU, NBCURR, WORK, LWORK, INFO )
            IF ( INFO .EQ. -12 )     INFO = -17
          ENDIF
*
          BCURR = BNEXT
          IF ( INFO .GE. 0 )     GOTO 100
*
        ENDIF
*
*          --- after the reduction, repack the band to leading
*              dimension lda and lower banded storage scheme   ---
*
        IF ( ( INFO .GE. 0 ) .AND.
     >       ( ( LDCURR .NE. LDA ) .OR. LSAME( ULCURR, 'Upper' ) ) )
     >  THEN
          CALL DSB2BI( ULCURR, N, BCURR, A, LDCURR, LDA, INFO )
        ENDIF
*
        IF ( INFO .GE. 0 )     INFO = 1
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYRDD( JOBU, UPLO, N, B2, A, LDA, DRPTOL,
     >                     ABAND, LDBAND, D, E, NSTEPS, B, NB,
     >                     WORK, LWORK, STEP, INFO )
*
* Description:
*
*   Driver routine for the multi-step reduction of symmetric matrices to
*   banded form.
*   Given a symmetric n-by-n matrix A, dsyrdd reduces A to a symmetric
*   banded matrix B with b2 sub(or super-) diagonals using a sequence of
*   orthogonal transformations.
*   If desired, the same transformations are also accumulated in an
*   orthogonal matrix U. That is, the resulting banded matrix B and the
*   accumulated matrix U fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK symmetric storage scheme with either
*   the upper or lower triangle stored explicitly, and B is returned in
*   lower banded storage (upper banded is not supported for output).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOBU, UPLO
        INTEGER               N, B2, LDA, LDBAND, NSTEPS, LWORK, STEP,
     >                        INFO
        INTEGER               B( * ), NB( * )
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), ABAND( LDBAND, * ),
     >                        D( * ), E( * ), WORK( * )
*
*   jobu    (in) character*1
*           Specifies whether U is required or not.
*           jobu = 'U' : Build U.
*                = 'N' : Do not build U.
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of a ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 < n, if n > 1.
*           b2 = 0     , if n <= 1.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the leading n-by-n portion of a contains the
*           symmetric matrix A in upper or lower symmetric storage.
*           If uplo='U' then the upper triangle of A is stored in
*           the upper triangle of the leading n-by-n portion of a;
*           if uplo='L' then the lower triangle of A is stored in
*           the lower triangle of the leading n-by-n portion of a.
*           On exit, A is destroyed.
*           If jobu='U' then the leading n-by-n portion of a holds
*           the orthogonal matrix U.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   drptol  (in) double precision
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   aband   (out) double precision array, dimension ( ldband, n )
*           On exit, the leading (b2+1)-by-n portion of aband holds the
*           symmetric banded matrix B in lower banded storage (i.e., for
*           j = 1, ..., n and i = j, ..., min( j+b2, n ), the matrix
*           element B( i, j ) is stored in location aband( i-j+1, j ).
*
*   ldband  (in) integer
*           The leading dimension of the array aband.
*           ldband >= b( 1 ) + 1, if nsteps > 1.
*                  >= b2 + 1    , otherwise.
*           For reasonable performance, set ldband >= 2 * b( 1 ) if
*           nsteps > 1, and ldband >= 50 if nsteps = 0.
*
*   d       (out) double precision array, dimension ( n )
*           If b2 = 1 then, on exit, d( 1 .. n ) contains the main
*           diagonal of the resulting tridiagonal matrix B.
*
*   e       (out) double precision array, dimension ( n-1 )
*           If b2 = 1 then, on exit, e( 1 .. n-1 ) contains the
*           subdiagonal of the resulting tridiagonal matrix B.
*
*   nsteps  (in) integer
*           The number of reduction steps.
*           nsteps >= 0.
*
*           If nsteps > 0 then the reduction from full to b2 diagonals
*           is done in exactly nsteps steps with user-specified
*           intermediate bandwidths and blocking factors (see paramaters
*           b and nb, below).
*           If nsteps = 0 then the routine tries to determine these
*           parameters on its own.
*           If you do not know or if you do not care, use 0.
*
*   b       (in) integer array, dimension ( nsteps-1 )
*           The sequence of intermediate bandwidths. The nsteps
*           bandwidth reduction steps are
*              n-1 --> b( 1 ),
*              b( 1 ) --> b( 2 ),
*              ...
*              b( nsteps-1 ) --> b2.
*           This array is accessed only if nsteps > 1.
*
*   nb      (in) integer array, dimension ( nsteps )
*           The blocking factors nb, as suggested by the user, for the
*           reduction and/or the accumulation of the transformations
*           in each of the nb reduction steps.
*           Note that the automatic selection of suitable blocking
*           factors is enabled by setting nb( i ) = 0 for some steps i.
*           This array is accessed only if nsteps > 0.
*
*   work    (workspace) double precision array, dimension ( lwork )
*
*   lwork   (in) integer
*           The length of the workspace array.
*           The exact amount of workspace required depends on the
*           sequence of intermediate bandwidths (i.e., b), on the
*           leading dimension of the array a (i.e., lda), and on the
*           blocking factors for the reduction steps (i.e., nb).
*           lwork >= maximum workspace requirement for any of the
*                    reduction steps.
*           Minimum requirement is 4 * n, but setting lwork this low may
*           severely degrade performance.
*           As a rule, lwork >= 50 * n should work fine; if you can
*           spare it, use lwork >= 100 * n.
*
*   step    (out) integer
*           On exit, step returns the number of the last reduction step
*           that was performed (or tried).
*
*   info    (out) integer
*           On exit, info indicates the status of the reduction.
*           info =   1 : All arguments were OK, and the reduction went
*                        without problems.
*                =  -1 : jobu is none of 'U', 'N' (upper/lower case).
*                =  -2 : uplo is none of 'U', 'L' (upper/lower case).
*                =  -3 : n is out of range (negative).
*                =  -4 : b2 is out of range ( < 0,
*                        or < 1 or >= n while n > 1 ).
*                =  -6 : lda is too small (see above).
*                =  -7 : drptol is out of range (negative).
*                =  -9 : ldband is out of range ( < b(1)+1 ).
*                = -12 : nsteps is out of range (negative).
*                = -13 : the sequence of bandwidths n-1, b( 1 ), b( 2 ),
*                        ..., b( nsteps-1 ), b2 is not monotonically
*                        decreasing
*                = -14 : nb contains negative entries
*                = -16 : lwork is too small (see above).
*           If info < 0 and step > 0 then the parameter for the step-th
*           reduction step was not OK.
*
* Local constants and variables:
*
        DOUBLE PRECISION      ZERO
        PARAMETER             ( ZERO = 0.0D0 )
*
        LOGICAL               NEEDU, UPPER
        INTEGER               BNEXT, NBCURR
*
*   needu   is U needed ?
*   upper   is the upper triangle of A stored ?
*   nbcurr  blocking factor for the current step
*   bnext   bandwidth after the next reduction step
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine intermediate bandwidth (SBR)
*
        EXTERNAL              DORGTR, DSBRDD, DSY2BC, DSYGTR, DSYRDB,
     >                        DSYTRD
*
*   dorgtr  accumulation of the transformations (LAPACK)
*   dsbrdd  bandwidth reduction for banded matrices (SBR)
*   dsy2bc  repacking from full to banded storage (SBR)
*   dsygtr  accumulation of the transformations (SBR)
*   dsyrdb  reduction full -> banded (SBR)
*   dsytrd  one-step reduction full -> tridiagonal (LAPACK)
*
        INTRINSIC             MAX
*
* ----------------------------------------------------------------------
*
        STEP = 1
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOBU, 'U' )
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -3
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B2 .LT. 1 ) .OR. ( B2 .GT. N-1 ) ) ) ) THEN
          INFO = -4
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = -6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -7
        ELSEIF ( ( LDBAND .LE. B2 ) .OR.
     >           ( ( NSTEPS .GT. 1 ) .AND. ( LDBAND .LE. B( 1 ) ) ) )
     >  THEN
          INFO = -9
        ELSEIF ( NSTEPS .LT. 0 ) THEN
          INFO = -12
        ELSEIF ( LWORK .LT. 4*N ) THEN
          INFO = -16
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 1 ) THEN
          IF ( ( B( 1 ) .GT. ( N-1 ) ) .OR.
     >         ( B2 .GT. B( NSTEPS-1 ) ) ) THEN
            INFO = -13
          ELSE
            DO 10 STEP = 1, NSTEPS-2
              IF ( B( STEP+1 ) .GT. B( STEP ) )     INFO = -13
   10       CONTINUE
          ENDIF
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 0 ) THEN
          DO 20 STEP = 1, NSTEPS
            IF ( NB( STEP ) .LT. 0 )     INFO = -14
   20     CONTINUE
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
        STEP = 1
*
*          --- determine first intermediate bandwidth and blocking
*              factor                                              ---
*
        IF ( NSTEPS .GT. 0 ) THEN
          IF ( NSTEPS .EQ. 1 ) THEN
            BNEXT = B2
          ELSE
            BNEXT = B( 1 )
          ENDIF
          NBCURR = NB( 1 )
        ELSE
*
*            --- automatic bandwidth selection ---
*
          BNEXT = NBDFLT( 'SYRDD', 'DoublePrec', 'Bandwidth',
     >                    N, N - 1, B2, NEEDU )
*
*              --- if the proposed intermediate bandwidth is out
*                  of range then do a one-step reduction         ---
*
          IF ( ( BNEXT .GT. N-1 ) .OR. ( BNEXT .LT. B2 ) .OR.
     >         ( LDBAND .LT. 2*BNEXT ) ) THEN
            BNEXT = B2
          ENDIF
          NBCURR = 0
        ENDIF
*
        IF ( BNEXT .EQ. 1 ) THEN
*
*            --- use LAPACK code for direct tridiagonalization ---
*
          CALL DSYTRD( UPLO, N, A, LDA, D, E, WORK( 1 ),
     >                 WORK( N ), LWORK-N+1, INFO )
          IF ( NEEDU ) THEN
            CALL DORGTR( UPLO, N, A, LDA, WORK( 1 ),
     >                   WORK( N ), LWORK-N+1, INFO )
          ENDIF
        ELSE
*
*            --- reduction to bandwidth > 1 width dsyrdb ---
*
          CALL DSYRDB( UPLO, 'NoU', N, BNEXT, A, LDA, DRPTOL,
     >                 WORK( 1 ), N, NBCURR, WORK( 1 ),
     >                 WORK( N+1 ), LWORK-N, INFO )
*
*            --- repack the reduced matrix to banded storage ---
*
          CALL DSY2BC( UPLO, N, BNEXT, A, LDA, ABAND, LDBAND, INFO )
*
*            --- accumulation of the transformations, if required ---
*
          IF ( NEEDU ) THEN
            CALL DSYGTR( UPLO, N, BNEXT, A, LDA, WORK( 1 ),
     >                   WORK( N+1 ), LWORK-N, INFO )
          ENDIF
*
*            --- further reduce the banded matrix, if required ---
*
          IF ( ( BNEXT .GT. B2 ) .AND. ( INFO .GE. 0 ) ) THEN
            IF ( NSTEPS .EQ. 0 ) THEN
              CALL DSBRDD( JOBU, 'Lower', N, BNEXT, B2, ABAND, LDBAND,
     >                     DRPTOL, D, E, A, LDA, 0, B, NB,
     >                     WORK, LWORK, STEP, INFO )
            ELSE
              CALL DSBRDD( JOBU, 'Lower', N, BNEXT, B2, ABAND, LDBAND,
     >                     DRPTOL, D, E, A, LDA, NSTEPS-1, B( 2 ),
     >                     NB( 2 ), WORK, LWORK, STEP, INFO )
            ENDIF
            STEP = STEP + 1
          ENDIF
        ENDIF
*
  999   IF ( INFO .GE. 0 )     INFO = 1
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DLBRFG( N, ALPHA, X, INCX, TAU, DRPTOL )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dlbrfg generates an elementary reflector H of order n, such that
*
*                                    T
*      H * ( alpha ) = ( beta ) ,   H  * H = I ,
*          (   x   )   (   0  )
*
*   where alpha and beta are scalars, and x is an ( n - 1 )-element
*   vector. H is represented in the form
*
*                                 T
*      H = I - tau * ( 1 ) * ( 1 v  ) ,
*                    ( v )
*
*   where tau is a scalar and v is an ( n - 1 )-element vector.
*
*   If the elements of x are all zero, or the 2-norm of x does not
*   exceed drptol, then x is simply zeroed out, tau is set to 0,
*   indicating that H is the identity matrix. In this case, the
*   transformation is effectively skipped.
*
*   Otherwise  1 <= tau <= 2.
*
*   This routine is a modified version of dlbrfg by Bischof/Sun which
*   in turn is a modified version of the LAPACK routine dlarfg.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               N, INCX
        DOUBLE PRECISION      ALPHA, TAU, DRPTOL
        DOUBLE PRECISION      X( * )
*
*   n       (in) integer
*           The order of the elementary reflector.
*           n >= 0.
*
*   alpha   (in/out) double precision
*           On entry, the value alpha.
*           On exit, it is overwritten with the value beta.
*
*   x       (in/out) double precision array, dimension ( 1+(n-2)*incx )
*           On entry, the vector x.
*           On exit, the "x elements" are overwritten with the vector v.
*
*   incx    (in) integer
*           The increment between elements of x.
*           incx > 0.
*
*   tau     (out) double precision
*           The scaling factor tau.
*
*   drptol  (in) double precision
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to eliminate is already <= drptol
*           then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        DOUBLE PRECISION      XNORM, BETA, SAFMIN, RSAFMN
        INTEGER               CNT, J
*
*   xnorm   2-norm of x
*   beta    the computed value beta
*   safmin  safe minimum (such that relative accuracy can be guaranteed)
*   rsafmn  1 / safmin
*   cnt     counts the rescaling steps
*
* Routines called:
*
        DOUBLE PRECISION      DLAMCH, DLAPY2, DNRM2
        EXTERNAL              DLAMCH, DLAPY2, DNRM2, DSCAL
*
*   dlamch        determine machine parameters (LAPACK)
*   dlapy2        stable 2-norm of 2-vector (LAPACK)
*   dnrm2         2-norm of a vector (BLAS)
*   dscal         vector scaling (BLAS)
*
        INTRINSIC             SIGN, ABS
*
* ----------------------------------------------------------------------
*
*            --- check for quick exit ---
*
        IF ( N .LE. 1 ) THEN
          TAU = ZERO
        ELSE
*
          XNORM = DNRM2( N-1, X, INCX )
*
          IF ( XNORM .LE. DRPTOL ) THEN
*
*              --- H = I ---
*
            TAU = ZERO
            DO 10 J = 1, N-1
              X( 1+(J-1)*INCX ) = ZERO
   10       CONTINUE
*
          ELSE
*
*              --- general case ---
*
            BETA = - SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
            SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
*
            IF ( ABS( BETA ) .LT. SAFMIN ) THEN
*
*                --- xnorm, beta may be inaccurate; scale x
*                    and recompute them                     ---
*
              RSAFMN = ONE / SAFMIN
              CNT = 0
*
  100         CONTINUE
                CNT = CNT + 1
                ALPHA = ALPHA * RSAFMN
                CALL DSCAL( N-1, RSAFMN, X, INCX )
                BETA = BETA * RSAFMN
              IF ( ABS( BETA ) .LT. SAFMIN )     GOTO 100
*
*                --- now abs( beta ) is at least safmin ---
*
              XNORM = DNRM2( N-1, X, INCX )
              BETA = - SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
              TAU = ( BETA - ALPHA ) / BETA
              CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
*
*                --- if alpha is subnormal, it may lose
*                    relative accuracy                  ---
*
              ALPHA = BETA
*
              DO 110 J = 1, CNT
                ALPHA = ALPHA * SAFMIN
  110         CONTINUE
*
            ELSE
*
              TAU = ( BETA - ALPHA ) / BETA
              CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
              ALPHA = BETA
*
            ENDIF
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYRF( UPLO, N, V, INCV, TAU,
     >                    A, LDA, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*                                                      T
*   Apply the Householder transform H = I - tau * v * v  from both
*   sides to the symmetric matrix A, i.e., update
*
*                            T
*      A := H * A * H   ( = H  * A * H )  .
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, INCV, LDA
        DOUBLE PRECISION      TAU
        DOUBLE PRECISION      V( * ), A( LDA, * ), WORK( * )
*
*  uplo     (in) character*1
*           Is the upper or lower triangle of A stored ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*  n        (in) integer
*           The dimension of the matrix A.
*           n >= 0.
*
*  v        (in) double precision array, dimension ( 1+(n-1)*incv )
*           The Householder vector associated with H.
*           Usually, v( 1 ) = 1, and v( 2:n ) contains the "mantissa" of
*           the transform.
*
*  incv     (in) integer
*           The increment between the elements of v.
*           incv > 0.
*
*  tau      (in) double precision
*           The scaling factor for the transform.
*
*  a        (in/out) double precision array, dimension ( lda, n )
*           On entry, an n-by-n symmetric matrix A with either the lower
*           or the upper triangle stored.
*           On exit, the leading A is overwritten with H * A * H.
*
*  lda      (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*  work     (workspace) double precision array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        DOUBLE PRECISION      ALPHA
*
*   alpha   auxiliary factor
*
* Routines called:
*
        DOUBLE PRECISION      DDOT
        EXTERNAL              DAXPY, DDOT, DSYMV, DSYR2
*
*   daxpy   add multiple of a vector to another vector (BLAS)
*   ddot    dot product of two vectors (BLAS)
*   dsymv   symmetric matrix-vector product (BLAS)
*   dsyr2   symmetric rank-2 update (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( N .GT. 0 ) .AND. ( TAU .NE. ZERO ) ) THEN
*
*              --- work( 1:n ) := x = tau * A * v ---
*
          CALL DSYMV( UPLO, N, TAU, A, LDA, V, INCV, ZERO, WORK, 1 )
*
*                                                        T
*              --- work( 1:n ) := w = x - 1/2 * tau * ( x  * v ) * v ---
*
          ALPHA = -0.5D0 * TAU * DDOT( N, WORK, 1, V, INCV )
          CALL DAXPY( N, ALPHA, V, INCV, WORK, 1 )
*
*                                T        T
*              --- A := A - v * w  - w * v  ---
*
          CALL DSYR2( UPLO, N, -ONE, V, INCV, WORK, 1, A, LDA )
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DGBQR2( M, N, D, A, LDA, TAU, DRPTOL, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given an m-by-n matrix A with d subdiagonals, dgeqr2 computes
*   a QR factorization of A.
*
*   The matrix Q is represented as a product of elementary reflectors
*
*      Q  =  H( 1 ) * ... * H( k )   ,   where k = min( m, n ).
*
*   Each H( j ) has the form
*
*                                  T
*      H( j )  =  I  -  tau * v * v
*
*   where tau is a scalar, and v is a vector of length m with
*   v( 1:j-1 ) = 0   and   v( j ) = 1.
*   On exit, v( j+1:m ) is stored in a( j+1:m, j ) and tau in tau( j ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               M, N, D, LDA
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), TAU( * ), WORK( * )
*
*   m       (in) integer
*           The number of rows in the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns in the matrix A.
*           n >= 0.
*
*   d       (in) integer
*           The number of subdiagonals of the matrix A.
*           0 <= d <= m - 1, if m > 0.
*           d = 0          , if m = 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the m-by-n matrix A with lower bandwidth b.
*           On exit, the elements on and above the diagonal contain the
*           min( m, n )-by-n upper trapezoidal matrix R (R is upper
*           triangular if m >= n); the elements below the diagonal,
*           together with the array tau, represent the orthogonal
*           matrix Q as a product of Householder transformations.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( m, 1 ).
*
*   tau     (out) double precision array, dimension ( min( m-1, n ) )
*           The scaling factors of the Householder transformations.
*
*   drptol  (in) double precision
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to be zeroed is already less than
*           drptol then the transform is skipped.
*           drptol >= 0.0.
*
*   work    (workspace) double precision array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        INTEGER               J, LEN
        DOUBLE PRECISION      AJJ
*
*   len     length of the current transform
*   ajj     temporary buffer for the element a( j, j )
*
* Routines called:
*
        EXTERNAL              DLARFX, DLBRFG
*
*   dlarfx  apply Householder transformation (LAPACK)
*   dlbrfg  generate Householder vector (SBR)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        DO 100 J = 1, MIN( M-1, N )
*
          LEN = MIN( D+1, M-J+1 )
*
*            --- generate Householder reflector H( j ) to zero
*                A( j+1:j+d, j )                               ---
*
          CALL DLBRFG( LEN, A( J, J ), A( J+1, J ), 1,
     >                 TAU( J ), DRPTOL )
*
*            --- apply the transform ---
*
          IF ( TAU( J ) .NE. ZERO ) THEN
*
            AJJ = A( J, J )
            A( J, J ) = ONE
            CALL DLARFX( 'Left', LEN, N-J, A( J, J ), TAU( J ),
     >                  A( J, J+1 ), LDA, WORK )
            A( J, J ) = AJJ
*
          ENDIF
*
  100   CONTINUE
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DGEQRL( DECOMP, M, N, A, LDA, DRPTOL,
     >                     TAU, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Compute the QR or QL factorization of the m-by-n matrix A,
*   where m >= n.
*
*   The matrix Q is represented as a product of elementary reflectors
*
*      Q  =  H( 1 ) * ... * H( n )        (QR decomposition)
*
*   or
*
*      Q  =  H( n ) * ... * H( 1 )        (QL decomposition).
*
*   Each H( j ) has the form
*
*                                  T
*      H( j )  =  I  -  tau * v * v
*
*   where tau is a scalar, and v is a vector of length m.
*
*   In the QR case,
*     v( 1:j-1 ) = 0   and   v( j ) = 1   and, on exit, v( j+1:m ) is
*     stored in a( j+1:m, j ) and tau in tau( j ).
*
*   In the QL case,
*     v( m-n+j+1:m ) = 0   and   v( m-n+j ) = 1   and, on exit,
*     v( 1:m-n+j-1 ) is stored in a( 1:m-n+j-1, j ) and tau in tau( j ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           DECOMP
        INTEGER               M, N, LDA
        DOUBLE PRECISION      DRPTOL
        DOUBLE PRECISION      A( LDA, * ), TAU( * ), WORK( * )
*
*   decomp  (in) character*1
*           Which decomposition is required ?
*           decomp = 'L' : QL decomposition.
*                  = 'R' : QR decomposition.
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           0 <= n <= m.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the m-by-n matrix A.
*           If decomp = 'R' then, on exit, the elements on and above the
*           diagonal contain the n-by-n upper triangular matrix R; the
*           elements below the diagonal, together with the array tau,
*           represent the orthogonal matrix Q as a product of
*           Householder transformations.
*           If decomp = 'L' then, on exit, the n-by-n matrix L is stored
*           in the lower triangle at the "bottom" of A, and the
*           Householder vectors are stored in the remaining trapezoid.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( m, 1 ).
*
*   tau     (out) double precision array, dimension ( n )
*           The scaling factors of the Householder transformations.
*
*   drptol  (in) double precision
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to be zeroed is already less than
*           drptol then the transform is skipped.
*           drptol >= 0.0.
*
*   work    (workspace) double precision array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ONE
        PARAMETER             ( ONE = 1.0D0 )
*
        INTEGER               I, J
        DOUBLE PRECISION      TMP
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              DLARFX, DLBRFG
*
*   dlarfx  apply Householder transform (LAPACK)
*   dlbrfg  generate Householder vector (SBR)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        IF ( N .GT. 0 ) THEN
*
          IF ( LSAME( DECOMP, 'L' ) ) THEN
*
*              --- QL factorization ---
*
            DO 100 J = N, 1, -1
*
*                --- generate Householder vector to zero out
*                    A( 1:m-n+j, j)                          ---
*
              I = M - N + J
              CALL DLBRFG( I, A( I, J ), A( 1, J ), 1, TAU( J ),
     >                     DRPTOL )
*
*                --- apply transformation from the left ---
*
              TMP = A( I, J )
              A( I, J ) = ONE
              CALL DLARFX( 'Left', I, J-1, A( 1, J ), TAU( J ),
     >                     A, LDA, WORK )
              A( I, J ) = TMP
*
  100       CONTINUE
*
          ELSE
*
*              --- QR factorization ---
*
            DO 200 J = 1, N
*
*                --- generate Householder vector to zero out
*                    A( j+1:m, j )                           ---
*
              CALL DLBRFG( M-J+1, A( J, J ),
     >                     A( MIN( J+1, M ), J ), 1, TAU( J ),
     >                     DRPTOL )
*
*                --- apply transformation from the left ---
*
              TMP = A( J, J )
              A( J, J ) = ONE
              CALL DLARFX( 'Left', M-J+1, N-J, A( J, J ), TAU( J ),
     >                     A( J, J+1 ), LDA, WORK )
              A( J, J ) = TMP
*
  200       CONTINUE
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DGBWYG( M, N, D, A, LDA, TAU,
     >                     W, LDW, Y, LDY, K )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a set of Householder vectors as returned by dgbqr2, this
*   routine returns W and Y such that
*
*                       T
*      Q  =  I  +  W * Y
*
*   where Q is the product of the Householder matrices.
*
*   Each Householder transformation is represented by a vector vj and
*   a scalar tau( j ) such that
*                                         T  T          T
*      H( j )  =  I  -  tau( j ) * ( 1, vj  )  * ( 1, vj  )  .
*
*   The matrix Q is accumulated as
*                                                  T
*      Q( j + 1 )  =  I  +  W( j + 1 ) * Y( j + 1 )   =  Q( j ) * H( j )
*
*   where
*                                            T          T
*      Y( j + 1 )  =  [ Y( j ), y ]   with  y  = [ 0, vj  ]   and
*
*      W( j + 1 )  =  [ W( j ), w ]   with  w = - tau( j ) * Q( j ) * y.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               M, N, D, LDA, LDW, LDY, K
        DOUBLE PRECISION      A( LDA, * ), TAU( * ),
     >                        W( LDW, * ), Y( LDY, * )
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           n >= 0.
*
*   d       (in) integer
*           The number of subdiagonals of the matrix A (as the vectors
*           vj are stored in these subdiagonals, d is the length of
*           these transforms, minus 1).
*           0 <= d <= m - 1, if m > 0.
*           d = 0          , if m = 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the d subdiagonals of the m-by-n matrix A contain
*           the Householder vectors vj.
*           On exit, A is zero below the main diagonal.
*
*   lda     (in) integer
*           The leading dimension of the array A.
*           lda >= max( m, 1 ).
*
*   tau     (in/out) double precision array, dimension ( n )
*           On entry, tau contains the scaling factors for the
*           Householder transforms.
*           On exit, tau is destroyed.
*
*   w       (out) double precision array, dimension ( ldw, n )
*           On exit, the first k columns of w contain the block
*           reflector W (zero below the d-th subdiagonal).
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ).
*
*   y       (out) double precision array, dimension ( ldy, n )
*           On exit, the first k columns of y contain the block
*           reflector Y (zero above the main diagonal and below the d-th
*           subdiagonal).
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ).
*
*   k       (out) integer
*           On exit, k is the "active blocksize"
*           = the number of valid columns in W and Y
*           = the number of nontrivial Householder transforms contained
*             in W and Y
*           = the number of nonzero tau entries in the input.
*           0 <= k <= n.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        INTEGER               I, J, LEN
*
*   len     length of the vector v( j )
*
* Routines called:
*
        EXTERNAL              DGEMV, DSWAP
*
*   dgemv   matrix-vector product (BLAS)
*   dswap   swap two vectors (BLAS)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        K = 0
*
        DO 200 J = 1, MIN( M-1, N )
*
          IF ( TAU( J ) .NE. ZERO ) THEN
*
*              --- W and Y grow ---
*
            K = K + 1
            LEN = MIN( M-J, D )
*
*              --- copy vj to Y( :, k ) and zero A( j+1:j+d, j ) ---
*
            DO 110 I = 1, M
              Y( I, K ) = ZERO
  110       CONTINUE
            Y( J, K ) = ONE
            CALL DSWAP( LEN, A( J+1, J ), 1, Y( J+1, K ), 1 )
*
*                --- W( :, k ) = - tau( j ) * Y( :, k ) ---
*
            DO 120 I = 1, J-1
              W( I, K ) = ZERO
  120       CONTINUE
            DO 130 I = J, J+LEN
              W( I, K ) = -TAU( J ) * Y( I, K )
  130       CONTINUE
            DO 140 I = J+LEN+1, M
              W( I, K ) = ZERO
  140       CONTINUE
*
*              --- W( :, k ) = - tau( j ) * Q( j-1 ) * y( j )
*                                                    T
*                         = ( I + W( j-1 ) * Y( k-1 )  ) * W( :, k ) ---
*
            CALL DGEMV( 'Transpose', LEN+J, K-1,
     >                  ONE, Y, LDY, W( 1, K ), 1, ZERO, TAU, 1 )
            CALL DGEMV( 'NoTranspose', LEN+J, K-1,
     >                  ONE, W, LDW, TAU, 1, ONE, W( 1, K ), 1 )
*
          ENDIF
*
  200   CONTINUE
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DGEWYG( UPLO, M, N, A, LDA, TAU,
     >                     W, LDW, Y, LDY, K,
     >                     WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a set of Householder vectors as returned by dgeqrl, this
*   routine returns W and Y such that
*
*                       T
*      Q  =  I  +  W * Y
*
*   where Q is the product of the Householder matrices.
*
*   Each Householder transformation is represented by a vector vj and
*   a scalar tau( j ) such that
*                                         T  T          T
*      H( j )  =  I  -  tau( j ) * ( 1, vj  )  * ( 1, vj  )  .
*
*   The matrix Q is accumulated as
*                                                  T
*      Q( j + 1 )  =  I  +  W( j + 1 ) * Y( j + 1 )   =  Q( j ) * H( j )
*
*   where
*                                            T          T
*      Y( j + 1 )  =  [ Y( j ), y ]   with  y  = [ 0, vj  ]   and
*
*      W( j + 1 )  =  [ W( j ), w ]   with  w = - tau( j ) * Q( j ) * y.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               M, N, LDA, LDW, LDY, K
        DOUBLE PRECISION      A( LDA, * ), TAU( * ),
     >                        W( LDW, * ), Y( LDY, * ), WORK( * )
*
*   uplo    (in) character*1
*           Are the Housholder vectors stored in the upper or lower
*           triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   m       (in) integer
*           The row dimension of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The column dimension of A.
*           0 <= n <= m.
*
*   a       (in) double precision array, dimension ( lda, n )
*           The matrix containing the Householder vectors.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( m, 1 ).
*
*   tau     (in) double precision array, dimension ( n )
*           The scaling factors for the Householder transformations.
*
*   w       (out) double precision array, dimension ( ldw, n )
*           On exit, the first k columns of w contain the block
*           reflector W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ).
*
*   y       (out) double precision array, dimension ( ldy, n )
*           On exit, the first k columns of y contain the block
*           reflector Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ).
*
*   k       (out) integer
*           On exit, k is the "active blocksize"
*           = the number of valid columns in W and Y
*           = the number of nontrivial Householder transforms contained
*             in W and Y
*           = the number of nonzero tau entries in the input.
*           0 <= k <= n.
*
*   work    (workspace) double precision array, dimension ( n-1 )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
        INTEGER               J, I
        DOUBLE PRECISION      TMP
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              DCOPY, DGEMV
*
*   dcopy   BLAS
*   dgemv   BLAS
*
* ----------------------------------------------------------------------
*
        K = 0
*
        IF ( ( M .GT. 0 ) .AND. ( N .GT. 0 ) ) THEN
*
          IF ( LSAME( UPLO, 'Lower' ) ) THEN
*
*              --- vectors come from a QR decomposition ---
*
            DO 200 J = 1, N
*
              TMP = - TAU( J )
*
              IF ( TMP .NE. ZERO ) THEN
                K = K + 1
*
*                  --- Y( :, k ) := vj ---
*
                DO 110 I = 1, J-1
                  Y( I, K ) = ZERO
  110           CONTINUE
                Y( J, K ) = ONE
                CALL DCOPY( M-J, A( J+1, J ), 1, Y( J+1, K ), 1 )
*
*                  --- W( :, k ) := - tau( j ) * vj ---
*
                DO 120 I = 1, J-1
                  W( I, K ) = ZERO
  120           CONTINUE
                DO 130 I = J, M
                  W( I, K ) = TMP * Y( I, K )
  130           CONTINUE
*
*                     --- apply previous transformations ---
*
                IF ( K .GT. 1 ) THEN
                  CALL DGEMV( 'Transpose', M, K-1,
     >                        ONE, Y, LDY, W( 1, K ), 1, ZERO, WORK, 1 )
                  CALL DGEMV( 'NoTranspose', M, K-1,
     >                        ONE, W, LDW, WORK, 1, ONE, W( 1, K ), 1 )
                ENDIF
              ENDIF
*
  200       CONTINUE
*
          ELSE
*
*                --- vectors come from a QL decomposition ---
*
            DO 400 J = N, 1, -1
*
              TMP = - TAU( J )
*
              IF ( TMP .NE. ZERO ) THEN
                K = K + 1
*
*                    --- Y( :, k ) := vj ---
*
                DO 310 I = M-N+J+1, M
                  Y( I, K ) = ZERO
  310           CONTINUE
                Y( M-N+J, K ) = ONE
                CALL DCOPY( M-N+J-1, A( 1, J ), 1, Y( 1, K ), 1 )
*
*                    --- W( :, k ) := - tau( j ) * vj ---
*
                DO 320 I = M-N+J+1, M
                  W( I, K ) = ZERO
  320           CONTINUE
                DO 330 I = 1, M-N+J
                  W( I, K ) = TMP * Y( I, K )
  330           CONTINUE
*
*                     --- apply previous transformations ---
*
                IF ( K .GT. 1 ) THEN
                  CALL DGEMV( 'Transpose', M, K-1,
     >                        ONE, Y, LDY, W( 1, K ), 1, ZERO, WORK, 1 )
                  CALL DGEMV( 'NoTranspose', M, K-1,
     >                        ONE, W, LDW, WORK, 1, ONE, W( 1, K ), 1 )
                ENDIF
              ENDIF
*
  400       CONTINUE
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DGEWY( SIDE, M, N, K, A, LDA,
     >                    W, LDW, Y, LDY,
     >                    WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Apply a WY block transform to the matrix A (from the left or from
*   the right), i.e., update A as
*
*                        T  T
*      A  :=  ( I + W * Y  )  * A   , or
*
*                            T
*      A  :=  A * ( I + W * Y  )    , resp.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           SIDE
        INTEGER               M, N, K, LDA, LDW, LDY
        DOUBLE PRECISION      A( LDA, * ), W( LDW, * ), Y( LDY, * ),
     >                        WORK( * )
*
*   side    (in) character*1
*           Apply the transforms from the left or from the right ?
*           side = 'L' : From the left.
*                = 'R' : From the right.
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           n >= 0.
*
*   k       (in) integer
*           The number of columns of the matrices W and Y.
*           k >= 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the matrix A.
*                               T  T
*           On exit, ( I + W * Y  )  * A, if side = 'L', or
*                                   T
*                    A * ( I + W * Y  ),  if side = 'R'.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( m, 1 ).
*
*   w       (in) double precision array, dimension ( ldw, k )
*           The matrix W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ), if side = 'L'.
*               >= max( n, 1 ), if side = 'R'.
*           (W has row dimension m or n, resp.)
*
*   y       (in) double precision array, dimension ( ldy, k )
*           The matrix Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ), if side = 'L'.
*               >= max( n, 1 ), if side = 'R'.
*           (Y has row dimension m or n, resp.)
*
*   work    (workspace) double precision array,
*           dimension ( n*k ), if side = 'L'.
*                     ( m*k ), if side = 'R'.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              DGEMM
*
*   dgemm   matrix-matrix product (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( K .GT. 0 ) .AND. ( M .GT. 0 ) .AND. ( N .GT. 0 ) ) THEN
*
          IF ( LSAME( SIDE, 'L' ) ) THEN
*
*                            T
*                --- work = W  * A ---
*
            CALL DGEMM( 'Transpose', 'NoTranspose', K, N, M,
     >                  ONE, W, LDW, A, LDA, ZERO, WORK, K )
*
*                --- A = Y * work + A ---
*
            CALL DGEMM( 'NoTranspose', 'NoTranspose', M, N, K,
     >                  ONE, Y, LDY, WORK, K, ONE, A, LDA )
*
          ELSE
*
*                --- work = A * W ---
*
            CALL DGEMM( 'NoTranspose', 'NoTranspose', M, K, N,
     >                  ONE, A, LDA, W, LDW, ZERO, WORK, M )
*
*                                    T
*                --- A = A + work * Y  ---
*
            CALL DGEMM( 'NoTranspose', 'Transpose', M, N, K,
     >                  ONE, WORK, M, Y, LDY, ONE, A, LDA )
*
          ENDIF
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DQRUPD( M, N, B, A, LDA, DRPTOL,
     >                     NEEDA1, M1, A1, LDA1, N2, A2,
     >                     NB, Y, W, LDWY, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   dqrupd forms the QR factorization
*
*      A  =  Q * R
*
*   of the m-by-n block A and overwrites A by R.
*   In addition, the matrices W and Y in the block representation
*
*                     T
*      Q  =  I + W * Y
*
*   are built from the Householder transforms that were used in the
*   QR decomposition, a matrix A1 may be updated via
*
*      A1 := A1 * Q  ,
*
*   and another matrix A2 is updated via
*
*             T
*      A2 := Q  * A2  .
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
* Parameters:
*
        INTEGER               M, N, B, LDA, M1, LDA1, N2, NB, LDWY
        DOUBLE PRECISION      DRPTOL
        LOGICAL               NEEDA1
        DOUBLE PRECISION      A( LDA, * ), A1( LDA1, * ), A2( LDA, * ),
     >                        Y( * ), W( * ), WORK( * )
*
*   m       (in) integer
*           The number of rows in the block A, for which a QR
*           decomposition is sought.
*           m > 0.
*
*   n       (in) integer
*           The number of columns in that block.
*           n > 0.
*
*   b       (in) integer
*           The number of nonzero subdiagonals in the block (the
*           subdiagonals below the b-th are supposed to be zero and are
*           not accessed.)
*           b > 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, A is a m-by-n matrix with lower bandwidth <= b.
*           Because of the banded storage scheme used in the calling
*           routine, the zero elements below the b-th subdiagonal may
*           not be explicitly stored. Therefore, they are not accessed
*           in this routine.
*           On exit, the subdiagonals 1, ..., b of A are zeroed out, and
*           the upper triangle of A is overwritten with the matrix R of
*           the factorization A = Q * R.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= m.
*
*   drptol  (in) double precision
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transformation is skipped.
*           drptol >= 0.0.
*
*   needa1  (in) logical
*           Is A1 required or not ?
*           needa1 = .true.  : Update A1.
*                  = .false. : Do not update A1.
*
*   m1      (in) integer
*           The number of rows of the matrix A1 (the number of columns
*           must be m). Accessed only if A1 is required.
*           m1 >= 0.
*
*   a1      (in/out) double precision array, dimension ( lda1, m )
*           On entry, the m1-by-m matrix A1.
*           On exit, A1 may be overwritten with A1 * Q.
*
*   lda1    (in) integer
*           The leading dimension of the array a1. Accessed only if A1
*           is required.
*           lda1 >= max( m1, 1 ).
*
*   n2      (in) integer
*           The number of columns in the block A2.
*           0 <= n2 <= lda.
*
*   a2      (in/out) double precision array, dimension ( lda, n2 )
*           On entry, the m-by-n2 matrix A2.
*                                            T
*           On exit, A2 is overwritten with Q  * A2.
*
*   nb      (out) integer
*           The number of non-zero Householder vectors contributing to
*           Q.
*           0 <= nb <= min( m-1, n ).
*
*   y       (out) double precision array, dimension ( ldwy, n )           T
*           The m-by-nb matrix Y in the representation Q = I + W * Y .
*
*   w       (out) double precision array, dimension ( ldwy, n )           T
*           The m-by-nb matrix W in the representation Q = I + W * Y .
*
*   ldwy    (out) integer
*           The leading dimension of the arrays w and y.
*           ldwy = m.
*
*   work    (workspace) double precision array,
*           dimension ( max( m1, m )*n + n ),   if A1 is required.
*                     ( m*n + n )           ,   otherwise.
*
* ----------------------------------------------------------------------
*
* Local variables :
*
        INTEGER               ITAU, IWORK
*
*  itau     points to the portion of work that will hold the scaling
*           values tau for the blocked transforms (required size for
*           this buffer : n elements)
*  iwork    points to the portion of work that will be used as workspace
*           for the routines dgbqr2 (n elements) and dgewy
*           ( max( m1, m ) * nb elements).
*
* Routines called:
*
        EXTERNAL              DGBQR2, DGBWYG, DGEWY
*
*   dgbqr2  QR factorization of a banded matrix (SBR)
*   dgbwyg  generate WY factors (SBR)
*   dgewy   apply WY transform (SBR)
*
* ----------------------------------------------------------------------
*
*            --- set pointers to subdivide workspace ---
*
        ITAU = 1
        IWORK = ITAU + N
*
*            --- factorize A = Q * R ---
*
        CALL DGBQR2( M, N, B, A, LDA, WORK( ITAU ), DRPTOL,
     >               WORK( IWORK ) )
*
*            --- build W and Y factors ---
*
        LDWY = M
        CALL DGBWYG( M, N, B, A, LDA, WORK( ITAU ),
     >               W, LDWY, Y, LDWY, NB )
*
        IF ( NB .GT. 0 ) THEN
*
*              --- update A1 ---
*
          IF ( NEEDA1 ) THEN
            CALL DGEWY( 'Right', M1, M, NB, A1, LDA1,
     >                  W, LDWY, Y, LDWY, WORK( IWORK ) )
          ENDIF
*
*              --- premultiply A2 ---
*
          IF ( N2 .GT. 0 ) THEN
            CALL DGEWY( 'Left', M, N2, NB, A2, LDA,
     >                  W, LDWY, Y, LDWY, WORK( IWORK ) )
          ENDIF
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE DSYWY( UPLO, N, K, A, LDA, W, LDW, Y, LDY, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Apply a two-sided WY block transform to the symmetric matrix A,
*                                   T  T                  T
*   i.e., replace A with ( I + W * Y  )  * A * ( I + W * Y  ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, K, LDA, LDW, LDY
        DOUBLE PRECISION      A( LDA, * ), W( LDW, * ), Y( LDY, * ),
     >                        WORK( * )
*
*   uplo    (in) character*1
*           Is the upper or lower triangle of A stored ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the block to transform.
*           n >= 0.
*
*   k       (in) integer
*           The number of nontrivial Householder transforms in the
*           block WY transform.
*           k >= 0.
*
*   a       (in/out) double precision array, dimension ( lda, n )
*           On entry, the n-by-n symmetric matrix A.
*                                                T  T             T
*           On exit, A is overwritten with ( I+WY  )  * A * ( I+WY  ).
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   w       (in) double precision array, dimension ( ldw, k )
*           Contains the block reflector W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( n, 1 ).
*
*   y       (in) double precision array, dimension ( ldy, k )
*           Contains the block reflector Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( n, 1 ).
*
*   work    (workspace) double precision array, dimension ( (n+k)*k )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        DOUBLE PRECISION      ZERO, ONE
        PARAMETER             ( ZERO = 0.0D0, ONE = 1.0D0 )
*
* Routines called:
*
        EXTERNAL              DGEMM, DSYMM, DSYR2K
*
*   dgemm   matrix-matrix product (BLAS)
*   dsymm   symmetric matrix-matrix product (BLAS)
*   dsyr2k  symmetric rank-2 update (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( N .GT. 0 ) .AND. ( K .GT. 0 ) ) THEN
*
*              --- work( 1 .. n*k ) := X1 = A * W ---
*
          CALL DSYMM( 'Left', UPLO, N, K,
     >                ONE, A, LDA, W, LDW, ZERO, WORK, N )
*
*                                                           T
*              --- work( n*k+1 .. n*k+k*k ) := X2 = 1/2 * X1  * W ---
*
          CALL DGEMM( 'Transpose', 'NoTranspose', K, K, N,
     >                0.5D0, WORK, N, W, LDW, ZERO, WORK( N*K+1 ), K )
*
*              --- work( 1 .. n*k ) := X3 = X1 + Y * X2 ---
*
          CALL DGEMM( 'NoTranspose', 'NoTranspose', N, K, K,
     >                ONE, Y, LDY, WORK( N*K+1 ), K, ONE, WORK, N )
*
*                                 T        T
*              --- A := A + X3 * Y + Y * X3  ---
*
          CALL DSYR2K( UPLO, 'NoTranspose', N, K,
     >                 ONE, WORK, N, Y, LDY, ONE, A, LDA )
*
        ENDIF
*
        RETURN
        END
SHAR_EOF
fi # end of overwriting check
cd ..
cd ..
if test ! -d 'Sp'
then
	mkdir 'Sp'
fi
cd 'Sp'
if test ! -d 'Drivers'
then
	mkdir 'Drivers'
fi
cd 'Drivers'
if test -f 'data1'
then
	echo shar: will not over-write existing file "'data1'"
else
cat << "SHAR_EOF" > 'data1'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for testing the SBR toolbox               -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  Format of the commands:
C
C  'Comment'     : The remainder of this line is treated as a comment.
C  'FileName'    : The following line contains the name of the output file
C			 (up to 7 characters). For example, if you specify 'OUTHCK'
C			 and run the double-precision test driver 'drun', then the
C			 output is directed to the file 'DOUTCHK', whereas the
C			 output of the single-precision driver 'srun' would be
C			 directed to 'SOUTCHK'.
C  'MaxDim'      : The following line determines a maximum matrix size for
C			 the runs. All runs with larger matrices will be skipped.
C			 This feature can be used to limit the execution time of
C			 the timing/tuning runs without much file editing.
C  'NoChecks'    : Switch off all numerical checks, even if they are
C			 requested in the following runs. This feature can be used
C			 to reduce the execution time of the timing/tuning runs
C			 without much file editing.
C  'OutputLevel' : The value in the following line determines how much output
C			 is produced.
C			 1 : Generate only the overall summary.
C			 2 : Generate also condensed summaries for selected
C			     computational routines (this mode should be used to
C			     obtain tuning information).
C			 3 : Generate a more detailed summary for each test run.
C			 4 : Generate summaries for each routine called.
C  'Print'       : The following line (up to 78 characters) is printed to
C			 the output file.
C  'Quit'        : Quit the test driver, ignore the remainder of the input
C			 file.
C
C  For the above commands, only the first character is relevant (see the
C  current comment lines), case is ignored.
C  The following commands trigger tests for computational routines. These
C  commands must be specified with all 5 characters (case is ignored), and
C  each requires at least two additional lines (see below).
C
C  'SYTRD' (cf. lines   86ff): Test run for the one-step reduction
C					 full -> tridiagonal (LAPACK) and, optionally,
C					 for the backward accumulation of the
C					 transformations (ORGTR from LAPACK)
C  'SBTRD' (cf. lines  138ff): Test run for the one-step reduction
C					 banded -> tridiagonal (LAPACK)
C  'SYRDB' (cf. lines  182ff): Test run for the one-step reduction
C					 full -> banded (SBR) and, optionally, for the
C					 backward accumulation of the transformations
C					 (SYGTR from SBR)
C  'SBRDB' (cf. lines  387ff): Test run for the one-step reduction
C					 banded -> banded (SBR)
C  'SBRDT' (cf. lines  591ff): Test run for the one-step reduction
C					 banded -> tridiagonal (SBR)
C  'SY2BC' (cf. lines  773ff): Test run for the copy full -> banded (SBR)
C  'SY2BI' (cf. lines  897ff): Test run for the in-place repacking
C					 full -> banded (SBR)
C  'SB2BC' (cf. lines 1021ff): Test run for the copy banded -> banded (SBR)
C  'SB2BI' (cf. lines 1123ff): Test run for the in-place repacking
C					 banded -> banded (SBR)
C  'SYRDD' (cf. lines 1225ff): Test run for the multi-step reduction driver
C					 full -> banded/tridiagonal (SBR)
C  'SBRDD' (cf. lines 1463ff): Test run for the multi-step reduction driver
C					 banded -> banded/tridiagonal (SBR)
C			
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTCHK'
C  --- set output level ---
'OutputLevel'
 1
C ------------------------------------------------------------------------------
C
C  SYTRD : one-step reduction full -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : nb1 = blocking factor for the reduction (nb1=0 : use default)
C     7 : nx1 = cross-over point to non-blocked algorithm for the reduction
C               (nx1=0 : use default)
C     8 : lwork1 = length of the workspace for the reduction
C     9 : xinfo1 = expected info value for the routine sytrd
C                  (xinfo1 <> 0 may be used for checking error exits)
C    10 : jobu = accumulate the transformations in a matrix U with the
C                routine orgtr (jobu='U') or not (jobu='N') ?
C    11 : nb2 = blocking factor for the accumulation (nb2=0 : use default)
C    12 : nx2 = cross-over point to non-blocked algorithm for the accumulation
C               (nb2=0 : use default)
C    13 : lwork2 = length of workspace for the accumulation
C    14 : xinfo2 = expected info value for the routine orgtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'SYTRD'
   'Rand'   0.0 'Upper'   30   30   8   8   10000   0 'Upd'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'   30   30   8   8   10000   0 'Upd'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Upper'   30   30   8   8   10000   0 'NoU'   8   8   10000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'   30   30   8   8   10000   0 'NoU'   8   8   10000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'SBTRD'
   'Rand'   0.0 'Upper'   30    7    8 'Upd'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'   30    7    8 'Upd'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Upper'   30    7    8 'NoU'   50   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'   30    7    8 'NoU'   50   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDB : one-step reduction full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : lwork1 = length of the workspace for the reduction
C    10 : xinfo1 = expected info value for the routine syrdb
C                  (xinfo1 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : jobu = accumulate the transformations in a matrix U or not ?
C                jobu = 'O' : do the accumulation 'on the fly' in syrdb
C		          = 'U' : do the accumulation after the reduction with
C					sygtr
C		     jobu = 'N' : no accumulation
C     2 : ldu = leading dimension of the array u
C     3 : lwork2 = length of workspace for the accumulation with sygtr
C     4 : xinfo2 = expected info value for the routine sygtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the fourth line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U' or 'O'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U' or 'O'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- nonblocked reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'Onf'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    6    0.0   1   10000   1
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    6    0.0   1   10000   1
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'OnF'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    7    0.0   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   30   30    7    0.0   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- autopilot, non-exact dimensions ---
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'OnF'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'OnF'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'Upd'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'Upd'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   29   31    8    0.0   0   10000   8
   'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   29   31    8    0.0   0   10000   8
   'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
C --- small workspace forcing blocksize reduction ---
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    8    0.0   6     300   4
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30    8    0.0   0     300   4
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SYRDB'
   'ISDA' 1.0E3 'Upper'   30   30    8  1.0E4   6   10000   6
   'Upd'   30   10000   1
   'Check'   10.0  1.0E4   10.0
'SYRDB'
   'ISDA' 1.0E3 'Upper'   30   30    8  1.0E4   6   10000   6
   'NoU'   30   10000   1
   'Check'   10.0   10.0  1.0E4
C --- checks for quick return ---
'SYRDB'
   'Rand'   0.0 'Upper'    1   30    0    0.0   1     600   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Upper'   30   30   29    0.0   1     600   1
   'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits : ---
C --- uplo is neither 'U' nor 'L' ---
'SYRDB'
   'Rand'   0.0 'Error'   10   10    4    0.0   4   10000  -1
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- jobu is neither 'U' nor 'N' ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4   10000  -2
   'Err'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SYRDB'
   'Rand'   0.0 'Lower'  -10   10    4    0.0   4   10000  -3
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SYRDB'
   'Rand'   0.0 'Lower'    1   10    4    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    0    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'   10   10   10    0.0   4   10000  -4
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10    8    4    0.0   4   10000  -6
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4   -1.0   4   10000  -7
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4   10000  -9
   'Upd'    7   10000   1
   'Check'   10.0   10.0   10.0
C --- nb negative ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0  -4   10000 -10
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- lwork is too small ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4      21 -13
   'NoU'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- this should be just enough ---
'SYRDB'
   'Rand'   0.0 'Lower'   10   10    4    0.0   4      22   1
   'NoU'   10   10000   1
   'Check'     10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDB : one-step reduction banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    10 : ldu = leading dimension of the array u
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine sbrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- nonblocked reduction ---
'SBRDB'
   'Rand'   0.0   30    8   13    4    0.0   1 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    8   13    4    0.0   1 'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction ---
'SBRDB'
   'Rand'   0.0   31    8   15    4    0.0   3 'Upd'   31   10000   3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   31    8   15    4    0.0   3 'NoU'   31   10000   3
   'Check'   10.0   10.0   10.0
C --- autopilot, nonexact dimensions ---
'SBRDB'
   'Rand'   0.0   29    8   23    4    0.0   0 'Upd'   32   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   29    8   23    4    0.0   0 'NoU'   32   10000   4
   'Check'   10.0   10.0   10.0
C --- force blocksize reduction by insufficient workspace ---
'SBRDB'
   'Rand'   0.0   30    8   20    5    0.0   5 'Upd'   30     200   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    8   20    5    0.0   5 'NoU'   30     100   3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   29   59    5    0.0   0 'Upd'   30     400   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   29   59    5    0.0   0 'NoU'   30     300   3
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SBRDB'
   'ISDA' 1.0E3   30   12   24    8  1.0E4   8 'Upd'   30   10000   8
   'Check'   10.0  1.0E4   10.0
'SBRDB'
   'ISDA' 1.0E3   30   12   24    8  1.0E4   8 'NoU'   30   10000   8
   'Check'   10.0   10.0  1.0E4
C --- now the workspace should fit exactly ---
'SBRDB'
   'Rand'   0.0   30   10   20    6    0.0   6 'Upd'   30     306   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30   10   20    6    0.0   6 'NoU'   30     216   6
   'Check'   10.0   10.0   10.0
C --- force buffering by providing very tight lda ---
'SBRDB'
   'Rand'   0.0   30    9   16    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   16    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   15    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   15    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   14    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   14    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   13    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   13    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   12    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   12    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   11    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   11    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   10    5    0.0   4 'Upd'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   30    9   10    5    0.0   4 'NoU'   30   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   20    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   20    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   13    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   12   13    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   19   20    5    0.0   4 'Upd'   20   10000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   20   19   20    5    0.0   4 'NoU'   20   10000   4
   'Check'   10.0   10.0   10.0
C --- checks for quick return ---
'SBRDB'
   'Rand'   0.0   10    6   10    6    0.0   1 'Upd'   10   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits : ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Err'   10   10000  -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDB'
   'Rand'   0.0  -10    6   10    3    0.0   1 'Upd'   10   10000  -2
   'Check'   10.0   10.0   10.0
C --- b1 is out of range ---
'SBRDB'
   'Rand'   0.0   10   -6   10    3    0.0   1 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10   10   10    3    0.0   1 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SBRDB'
   'Rand'   0.0   10    6   10   -3    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    0    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    7    0.0   1 'Upd'   10   10000  -4
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDB'
   'Rand'   0.0   10    6    6    3    0.0   1 'Upd'   10   10000  -6
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SBRDB'
   'Rand'   0.0   10    6   10    3   -1.0   1 'Upd'   10   10000  -7
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'    8   10000  -9
   'Check'   10.0   10.0   10.0
C --- nb is negative ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0  -1 'Upd'   10   10000 -10
   'Check'   10.0   10.0   10.0
C --- lwork is too small ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'   10      22 -12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'NoU'   10      20 -12
   'Check'   10.0   10.0   10.0
C --- for these, workspace should be just sufficient ---
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'Upd'   10      23   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0   10    6   10    3    0.0   1 'NoU'   10      21   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- non-blocked reduction/update ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   1 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   1 'NoU'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- blocked reduction/update ---
'SBRDT'
   'Rand'   0.0   31    8   16    0.0   8 'Upd'   31   10000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   31    8   16    0.0   8 'NoU'   31   10000   1
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SBRDT'
   'Rand'   0.0   29    4    5    0.0   0 'Upd'   32   10000   3
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    4    5    0.0   0 'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    8   18    0.0   0 'Upd'   32   10000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   29    8   18    0.0   0 'NoU'   32   10000   1
   'Check'   10.0   10.0   10.0
C --- ISDA-type matrix ---
'SBRDT'
   'ISDA' 1.0E3   30    8   16  1.0E4   8 'Upd'   30   10000   8
   'Check'   10.0  1.0E4   10.0
'SBRDT'
   'ISDA' 1.0E3   30    8   16  1.0E4   8 'NoU'   30   10000   1
   'Check'   10.0   10.0  1.0E4
C --- force repacking by providing rather tight lda ---
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'Upd'   30     517   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'NoU'   30      17   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'Upd'   30     522   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'NoU'   30      23   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   13    0.0   6 'Upd'   30     531   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   13    0.0   6 'NoU'   30      31   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   12    0.0   6 'Upd'   30     544   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   12    0.0   6 'NoU'   30      44   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   11    0.0   6 'Upd'   30     561   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   11    0.0   6 'NoU'   30      61   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   10    0.0   6 'Upd'   30     582   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   10    0.0   6 'NoU'   30      82   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'Upd'   30     607   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'NoU'   30     107   1
   'Check'   10.0   10.0   10.0
C --- force blocksize reduction by providing too small workspace ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'Upd'   30     350   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30   13   26    0.0   0 'Upd'   30     370   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   14    0.0   6 'Upd'   30     250   3
   'Check'   10.0   10.0   10.0
C --- checks for quick return ---
'SBRDT'
   'Rand'   0.0    0    0    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    0    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    1    2    0.0   6 'Upd'   30   10000   1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0   6 'Err'   10   10000  -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDT'
   'Rand'   0.0  -10    6   12    0.0   6 'Upd'   10   10000  -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SBRDT'
   'Rand'   0.0   10   -6   12    0.0   6 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   10   10   12    0.0   6 'Upd'   10   10000  -3
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDT'
   'Rand'   0.0   10    6    6    0.0   6 'Upd'   10   10000  -5
   'Check'   10.0   10.0   10.0
C --- drptol is negative ---
'SBRDT'
   'Rand'   0.0   10    6   12   -1.0   6 'Upd'   10   10000  -6
   'Check'   10.0   10.0   10.0
C --- ldu is too small ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0   6 'Upd'    8   10000 -10
   'Check'   10.0   10.0   10.0
C --- nb is negative ---
'SBRDT'
   'Rand'   0.0   10    6   12    0.0  -6 'Upd'   10   10000 -11
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'Upd'   50      37 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   16    0.0   6 'NoU'   50      15 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'Upd'   50      38 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8   15    0.0   6 'NoU'   50      16 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'Upd'   50     128 -13
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0   30    8    9    0.0   6 'NoU'   50     106 -13
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SY2BC : copy full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the array a in full storage
C     7 : lda2 = leading dimension of the array holding A in packed storage
C     8 : xinfo = expected info value for the routine sy2bc
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack to a tightly fitting band ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with leading dimension larger by 1 ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
C --- and now the same tests again, with inexact lda ---
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Upper'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SY2BC'
   'Rand'   0.0 'Lower'    0    8   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SY2BC'
   'Rand'   0.0 'Error'   25    8   30    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SY2BC'
   'Rand'   0.0 'Lower'  -25    8   30    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SY2BC'
   'Rand'   0.0 'Lower'   25   -8   30    9   -3
   'Check'   10.0   10.0   10.0
'SY2BC'
   'Rand'   0.0 'Lower'   25   25   30    9   -3
   'Check'   10.0   10.0   10.0
C --- ldfull is too small ---
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   23    9   -5
   'Check'   10.0   10.0   10.0
C --- ldband is too small ---
'SY2BC'
   'Rand'   0.0 'Lower'   25    8   30    8   -7
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SY2BI : in-place copy full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the array a in full storage
C     7 : lda2 = leading dimension of the array holding A in packed storage
C     8 : xinfo = expected info value for the routine sy2bi
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack to a tightly fitting band ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   25    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with leading dimension larger by 1 ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   26    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   25   33    1
   'Check'   10.0   10.0   10.0
C --- and now the same tests again, with inexact lda ---
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30    9    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   12    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   30    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   31    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Upper'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30   35    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SY2BI'
   'Rand'   0.0 'Lower'    0    8   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SY2BI'
   'Rand'   0.0 'Error'   25    8   30    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SY2BI'
   'Rand'   0.0 'Lower'  -25    8   30    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SY2BI'
   'Rand'   0.0 'Lower'   25   -8   30    9   -3
   'Check'   10.0   10.0   10.0
'SY2BI'
   'Rand'   0.0 'Lower'   25   25   30    9   -3
   'Check'   10.0   10.0   10.0
C --- ldfull is too small ---
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   23    9   -5
   'Check'   10.0   10.0   10.0
C --- ldband is too small ---
'SY2BI'
   'Rand'   0.0 'Lower'   25    8   30    8   -6
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SB2BC : copy banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the source array a
C     7 : lda2 = leading dimension of the destination array
C     8 : xinfo = expected info value for the routine sb2bc
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack a tightly fitting band ---
C --- repack to a tightly fitting band ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
C --- and now repack a band with diagonals to spare ---
C --- repack to tight fit ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SB2BC'
   'Rand'   0.0 'Upper'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SB2BC'
   'Rand'   0.0 'Lower'    0    0   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SB2BC'
   'Rand'   0.0 'Error'   25    8   12    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SB2BC'
   'Rand'   0.0 'Lower'  -25    8   12    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SB2BC'
   'Rand'   0.0 'Lower'   25   -8   12    9   -3
   'Check'   10.0   10.0   10.0
'SB2BC'
   'Rand'   0.0 'Lower'   25   25   25    9   -3
   'Check'   10.0   10.0   10.0
C --- ldsrc is too small ---
'SB2BC'
   'Rand'   0.0 'Lower'   25    8    6    9   -5
   'Check'   10.0   10.0   10.0
C --- lddst is too small ---
'SB2BC'
   'Rand'   0.0 'Lower'   25    8   11    7   -7
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SB2BI : in-place copy banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda1 = leading dimension of the source array a
C     7 : lda2 = leading dimension of the destination array
C     8 : xinfo = expected info value for the routine sb2bi
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- repack a tightly fitting band ---
C --- repack to a tightly fitting band ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    9    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    9   12    1
   'Check'   10.0   10.0   10.0
C --- and now repack a band with diagonals to spare ---
C --- repack to tight fit ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15    9    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with spare diagonals ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   12    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with the same leading dimension ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   15    1
   'Check'   10.0   10.0   10.0
C --- repack to a band with larger leading dimension ---
'SB2BI'
   'Rand'   0.0 'Upper'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   15   25    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SB2BI'
   'Rand'   0.0 'Lower'    0    0   30    9    1
   'Check'   10.0   10.0   10.0
C --- checks for error exits ---
C --- uplo is neither 'U' nor 'L' ---
'SB2BI'
   'Rand'   0.0 'Error'   25    8   12    9   -1
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SB2BI'
   'Rand'   0.0 'Lower'  -25    8   12    9   -2
   'Check'   10.0   10.0   10.0
C --- b is out of range ---
'SB2BI'
   'Rand'   0.0 'Lower'   25   -8   12    9   -3
   'Check'   10.0   10.0   10.0
'SB2BI'
   'Rand'   0.0 'Lower'   25   25   25    9   -3
   'Check'   10.0   10.0   10.0
C --- ldsrc is too small ---
'SB2BI'
   'Rand'   0.0 'Lower'   25    8    6    9   -5
   'Check'   10.0   10.0   10.0
C --- lddst is too small ---
'SB2BI'
   'Rand'   0.0 'Lower'   25    8   11    7   -6
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- one-step reduction ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8    9    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8    9    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8    9    1    0.0 'Upd'   10000    1
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8    9    1    0.0 'NoU'   10000    1
       5
   'Check'   10.0   10.0   10.0
C --- two-step reduction ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1   16    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1   16    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1   16    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1   16    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8   14    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    8   14    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8   14    2    0.0 'Upd'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    8   14    2    0.0 'NoU'   10000    1
      12
       5     4
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    1    2    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    1    2    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    5    6    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'   30   30    5    6    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    5    6    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   30   30    5    6    0    0.0 'NoU'   10000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  300  300    1   64    0    0.0 'Upd'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  300  300    1   64    0    0.0 'NoU'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'  300  300    1   64    0    0.0 'Upd'   20000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'  300  300    1   64    0    0.0 'NoU'   20000    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SYRDD'
   'Rand'   0.0 'Lower'    0    4    1    2    0    0.0 'Upd'   10000    1
   'Check'   10.0   10.0   10.0
C --- check for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Err'   10000   -1
       5
   'Check'   10.0   10.0   10.0
C --- uplo is neither 'U' nor 'L' ---
'SYRDD'
   'Rand'   0.0 'Error'   10   10    4    8    1    0.0 'Upd'   10000   -2
       5
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SYRDD'
   'Rand'   0.0 'Lower'  -10   10    4    8    1    0.0 'Upd'   10000   -3
       5
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10   -1    8    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    0    8    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10   10   20    1    0.0 'Upd'   10000   -4
       5
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SYRDD'
   'Rand'   0.0 'Lower'   10    8    4    8    1    0.0 'Upd'   10000   -6
       5
   'Check'   10.0   10.0   10.0
C --- drptol is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1   -1.0 'Upd'   10000   -7
       5
   'Check'   10.0   10.0   10.0
C --- ldband is out of range ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    4    1    0.0 'Upd'   10000   -9
       5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    6    2    0.0 'Upd'   10000   -9
       6
       5    3
   'Check'   10.0   10.0   10.0
C --- nsteps is negative ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8   -1    0.0 'Upd'   10000  -12
   'Check'   10.0   10.0   10.0
C --- sequence of bandwidths is non-decreasing ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    1   20    3    0.0 'Upd'   10000  -13
      10    3
       5    5    5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    3    8    3    0.0 'Upd'   10000  -13
       6    2
       5    5    5
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    1    8    3    0.0 'Upd'   10000  -13
       4    5
       5    5    5
   'Check'   10.0   10.0   10.0
C --- sequence of blocking factors contains negative entries ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Upd'   10000  -14
      -5
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SYRDD'
   'Rand'   0.0 'Lower'   10   10    4    8    1    0.0 'Upd'      38  -16
       5
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C --- one-step reduction ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30    4    8    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30    4    8    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30    4    8    1    1    0.0 'Upd'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30    4    8    1    1    0.0 'NoU'   30   10000    1
       5
   'Check'   10.0   10.0   10.0
C --- two-step reduction ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    3    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    3    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    3    2    0.0 'Upd'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    3    2    0.0 'NoU'   30   10000    1
      12
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'Upd'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   30    1    2    0.0 'NoU'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'NoU'   30   10000    1
       3
       5    3
   'Check'   10.0   10.0   10.0
C --- doubling sequence ---
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   16    1    4    0.0 'Upd'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   15   16    1    4    0.0 'NoU'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   16    1    4    0.0 'Upd'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   16    1    4    0.0 'NoU'   30   10000    1
      14   12    8
       0    0    0    0
   'Check'   10.0   10.0   10.0
C --- autopilot ---
'SBRDD'
   'Rand'   0.0 'Upper'   80   70   80    1    0    0.0 'Upd'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   80   70   80    1    0    0.0 'NoU'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   80   70   80    1    0    0.0 'Upd'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   80   70   80    1    0    0.0 'NoU'   80   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   12   30    1    0    0.0 'Upd'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Upper'   30   12   30    1    0    0.0 'NoU'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   12   30    1    0    0.0 'Upd'   30   10000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   12   30    1    0    0.0 'NoU'   30   10000    1
   'Check'   10.0   10.0   10.0
C --- check for quick return ---
'SBRDD'
   'Rand'   0.0 'Lower'    0    4    8    1    0    0.0 'Upd'   10   10000    1
   'Check'   10.0   10.0   10.0
C --- check for error exits ---
C --- jobu is neither 'U' nor 'N' ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Err'   10   10000   -1
       5
   'Check'   10.0   10.0   10.0
C --- uplo is neither 'U' nor 'L' ---
'SBRDD'
   'Rand'   0.0 'Error'   10    4    8    1    1    0.0 'Upd'   10   10000   -2
       5
   'Check'   10.0   10.0   10.0
C --- n is negative ---
'SBRDD'
   'Rand'   0.0 'Lower'  -10    4    8    1    1    0.0 'Upd'   10   10000   -3
       5
   'Check'   10.0   10.0   10.0
C --- b1 is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10   -4    8    1    1    0.0 'Upd'   10   10000   -4
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10   10   18    1    1    0.0 'Upd'   10   10000   -4
       5
   'Check'   10.0   10.0   10.0
C --- b2 is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    0    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'    0    0    8    1    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    5    1    0.0 'Upd'   10   10000   -5
       5
   'Check'   10.0   10.0   10.0
C --- lda is too small ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    4    1    1    0.0 'Upd'   10   10000   -7
       5
   'Check'   10.0   10.0   10.0
C --- drptol is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1   -1.0 'Upd'   10   10000   -8
       5
   'Check'   10.0   10.0   10.0
C --- ldu is out of range ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Upd'    8   10000  -12
       5
   'Check'   10.0   10.0   10.0
C --- nsteps is negative ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1   -1    0.0 'Upd'   10   10000  -13
   'Check'   10.0   10.0   10.0
C --- sequence of bandwidths is non-decreasing ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       5    3    2
       5    5    5    5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       3    5    2
       5    5    5    5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    4    0.0 'Upd'   10   10000  -14
       3    2    5
       5    5    5    5
   'Check'   10.0   10.0   10.0
C --- negative blocking factors ---
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    3    0.0 'Upd'   10   10000  -15
       3    2
       5   -5    5
   'Check'   10.0   10.0   10.0
C --- workspace is too small ---
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    1    0.0 'Upd'   30      42  -17
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   10    4    8    1    1    0.0 'Upd'   10       8  -17
       5
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'   30   15   30    1    2    0.0 'Upd'   30      55  -17
       8
       5    5
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data2'
then
	echo shar: will not over-write existing file "'data2'"
else
cat << "SHAR_EOF" > 'data2'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for timing the SBR toolbox               -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C800
C  --- if you are in a real hurry, uncomment the following two lines ---
'MaxDim'
400
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTIM'
C  --- set output level ---
'OutputLevel'
 3
C  -----------------------------------------------------------------------------
C
C  SYTRD : one-step reduction full -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : nb1 = blocking factor for the reduction (nb1=0 : use default)
C     7 : nx1 = cross-over point to non-blocked algorithm for the reduction
C               (nx1=0 : use default)
C     8 : lwork1 = length of the workspace for the reduction
C     9 : xinfo1 = expected info value for the routine sytrd
C                  (xinfo1 <> 0 may be used for checking error exits)
C    10 : jobu = accumulate the transformations in a matrix U with the
C                routine orgtr (jobu='U') or not (jobu='N') ?
C    11 : nb2 = blocking factor for the accumulation (nb2=0 : use default)
C    12 : nx2 = cross-over point to non-blocked algorithm for the accumulation
C               (nb2=0 : use default)
C    13 : lwork2 = length of workspace for the accumulation
C    14 : xinfo2 = expected info value for the routine orgtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Timing the LAPACK reduction full -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SYTRD'
   'Rand'   0.0 'Lower'  200  200   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  400  400   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  600  600   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  800  800   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower' 1000 1000   0   0 1000000   0 'NoU'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SYTRD'
   'Rand'   0.0 'Lower'  200  200   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  400  400   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  600  600   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower'  800  800   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
'SYTRD'
   'Rand'   0.0 'Lower' 1000 1000   0   0 1000000   0 'Upd'   0   0 1000000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR driver full -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SYRDD'
   'Rand'   0.0 'Upper'  200  200    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  400  400    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  600  600    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  800  800    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper' 1000 1000    1    2    0    0.0 'NoU' 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SYRDD'
   'Rand'   0.0 'Upper'  200  200    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  400  400    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  600  600    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper'  800  800    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
'SYRDD'
   'Rand'   0.0 'Upper' 1000 1000    1    2    0    0.0 'Upd' 1000000    1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the LAPACK reduction banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  800    4    5 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800    8    9 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   12   13 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   16   17 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   24   25 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   32   33 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   48   49 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   64   65 'NoU'  800   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower' 1000    4    5 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000    8    9 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   12   13 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   16   17 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   24   25 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   32   33 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   48   49 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   64   65 'NoU' 1000   0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower'  800    4    5 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800    8    9 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   12   13 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   16   17 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   24   25 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   32   33 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   48   49 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower'  800   64   65 'Upd'  800   0
   'Check'   10.0   10.0   10.0
'Print'
''
'SBTRD'
   'Rand'   0.0 'Lower' 1000    4    5 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000    8    9 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   12   13 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   16   17 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   24   25 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   32   33 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   48   49 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
'SBTRD'
   'Rand'   0.0 'Lower' 1000   64   65 'Upd' 1000   0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR reduction banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  800    4    8    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800    8   16    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   12   24    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   16   32    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   24   48    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   32   64    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   48   96    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   64  128    0.0   0 'NoU'  800 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0 1000    4    8    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000    8   16    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   12   24    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   16   32    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   24   48    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   32   64    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   48   96    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   64  128    0.0   0 'NoU' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
'      *** ignore messages about tests failing because ***'
'Print'
'      *** SBRDT returned a wrong (but positive) info  ***'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  800    4    8    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800    8   16    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   12   24    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   16   32    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   24   48    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   32   64    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   48   96    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  800   64  128    0.0   0 'Upd'  800 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0 1000    4    8    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000    8   16    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   12   24    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   16   32    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   24   48    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   32   64    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   48   96    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0 1000   64  128    0.0   0 'Upd' 1000 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Timing the SBR driver banded -> tridiagonal ***'
'Print'
''
'Print'
'   no update'
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  200    4    8    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200    8   16    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   12   24    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   16   32    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   24   48    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   48   96    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  400    4    8    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400    8   16    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   12   24    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   16   32    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   24   48    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   48   96    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  600    4    8    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600    8   16    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   12   24    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   16   32    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   24   48    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   48   96    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  800    4    8    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800    8   16    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   12   24    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   16   32    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   24   48    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   32   64    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   48   96    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   64  128    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower' 1000    4    8    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000    8   16    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   12   24    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   16   32    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   24   48    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   32   64    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   48   96    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   64  128    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'   with update'
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  200    4    8    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200    8   16    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   12   24    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   16   32    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   24   48    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   48   96    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    0    0.0 'NoU'  200 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  400    4    8    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400    8   16    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   12   24    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   16   32    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   24   48    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   48   96    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    0    0.0 'NoU'  400 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  600    4    8    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600    8   16    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   12   24    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   16   32    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   24   48    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   48   96    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    0    0.0 'NoU'  600 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower'  800    4    8    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800    8   16    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   12   24    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   16   32    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   24   48    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   32   64    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   48   96    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower'  800   64  128    1    0    0.0 'NoU'  800 1000000    1
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDD'
   'Rand'   0.0 'Lower' 1000    4    8    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000    8   16    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   12   24    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   16   32    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   24   48    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   32   64    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   48   96    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
'SBRDD'
   'Rand'   0.0 'Lower' 1000   64  128    1    0    0.0 'NoU' 1000 1000000    1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data3'
then
	echo shar: will not over-write existing file "'data3'"
else
cat << "SHAR_EOF" > 'data3'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for tuning the SBR toolbox                -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C400
C  --- if you are in a real hurry, uncomment the following two lines ---
'MaxDim'
200
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTUN1'
C  --- set output level ---
'OutputLevel'
 2
C ------------------------------------------------------------------------------
C
C  SYRDB : one-step reduction full -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : lwork1 = length of the workspace for the reduction
C    10 : xinfo1 = expected info value for the routine syrdb
C                  (xinfo1 <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : jobu = accumulate the transformations in a matrix U or not ?
C                jobu = 'O' : do the accumulation 'on the fly' in syrdb
C		          = 'U' : do the accumulation after the reduction with
C					sygtr
C		     jobu = 'N' : no accumulation
C     2 : ldu = leading dimension of the array u
C     3 : lwork2 = length of workspace for the accumulation with sygtr
C     4 : xinfo2 = expected info value for the routine sygtr
C                  (xinfo2 <> 0 may be used for checking error exits)
C
C  Parameters in the fourth line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U' or 'O'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U' or 'O'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Setting nb for SYRDB ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   1 1000000   1
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   4 1000000   4
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   6 1000000   6
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   8 1000000   8
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  12 1000000  12
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  16 1000000  16
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  20 1000000  20
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  24 1000000  24
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  32 1000000  32
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  40 1000000  40
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  48 1000000  48
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  64 1000000  64
   'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   1 1000000   1
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   4 1000000   4
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   6 1000000   6
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   8 1000000   8
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  12 1000000  12
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  16 1000000  16
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  20 1000000  20
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  24 1000000  24
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  32 1000000  32
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  40 1000000  40
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  48 1000000  48
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  64 1000000  64
   'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   1 1000000   1
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   4 1000000   4
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   6 1000000   6
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   8 1000000   8
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  12 1000000  12
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  16 1000000  16
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  20 1000000  20
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  24 1000000  24
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  32 1000000  32
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  40 1000000  40
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  48 1000000  48
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  64 1000000  64
   'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   1 1000000   1
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   4 1000000   4
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   6 1000000   6
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0   8 1000000   8
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  12 1000000  12
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  16 1000000  16
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  20 1000000  20
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  24 1000000  24
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  32 1000000  32
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  40 1000000  40
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  48 1000000  48
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  200  200   64    0.0  64 1000000  64
   'OnF'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   1 1000000   1
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   4 1000000   4
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   6 1000000   6
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0   8 1000000   8
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  12 1000000  12
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  16 1000000  16
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  20 1000000  20
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  24 1000000  24
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  32 1000000  32
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  40 1000000  40
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  48 1000000  48
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  400  400   64    0.0  64 1000000  64
   'OnF'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   1 1000000   1
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   4 1000000   4
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   6 1000000   6
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0   8 1000000   8
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  12 1000000  12
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  16 1000000  16
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  20 1000000  20
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  24 1000000  24
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  32 1000000  32
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  40 1000000  40
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  48 1000000  48
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SYRDB'
   'Rand'   0.0 'Lower'  600  600   64    0.0  64 1000000  64
   'OnF'  600 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDB : one-step reduction banded -> banded (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     8 : nb = blocking factor for the reduction (nb=0 : use default)
C     9 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    10 : ldu = leading dimension of the array u
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine sbrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting nb for SBRDB ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  10 'NoU'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  12 'NoU'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  16 'NoU'  200 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   1 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   4 'NoU'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   6 'NoU'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   8 'NoU'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  10 'NoU'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  12 'NoU'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  16 'NoU'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  20 'NoU'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  24 'NoU'  200 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  32 'NoU'  200 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  10 'NoU'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  12 'NoU'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  16 'NoU'  400 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   1 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   4 'NoU'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   6 'NoU'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   8 'NoU'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  10 'NoU'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  12 'NoU'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  16 'NoU'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  20 'NoU'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  24 'NoU'  400 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  32 'NoU'  400 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  10 'NoU'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  12 'NoU'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  16 'NoU'  600 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   1 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   4 'NoU'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   6 'NoU'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   8 'NoU'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  10 'NoU'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  12 'NoU'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  16 'NoU'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  20 'NoU'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  24 'NoU'  600 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  32 'NoU'  600 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   16   32    8    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   32   64   16    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  24 'Upd'  200 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  200   64  128   32    0.0  32 'Upd'  200 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   16   32    8    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   32   64   16    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  24 'Upd'  400 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  400   64  128   32    0.0  32 'Upd'  400 1000000  32
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   16   32    8    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   32   64   16    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  24 'Upd'  600 1000000  24
   'Check'   10.0   10.0   10.0
'SBRDB'
   'Rand'   0.0  600   64  128   32    0.0  32 'Upd'  600 1000000  32
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting nb for SBRDT ***'
'Print'
''
'Print'
'    with update'
'Print'
''
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0  24 'Upd'  200 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   1 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   4 'Upd'  200 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   6 'Upd'  200 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   8 'Upd'  200 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  10 'Upd'  200 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  12 'Upd'  200 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  16 'Upd'  200 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  20 'Upd'  200 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  32 'Upd'  200 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0  40 'Upd'  200 1000000  40
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0  24 'Upd'  400 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   1 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   4 'Upd'  400 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   6 'Upd'  400 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   8 'Upd'  400 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  10 'Upd'  400 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  12 'Upd'  400 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  16 'Upd'  400 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  20 'Upd'  400 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  32 'Upd'  400 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0  40 'Upd'  400 1000000  40
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0  24 'Upd'  600 1000000  24
   'Check'   10.0   10.0   10.0
'Print'
''
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   1 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   4 'Upd'  600 1000000   4
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   6 'Upd'  600 1000000   6
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   8 'Upd'  600 1000000   8
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  10 'Upd'  600 1000000  10
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  12 'Upd'  600 1000000  12
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  16 'Upd'  600 1000000  16
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  20 'Upd'  600 1000000  20
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  32 'Upd'  600 1000000  32
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0  40 'Upd'  600 1000000  40
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'data4'
then
	echo shar: will not over-write existing file "'data4'"
else
cat << "SHAR_EOF" > 'data4'
C  -----------------------------------------------------------------------------
C  -                                                                           -
C  -              Default input file for tuning the SBR toolbox                -
C  -                                                                           -
C  -----------------------------------------------------------------------------
C
C  Author: Bruno Lang
C          Aachen University of Technology
C          na.blang@na-net.ornl.gov
C  Date: May 17, 2000
C  Version: SBR Toolbox, Rev. 1.4.1
C
C  -----------------------------------------------------------------------------
C
C  For the format of the commands, see the file INCHK
C
C  --- if you are in a hurry, uncomment the following two lines ---
C'MaxDim'
C400
C  --- if you are in a real hurry, uncomment the following two lines ---
'MaxDim'
200
C  --- if you want result checking, comment out the following line ---
'NoChecks'
C  -----------------------------------------------------------------------------
C
C  --- name of the output file ---
C'FileName'
C'OUTTUN2'
C  --- set output level ---
'OutputLevel'
 2
C ------------------------------------------------------------------------------
C
C  SYRDD : driver routine for the reduction full -> banded/tridiagonal
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : lda1 = leading dimension of the array a
C     6 : b2 = (semi-)bandwidth of the reduced matrix B
C     7 : lda2 = leading dimension of the array holding the banded matrix
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : lwork = length of workspace for the reduction and accumulation
C    12 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
'*** Setting intermediate bandwidth for SYRDD ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1    2    1    0.0 'NoU' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   24    2    0.0 'NoU' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   32    2    0.0 'NoU' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   40    2    0.0 'NoU' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   48    2    0.0 'NoU' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   64    2    0.0 'NoU' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   80    2    0.0 'NoU' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   96    2    0.0 'NoU' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1  128    2    0.0 'NoU' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  200  200    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  400  400    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1    2    1    0.0 'Upd' 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   24    2    0.0 'Upd' 1000000    1
      12
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   32    2    0.0 'Upd' 1000000    1
      16
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=20:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   40    2    0.0 'Upd' 1000000    1
      20
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   48    2    0.0 'Upd' 1000000    1
      24
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   64    2    0.0 'Upd' 1000000    1
      32
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=40:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   80    2    0.0 'Upd' 1000000    1
      40
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1   96    2    0.0 'Upd' 1000000    1
      48
       0     0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SYRDD'
   'Rand'   0.0 'Lower'  600  600    1  128    2    0.0 'Upd' 1000000    1
      64
       0     0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBRDD : driver routine for the reduction banded -> banded/tridiagonal
C 
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the matrix A
C     6 : lda = leading dimension of the array a
C     7 : b2 = (seim-)bandwidth of the reduced matrix B
C     8 : nsteps = number of reduction steps
C     9 : drptol = threshold for dropping Householder transforms (in multiples
C			 of macheps)
C    10 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C    11 : ldu = leading dimension of the array u
C    12 : lwork = length of workspace for the reduction and accumulation
C    13 : xinfo = expected info value for the routine syrdb
C                 (xinfo <> 0 may be used for checking error exits)
C
C  If nsteps > 1 then the second line contains the nstep-1 intermediate
C    bandwidths, and the third line contains the nsteps blocking factors for the
C    reduction steps.
C  If nsteps = 1 then the second line contains the blocking factor for the
C    reduction step (the line specifying intermediate bandwidths is missing).
C  If nsteps = 0 then no intermediate bandwidths or blocking factors are
C    specified (so both lines are missing).
C
C  Parameters in the last line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C		       (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Setting intermediate bandwidth for SBRDD ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'NoU'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    1    0.0 'NoU'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'NoU'  200 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'NoU'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    1    0.0 'NoU'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'NoU'  400 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'NoU'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    1    0.0 'NoU'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'NoU'  600 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   32   64    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   64  128    1    2    0.0 'Upd'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    1    0.0 'Upd'  200 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  200   96  192    1    2    0.0 'Upd'  200 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   32   64    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   64  128    1    2    0.0 'Upd'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    1    0.0 'Upd'  400 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  400   96  192    1    2    0.0 'Upd'  400 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   32   64    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   64  128    1    2    0.0 'Upd'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'one-step (b=1):'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    1    0.0 'Upd'  600 1000000    1
       0
   'Check'   10.0   10.0   10.0
'Print'
'b=8:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
       8
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=12:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      12
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=16:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      16
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=24:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      24
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=32:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      32
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=48:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      48
       0    0
   'Check'   10.0   10.0   10.0
'Print'
'b=64:'
'SBRDD'
   'Rand'   0.0 'Lower'  600   96  192    1    2    0.0 'Upd'  600 1000000    1
      64
       0    0
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C  SBTRD : one-step reduction banded -> tridiagonal (LAPACK)
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : uplo = use upper (uplo='U') or lower triangle (uplo='L') of the
C                matrix A ?
C     4 : n = dimension of the matrix A
C     5 : b1 = (semi-)bandwidth of the banded matrix A
C     6 : lda = leading dimension of the array a
C     7 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     8 : ldu = leading dimension of the array u
C     9 : xinfo = expected info value for the routine sbtrd
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
C
C  SBRDT : one-step reduction banded -> tridiagonal (SBR)
C
C  Parameters in the second line:
C     1 : mtype = matrix type (mtype='R' : random, mtype='I' : isda)
C     2 : diam = diameter of the eigenvalue clusters (in multiples of macheps;
C                used only if mtype='I'
C     3 : n = dimension of the matrix A
C     4 : b1 = (semi-)bandwidth of the matrix A
C     5 : lda = leading dimension of the array a
C     6 : drptol = threshold for dropping Householder transforms (in multiples
C                  of macheps)
C     7 : nb = blocking factor for the reduction (nb=0 : use default)
C     8 : jobu = accumulate the transformations in a matrix U (jobu='U') or
C                not (jobu='N') ?
C     9 : ldu = leading dimension of the array u
C    10 : lwork = length of workspace for the reduction and accumulation
C    11 : xinfo = expected info value for the routine sbrdt
C                 (xinfo <> 0 may be used for checking error exits)
C
C  Parameters in the third line:
C     1 : check = check the results (check='C') or not (check='N') ?
C     2 : torthu = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps);
C                  used only if check='C' and jobu='U'
C     3 : tres = threshold for the residual error F-norm( U * A - B * U )
C                (in multiples of n * macheps * F-norm( A ));
C                used only if check='C' and jobu='U'
C     4 : tdevls = threshold for the orthogonality error F-norm( U' * U - I )
C                  (in multiples of n * macheps * F-norm( A ));
C                  used only if check='C' and jobu='N'
C
C ------------------------------------------------------------------------------
'Print'
''
'Print'
'*** Where to switch from SYTRD to SYRDT ? ***'
'Print'
''
'Print'
'    no update'
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  200    6    7 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    6   12    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  200   10   11 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   10   20    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  200   20   21 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   20   40    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  200   40   41 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   40   80    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'NoU'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'NoU'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  400    6    7 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    6   12    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  400   10   11 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   10   20    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  400   20   21 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   20   40    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  400   40   41 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   40   80    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'NoU'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'NoU'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  600    6    7 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    6   12    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  600   10   11 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   10   20    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  600   20   21 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   20   40    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  600   40   41 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   40   80    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'NoU'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'NoU'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'    with update'
'Print'
'      *** ignore messages about tests failing because ***'
'Print'
'      *** SBRDT returned a wrong (but positive) info  ***'
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  200    4    5 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    4    8    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  200    6    7 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    6   12    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  200    8    9 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200    8   16    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  200   10   11 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   10   20    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  200   12   13 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   12   24    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  200   16   17 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   16   32    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  200   20   21 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   20   40    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  200   24   25 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   24   48    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  200   32   33 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   32   64    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  200   40   41 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   40   80    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  200   48   49 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   48   96    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  200   64   65 'Upd'  200   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  200   64  128    0.0   0 'Upd'  200 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  400    4    5 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    4    8    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  400    6    7 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    6   12    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  400    8    9 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400    8   16    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  400   10   11 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   10   20    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  400   12   13 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   12   24    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  400   16   17 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   16   32    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  400   20   21 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   20   40    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  400   24   25 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   24   48    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  400   32   33 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   32   64    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  400   40   41 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   40   80    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  400   48   49 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   48   96    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  400   64   65 'Upd'  400   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  400   64  128    0.0   0 'Upd'  400 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
''
'Print'
'b=4'
'SBTRD'
   'Rand'   0.0 'Lower'  600    4    5 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    4    8    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=6'
'SBTRD'
   'Rand'   0.0 'Lower'  600    6    7 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    6   12    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=8'
'SBTRD'
   'Rand'   0.0 'Lower'  600    8    9 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600    8   16    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=10'
'SBTRD'
   'Rand'   0.0 'Lower'  600   10   11 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   10   20    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=12'
'SBTRD'
   'Rand'   0.0 'Lower'  600   12   13 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   12   24    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=16'
'SBTRD'
   'Rand'   0.0 'Lower'  600   16   17 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   16   32    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=20'
'SBTRD'
   'Rand'   0.0 'Lower'  600   20   21 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   20   40    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=24'
'SBTRD'
   'Rand'   0.0 'Lower'  600   24   25 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   24   48    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=32'
'SBTRD'
   'Rand'   0.0 'Lower'  600   32   33 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   32   64    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=40'
'SBTRD'
   'Rand'   0.0 'Lower'  600   40   41 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   40   80    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=48'
'SBTRD'
   'Rand'   0.0 'Lower'  600   48   49 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   48   96    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
'Print'
'b=64'
'SBTRD'
   'Rand'   0.0 'Lower'  600   64   65 'Upd'  600   0
   'Check'   10.0   10.0   10.0
'SBRDT'
   'Rand'   0.0  600   64  128    0.0   0 'Upd'  600 1000000   1
   'Check'   10.0   10.0   10.0
C ------------------------------------------------------------------------------
C
C --- quit ---
'Quit'
C
SHAR_EOF
fi # end of overwriting check
if test -f 'driver.f'
then
	echo shar: will not over-write existing file "'driver.f'"
else
cat << "SHAR_EOF" > 'driver.f'
      SUBROUTINE SORQLX( NB0, NX0,
     >                   M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            NB0, NX0, INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  sORQLx generates an M-by-N real matrix Q with orthonormal columns,
C*  DORGQL generates an M-by-N real matrix Q with orthonormal columns,
*  which is defined as the last N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by DGEQLF.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the nonblocked algorithm.
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) real array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the (n-k+i)-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by DGEQLF in the last k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) real array, dimension (K)
C*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DGEQLF.
*
*  WORK    (workspace/output) real array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
C      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
C      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
     $                   NB, NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLARFB, SLARFT, SORG2L, XERBLA
C      EXTERNAL           DLARFB, DLARFT, DORG2L, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF ( NB0 .GT. 0 ) THEN
        NB = NB0
      ELSE
        NB = ILAENV( 1, 'sORGQL', ' ', M, N, K, -1 )
      ENDIF
C      NB = ILAENV( 1, 'DORGQL', ' ', M, N, K, -1 )
      LWKOPT = MAX( 1, N )*NB
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'sORGQL', -INFO )
C         CALL XERBLA( 'DORGQL', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      NX = 0
      IWS = N
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         IF ( NX0 .GT. 0 ) THEN
           NX = NX0
         ELSE
           NX = MAX( 0, ILAENV( 3, 'sORGQL', ' ', M, N, K, -1 ) )
         ENDIF
C         NX = MAX( 0, ILAENV( 3, 'DORGQL', ' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = 2
C               NBMIN = MAX( 2, ILAENV( 2, 'DORGQL', ' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
*
*        Use blocked code after the first block.
*        The last kk columns are handled by the block method.
*
         KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
*
*        Set A(m-kk+1:m,1:n-kk) to zero.
*
         DO 20 J = 1, N - KK
            DO 10 I = M - KK + 1, M
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the first or only block.
*
      CALL SORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
C      CALL DORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = K - KK + 1, K, NB
            IB = MIN( NB, K-I+1 )
            IF( N-K+I.GT.1 ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i+ib-1) . . . H(i+1) H(i)
*
               CALL SLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
     $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
C               CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
C     $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
*
               CALL SLARFB( 'Left', 'No transpose', 'Backward',
     $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
     $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
     $                      WORK( IB+1 ), LDWORK )
C               CALL DLARFB( 'Left', 'No transpose', 'Backward',
C     $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
C     $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
C     $                      WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H to rows 1:m-k+i+ib-1 of current block
*
            CALL SORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
     $                   TAU( I ), WORK, IINFO )
C            CALL DORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
C     $                   TAU( I ), WORK, IINFO )
*
*           Set rows m-k+i+ib:m of current block to zero
*
            DO 40 J = N - K + I, N - K + I + IB - 1
               DO 30 L = M - K + I + IB, M
                  A( L, J ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of sORQLx
C*     End of DORGQL
*
      END
      SUBROUTINE SORQRX( NB0, NX0,
     >                   M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      INTEGER            NB0, NX0, INFO, K, LDA, LWORK, M, N
C      INTEGER            INFO, K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  sORQRx generates an M-by-N real matrix Q with orthonormal columns,
C*  DORGQR generates an M-by-N real matrix Q with orthonormal columns,
*  which is defined as the first N columns of a product of K elementary
*  reflectors of order M
*
*        Q  =  H(1) H(2) . . . H(k)
*
*  as returned by sGEQRF.
C*  as returned by DGEQRF.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the non-blocked algorithm.
*
*  M       (input) INTEGER
*          The number of rows of the matrix Q. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix Q. M >= N >= 0.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. N >= K >= 0.
*
*  A       (input/output) real array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the i-th column must contain the vector which
*          defines the elementary reflector H(i), for i = 1,2,...,k, as
*          returned by sGEQRF in the first k columns of its array
C*          returned by DGEQRF in the first k columns of its array
*          argument A.
*          On exit, the M-by-N matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) real array, dimension (K)
C*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by sGEQRF.
C*          reflector H(i), as returned by DGEQRF.
*
*  WORK    (workspace/output) real array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N).
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO
C      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0E+0 )
C      PARAMETER          ( ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
     $                   LWKOPT, NB, NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLARFB, SLARFT, SORG2R, XERBLA
C      EXTERNAL           DLARFB, DLARFT, DORG2R, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF ( NB0 .GT. 0 ) THEN
        NB = NB0
      ELSE
        NB = ILAENV( 1, 'sORGQR', ' ', M, N, K, -1 )
      ENDIF
C      NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
      LWKOPT = MAX( 1, N )*NB
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
         INFO = -2
      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -5
      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'sORGQR', -INFO )
C         CALL XERBLA( 'DORGQR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NBMIN = 2
      NX = 0
      IWS = N
      IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
*        Determine when to cross over from blocked to unblocked code.
*
         IF ( NX0 .GT. 0 ) THEN
           NX = NX0
         ELSE
           NX = MAX( 0, ILAENV( 3, 'sORGQR', ' ', M, N, K, -1 ) )
         ENDIF
C         NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) )
         IF( NX.LT.K ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  reduce NB and
*              determine the minimum value of NB.
*
               NB = LWORK / LDWORK
               NBMIN = 2
C               NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) )
            END IF
         END IF
      END IF
*
      IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
*
*        Use blocked code after the last block.
*        The first kk columns are handled by the block method.
*
         KI = ( ( K-NX-1 ) / NB )*NB
         KK = MIN( K, KI+NB )
*
*        Set A(1:kk,kk+1:n) to zero.
*
         DO 20 J = KK + 1, N
            DO 10 I = 1, KK
               A( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
      ELSE
         KK = 0
      END IF
*
*     Use unblocked code for the last or only block.
*
      IF( KK.LT.N )
     $   CALL SORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
     $                TAU( KK+1 ), WORK, IINFO )
C     $   CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
C     $                TAU( KK+1 ), WORK, IINFO )
*
      IF( KK.GT.0 ) THEN
*
*        Use blocked code
*
         DO 50 I = KI + 1, 1, -NB
            IB = MIN( NB, K-I+1 )
            IF( I+IB.LE.N ) THEN
*
*              Form the triangular factor of the block reflector
*              H = H(i) H(i+1) . . . H(i+ib-1)
*
               CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB,
     $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
C               CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
C     $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
*
*              Apply H to A(i:m,i+ib:n) from the left
*
               CALL SLARFB( 'Left', 'No transpose', 'Forward',
     $                      'Columnwise', M-I+1, N-I-IB+1, IB,
     $                      A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
     $                      LDA, WORK( IB+1 ), LDWORK )
C               CALL DLARFB( 'Left', 'No transpose', 'Forward',
C     $                      'Columnwise', M-I+1, N-I-IB+1, IB,
C     $                      A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
C     $                      LDA, WORK( IB+1 ), LDWORK )
            END IF
*
*           Apply H to rows i:m of current block
*
            CALL SORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
     $                   IINFO )
C            CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
C     $                   IINFO )
*
*           Set rows 1:i-1 of current block to zero
*
            DO 40 J = I, I + IB - 1
               DO 30 L = 1, I - 1
                  A( L, J ) = ZERO
   30          CONTINUE
   40       CONTINUE
   50    CONTINUE
      END IF
*
      WORK( 1 ) = IWS
      RETURN
*
*     End of sORQRx
C*     End of DORGQR
*
      END
      SUBROUTINE SORGTX( NB0, NX0,
     >                   UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            NB0, NX0, INFO, LDA, LWORK, N
C      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), TAU( * ), WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  sORGTx generates a real orthogonal matrix Q which is defined as the
C*  DORGTR generates a real orthogonal matrix Q which is defined as the
*  product of n-1 elementary reflectors of order N, as returned by
*  sSYTRD:
C*  DSYTRD:
*
*  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point for the nonblocked algorithm.
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangle of A contains elementary reflectors
*                 from sSYTRD;
C*                 from DSYTRD;
*          = 'L': Lower triangle of A contains elementary reflectors
*                 from sSYTRD.
C*                 from DSYTRD.
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  A       (input/output) sPreicision array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the vectors which define the elementary reflectors,
*          as returned by sSYTRD.
C*          as returned by DSYTRD.
*          On exit, the N-by-N orthogonal matrix Q.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,N).
*
*  TAU     (input) sPreicision array, dimension (N-1)
C*  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by sSYTRD.
C*          reflector H(i), as returned by DSYTRD.
*
*  WORK    (workspace/output) real array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,N-1).
*          For optimum performance LWORK >= (N-1)*NB, where NB is
*          the optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
C      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
C      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, J, LWKOPT, NB
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           SORQLX, SORQRX, XERBLA
C      EXTERNAL           DORGQL, DORGQR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
         INFO = -7
      END IF
*
      IF( INFO.EQ.0 ) THEN
         IF( UPPER ) THEN
            IF ( NB0 .GT. 0 ) THEN
              NB = NB0
            ELSE
              NB = ILAENV( 1, 'sORGQL', ' ', N-1, N-1, N-1, -1 )
            ENDIF
C            NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
         ELSE
            IF ( NB0 .GT. 0 ) THEN
              NB = NB0
            ELSE
              NB = ILAENV( 1, 'sORGQR', ' ', N-1, N-1, N-1, -1 )
            ENDIF
C            NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
         END IF
         LWKOPT = MAX( 1, N-1 )*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'sORGTR', -INFO )
C         CALL XERBLA( 'DORGTR', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      IF( UPPER ) THEN
*
*        Q was determined by a call to sSYTRD with UPLO = 'U'
C*        Q was determined by a call to DSYTRD with UPLO = 'U'
*
*        Shift the vectors which define the elementary reflectors one
*        column to the left, and set the last row and column of Q to
*        those of the unit matrix
*
         DO 20 J = 1, N - 1
            DO 10 I = 1, J - 1
               A( I, J ) = A( I, J+1 )
   10       CONTINUE
            A( N, J ) = ZERO
   20    CONTINUE
         DO 30 I = 1, N - 1
            A( I, N ) = ZERO
   30    CONTINUE
         A( N, N ) = ONE
*
*        Generate Q(1:n-1,1:n-1)
*
         CALL SORQLX( NB0, NX0,
     >                N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
C         CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
*
      ELSE
*
*        Q was determined by a call to sSYTRD with UPLO = 'L'.
C*        Q was determined by a call to DSYTRD with UPLO = 'L'.
*
*        Shift the vectors which define the elementary reflectors one
*        column to the right, and set the first row and column of Q to
*        those of the unit matrix
*
         DO 50 J = N, 2, -1
            A( 1, J ) = ZERO
            DO 40 I = J + 1, N
               A( I, J ) = A( I, J-1 )
   40       CONTINUE
   50    CONTINUE
         A( 1, 1 ) = ONE
         DO 60 I = 2, N
            A( I, 1 ) = ZERO
   60    CONTINUE
         IF( N.GT.1 ) THEN
*
*           Generate Q(2:n,2:n)
*
            CALL SORQRX( NB0, NX0,
     >                   N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
     $                   LWORK, IINFO )
C            CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
C     $                   LWORK, IINFO )
         END IF
      END IF
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of sORGTR
C*     End of DORGTR
*
      END
C      SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
      SUBROUTINE SSBTRX( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
     $                   WORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO, VECT
      INTEGER            INFO, KD, LDAB, LDQ, N
*     ..
*     .. Array Arguments ..
C      DOUBLE PRECISION   AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ),
      REAL   AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ),
     $                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
C*  DSBTRD reduces a real symmetric band matrix A to symmetric
*  sSBTRD reduces a real symmetric band matrix A to symmetric
*  tridiagonal form T by an orthogonal similarity transformation:
*  Q**T * A * Q = T.
*
*  Arguments
*  =========
*
*  VECT    (input) CHARACTER*1
*          = 'N':  do not form Q;
*          = 'V':  form Q;
*          = 'U':  update a matrix X, by forming X*Q.
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
C*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*  AB      (input/output) real array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*          On exit, the diagonal elements of AB are overwritten by the
*          diagonal elements of the tridiagonal matrix T; if KD > 0, the
*          elements on the first superdiagonal (if UPLO = 'U') or the
*          first subdiagonal (if UPLO = 'L') are overwritten by the
*          off-diagonal elements of T; the rest of AB is overwritten by
*          values generated during the reduction.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
C*  D       (output) DOUBLE PRECISION array, dimension (N)
*  D       (output) real array, dimension (N)
*          The diagonal elements of the tridiagonal matrix T.
*
C*  E       (output) DOUBLE PRECISION array, dimension (N-1)
*  E       (output) real array, dimension (N-1)
*          The off-diagonal elements of the tridiagonal matrix T:
*          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
*
C*  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
*  Q       (input/output) real array, dimension (LDQ,N)
*          On entry, if VECT = 'U', then Q must contain an N-by-N
*          matrix X; if VECT = 'N' or 'V', then Q need not be set.
*
*          On exit:
*          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
*          if VECT = 'U', Q contains the product X*Q;
*          if VECT = 'N', the array Q is not referenced.
*
*  LDQ     (input) INTEGER
*          The leading dimension of the array Q.
*          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
*
C*  WORK    (workspace) DOUBLE PRECISION array, dimension (N)
*  WORK    (workspace) real array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  Further Details
*  ===============
*
*  Modified by Linda Kaufman, Bell Labs.
*
*  =====================================================================
*
*     .. Parameters ..
C      DOUBLE PRECISION   ZERO, ONE
      REAL   ZERO, ONE
C      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            INITQ, UPPER, WANTQ
      INTEGER            I, I2, IBL, INCA, INCX, IQAEND, IQB, IQEND, J,
     $                   J1, J1END, J1INC, J2, JEND, JIN, JINC, K, KD1,
     $                   KDM1, KDN, L, LAST, LEND, NQ, NR, NRT
C      DOUBLE PRECISION   TEMP
      REAL   TEMP
*     ..
*     .. External Subroutines ..
C      EXTERNAL           DLAR2V, DLARGV, DLARTG, DLARTV, DLASET, DROT,
      EXTERNAL           SLAR2V, SLARGV, SLARTG, SLARTV, SLASET, SROT,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INITQ = LSAME( VECT, 'V' )
      WANTQ = INITQ .OR. LSAME( VECT, 'U' )
      UPPER = LSAME( UPLO, 'U' )
      KD1 = KD + 1
      KDM1 = KD - 1
      INCX = LDAB - 1
      IQEND = 1
*
      INFO = 0
      IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'N' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( KD.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD1 ) THEN
         INFO = -6
      ELSE IF( LDQ.LT.MAX( 1, N ) .AND. WANTQ ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
C         CALL XERBLA( 'DSBTRD', -INFO )
         CALL XERBLA( 'sSBTRD', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Initialize Q to the unit matrix, if needed
*
      IF( INITQ )
C     $   CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
     $   CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
*
*     Wherever possible, plane rotations are generated and applied in
*     vector operations of length NR over the index set J1:J2:KD1.
*
*     The cosines and sines of the plane rotations are stored in the
*     arrays D and WORK.
*
      INCA = KD1*LDAB
      KDN = MIN( N-1, KD )
      IF( UPPER ) THEN
*
         IF( KD.GT.1 ) THEN
*
*           Reduce to tridiagonal form, working with upper triangle
*
            NR = 0
            J1 = KDN + 2
            J2 = 1
*
            DO 90 I = 1, N - 2
*
*              Reduce i-th row of matrix to tridiagonal form
*
               DO 80 K = KDN + 1, 2, -1
                  J1 = J1 + KDN
                  J2 = J2 + KDN
*
                  IF( NR.GT.0 ) THEN
*
*                    generate plane rotations to annihilate nonzero
*                    elements which have been created outside the band
*
C                     CALL DLARGV( NR, AB( 1, J1-1 ), INCA, WORK( J1 ),
                     CALL SLARGV( NR, AB( 1, J1-1 ), INCA, WORK( J1 ),
     $                            KD1, D( J1 ), KD1 )
*
*                    apply rotations from the right
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    sLARTV or sROT is used
*
                     IF( NR.GE.2*KD-1 ) THEN
                        DO 10 L = 1, KD - 1
C                           CALL DLARTV( NR, AB( L+1, J1-1 ), INCA,
                           CALL SLARTV( NR, AB( L+1, J1-1 ), INCA,
     $                                  AB( L, J1 ), INCA, D( J1 ),
     $                                  WORK( J1 ), KD1 )
   10                   CONTINUE
*
                     ELSE
                        JEND = J1 + ( NR-1 )*KD1
                        DO 20 JINC = J1, JEND, KD1
C                           CALL DROT( KDM1, AB( 2, JINC-1 ), 1,
                           CALL SROT( KDM1, AB( 2, JINC-1 ), 1,
     $                                AB( 1, JINC ), 1, D( JINC ),
     $                                WORK( JINC ) )
   20                   CONTINUE
                     END IF
                  END IF
*
*
                  IF( K.GT.2 ) THEN
                     IF( K.LE.N-I+1 ) THEN
*
*                       generate plane rotation to annihilate a(i,i+k-1)
*                       within the band
*
C                        CALL DLARTG( AB( KD-K+3, I+K-2 ),
                        CALL SLARTG( AB( KD-K+3, I+K-2 ),
     $                               AB( KD-K+2, I+K-1 ), D( I+K-1 ),
     $                               WORK( I+K-1 ), TEMP )
                        AB( KD-K+3, I+K-2 ) = TEMP
*
*                       apply rotation from the right
*
C                        CALL DROT( K-3, AB( KD-K+4, I+K-2 ), 1,
                        CALL SROT( K-3, AB( KD-K+4, I+K-2 ), 1,
     $                             AB( KD-K+3, I+K-1 ), 1, D( I+K-1 ),
     $                             WORK( I+K-1 ) )
                     END IF
                     NR = NR + 1
                     J1 = J1 - KDN - 1
                  END IF
*
*                 apply plane rotations from both sides to diagonal
*                 blocks
*
                  IF( NR.GT.0 )
C     $               CALL DLAR2V( NR, AB( KD1, J1-1 ), AB( KD1, J1 ),
     $               CALL SLAR2V( NR, AB( KD1, J1-1 ), AB( KD1, J1 ),
     $                            AB( KD, J1 ), INCA, D( J1 ),
     $                            WORK( J1 ), KD1 )
*
*                 apply plane rotations from the left
*
                  IF( NR.GT.0 ) THEN
                     IF( 2*KD-1.LT.NR ) THEN
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    sLARTV or sROT is used
*
                        DO 30 L = 1, KD - 1
                           IF( J2+L.GT.N ) THEN
                              NRT = NR - 1
                           ELSE
                              NRT = NR
                           END IF
                           IF( NRT.GT.0 )
C     $                        CALL DLARTV( NRT, AB( KD-L, J1+L ), INCA,
     $                        CALL SLARTV( NRT, AB( KD-L, J1+L ), INCA,
     $                                     AB( KD-L+1, J1+L ), INCA,
     $                                     D( J1 ), WORK( J1 ), KD1 )
   30                   CONTINUE
                     ELSE
                        J1END = J1 + KD1*( NR-2 )
                        IF( J1END.GE.J1 ) THEN
                           DO 40 JIN = J1, J1END, KD1
C                              CALL DROT( KD-1, AB( KD-1, JIN+1 ), INCX,
                              CALL SROT( KD-1, AB( KD-1, JIN+1 ), INCX,
     $                                   AB( KD, JIN+1 ), INCX,
     $                                   D( JIN ), WORK( JIN ) )
   40                      CONTINUE
                        END IF
                        LEND = MIN( KDM1, N-J2 )
                        LAST = J1END + KD1
                        IF( LEND.GT.0 )
C     $                     CALL DROT( LEND, AB( KD-1, LAST+1 ), INCX,
     $                     CALL SROT( LEND, AB( KD-1, LAST+1 ), INCX,
     $                                AB( KD, LAST+1 ), INCX, D( LAST ),
     $                                WORK( LAST ) )
                     END IF
                  END IF
*
                  IF( WANTQ ) THEN
*
*                    accumulate product of plane rotations in Q
*
                     IF( INITQ ) THEN
*
*                 take advantage of the fact that Q was
*                 initially the Identity matrix
*
                        IQEND = MAX( IQEND, J2 )
                        I2 = MAX( 0, K-3 )
                        IQAEND = 1 + I*KD
                        IF( K.EQ.2 )
     $                     IQAEND = IQAEND + KD
                        IQAEND = MIN( IQAEND, IQEND )
                        DO 50 J = J1, J2, KD1
                           IBL = I - I2 / KDM1
                           I2 = I2 + 1
                           IQB = MAX( 1, J-IBL )
                           NQ = 1 + IQAEND - IQB
                           IQAEND = MIN( IQAEND+KD, IQEND )
C                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
                           CALL SROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
     $                                1, D( J ), WORK( J ) )
   50                   CONTINUE
                     ELSE
*
                        DO 60 J = J1, J2, KD1
C                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
                           CALL SROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
     $                                D( J ), WORK( J ) )
   60                   CONTINUE
                     END IF
*
                  END IF
*
                  IF( J2+KDN.GT.N ) THEN
*
*                    adjust J2 to keep within the bounds of the matrix
*
                     NR = NR - 1
                     J2 = J2 - KDN - 1
                  END IF
*
                  DO 70 J = J1, J2, KD1
*
*                    create nonzero element a(j-1,j+kd) outside the band
*                    and store it in WORK
*
                     WORK( J+KD ) = WORK( J )*AB( 1, J+KD )
                     AB( 1, J+KD ) = D( J )*AB( 1, J+KD )
   70             CONTINUE
   80          CONTINUE
   90       CONTINUE
         END IF
*
         IF( KD.GT.0 ) THEN
*
*           copy off-diagonal elements to E
*
            DO 100 I = 1, N - 1
               E( I ) = AB( KD, I+1 )
  100       CONTINUE
         ELSE
*
*           set E to zero if original matrix was diagonal
*
            DO 110 I = 1, N - 1
               E( I ) = ZERO
  110       CONTINUE
         END IF
*
*        copy diagonal elements to D
*
         DO 120 I = 1, N
            D( I ) = AB( KD1, I )
  120    CONTINUE
*
      ELSE
*
         IF( KD.GT.1 ) THEN
*
*           Reduce to tridiagonal form, working with lower triangle
*
            NR = 0
            J1 = KDN + 2
            J2 = 1
*
            DO 210 I = 1, N - 2
*
*              Reduce i-th column of matrix to tridiagonal form
*
               DO 200 K = KDN + 1, 2, -1
                  J1 = J1 + KDN
                  J2 = J2 + KDN
*
                  IF( NR.GT.0 ) THEN
*
*                    generate plane rotations to annihilate nonzero
*                    elements which have been created outside the band
*
C                     CALL DLARGV( NR, AB( KD1, J1-KD1 ), INCA,
                     CALL SLARGV( NR, AB( KD1, J1-KD1 ), INCA,
     $                            WORK( J1 ), KD1, D( J1 ), KD1 )
*
*                    apply plane rotations from one side
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    sLARTV or sROT is used
*
                     IF( NR.GT.2*KD-1 ) THEN
                        DO 130 L = 1, KD - 1
C                           CALL DLARTV( NR, AB( KD1-L, J1-KD1+L ), INCA,
                           CALL SLARTV( NR, AB( KD1-L, J1-KD1+L ), INCA,
     $                                  AB( KD1-L+1, J1-KD1+L ), INCA,
     $                                  D( J1 ), WORK( J1 ), KD1 )
  130                   CONTINUE
                     ELSE
                        JEND = J1 + KD1*( NR-1 )
                        DO 140 JINC = J1, JEND, KD1
C                           CALL DROT( KDM1, AB( KD, JINC-KD ), INCX,
                           CALL SROT( KDM1, AB( KD, JINC-KD ), INCX,
     $                                AB( KD1, JINC-KD ), INCX,
     $                                D( JINC ), WORK( JINC ) )
  140                   CONTINUE
                     END IF
*
                  END IF
*
                  IF( K.GT.2 ) THEN
                     IF( K.LE.N-I+1 ) THEN
*
*                       generate plane rotation to annihilate a(i+k-1,i)
*                       within the band
*
C                        CALL DLARTG( AB( K-1, I ), AB( K, I ),
                        CALL SLARTG( AB( K-1, I ), AB( K, I ),
     $                               D( I+K-1 ), WORK( I+K-1 ), TEMP )
                        AB( K-1, I ) = TEMP
*
*                       apply rotation from the left
*
C                        CALL DROT( K-3, AB( K-2, I+1 ), LDAB-1,
                        CALL SROT( K-3, AB( K-2, I+1 ), LDAB-1,
     $                             AB( K-1, I+1 ), LDAB-1, D( I+K-1 ),
     $                             WORK( I+K-1 ) )
                     END IF
                     NR = NR + 1
                     J1 = J1 - KDN - 1
                  END IF
*
*                 apply plane rotations from both sides to diagonal
*                 blocks
*
                  IF( NR.GT.0 )
C     $               CALL DLAR2V( NR, AB( 1, J1-1 ), AB( 1, J1 ),
     $               CALL SLAR2V( NR, AB( 1, J1-1 ), AB( 1, J1 ),
     $                            AB( 2, J1-1 ), INCA, D( J1 ),
     $                            WORK( J1 ), KD1 )
*
*                 apply plane rotations from the right
*
*
*                    Dependent on the the number of diagonals either
C*                    DLARTV or DROT is used
*                    sLARTV or sROT is used
*
                  IF( NR.GT.0 ) THEN
                     IF( NR.GT.2*KD-1 ) THEN
                        DO 150 L = 1, KD - 1
                           IF( J2+L.GT.N ) THEN
                              NRT = NR - 1
                           ELSE
                              NRT = NR
                           END IF
                           IF( NRT.GT.0 )
C     $                        CALL DLARTV( NRT, AB( L+2, J1-1 ), INCA,
     $                        CALL SLARTV( NRT, AB( L+2, J1-1 ), INCA,
     $                                     AB( L+1, J1 ), INCA, D( J1 ),
     $                                     WORK( J1 ), KD1 )
  150                   CONTINUE
                     ELSE
                        J1END = J1 + KD1*( NR-2 )
                        IF( J1END.GE.J1 ) THEN
                           DO 160 J1INC = J1, J1END, KD1
C                              CALL DROT( KDM1, AB( 3, J1INC-1 ), 1,
                              CALL SROT( KDM1, AB( 3, J1INC-1 ), 1,
     $                                   AB( 2, J1INC ), 1, D( J1INC ),
     $                                   WORK( J1INC ) )
  160                      CONTINUE
                        END IF
                        LEND = MIN( KDM1, N-J2 )
                        LAST = J1END + KD1
                        IF( LEND.GT.0 )
C     $                     CALL DROT( LEND, AB( 3, LAST-1 ), 1,
     $                     CALL SROT( LEND, AB( 3, LAST-1 ), 1,
     $                                AB( 2, LAST ), 1, D( LAST ),
     $                                WORK( LAST ) )
                     END IF
                  END IF
*
*
*
                  IF( WANTQ ) THEN
*
*                    accumulate product of plane rotations in Q
*
                     IF( INITQ ) THEN
*
*                 take advantage of the fact that Q was
*                 initially the Identity matrix
*
                        IQEND = MAX( IQEND, J2 )
                        I2 = MAX( 0, K-3 )
                        IQAEND = 1 + I*KD
                        IF( K.EQ.2 )
     $                     IQAEND = IQAEND + KD
                        IQAEND = MIN( IQAEND, IQEND )
                        DO 170 J = J1, J2, KD1
                           IBL = I - I2 / KDM1
                           I2 = I2 + 1
                           IQB = MAX( 1, J-IBL )
                           NQ = 1 + IQAEND - IQB
                           IQAEND = MIN( IQAEND+KD, IQEND )
C                           CALL DROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
                           CALL SROT( NQ, Q( IQB, J-1 ), 1, Q( IQB, J ),
     $                                1, D( J ), WORK( J ) )
  170                   CONTINUE
                     ELSE
*
                        DO 180 J = J1, J2, KD1
C                           CALL DROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
                           CALL SROT( N, Q( 1, J-1 ), 1, Q( 1, J ), 1,
     $                                D( J ), WORK( J ) )
  180                   CONTINUE
                     END IF
                  END IF
*
                  IF( J2+KDN.GT.N ) THEN
*
*                    adjust J2 to keep within the bounds of the matrix
*
                     NR = NR - 1
                     J2 = J2 - KDN - 1
                  END IF
*
                  DO 190 J = J1, J2, KD1
*
*                    create nonzero element a(j+kd,j-1) outside the
*                    band and store it in WORK
*
                     WORK( J+KD ) = WORK( J )*AB( KD1, J )
                     AB( KD1, J ) = D( J )*AB( KD1, J )
  190             CONTINUE
  200          CONTINUE
  210       CONTINUE
         END IF
*
         IF( KD.GT.0 ) THEN
*
*           copy off-diagonal elements to E
*
            DO 220 I = 1, N - 1
               E( I ) = AB( 2, I )
  220       CONTINUE
         ELSE
*
*           set E to zero if original matrix was diagonal
*
            DO 230 I = 1, N - 1
               E( I ) = ZERO
  230       CONTINUE
         END IF
*
*        copy diagonal elements to D
*
         DO 240 I = 1, N
            D( I ) = AB( 1, I )
  240    CONTINUE
      END IF
*
      RETURN
*
C*     End of DSBTRD
*     End of sSBTRD
*
      END
      SUBROUTINE SSYTRX( NB0, NX0,
     >                   UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
C      SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            NB0, NX0, INFO, LDA, LWORK, N
C      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), D( * ), E( * ), TAU( * ),
     $                   WORK( * )
C      DOUBLE PRECISION   A( LDA, * ), D( * ), E( * ), TAU( * ),
C     $                   WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  sSYTRx reduces a real symmetric matrix A to real symmetric
C*  DSYTRD reduces a real symmetric matrix A to real symmetric
*  tridiagonal form T by an orthogonal similarity transformation:
*  Q**T * A * Q = T.
*
*  Arguments
*  =========
*
*  nb0     (input) integer
*          The blocking factor.
*
*  nx0     (input) integer
*          The cross-over point to the nonblocked algorithm.
C
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) real array, dimension (LDA,N)
C*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
*          N-by-N upper triangular part of A contains the upper
*          triangular part of the matrix A, and the strictly lower
*          triangular part of A is not referenced.  If UPLO = 'L', the
*          leading N-by-N lower triangular part of A contains the lower
*          triangular part of the matrix A, and the strictly upper
*          triangular part of A is not referenced.
*          On exit, if UPLO = 'U', the diagonal and first superdiagonal
*          of A are overwritten by the corresponding elements of the
*          tridiagonal matrix T, and the elements above the first
*          superdiagonal, with the array TAU, represent the orthogonal
*          matrix Q as a product of elementary reflectors; if UPLO
*          = 'L', the diagonal and first subdiagonal of A are over-
*          written by the corresponding elements of the tridiagonal
*          matrix T, and the elements below the first subdiagonal, with
*          the array TAU, represent the orthogonal matrix Q as a product
*          of elementary reflectors. See Further Details.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  D       (output) real array, dimension (N)
C*  D       (output) DOUBLE PRECISION array, dimension (N)
*          The diagonal elements of the tridiagonal matrix T:
*          D(i) = A(i,i).
*
*  E       (output) real array, dimension (N-1)
C*  E       (output) DOUBLE PRECISION array, dimension (N-1)
*          The off-diagonal elements of the tridiagonal matrix T:
*          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
*
*  TAU     (output) real array, dimension (N-1)
C*  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
*          The scalar factors of the elementary reflectors (see Further
*          Details).
*
*  WORK    (workspace/output) real array, dimension (LWORK)
C*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.  LWORK >= 1.
*          For optimum performance LWORK >= N*NB, where NB is the
*          optimal blocksize.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  Further Details
*  ===============
*
*  If UPLO = 'U', the matrix Q is represented as a product of elementary
*  reflectors
*
*     Q = H(n-1) . . . H(2) H(1).
*
*  Each H(i) has the form
*
*     H(i) = I - tau * v * v'
*
*  where tau is a real scalar, and v is a real vector with
*  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
*  A(1:i-1,i+1), and tau in TAU(i).
*
*  If UPLO = 'L', the matrix Q is represented as a product of elementary
*  reflectors
*
*     Q = H(1) H(2) . . . H(n-1).
*
*  Each H(i) has the form
*
*     H(i) = I - tau * v * v'
*
*  where tau is a real scalar, and v is a real vector with
*  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
*  and tau in TAU(i).
*
*  The contents of A on exit are illustrated by the following examples
*  with n = 5:
*
*  if UPLO = 'U':                       if UPLO = 'L':
*
*    (  d   e   v2  v3  v4 )              (  d                  )
*    (      d   e   v3  v4 )              (  e   d              )
*    (          d   e   v4 )              (  v1  e   d          )
*    (              d   e  )              (  v1  v2  e   d      )
*    (                  d  )              (  v1  v2  v3  e   d  )
*
*  where d and e denote diagonal and off-diagonal elements of T, and vi
*  denotes an element of the vector defining H(i).
*
*  =====================================================================
*
*     .. Parameters ..
      REAL                ONE
C      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0E+0 )
C      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER
      INTEGER            I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB,
     $                   NBMIN, NX
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLATRD, SSYR2K, SSYTD2, XERBLA
C      EXTERNAL           DLATRD, DSYR2K, DSYTD2, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      LQUERY = ( LWORK.EQ.-1 )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
         INFO = -9
      END IF
*
      IF( INFO.EQ.0 ) THEN
*
*        Determine the block size.
*
         IF ( NB0 .GT. 0 ) THEN
           NB = NB0
         ELSE
           NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         ENDIF
C         NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         LWKOPT = N*NB
         WORK( 1 ) = LWKOPT
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'sSYTRD', -INFO )
C         CALL XERBLA( 'DSYTRD', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         WORK( 1 ) = 1
         RETURN
      END IF
*
      NX = N
      IWS = 1
      IF( NB.GT.1 .AND. NB.LT.N ) THEN
*
*        Determine when to cross over from blocked to unblocked code
*        (last block is always handled by unblocked code).
*
         IF ( NX0 .GT. 0 ) THEN
           NX = MAX( NB, NX0 )
         ELSE
           NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
         ENDIF
C         NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
         IF( NX.LT.N ) THEN
*
*           Determine if workspace is large enough for blocked code.
*
            LDWORK = N
            IWS = LDWORK*NB
            IF( LWORK.LT.IWS ) THEN
*
*              Not enough workspace to use optimal NB:  determine the
*              minimum value of NB, and reduce NB or force use of
*              unblocked code by setting NX = N.
*
               NB = MAX( LWORK / LDWORK, 1 )
               NBMIN = 2
C               NBMIN = ILAENV( 2, 'DSYTRD', UPLO, N, -1, -1, -1 )
               IF( NB.LT.NBMIN )
     $            NX = N
            END IF
         ELSE
            NX = N
         END IF
      ELSE
         NB = 1
      END IF
*
      IF( UPPER ) THEN
*
*        Reduce the upper triangle of A.
*        Columns 1:kk are handled by the unblocked method.
*
         KK = N - ( ( N-NX+NB-1 ) / NB )*NB
         DO 20 I = N - NB + 1, KK + 1, -NB
*
*           Reduce columns i:i+nb-1 to tridiagonal form and form the
*           matrix W which is needed to update the unreduced part of
*           the matrix
*
            CALL SLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK,
     $                   LDWORK )
C            CALL DLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK,
C     $                   LDWORK )
*
*           Update the unreduced submatrix A(1:i-1,1:i-1), using an
*           update of the form:  A := A - V*W' - W*V'
*
            CALL SSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
     $                   LDA, WORK, LDWORK, ONE, A, LDA )
C            CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
C     $                   LDA, WORK, LDWORK, ONE, A, LDA )
*
*           Copy superdiagonal elements back into A, and diagonal
*           elements into D
*
            DO 10 J = I, I + NB - 1
               A( J-1, J ) = E( J-1 )
               D( J ) = A( J, J )
   10       CONTINUE
   20    CONTINUE
*
*        Use unblocked code to reduce the last or only block
*
         CALL SSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO )
C         CALL DSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO )
      ELSE
*
*        Reduce the lower triangle of A
*
         DO 40 I = 1, N - NX, NB
*
*           Reduce columns i:i+nb-1 to tridiagonal form and form the
*           matrix W which is needed to update the unreduced part of
*           the matrix
*
            CALL SLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ),
     $                   TAU( I ), WORK, LDWORK )
C            CALL DLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ),
C     $                   TAU( I ), WORK, LDWORK )
*
*           Update the unreduced submatrix A(i+ib:n,i+ib:n), using
*           an update of the form:  A := A - V*W' - W*V'
*
            CALL SSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
     $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
     $                   A( I+NB, I+NB ), LDA )
C            CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
C     $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
C     $                   A( I+NB, I+NB ), LDA )
*
*           Copy subdiagonal elements back into A, and diagonal
*           elements into D
*
            DO 30 J = I, I + NB - 1
               A( J+1, J ) = E( J )
               D( J ) = A( J, J )
   30       CONTINUE
   40    CONTINUE
*
*        Use unblocked code to reduce the last or only block
*
         CALL SSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ),
     $                TAU( I ), IINFO )
C         CALL DSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ),
C     $                TAU( I ), IINFO )
      END IF
*
      WORK( 1 ) = LWKOPT
      RETURN
*
*     End of sSYTRD
C*     End of DSYTRD
*
      END
      SUBROUTINE SLAGSY( N, K, D, A, LDA, ISEED, WORK, INFO )
*
*  -- LAPACK auxiliary test routine (version 3.0)
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      INTEGER            INFO, K, LDA, N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      REAL               A( LDA, * ), D( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  SLAGSY generates a real symmetric matrix A, by pre- and post-
*  multiplying a real diagonal matrix D with a random orthogonal matrix:
*  A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
*  orthogonal transformations.
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  K       (input) INTEGER
*          The number of nonzero subdiagonals within the band of A.
*          0 <= K <= N-1.
*
*  D       (input) REAL array, dimension (N)
*          The diagonal elements of the diagonal matrix D.
*
*  A       (output) REAL array, dimension (LDA,N)
*          The generated n by n symmetric matrix A (the full matrix is
*          stored).
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= N.
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry, the seed of the random number generator; the array
*          elements must be between 0 and 4095, and ISEED(4) must be
*          odd.
*          On exit, the seed is updated.
*
*  WORK    (workspace) REAL array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE, HALF
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, HALF = 0.5E+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      REAL               ALPHA, TAU, WA, WB, WN
*     ..
*     .. External Subroutines ..
      EXTERNAL           SAXPY, SGEMV, SGER, SLARNV, SSCAL, SSYMV,
     $                   SSYR2, XERBLA
*     ..
*     .. External Functions ..
      REAL               SDOT, SNRM2
      EXTERNAL           SDOT, SNRM2
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SIGN
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      END IF
      IF( INFO.LT.0 ) THEN
         CALL XERBLA( 'SLAGSY', -INFO )
         RETURN
      END IF
*
*     initialize lower triangle of A to diagonal matrix
*
      DO 20 J = 1, N
         DO 10 I = J + 1, N
            A( I, J ) = ZERO
   10    CONTINUE
   20 CONTINUE
      DO 30 I = 1, N
         A( I, I ) = D( I )
   30 CONTINUE
*
*     Generate lower triangle of symmetric matrix
*
      DO 40 I = N - 1, 1, -1
*
*        generate random reflection
*
         CALL SLARNV( 3, ISEED, N-I+1, WORK )
         WN = SNRM2( N-I+1, WORK, 1 )
         WA = SIGN( WN, WORK( 1 ) )
         IF( WN.EQ.ZERO ) THEN
            TAU = ZERO
         ELSE
            WB = WORK( 1 ) + WA
            CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
            WORK( 1 ) = ONE
            TAU = WB / WA
         END IF
*
*        apply random reflection to A(i:n,i:n) from the left
*        and the right
*
*        compute  y := tau * A * u
*
         CALL SSYMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO,
     $               WORK( N+1 ), 1 )
*
*        compute  v := y - 1/2 * tau * ( y, u ) * u
*
         ALPHA = -HALF*TAU*SDOT( N-I+1, WORK( N+1 ), 1, WORK, 1 )
         CALL SAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 )
*
*        apply the transformation as a rank-2 update to A(i:n,i:n)
*
         CALL SSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
     $               A( I, I ), LDA )
   40 CONTINUE
*
*     Reduce number of subdiagonals to K
*
      DO 60 I = 1, N - 1 - K
*
*        generate reflection to annihilate A(k+i+1:n,i)
*
         WN = SNRM2( N-K-I+1, A( K+I, I ), 1 )
         WA = SIGN( WN, A( K+I, I ) )
         IF( WN.EQ.ZERO ) THEN
            TAU = ZERO
         ELSE
            WB = A( K+I, I ) + WA
            CALL SSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 )
            A( K+I, I ) = ONE
            TAU = WB / WA
         END IF
*
*        apply reflection to A(k+i:n,i+1:k+i-1) from the left
*
         CALL SGEMV( 'Transpose', N-K-I+1, K-1, ONE, A( K+I, I+1 ), LDA,
     $               A( K+I, I ), 1, ZERO, WORK, 1 )
         CALL SGER( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1,
     $              A( K+I, I+1 ), LDA )
*
*        apply reflection to A(k+i:n,k+i:n) from the left and the right
*
*        compute  y := tau * A * u
*
         CALL SSYMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA,
     $               A( K+I, I ), 1, ZERO, WORK, 1 )
*
*        compute  v := y - 1/2 * tau * ( y, u ) * u
*
         ALPHA = -HALF*TAU*SDOT( N-K-I+1, WORK, 1, A( K+I, I ), 1 )
         CALL SAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 )
*
*        apply symmetric rank-2 update to A(k+i:n,k+i:n)
*
         CALL SSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
     $               A( K+I, K+I ), LDA )
*
         A( K+I, I ) = -WA
         DO 50 J = K + I + 1, N
            A( J, I ) = ZERO
   50    CONTINUE
   60 CONTINUE
*
*     Store full symmetric matrix
*
      DO 80 J = 1, N
         DO 70 I = J + 1, N
            A( J, I ) = A( I, J )
   70    CONTINUE
   80 CONTINUE
      RETURN
*
*     End of SLAGSY
*
      END
      REAL FUNCTION SLARAN( ISEED )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
*     ..
*
*  Purpose
*  =======
*
*  SLARAN returns a random real number from a uniform (0,1)
*  distribution.
*
*  Arguments
*  =========
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry, the seed of the random number generator; the array
*          elements must be between 0 and 4095, and ISEED(4) must be
*          odd.
*          On exit, the seed is updated.
*
*  Further Details
*  ===============
*
*  This routine uses a multiplicative congruential method with modulus
*  2**48 and multiplier 33952834046453 (see G.S.Fishman,
*  'Multiplicative congruential random number generators with modulus
*  2**b: an exhaustive analysis for b = 32 and a partial analysis for
*  b = 48', Math. Comp. 189, pp 331-344, 1990).
*
*  48-bit integers are stored in 4 integer array elements with 12 bits
*  per element. Hence the routine is portable across machines with
*  integers of 32 bits or more.
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            M1, M2, M3, M4
      PARAMETER          ( M1 = 494, M2 = 322, M3 = 2508, M4 = 2549 )
      REAL               ONE
      PARAMETER          ( ONE = 1.0E+0 )
      INTEGER            IPW2
      REAL               R
      PARAMETER          ( IPW2 = 4096, R = ONE / IPW2 )
*     ..
*     .. Local Scalars ..
      INTEGER            IT1, IT2, IT3, IT4
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MOD, REAL
*     ..
*     .. Executable Statements ..
*
*     multiply the seed by the multiplier modulo 2**48
*
      IT4 = ISEED( 4 )*M4
      IT3 = IT4 / IPW2
      IT4 = IT4 - IPW2*IT3
      IT3 = IT3 + ISEED( 3 )*M4 + ISEED( 4 )*M3
      IT2 = IT3 / IPW2
      IT3 = IT3 - IPW2*IT2
      IT2 = IT2 + ISEED( 2 )*M4 + ISEED( 3 )*M3 + ISEED( 4 )*M2
      IT1 = IT2 / IPW2
      IT2 = IT2 - IPW2*IT1
      IT1 = IT1 + ISEED( 1 )*M4 + ISEED( 2 )*M3 + ISEED( 3 )*M2 +
     $      ISEED( 4 )*M1
      IT1 = MOD( IT1, IPW2 )
*
*     return updated seed
*
      ISEED( 1 ) = IT1
      ISEED( 2 ) = IT2
      ISEED( 3 ) = IT3
      ISEED( 4 ) = IT4
*
*     convert 48-bit integer to a real number in the interval (0,1)
*
      SLARAN = R*( REAL( IT1 )+R*( REAL( IT2 )+R*( REAL( IT3 )+R*
     $         ( REAL( IT4 ) ) ) ) )
      RETURN
*
*     End of SLARAN
*
      END
* **********************************************************************
*
        PROGRAM SRUN
*
* Description:
*
*   This is the testing and timing driver for the SBR toolbox.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Local constants and variables:
*
        REAL                  ONE
        PARAMETER             ( ONE = 1.0E0 )
*
*          --- array dimensions ---
*
        INTEGER               NMAX, SZA, SZACPY, SZU, SZWORK
        PARAMETER             ( NMAX = 1400 ,
     >                          SZA = NMAX * NMAX ,
     >                          SZACPY = 500 * NMAX ,
     >                          SZU = NMAX * NMAX ,
     >                          SZWORK = NMAX * NMAX  )
        REAL                  A( SZA ), ACPY( SZACPY ), U( SZU ),
     >                        EVLS( NMAX ), D( NMAX ), E( NMAX ),
     >                        TAU( NMAX ), WORK( SZWORK )
        COMMON    /ARRAYS/    A, ACPY, U, EVLS, D, E, TAU, WORK
*
*   nmax    maximum matrix size
*   a       holds the matrix A to be reduced (full or banded)
*   sza     size of the array a.
*           sza >= nmax * nmax,       if full matrices are handled
*               >= ( bmax+1 ) * nmax, if only banded matrices with
*                                     semibandwidth <= bmax are handled
*   acpy    holds the reduced matrix (banded)
*   szacpy  size of the array acpy.
*           szacpy >= ( bmax+1 ) * nmax, where bmax is the maximum
*                                        semibandwith
*   u       holds the accumulated transformation matrix U, if required
*   szu     size of the array u.
*           szu >= nmax * nmax, if U is accumulated
*               >= 0,           otherwise
*   evls    the eigenvalues of the matrix A (accessed during
*           initialization)
*   d       main diagonal of the reduced tridiagonal matrix
*   e       sub(super)diagonal of the reduced tridiagonal matrix
*   tau     scaling factors in the reduction full -> banded/tridiagonal
*   work    workspace
*   szwork  size of the array work.
*           szwork depends on the reduction algorithms that are run, on
*           the matrix sizes, on the blocking factors, and on the
*           leading dimensions of the matrices.
*           Recomended: szwork >= 100 * nmax.
*   arrays  common block is used only because some machines cannot
*           handle large arrays on the stack
*
*          --- I/O control ---
*
        INTEGER               IUNIT, OUNIT, OUNITF
	INTEGER               I1MACH
*       PARAMETER             ( IUNIT = 5, OUNITF = 8 )
*       CHARACTER*8           IFILE, OFILE
        CHARACTER*8           OFILE
*       PARAMETER             ( IFILE = 'INFILE' )
        INTEGER               OLEVEL, OUTSUM, OUTTUN, OUTRUN, OUTDET,
     >                        LINENO, LINE0
        PARAMETER             ( OUTSUM = 1, OUTTUN = 2, OUTRUN = 3,
     >                          OUTDET = 4 )
        CHARACTER*78          MBUF
*
*   iunit   unit number for input file
*   ounit   unit number for output
*   ounitf  unit number for output file
*   ifile   name of input file
*   ofile   name of output file
*   olevel  level of output
*           olevel = outsum : only summary for all the runs
*                  = outtun : short summaries for tuning
*                  = outrun : summary for each run
*                  = outdet : detailed output for each run
*   lineno  number of current input line
*   line0   first input line corresponding to the current run
*   mbuf    buffer for messages
*
*          --- for statistics ---
*
        INTEGER               SYTRD, ORGTR, SBTRD, SYRDB, SYGTR, SBRDB,
     >                        SBRDT, SY2BC, SY2BI, SB2BC, SB2BI, SYRDD,
     >                        SBRDD, TOTAL
        PARAMETER             ( SYTRD = 1, ORGTR = 2, SBTRD = 3,
     >                          SYRDB = 4, SYGTR = 5, SBRDB = 6,
     >                          SBRDT = 7, SY2BC = 8, SY2BI = 9,
     >                          SB2BC = 10, SB2BI = 11, SYRDD = 12,
     >                          SBRDD = 13, TOTAL = 14 )
        INTEGER               TRY( TOTAL ), SKIP( TOTAL ), FAIL( TOTAL )
        CHARACTER*6           PRBLMN( TOTAL )
        CHARACTER*40          COMMNT( TOTAL )
*
*   sytrd   tests for ssytrd (full -> tridiagonal, LAPACK)
*   orgtr   tests for sorgtr (backward accumulation, LAPACK)
*   sbtrd   tests for ssbtrd (banded -> tridiagonal, LAPACK)
*   syrdb   tests for ssyrdb (full -> banded, SBR)
*   sygtr   tests for ssygtr (backward accumulation, SBR)
*   sbrdb   tests for ssbrdb (banded -> banded, SBR)
*   sbrdt   tests for ssbrdt (banded -> tridiagonal, SBR)
*   sy2bc   tests for ssy2bc (full -> banded copy, SBR)
*   sy2bi   tests for ssy2bi (full -> banded repacking, SBR)
*   sb2bc   tests for ssb2bc (banded -> banded copy, SBR)
*   sb2bi   tests for ssb2bi (banded -> banded repacking, SBR)
*   syrdd   tests for ssyrdd (reduction driver for full matrices, SBR)
*   sbrdd   tests for ssbrdd (reduction driver for banded matrices, SBR)
*   total   all tests
*   count   counters for all tests
*   fail    counters for failed tests
*   skip    counters for skipped tests
*   prblmn  names of the reduction paths (for output)
*   commnt  comments to the reduction paths (for output)
*
        DOUBLE PRECISION      STIME, BTIME, CTIME, RTIME
*
*   stime   time before all the tests
*   btime   time before the procedure call
*   ctime   time for the procedure call
*   rtime   time for a full reduction/accumulation path
*
*        --- controlling the test runs ---
*
        REAL                  EPS, NOTUSD
*
*   eps     machine epsilon
*   notusd  (large) value for marking memory that should not be accessed
*
        CHARACTER*5           PNAME
        INTEGER               MAXDIM, PRBLM, N, B1, LDA1, B2, LDA2, LDU,
     >                        NSTEPS, STEP, LWORK1, LWORK2, NX1, NX2,
     >                        XINFO1, XINFO2, INFO
        CHARACTER             MTYPE, UPLO, FRMT1, FRMT2, JOBU, JOBU0
        REAL                  DIAM, DRPTOL
        INTEGER               B( 100 ), NB( 100 )
*
*   pname   name of the routine to test (without precision specifier)
*   maxdim  maximum matrix size for the runs (runs with larger matrices
*           are skipped)
*   prblm   number of the routine to test (numbering sytrd=1, etc. as
*           above)
*   mtype   matrix type
*           mtype = 'R' : Eigenvalues are uniformly random in [ -1, 1 ).
*                 = 'I' : ISDA-type matrix: eigenvalues are clustered
*                         around 0 and 1.
*   diam    diameter of the eigenvalue clusters in multiples of the
*           machine precision (used only for ISDA-type matrices)
*   uplo    use upper or lower triangle of the matrix ?
*   n       matrix dimension
*   frmt1   format of the matrix before the reduction ('F'ull/'B'anded)
*   b1      semibandwidth before the reduction
*   lda1    leading dimension before the reductino
*   frmt2   format after the reduction ('B'anded/'T'ridiagonal)
*   b2      semibandwidth after the reduction
*   lda2    leading dimension after the reduction
*   jobu0   accumulate the transformations in an orthogonal matrix ?
*   jobu    accumulate in the current routine ?
*   ldu     leading dimension of the array u
*   nsteps  number of reduction steps (used only in the driver routines)
*   step    number of the last step performed or tried
*   b       intermediate bandwidths for multi-step reduction
*   nb      blocking factors for the reduction/accumulation steps
*   drptol  threshold for skipping ransformations
*   lwork1  length of workspace for the reduction
*   lwork2  length of workspace for backward accumulation
*   nx1     cross-over point for LAPACK tridiagonalization ssytrd
*   nx2     cross-over point for LAPACK backward accumulation sorgtr
*   xinfo1  error code expected from the reduction routine
*   xinfo2  error code expected from backward accumulation
*   info    actual error code returned from the routines
*
        CHARACTER             CHECK
        REAL                  ORTHU, SORTHU, TORTHU, RES, SRES, TRES,
     >                        DEVLS, SDEVLS, TDEVLS
        LOGICAL               CHECKS, ERRCHK, OK
        INTEGER               NUSED
*
*   check   is result checking required ? ('C'check/'N'oCheck)
*   checks  are checks enabled ?
*   orthu   ortogonality error, i.e., (Frobenius) norm of U' * U - I
*   sorthu  = orthu / ( n * eps ), the scaled orthogonality error
*   torthu  threshold on sorthu for accepting the run
*   res     residual, i.e., (Frobenius) norm of U * B - A * U, where
*           A is the original matrix and B is the reduced matrix
*   sres    = res / ( n * eps * norm( A ) ), the scaled residual
*   tres    threshold on sres
*   devls   deviation of the eigenvalues, i.e., (Frobenius) norm of
*           spec( A ) - spec( B ), where spec( A ) and spec( B ) are
*           the (ascendingly sorted) eigenvalues of the original matrix
*           and the reduced matrix, respectively
*   sdevls  = devls / ( n * eps * norm( A ) ), the scaled deviation
*   tdevls  threshold on devls
*   errchk  was it a check for error exit ?
*   ok      did the numerical checks meet the thresholds ?
*   nused   number of workspace elements that were modified
*
      INTEGER                 I
*
* Routines called:
*
	REAL                  SECOND
        REAL                  R1MACH
        LOGICAL               LSAME, LXSAME
        EXTERNAL              SECOND, R1MACH, LSAME, LXSAME
*
*   dsecnd  timer (LAPACK)
*   slamch  determine machine parameters (LAPACK)
*   lsame   case-insensitive character-matching (BLAS)
*   lxsame  case-insensitive string matching (this file)
*
        EXTERNAL              SLACPY, SORGTX, SSB2BC, SSB2BI, SSBRDB,
     >                        SSBRDD, SSBRDT, SSBTRX, SSY2BC, SSY2BI,
     >                        SSYGTR, SSYINI, SSYNCK, SSYRDB, SSYRDD,
     >                        SSYTRX
*
*   slacpy  copy matrix (LAPACK)
*   sorgtx  backward accumulation of transformations (LAPACK, modified)
*   ssb2bc  banded -> banded copy (SBR)
*   ssb2bi  banded -> banded repacking (SBR)
*   ssbrdb  banded -> banded reduction (SBR)
*   ssbrdd  reduction driver for banded matrices (SBR)
*   ssbrdt  banded -> tridiagonal reduction (SBR)
*   ssbtrx  banded -> tridiagonal reduction (LAPACK, modified)
*   ssy2bc  full -> banded copy (SBR)
*   ssy2bi  full -> banded repacking (SBR)
*   ssygtr  backward accumulation of transformations (SBR)
*   ssyini  initialize symmetric (full or banded) matrix
*   ssynck  numerical checks for the reduction
*   ssyrdb  full -> banded reduction (SBR)
*   ssyrdd  reduction driver for full matrices (SBR)
*   ssytrx  full -> tridiagonal reduction (LAPACK, modified)
*
        INTRINSIC             MAX, MIN
*
*          --- names and explanations for the test paths ---
*
        DATA
     >      PRBLMN( SYTRD )/'ssytrd'/,
     >      COMMNT( SYTRD )/'full -> tridiagonal, one-step (LAPACK)'/,
     >      PRBLMN( ORGTR )/'sorgtr'/,
     >      COMMNT( ORGTR )/'accumulation of transformations (LAPACK)'/,
     >      PRBLMN( SBTRD )/'ssbtrd'/,
     >      COMMNT( SBTRD )/'banded -> tridiagonal, one-step (LAPACK)'/
        DATA
     >      PRBLMN( SYRDB )/'ssyrdb'/,
     >      COMMNT( SYRDB )/'full -> banded, one-step (SBR)'/,
     >      PRBLMN( SYGTR )/'ssygtr'/,
     >      COMMNT( SYGTR )/'accumulation of transformations (SBR)'/,
     >      PRBLMN( SBRDB )/'ssbrdb'/,
     >      COMMNT( SBRDB )/'banded -> banded, one-step (SBR)'/,
     >      PRBLMN( SBRDT )/'ssbrdt'/,
     >      COMMNT( SBRDT )/'banded -> tridiagonal, one-step (SBR)'/
        DATA
     >      PRBLMN( SY2BC )/'ssy2bc'/,
     >      COMMNT( SY2BC )/'copy full -> banded (SBR)'/,
     >      PRBLMN( SY2BI )/'ssy2bi'/,
     >      COMMNT( SY2BI )/'in-place copy full -> banded (SBR)'/,
     >      PRBLMN( SB2BC )/'ssb2bc'/,
     >      COMMNT( SB2BC )/'copy banded -> banded (SBR)'/,
     >      PRBLMN( SB2BI )/'ssb2bi'/,
     >      COMMNT( SB2BI )/'in-place copy banded -> banded (SBR)'/
        DATA
     >      PRBLMN( SYRDD )/'ssyrdd'/,
     >      COMMNT( SYRDD )/'reduction driver for full matrices (SBR)'/,
     >      PRBLMN( SBRDD )/'ssbrdd'/,
     >      COMMNT( SBRDD )/'reduction driver for banded matrcs (SBR)'/,
     >      PRBLMN( TOTAL )/'Total '/,
     >      COMMNT( TOTAL )/' '/
*
* ----------------------------------------------------------------------
*
        STIME = SECOND()
*
*          --- initialize ---
*
        DO 1000 I = 1, TOTAL
          TRY( I ) = 0
          SKIP( I ) = 0
          FAIL( I ) = 0
 1000   CONTINUE
*
*       EPS = SLAMCH( 'Epsilon' )
*       NOTUSD = ONE / SLAMCH( 'SafeMinimum' )
        EPS = R1MACH(4)
	NOTUSD = ONE/(R1MACH(1)*(ONE + EPS))
*
*          --- open input and output files ---
*
*       OPEN( UNIT=IUNIT, FILE=IFILE )
        LINENO = 0
*
	IUNIT = I1MACH(1)
        OUNIT = I1MACH(2)
        OLEVEL = OUTSUM
        MAXDIM = NMAX
        CHECKS = .TRUE.
*
 2000   CONTINUE
*
*            --- read next line from input file ---
*
          LINENO = LINENO + 1
          LINE0 = LINENO
          READ( IUNIT, * ) PNAME
*         WRITE( *, * ) LINE0
*
*            --- if comment line then just skip it ---
*
          IF ( LSAME( PNAME( 1:1 ), 'Comment' ) ) THEN
            GOTO 2000
*
*            --- filename for output file ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'FileName' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) OFILE( 2:8 )
            OFILE( 1:1 ) = 'SinglePrec'
            OUNIT = OUNITF
            OPEN( UNIT=OUNIT, FILE=OFILE )
            GOTO 2000
*
*            --- set output level ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'OutputLevel' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) I
            IF ( ( I .LT. OUTSUM ) .OR. ( I .GT. OUTDET ) ) THEN
              WRITE( OUNIT, 9300 ) LINENO, 'Output level out of range'
            ELSE
              OLEVEL = I
            ENDIF
            GOTO 2000
*
*            --- message to print ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'Print' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) MBUF
            WRITE( OUNIT, 9100 ) MBUF
            GOTO 2000
*
*            --- maximum matrix size ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'MaxDim' ) ) THEN
            LINENO = LINENO + 1
            READ( IUNIT, * ) MAXDIM
            GOTO 2000
*
*            --- disable checks ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'NoChecks' ) ) THEN
            CHECKS = .FALSE.
            GOTO 2000
*
*            --- test run ?
*                If so then read and set parameters for the run ---
*
          ELSEIF ( LXSAME( PNAME, 'SYTRD' ) ) THEN
*
*              --- LAPACK reduction full -> tridiagonal ---
*
            PRBLM = SYTRD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, NB( 1 ), NX1,
     >                       LWORK1, XINFO1, JOBU, NB( 2 ), NX2, LWORK2,
     >                       XINFO2
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SBTRD' ) ) THEN
*
*              --- LAPACK reduction banded -> tridiagonal ---
*
            PRBLM = SBTRD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, JOBU, LDU,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
            LWORK1 = N
          ELSEIF ( LXSAME( PNAME, 'SYRDB' ) ) THEN
*
*              --- SBR reduction full -> banded ---
*
            PRBLM = SYRDB
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, B2, DRPTOL,
     >                       NB( 1 ), LWORK1, XINFO1
            LINENO = LINENO + 1
            READ( IUNIT, * ) JOBU0, LDU, LWORK2, XINFO2
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Banded'
            LDA2 = B2 + 1
            IF ( LSAME( JOBU0, 'OnFly' ) ) THEN
              JOBU = 'Update'
            ELSEIF ( LSAME( JOBU0, 'Update' ) ) THEN
              JOBU = 'NoU'
            ELSE
              JOBU = JOBU0
            ENDIF
          ELSEIF ( LXSAME( PNAME, 'SBRDB' ) ) THEN
*
*              --- SBR reduction banded -> banded ---
*
            PRBLM = SBRDB
            READ( IUNIT, * ) MTYPE, DIAM, N, B1, LDA1, B2, DRPTOL,
     >                       NB( 1 ), JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            UPLO = 'Lower'
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Banded'
            LDA2 = B2 + 1
          ELSEIF ( LXSAME( PNAME, 'SBRDT' ) ) THEN
*
*              --- SBR reduction banded -> tridiagonal ---
*
            PRBLM = SBRDT
            READ( IUNIT, * ) MTYPE, DIAM, N, B1, LDA1, DRPTOL, NB( 1 ),
     >                       JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            UPLO = 'Lower'
            DRPTOL = DRPTOL * EPS
            FRMT2 = 'Tridiagonal'
            B2 = 1
            LDA2 = B2 + 1
          ELSEIF ( LXSAME( PNAME, 'SY2BC' ) ) THEN
*
*              --- SBR copy full -> banded ---
*
            PRBLM = SY2BC
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Full'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SY2BI' ) ) THEN
*
*              --- SBR in-place copy full -> banded ---
*
            PRBLM = SY2BI
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Full'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SB2BC' ) ) THEN
*
*              --- SBR copy banded -> banded ---
*
            PRBLM = SB2BC
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SB2BI' ) ) THEN
*
*              --- SBR in-place copy full -> banded ---
*
            PRBLM = SB2BI
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, LDA2,
     >                       XINFO1
            FRMT1 = 'Banded'
            FRMT2 = 'Banded'
            B2 = B1
            LWORK1 = 0
            JOBU = 'NoU'
            LDU = N
          ELSEIF ( LXSAME( PNAME, 'SYRDD' ) ) THEN
*
*              --- SBR driver for full matrices ---
*
            PRBLM = SYRDD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, LDA1, B2, LDA2,
     >                       NSTEPS, DRPTOL, JOBU, LWORK1, XINFO1
            FRMT1 = 'Full'
            B1 = MAX( N-1, 0 )
            DRPTOL = DRPTOL * EPS
            IF ( B2 .EQ. 1 ) THEN
              FRMT2 = 'Tridiagonal'
            ELSE
              FRMT2 = 'Banded'
            ENDIF
            LDU = N
            IF ( NSTEPS .GT. 1 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( B( I ), I = 1, NSTEPS-1 )
            ENDIF
            IF ( NSTEPS .GT. 0 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( NB( I ), I = 1, NSTEPS )
            ENDIF
          ELSEIF ( LXSAME( PNAME, 'SBRDD' ) ) THEN
*
*              --- SBR driver for banded matrices ---
*
            PRBLM = SBRDD
            READ( IUNIT, * ) MTYPE, DIAM, UPLO, N, B1, LDA1, B2, NSTEPS,
     >                       DRPTOL, JOBU, LDU, LWORK1, XINFO1
            FRMT1 = 'Banded'
            DRPTOL = DRPTOL * EPS
            IF ( B2 .EQ. 1 ) THEN
              FRMT2 = 'Tridiagonal'
            ELSE
              FRMT2 = 'Banded'
            ENDIF
            LDA2 = B2 + 1
            IF ( NSTEPS .GT. 1 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( B( I ), I = 1, NSTEPS-1 )
            ENDIF
            IF ( NSTEPS .GT. 0 ) THEN
              LINENO = LINENO + 1
              READ( IUNIT, * ) ( NB( I ), I = 1, NSTEPS )
            ENDIF
*
*            --- done ? ---
*
          ELSEIF ( LSAME( PNAME( 1:1 ), 'Quit' ) ) THEN
            GOTO 8000
          ELSE
            WRITE( OUNIT, 9300 ) LINENO, 'Command not recognized'
            GOTO 2000
          ENDIF
*
*  - - - - - - - - if we get here then a test run is required - - - - -
*
          LINENO = LINENO + 2
          READ ( IUNIT, * ) CHECK, TORTHU, TRES, TDEVLS
          ERRCHK = .FALSE.
*
          TRY( PRBLM ) = TRY( PRBLM ) + 1
*
*            --- is the problem too large ? ---
*
          IF ( N .GT. MAXDIM ) THEN
            SKIP( PRBLM ) = SKIP( PRBLM ) + 1
            WRITE( OUNIT, 9310 ) LINE0
            GOTO 2000
          ENDIF
*
*            ---  initialize matrices ---
*
          INFO = 0
          BTIME = SECOND()
          CALL SSYINI( MTYPE, EVLS, NMAX, DIAM,
     >                 FRMT1, UPLO, N, B1, A, LDA1, SZA,
     >                 JOBU, U, LDU, SZU,
     >                 NOTUSD, WORK, SZWORK, INFO )
          CTIME = SECOND() - BTIME
*
*            --- protocol output, if required ---
*
          IF ( OLEVEL .GE. OUTDET ) THEN
            WRITE( OUNIT, 9500 ) MTYPE, NMAX, DIAM, FRMT1, UPLO, N
            WRITE( OUNIT, 9501 ) B1, LDA1, SZA, JOBU, LDU, SZU
            WRITE( OUNIT, 9502 ) NOTUSD, SZWORK
            WRITE( OUNIT, 9400 ) INFO, CTIME
          ENDIF
*
          IF ( ( INFO .EQ. -3 ) .OR. ( INFO .EQ. -11 ) .OR.
     >         ( INFO .EQ. -15 ) .OR. ( INFO .EQ. -18 ) ) THEN
*
*              --- test problem is too large : skip ---
*
            SKIP( PRBLM ) = SKIP( PRBLM ) + 1
            WRITE( OUNIT, 9310 ) LINE0
            GOTO 3000
          ENDIF
*
*            --- mark workspace "unused" ---
*
          DO 2100 I = 1, MIN( MAX( 2*LWORK1, 10000 ), SZWORK )
            WORK( I ) = NOTUSD
 2100     CONTINUE
*
*  - - - - - - - - do the reduction / repacking - - - - - - - - - - - -
*
          INFO = 0
          BTIME = SECOND()
          IF ( PRBLM .EQ. SYTRD ) THEN
            CALL SSYTRX( NB( 1 ), NX1, UPLO, N, A, LDA1, D, E,
     >                   TAU, WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBTRD ) THEN
            CALL SSBTRX( JOBU, UPLO, N, B1, A, LDA1, D, E,
     >                   U, LDU, WORK, INFO )
          ELSEIF ( PRBLM .EQ. SYRDB ) THEN
            CALL SSYRDB( UPLO, JOBU, N, B2, A, LDA1, DRPTOL,
     >                   U, LDU, NB( 1 ), TAU, WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBRDB ) THEN
            CALL SSBRDB( JOBU, N, B1, B2, A, LDA1, DRPTOL,
     >                   U, LDU, NB( 1 ), WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SBRDT ) THEN
            CALL SSBRDT( JOBU, N, B1, A, LDA1, DRPTOL, D, E,
     >                   U, LDU, NB( 1 ), WORK, LWORK1, INFO )
          ELSEIF ( PRBLM .EQ. SY2BC ) THEN
            CALL SSY2BC( UPLO, N, B1, A, LDA1, ACPY, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SY2BI ) THEN
            CALL SSY2BI( UPLO, N, B1, A, LDA1, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SB2BC ) THEN
            CALL SSB2BC( UPLO, N, B1, A, LDA1, ACPY, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SB2BI ) THEN
            CALL SSB2BI( UPLO, N, B1, A, LDA1, LDA2, INFO )
          ELSEIF ( PRBLM .EQ. SYRDD ) THEN
            CALL SSYRDD( JOBU, UPLO, N, B2, A, LDA1, DRPTOL,
     >                   ACPY, LDA2, D, E, NSTEPS, B, NB,
     >                   WORK, LWORK1, STEP, INFO )
          ELSEIF ( PRBLM .EQ. SBRDD ) THEN
            CALL SSBRDD( JOBU, UPLO, N, B1, B2, A, LDA1, DRPTOL,
     >                   D, E, U, LDU, NSTEPS, B, NB,
     >                   WORK, LWORK1, STEP, INFO )
          ENDIF
          CTIME = SECOND() - BTIME
          RTIME = CTIME
*
*            --- protocol output, if required ---
*
          IF ( OLEVEL .GE. OUTDET ) THEN
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9510 ) UPLO, N, LDA1, NB( 1 ), NX1, LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9520 ) JOBU, UPLO, N, B1, LDA1, LDU
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9530 ) UPLO, JOBU, N, B2, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9540 ) JOBU, N, B1, B2, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9550 ) JOBU, N, B1, LDA1, DRPTOL
              WRITE( OUNIT, 9531 ) LDU, NB( 1 ), LWORK1
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SY2BC ) THEN
              WRITE( OUNIT, 9560 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SY2BI ) THEN
              WRITE( OUNIT, 9570 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SB2BC ) THEN
              WRITE( OUNIT, 9580 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SB2BI ) THEN
              WRITE( OUNIT, 9590 ) UPLO, N, B1, LDA1, LDA2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9600 ) JOBU, UPLO, N, B2, LDA1
              WRITE( OUNIT, 9601 ) DRPTOL, LDA2, NSTEPS, LWORK1
              WRITE( OUNIT, 9401 ) STEP, INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9610 ) JOBU, UPLO, N, B1, B2, LDA1
              WRITE( OUNIT, 9611 ) DRPTOL, LDU, NSTEPS, LWORK1
              WRITE( OUNIT, 9401 ) STEP, INFO, CTIME
            ENDIF
          ELSEIF ( OLEVEL .EQ. OUTTUN ) THEN
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9515 ) UPLO, N, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9525 ) UPLO, JOBU, N, B1, INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9535 ) UPLO, JOBU, N, B2, NB( 1 ), INFO,
     >                             CTIME
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9545 ) JOBU, N, B1, B2, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9555 ) JOBU, N, B1, NB( 1 ), INFO, CTIME
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9605 ) UPLO, JOBU, N, B2, NSTEPS, STEP,
     >                             INFO, CTIME
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9615 ) UPLO, JOBU, N, B1, B2, NSTEPS, STEP,
     >                             INFO, CTIME
            ENDIF
          ENDIF
*
*  - - - - - - - - check if the error code is as expected - - - - - - -
*
          IF ( INFO .NE. XINFO1 ) THEN
*
*              --- wrong error code ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            IF ( ( PRBLM .EQ. SYRDD ) .OR. ( PRBLM .EQ. SBRDD ) ) THEN
              WRITE( OUNIT, 9900 ) LINE0, PRBLMN( PRBLM ), INFO, STEP,
     >                             XINFO1
            ELSE
              WRITE( OUNIT, 9901 ) LINE0, PRBLMN( PRBLM ), INFO, XINFO1
            ENDIF
            GOTO 3000
          ELSEIF ( ( ( PRBLM .EQ. SYRDD ) .OR. ( PRBLM .EQ. SBRDD ) )
     >             .AND. ( INFO .EQ. 1 ) .AND. ( NSTEPS .GT. 0 )
     >             .AND. ( STEP .NE. NSTEPS ) ) THEN
*
*              --- error code was ok, but the driver took a wrong
*                  number of steps                                ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            WRITE( OUNIT, 9910 ) LINE0, PRBLMN( PRBLM ), STEP,
     >                           NSTEPS
            GOTO 3000
          ELSEIF ( INFO .LT. 0 ) THEN
*
*              --- successful error exit ---
*
            ERRCHK = .TRUE.
            GOTO 3000
          ENDIF
*
*  - - - - - - - - check workspace usage - - - - - - - - - - - - - - - -
*
          NUSED = 0
          DO 2200 I = 1, MIN( MAX( 2*LWORK1, 10000 ), SZWORK )
            IF ( .NOT. ( WORK( I ) .EQ. NOTUSD ) )     NUSED = I
 2200     CONTINUE
*
          IF ( NUSED .GT. LWORK1 ) THEN
*
*              --- ran over the workspace bounds ---
*
            FAIL( PRBLM ) = FAIL( PRBLM ) + 1
            WRITE( OUNIT, 9920 ) LINE0, PRBLMN( PRBLM ), NUSED, LWORK1
            GOTO 3000
          ELSEIF ( OLEVEL .GE. OUTDET ) THEN
*
*            --- write protocol ---
*
            WRITE( OUNIT, 9410 ) NUSED, LWORK1
          ENDIF
*
*  - - - - - - - - accumulate transformations, if required - - - - - - -
*
          IF ( ( PRBLM .EQ. SYTRD ) .AND. LSAME( JOBU, 'Update' ) ) THEN
*
*              --- copy the Householder vectors into the array u ---
*
            CALL SLACPY( UPLO, N, N, A, LDA1, U, LDU )
*
*              --- backward accumulation ---
*
            TRY( ORGTR ) = TRY( ORGTR ) + 1
            INFO = 0
            BTIME = SECOND()
            CALL SORGTX( NB( 2 ), NX2, UPLO, N, U, LDU, TAU,
     >                   WORK, LWORK2, INFO )
            CTIME = SECOND() - BTIME
            RTIME = RTIME + CTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9620 ) UPLO, N, LDU, NB( 2 ), NX2, LWORK2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- is the error code as expected ? ---
*
            IF ( INFO .NE. XINFO2 ) THEN
              FAIL( ORGTR ) = FAIL( ORGTR ) + 1
              WRITE( OUNIT, 9901 ) LINE0, 'sorgtr', INFO, XINFO2
              GOTO 3000
            ELSEIF ( INFO .NE. 0 ) THEN
              ERRCHK = .TRUE.
              GOTO 3000
            ENDIF
*
          ELSEIF ( ( PRBLM .EQ. SYRDB ) .AND. LSAME( JOBU0, 'Update' ) )
     >    THEN
*
*              --- copy the Householder vectors into the array u ---
*
            CALL SLACPY( UPLO, N, N, A, LDA1, U, LDU )
*
*              --- backward accumulation ---
*
            TRY( SYGTR ) = TRY( SYGTR ) + 1
            INFO = 0
            BTIME = SECOND()
            CALL SSYGTR( UPLO, N, B2, U, LDU, TAU, WORK, LWORK2, INFO )
            CTIME = SECOND() - BTIME
            RTIME = RTIME + CTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9630 ) UPLO, N, B2, LDU, LWORK2
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- is the error code as expected ? ---
*
            IF ( INFO .NE. XINFO2 ) THEN
              FAIL( SYGTR ) = FAIL( SYGTR ) + 1
              WRITE( OUNIT, 9901 ) LINE0, 'ssygtr', INFO, XINFO2
              GOTO 3000
            ELSEIF ( INFO .NE. 1 ) THEN
              GOTO 3000
            ENDIF
          ENDIF
*
*  - - - - - - - - check results - - - - - - - - - - - - - - - - - - - -
*
          ORTHU = -ONE
          SORTHU = -ONE
          RES = -ONE
          SRES = -ONE
          DEVLS = -ONE
          SDEVLS = -ONE
*
          IF ( ( .NOT. ERRCHK ) .AND.
     >         CHECKS .AND. LSAME( CHECK, 'Check' ) ) THEN
            OK = .TRUE.
*
*              --- if the reduced matrix is banded then copy it
*                  into the array acpy                          ---
*
            IF ( PRBLM .EQ. SYRDB ) THEN
              INFO = 0
              BTIME = SECOND()
              CALL SSY2BC( UPLO, N, B2, A, LDA1, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9560 ) UPLO, N, B2, LDA1, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
              IF ( LSAME( JOBU0, 'Update' ) )      JOBU = 'Update'
            ELSEIF ( ( PRBLM .EQ. SBRDB ) .OR.
     >               ( ( PRBLM .EQ. SBRDD ) .AND. ( B2 .GT. 1 ) ) ) THEN
              INFO = 0
              BTIME = SECOND()
              CALL SSB2BC( 'Lower', N, B2, A, LDA1, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9580 ) 'Lower', N, B2, LDA1, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
            ELSEIF ( ( PRBLM .EQ. SY2BI ) .OR. ( PRBLM .EQ. SB2BI ) )
     >      THEN
              INFO = 0
              BTIME = SECOND()
              CALL SSB2BC( 'Lower', N, B2, A, LDA2, ACPY, LDA2, INFO )
              CTIME = SECOND() - BTIME
              IF ( OLEVEL .GE. OUTDET ) THEN
                WRITE( OUNIT, 9580 ) UPLO, N, B2, LDA2, LDA2
                WRITE( OUNIT, 9400 ) INFO, CTIME
              ENDIF
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
*
*                --- copy orthogonal matrix into u ---
*
              CALL SLACPY( 'Full', N, N, A, LDA1, U, LDU )
            ENDIF
*
*              --- perform numerical checks ---
*
            INFO = 0
            BTIME = SECOND()
            CALL SSYNCK( EVLS, FRMT1, UPLO, N, B1, A, LDA1, SZA,
     >                   FRMT2, B2, ACPY, LDA2, D, E, JOBU, U, LDU,
     >                   ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                   NOTUSD, WORK, SZWORK, INFO )
            CTIME = SECOND() - BTIME
*
*              --- protocol output, if required ---
*
            IF ( OLEVEL .GE. OUTDET ) THEN
              WRITE( OUNIT, 9640 ) FRMT1, UPLO, N, B1, LDA1, SZA
              WRITE( OUNIT, 9641 ) FRMT2, B2, LDA2, JOBU, LDU
              WRITE( OUNIT, 9642 ) ORTHU, SORTHU
              WRITE( OUNIT, 9643 ) RES, SRES
              WRITE( OUNIT, 9644 ) DEVLS, SDEVLS
              WRITE( OUNIT, 9645 ) NOTUSD, SZWORK
              WRITE( OUNIT, 9400 ) INFO, CTIME
            ENDIF
*
*              --- failed any computational check ? ---
*
            IF ( .NOT. ( SORTHU .LE. TORTHU ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'orhogonality', SORTHU, TORTHU
              OK = .FALSE.
            ENDIF
            IF ( .NOT. ( SRES .LE. TRES ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'residual', SRES, TRES
              OK = .FALSE.
            ENDIF
            IF ( .NOT. ( SDEVLS .LE. TDEVLS ) ) THEN
              WRITE( OUNIT, 9930 ) LINE0, 'eigenvalues', SDEVLS, TDEVLS
              OK = .FALSE.
            ENDIF
            IF ( .NOT. OK )     FAIL( PRBLM ) = FAIL( PRBLM ) + 1
          ENDIF
*
*  - - - - - - - - print summary for this run - - - - - - - - - - - - -
*
 3000     IF ( OLEVEL .GE. OUTRUN ) THEN
            WRITE( OUNIT, 9700 ) LINE0, PRBLMN( PRBLM ), COMMNT( PRBLM )
*
            IF ( PRBLM .EQ. SYTRD ) THEN
              WRITE( OUNIT, 9710 ) MTYPE, DIAM, UPLO, N, LDA1
              WRITE( OUNIT, 9711 ) NB( 1 ), NX1, LWORK1, XINFO1
              WRITE( OUNIT, 9712 ) JOBU, NB( 2 ), NX2, LWORK2, XINFO2
            ELSEIF ( PRBLM .EQ. SBTRD ) THEN
              WRITE( OUNIT, 9720 ) MTYPE, DIAM, UPLO, N, B1, LDA1
              WRITE( OUNIT, 9721 ) JOBU, LDU, XINFO1
            ELSEIF ( PRBLM .EQ. SYRDB ) THEN
              WRITE( OUNIT, 9730 ) MTYPE, DIAM, UPLO, N, LDA1, B2
              WRITE( OUNIT, 9731 ) DRPTOL, NB( 1 ), LWORK1, XINFO1
              WRITE( OUNIT, 9732 ) JOBU, LDU, LWORK2, XINFO2
            ELSEIF ( PRBLM .EQ. SBRDB ) THEN
              WRITE( OUNIT, 9740 ) MTYPE, DIAM, N, B1, LDA1, B2
              WRITE( OUNIT, 9741 ) DRPTOL, NB( 1 ), JOBU, LDU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
            ELSEIF ( PRBLM .EQ. SBRDT ) THEN
              WRITE( OUNIT, 9750 ) MTYPE, DIAM, N, B1, LDA1
              WRITE( OUNIT, 9741 ) DRPTOL, NB( 1 ), JOBU, LDU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
            ELSEIF ( ( PRBLM .EQ. SY2BC )
     >               .OR. ( PRBLM .EQ. SY2BI )
     >               .OR. ( PRBLM .EQ. SB2BC )
     >               .OR. ( PRBLM .EQ. SB2BI ) ) THEN
              WRITE( OUNIT, 9760 ) MTYPE, DIAM, UPLO, N, B1, LDA1
              WRITE( OUNIT, 9761 ) LDA2, XINFO1
            ELSEIF ( PRBLM .EQ. SYRDD ) THEN
              WRITE( OUNIT, 9770 ) MTYPE, DIAM, UPLO, N, LDA1, B2
              WRITE( OUNIT, 9771 ) LDA2, NSTEPS, DRPTOL, JOBU, LWORK1
              WRITE( OUNIT, 9742 ) XINFO1
              IF ( NSTEPS .GT. 1 ) THEN
                WRITE( OUNIT, 9772 ) ( B( I ), I = 1, NSTEPS-1 )
              ENDIF
              IF ( NSTEPS .GT. 0 ) THEN
                WRITE( OUNIT, 9773 ) ( NB( I ), I = 1, NSTEPS )
              ENDIF
            ELSEIF ( PRBLM .EQ. SBRDD ) THEN
              WRITE( OUNIT, 9780 ) MTYPE, DIAM, UPLO, N, B1, LDA1, B2
              WRITE( OUNIT, 9781 ) NSTEPS, DRPTOL, JOBU, LDU
              WRITE( OUNIT, 9782 ) LWORK1, XINFO1
              IF ( NSTEPS .GT. 1 ) THEN
                WRITE( OUNIT, 9772 ) ( B( I ), I = 1, NSTEPS-1 )
              ENDIF
              IF ( NSTEPS .GT. 0 ) THEN
                WRITE( OUNIT, 9773 ) ( NB( I ), I = 1, NSTEPS )
              ENDIF
            ENDIF
*
*              --- print available information on numerical checks ---
*
            IF ( ERRCHK ) THEN
              WRITE( OUNIT, 9420 )
            ELSE
              IF ( .NOT. ( SORTHU .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9430 ) ORTHU, SORTHU, TORTHU
              ENDIF
              IF ( .NOT. ( SRES .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9431 ) RES, SRES, TRES
              ENDIF
              IF ( .NOT. ( SDEVLS .EQ. -ONE ) ) THEN
                WRITE( OUNIT, 9432 ) DEVLS, SDEVLS, TDEVLS
              ENDIF
            ENDIF
*
            WRITE( OUNIT, 9440 ) RTIME
          ENDIF
*
          IF ( OLEVEL .GE. OUTDET )     WRITE( OUNIT, 9000 )
*
*            --- end of the main loop ---
*
        GOTO 2000
*
*  - - - - - - - - print "global" summary - - - - - - - - - - - - - - -
*
 8000   WRITE( OUNIT, * )
        WRITE( OUNIT, 9010 )
        WRITE( OUNIT, 9020 )
        WRITE( OUNIT, 9000 )
        DO 8100 PRBLM = SYTRD, TOTAL-1
          WRITE( OUNIT, 9030 ) PRBLMN( PRBLM ), COMMNT( PRBLM ),
     >                         TRY( PRBLM ), SKIP( PRBLM ),
     >                         FAIL( PRBLM )
          TRY( TOTAL ) = TRY( TOTAL ) + TRY( PRBLM )
          SKIP( TOTAL ) = SKIP( TOTAL ) + SKIP( PRBLM )
          FAIL( TOTAL ) = FAIL( TOTAL ) + FAIL( PRBLM )
 8100   CONTINUE
        WRITE( OUNIT, 9000 )
        WRITE( OUNIT, 9030 ) PRBLMN( TOTAL ), COMMNT( TOTAL ),
     >                       TRY( TOTAL ), SKIP( TOTAL ), FAIL( TOTAL )
        WRITE( OUNIT, 9000 )
        WRITE( OUNIT, 9040 ) SECOND() - STIME
*
*  - - - - - - - - formats - - - - - - - - - - - - - - - - - - - - - - -
*
*          --- "global" summary" ---
*
 9000   FORMAT( 1X, '----------------------------------------',
     >          '---------------------------------------' )
 9010   FORMAT( 1X, '========================================',
     >          '=======================================' )
*
 9020   FORMAT( 1X, 'Tests for                               ',
     >          '              Total Skipped  Failed' )
 9030   FORMAT( 1X, A6, ' : ', A40, ' :', I8, I8, I8 )
*
 9040   FORMAT( 1X, 'Total time : ', F8.2, ' seconds' )
*
*          --- messages ---
*
 9100   FORMAT( 1X, A )
*
*          --- problems with the input file ---
*
 9300   FORMAT( 1X, '*** Error in line ', I5, ' : ', A40 )
 9310   FORMAT( 1X, '+++ Line ', I5, ' : Test too large - skipped' )
*
*          --- general status reporting ---
*
 9400   FORMAT( 1X, '          info=', I5, ', time=', F12.6 )
 9401   FORMAT( 1X, '          step=', I5, ', info=', I5,
     >          ', time=', F12.6 )
*
 9410   FORMAT( 1X, '          used ', I8, ' out of ',
     >          I8, ' workspace' )
*
 9420   FORMAT( 1X, '    ((( check for error exit ))),' )
*
 9430   FORMAT( 1X, '    Norm(U''*U-I) =', E10.3, '=',
     >          E10.3, '*n*macheps         (thresh=', E10.3, '),' )
 9431   FORMAT( 1X, '    Norm(U*B-A*U)=', E10.3, '=',
     >          E10.3, '*n*macheps*Norm(A) (thresh=', E10.3, '),' )
 9432   FORMAT( 1X, '    Norm(Dlambda)=', E10.3, '=',
     >          E10.3, '*n*macheps*Norm(A) (thresh=', E10.3, '),' )
*
 9440   FORMAT( 1X, '    reduction time=', F12.6 )
*
*          --- formats for tracing single routine calls ---
*
 9500   FORMAT( 1X, '  ssyini: mtype=', A1, ', szevls=', I5,
     >          ', diam=', E11.4, ', frmt=', A1, ', uplo=', A1,
     >          ', n=', I5, ',' )
 9501   FORMAT( 1X, '          b=', I5, ', lda=', I5, ', sza=', I8,
     >          ', jobu=', A1, ', ldu=', I5, ', szu=', I8, ',' )
 9502   FORMAT( 1X, '          notusd=', E11.4, ', szwork=', I8, ',' )
*
 9510   FORMAT( 1X, '  ssytrd: uplo=', A1, ', n=', I5, ', lda=', I5,
     >          ', nb0=', I5, ', nx0=', I5, ', lwork=', I8, ',' )
 9515   FORMAT( 1X, 'ssytrd: uplo=', A1, ', n=', I5, ', nb=', I3,
     >          ', info=', I3, ', time=', F9.3 )
*
 9520   FORMAT( 1X, '  ssbtrd: vect=', A1, ', uplo=', A1, ', n=', I5,
     >          ', kd=', I5, ', ldab=', I5, ', ldu=', I5, ',' )
 9525   FORMAT( 1X, 'ssbtrd: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b1=', I3, ', info=', I3, ', time=', F9.3 )
*
 9530   FORMAT( 1X, '  ssyrdb: uplo=', A1, ', job=', A1, ', n=', I5,
     >          ', b=', I5, ', lda=', I5, ', drptol=', E11.4, ',' )
 9531   FORMAT( 1X, '          ldu=', I5, ', nb=', I5, ', lwork=', I8,
     >          ',' )
 9535   FORMAT( 1X, 'ssyrdb: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b2=', I3, ', nb=', I3, ', info=', I3,
     >          ', time=', F9.3 )
*
 9540   FORMAT( 1X, '  ssbrdb: job=', A1, ', n=', I5, ', b1=', I5,
     >          ', b2=', I5, ', lda=', I5, ', drptol=', E11.4, ',' )
 9545   FORMAT( 1X, 'ssbrdb: jobu=', A1, ', n=', I5, ', b1=', I3,
     >          ', b2=', I3, ', nb=',I3, ', info=', I3,
     >          ', time=', F9.3 )
*
 9550   FORMAT( 1X, '  ssbrdt: job=', A1, ', n=', I5, ', b=', I5,
     >          ', lda=', I5, ', drptol=', E11.4, ',' )
 9555   FORMAT( 1X, 'ssbrdt: jobu=', A1, ', n=', I5, ', b1=', I3,
     >          ', nb=', I3, ', info=', I3, ', time=', F9.3 )
*
 9560   FORMAT( 1X, '  ssy2bc: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldfull=', I5, ', ldband=', I5, ',' )
*
 9570   FORMAT( 1X, '  ssy2bi: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldfull=', I5, ', ldband=', I5, ',' )
*
 9580   FORMAT( 1X, '  ssb2bc: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldsrc=', I5, ', lddst=', I5, ',' )
*
 9590   FORMAT( 1X, '  ssb2bi: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', ldsrc=', I5, ', lddst=', I5, ',' )
*
 9600   FORMAT( 1X, '  ssyrdd: job=', A1, ', uplo=', A1, ', n=', I5,
     >          ', b2=', I5, ', lda=', I5, ',' )
 9601   FORMAT( 1X, '          drptol=', E11.4, ', ldband=', I5,
     >          ', nsteps=', I5, ', lwork=', I8, ',' )
 9605   FORMAT( 1X, 'ssyrdd: uplo=', A1, ', job=', A1, ', n=', I5,
     >          ', b2=', I3, ', nsteps=', I2, ', step=', I2,
     >          ', info=', I3, ', time=', F9.3 )
*
 9610   FORMAT( 1X, '  ssbrdd: jobu=', A1, ', uplo=', A1, ', n=', I5,
     >          ', b1=', I5, ', b2=', I5, ', lda=', I5, ',' )
 9611   FORMAT( 1X, '          drptol=', E11.4, ', ldu=', I5,
     >          ', nsteps=', I5, ', lwork=', I8, ',' )
 9615   FORMAT( 1X, 'ssbrdd: uplo=', A1, ', jobu=', A1, ', n=', I5,
     >          ', b1=', I3, ', b2=', I3, ', nsteps=', I2,
     >          ', step=', I2, ', info=', I3, ', time=', F9.3 )
*
 9620   FORMAT( 1X, '  sorgtr: uplo=', A1, ', n=', I5, ', lda=', I5,
     >          ', nb=', I5, ', nx=', I5, ', lwork=', I8, ',' )
*
 9630   FORMAT( 1X, '  ssygtr: uplo=', A1, ', n=', I5, ', b=', I5,
     >          ', lda=', I5, ', lwork=', I8, ',' )
*
 9640   FORMAT( 1X, '  ssynck: frmt1=', A1, ', uplo1=', A1, ', n=', I5,
     >          ', b1=', I5, ', lda1=', I5, ', sza1=', I8, ',' )
 9641   FORMAT( 1X, '          frmt2=', A1, ', b2=', I5, ', lda2=', I5,
     >          ', jobu=', A1, ', ldu=', I5, ',' )
 9642   FORMAT( 1X, '          Norm( U''*U - I ) =', E11.4,
     >          ' = ', E11.4, '*n*macheps,' )
 9643   FORMAT( 1X, '          Norm( U*B - A*U )=', E11.4,
     >          ' = ', E11.4, '*n*macheps*Norm( A ),' )
 9644   FORMAT( 1X, '          Norm( Dlambda )  =', E11.4,
     >          ' = ', E11.4, '*n*macheps*Norm( A ),' )
 9645   FORMAT( 1X, '          notusd=', E11.4, ', szwork=', I8, ',' )
*
*          --- formats for tracing single runs ---
*
 9700   FORMAT( 1X, 'Line ', I5, ' / ', A, ' : ', A, ',' )
*
 9710   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4,
     >          ', uplo=', A1, ', n=', I5, ', lda=', I5, ',' )
 9711   FORMAT( 1X, '    nb1=', I5, ', nx1=', I5, ', lwork1=', I8,
     >          ', xinfo1=', I5, ',' )
 9712   FORMAT( 1X, '    jobu=', A1, ', nb2=', I5, ', nx2=', I5,
     >          ', lwork2=', I8, ', xinfo2=', I5, ',' )
*
 9720   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ',' )
 9721   FORMAT( 1X, '    jobu=', A1, ', ldu=', I5, ', xinfo=', I5, ',' )
*
 9730   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', lda=', I5, ', b2=', I5, ',' )
 9731   FORMAT( 1X, '    drptol=', E11.4, ', nb=', I5, ', lwork1=', I8,
     >          ', xinfo1=', I5, ',' )
 9732   FORMAT( 1X, '    jobu=', A1, ', ldu=', I5, ', lwork2=', I8,
     >          ', xinfo2=', I5, ',' )
*
 9740   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', n=', I5,
     >          ', b1=', I5, ', lda=', I5, ', b2=', I5, ',' )
 9741   FORMAT( 1X, '    drptol=', E11.4, ', nb=', I5, ', jobu=', A1,
     >          ', ldu=', I5, ', lwork=', I8, ',' )
 9742   FORMAT( 1X, '    xinfo=', I5, ',' )
*
 9750   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ',' )
*
 9760   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda1=', I5, ',' )
 9761   FORMAT( 1X, '    lda2=', I5, ', xinfo=', I5, ',' )
*
 9770   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', lda1=', I5, ', b2=', I5, ',' )
 9771   FORMAT( 1X, '    lda2=', I5, ', nsteps=', I5,
     >          ', drptol=', E11.4, ', jobu=', A1, ', lwork=', I8, ',' )
 9772   FORMAT( 1X, '    b ( 2: )=', 100(I5, ',') )
 9773   FORMAT( 1X, '    nb( 1: )=', 100(I5, ',') )
*
 9780   FORMAT( 1X, '    mtype=', A1, ', diam=', E11.4, ', uplo=', A1,
     >          ', n=', I5, ', b1=', I5, ', lda=', I5, ', b2=', I5,
     >          ',' )
 9781   FORMAT( 1X, '    nsteps=', I5, ', drptol=', E11.4,
     >          ', jobu=', A1, ', ldu=', I5, ',' )
 9782   FORMAT( 1X, '    lwork=', I8, ', xinfo=', I5, ',' )
*
*          --- unexpected behaviour of the routines ---
*
 9900   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned info=', I5, ' in step ', I5,
     >          ' (expected ', I5, ')' )
 9901   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned info=', I5, ' (expected ', I5, ')' )
*
 9910   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' returned step=', I5, ' (expected ', I5, ')' )
*
 9920   FORMAT( 1X, '*** Test in line ', I5, ' failed : ', A6,
     >          ' used ', I8, ' workspace (allowed ', I8, ')' )
*
 9930   FORMAT( 1X, '*** Test in line ', I5, ' failed ', A,
     >          ' test: ', E10.3, ' (thresh=', E10.3, ')' )
*
*  - - - - - - - - done - - - - - - - - - - - - - - - - - - - - - - - -
*
        STOP
        END
*
* **********************************************************************
*
        SUBROUTINE SSYINI( MTYPE, EVLS, SZEVLS, DIAM,
     >                     FRMT, UPLO, N, B, A, LDA, SZA,
     >                     JOBU, U, LDU, SZU,
     >                     NOTUSD, WORK, SZWORK, INFO )
*
* Description:
*
*   Generates a symmetric (full or banded) matrix A with either
*   prescribed eigenvalues, random eigenvalues, or two clusters of
*   eigenvalues. The matrix is returned either in (upper or lower)
*   symmetric full storage or in (upper or lower) symmetric banded
*   storage. In addition, U can be set to the identity matrix.
*
*   Note: In contrast to the LAPACK routine slagsy, this routine
*         generates the banded matrix within an n-by-(b+1) array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           MTYPE, FRMT, UPLO, JOBU
        INTEGER               N, B, LDA, SZA, LDU, SZU, SZWORK, SZEVLS,
     >                        INFO
        REAL                  DIAM, NOTUSD
        REAL                  A( LDA, * ), U( LDU, * ), EVLS( * ),
     >                        WORK( * )
*
*   mtype   (in) character*1
*           The matrix type.
*           mtype = 'S' : Generate a matrix with prescribed eigenvalues.
*                 = 'R' : Eigenvalues are uniformly random in [ -1, 1 ).
*                 = 'I' : ISDA-type matrix: eigenvalues are clustered
*                         around 0 and 1.
*
*   evls    (in OR out) real array, dimension ( szevls )
*           The eigenvalues of the matrix A.
*           If mtype = 'S' then evls is an input parameter, and the
*           first n elements of evls are taken as eigenvalues for the
*           matrix A.
*           If mtype = 'R' or 'I', then evls is an output parameter and
*           contains the eigenvalues of the matrix A.
*
*   szevls  (in) integer
*           The size of the array evls.
*           szevls >= n.
*
*   diam    (in) real
*           The diameter of the eigenvalue clusters (in multiples of
*           machine_epsilon).
*           Accessed only if mtype = 'I'.
*
*   frmt    (in) character*1
*           The storage format for the matrix A.
*           frmt = 'F' : (Symmetric upper or lower) full storage.
*                = 'B' : (Symmetric upper or lower) banded storage.
*
*   uplo    (in) character*1
*           Which triangle of the matrix is used?
*           uplo = 'U' : Initialize the upper triangle.
*                = 'L' : Initialize the lower triangle.
*           In banded storage (frmt = 'B'), uplo also determines
*           whether the upper or lower banded storage scheme is used.
*
*   n       (in) integer
*           The dimension of the matrix.
*           n >= 0.
*
*   b       (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           matrix A.
*           0 <= b <= max( n-1, 0 ).
*
*   a       (out) real array, dimension ( lda, n )
*           The n-by-n symmetric matrix with semibandwidth b.
*           If frmt = 'F' then A is returned in the leading n-by-n
*           subarray - that is, matrix element A( i, j ) is stored at
*           array position a( i, j ) -, with the strict lower
*           (uplo = 'U') or the strictly upper (uplo = 'L') triangle set
*           to some large value (NOT_USED).
*           If frmt = 'B' then A is returned in banded format in the
*           leading (b+1)-times-n subarray - that is, matrix element
*           A( i, j ) is stored at array position a( b+1+i-j, j ) if
*           uplo = 'U', and at position a( 1+i-j, j ) if uplo = 'L'.
*           In any case, the remainder of the first n columns is set
*           to the same large value mentioned above.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= n,   if frmt = 'F'
*               >= b+1, if frmt = 'B'.
*
*   sza     (in) integer
*           The total size (in elements) of the array (not matrix!) a.
*           sza >= lda * n.
*
*   jobu    (in) character*1
*           Set the matrix U to identity?
*           jobu = 'U' : Yes.
*                = 'N' : No.
*
*   u       (out) real array, dimension ( ldu, n )
*           If jobu = 'U' then the leading n-by-n subarray is set to
*           an n-by-n identity matrix.
*           If jobu = 'N' then u is not accessed.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= n.
*
*   szu     (in) integer
*           The total size (in elements) of the array (not matrix!) u.
*           szu >= ldu * n, if jobu = 'U'
*               >= 0      , if jobu = 'N'.
*
*   notusd  (in) real
*           Value for marking elements that should not be used.
*           Typically a rather large number.
*
*   work    (workspace) real array, dimension ( szwork )
*
*   szwork  (in) integer
*           The size of the array work.
*           szwork >= 2 * n.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           =   0 : All arguments are OK.
*           =  -1 : mtype is none of 'S', 'R', 'I' (upper/lower case).
*           =  -3 : szevls is too small ( < n ).
*           =  -4 : diam is out of range (negative).
*           =  -5 : frmt is none of 'F', 'B' (upper or lower case).
*           =  -6 : uplo is none of 'U', 'L' (upper or lower case).
*           =  -7 : n is out of range ( < 0 ).
*           =  -8 : b is out of range ( < 0 or > max( n-1, 0 ) ).
*           = -10 : lda is too small ( < n, if full, < b+1, if banded).
*           = -11 : sza is too small ( < n*lda ).
*           = -12 : jobu is none of 'U', 'N' (upper or lower case).
*           = -14 : ldu is too small ( < n ).
*           = -15 : szu is too small ( < n*ldu, if U is required).
*           = -18 : szwork is too small (see above).
*
* ----------------------------------------------------------------------
*
* Local constants and variables:
*
        REAL                  ZERO, HALF, ONE, TWO
        PARAMETER             ( ZERO = 0.0E0, HALF = 0.5E0,
     >                          ONE = 1.0E0, TWO = 2.0E0 )
*
        LOGICAL               SPEC, ISDA, FULL, UPPER, NEEDU
        INTEGER               ISEED( 4 )
        REAL                  SDIAM
*
*   spec    matrix with prescribed spectrum ?
*   isda    ISDA-type matrix or random matrix ?
*   full    store the matrix in full or banded format ?
*   upper   use upper or lower triangle ?
*   needu   update I or not ?
*   iseed   seed for the random number generator
*   sdiam   scaled diameter
*
        INTEGER               D, I, J, K, Q
        REAL                  C, S, FILL, A11, A12, A21, A22, TMP
*
*   d       the number of the new diagonal
*   c       cosine of the rotation angle
*   s       sine of the rotation angle
*   fill    new fill-in element
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        REAL                  R1MACH, SLARAN
        EXTERNAL              SCOPY, SLAGSY, R1MACH, SLARAN, SLARTG,
     >                        SLASET
*
*   scopy   vector copy (BLAS)
*   slagsy  generate symmetric matrix (LAPACK TMG)
*   slamch  inquire machine parameters (LAPACK)
*   slaran  random number generator (LAPACK TMG)
*   slartg  generate rotation (LAPACK)
*   slaset  initialize diagonal matrix (LAPACK)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- sanity check for the arguments ---
*
        SPEC = LSAME( MTYPE, 'Spectrum' )
        ISDA = LSAME( MTYPE, 'Isda' )
        FULL = LSAME( FRMT, 'Full' )
        UPPER = LSAME( UPLO, 'Upper' )
        NEEDU = LSAME( JOBU, 'Update' )
*
        IF ( .NOT. ( ISDA .OR. SPEC .OR. LSAME( MTYPE, 'Random' ) ) )
     >  THEN
          INFO = -1
        ELSEIF ( SZEVLS .LT. N ) THEN
          INFO = -3
        ELSEIF ( DIAM .LT. ZERO ) THEN
          INFO = -4
        ELSEIF ( .NOT. ( FULL .OR. LSAME( FRMT, 'Banded' ) ) ) THEN
          INFO = -5
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -6
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -7
        ELSEIF ( ( B .LT. 0 ) .OR. ( B .GT. MAX( N-1, 0 ) ) ) THEN
          INFO = -8
        ELSEIF ( ( FULL .AND. ( LDA .LT. N ) )
     >           .OR. ( LDA .LT. B+1 ) ) THEN
          INFO = -10
        ELSEIF ( SZA .LT. N*LDA ) THEN
          INFO = -11
        ELSEIF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'NoUpdate' ) ) ) THEN
          INFO = -12
        ELSEIF ( LDU .LT. N ) THEN
          INFO = -14
        ELSEIF ( NEEDU .AND. ( SZU .LT. N*LDU ) ) THEN
          INFO = -15
        ELSEIF ( SZWORK .LT. 2*N ) THEN
          INFO = -18
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .NE. 0 )     GOTO 9999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 9999
*
        IF ( .NOT. SPEC ) THEN
*
*            --- set up eigenvalue distribution ---
*
          ISEED( 1 ) = 4001
          ISEED( 2 ) = 3001
          ISEED( 3 ) = 2001
          ISEED( 4 ) = 1001
*
          SDIAM = TWO * DIAM * R1MACH(4)
          DO 1000 I = 1, N
            IF ( ISDA ) THEN
              EVLS( I ) = SDIAM * ( SLARAN( ISEED ) - HALF )
              IF ( SLARAN( ISEED ) .LT. HALF ) THEN
                EVLS( I ) = EVLS( I ) + ONE
              ENDIF
            ELSE
              EVLS( I ) = TWO * ( SLARAN( ISEED ) - HALF )
            ENDIF
 1000     CONTINUE
        ENDIF
*
*          --- initialize random number generator ---
*
        ISEED( 1 ) = 1001
        ISEED( 2 ) = 2001
        ISEED( 3 ) = 3001
        ISEED( 4 ) = 4001
*
        IF ( FULL ) THEN
*
*  - - - - - - - initialize matrix in full storage - - - - - - - - - - -
*
          CALL SLAGSY( N, B, EVLS, A, LDA, ISEED, WORK, INFO )
*
          IF ( UPPER ) THEN
*
*              --- mark lower triangle "not used" ---
*
            DO 2100 J = 1, N-1
              DO 2010 I = J+1, N
                A( I, J ) = NOTUSD
 2010         CONTINUE
 2100       CONTINUE
          ELSE
*
*              --- mark upper triangle "not used" ---
*
            DO 2300 J = 2, N
              DO 2210 I = 1, J-1
                A( I, J ) = NOTUSD
 2210         CONTINUE
 2300       CONTINUE
          ENDIF
*
        ELSE
*
* - - - - - - - - initialize matrix in banded storage - - - - - - - - -
*
* - - - - - - - - first initialize in lower packed storage - - - - - - -
*
          CALL SCOPY( N, EVLS, 1, A( 1, 1 ), LDA )
*
          DO 3500 D = 1, B
*
*              --- add d-th diagonal ---
*
            DO 3300 I = N-1, 1, -1
*
*                --- to generate an new element at position
*                    ( i+1, i-d ), ...                      ---
*
*                --- ... first determine a random rotation, ... ---
*
              A11 = SLARAN( ISEED )
              A12 = SLARAN( ISEED )
              CALL SLARTG( A11, A12, C, S, TMP )
*
*                --- ... apply it to rows i and i+1, ... ---
*
              DO 3010 Q = MAX( I-D+1, 1 ), I-1
                IF ( Q .EQ. ( I-D+1 ) ) THEN
                  A( D+1, Q ) = -S * A( D, Q )
                  A( D, Q ) = C * A( D, Q )
                ELSE
                  TMP = C * A( I-Q+2, Q ) - S * A( I-Q+1, Q )
                  A( I-Q+1, Q ) = C * A( I-Q+1, Q ) + S * A( I-Q+2, Q )
                  A( I-Q+2, Q ) = TMP
                ENDIF
 3010         CONTINUE
*
*                --- ... apply it to A( i:i+1, i:i+1 ), ... ---
*
              IF ( D .EQ. 1 ) THEN
                A11 = C * A( 1, I )
                A21 = -S * A( 1, I )
                A12 = S * A( 1, I+1 )
                A22 = C * A( 1, I+1 )
              ELSE
                A11 = C * A( 1, I ) + S * A( 2, I )
                A21 = C * A( 2, I ) - S * A( 1, I )
                A12 = C * A( 2, I ) + S * A( 1, I+1 )
                A22 = C * A( 1, I+1 ) - S * A( 2, I )
              ENDIF
              A( 1, I ) = C * A11 + S * A12
              A( 2, I ) = C * A21 + S * A22
              A( 1, I+1 ) = C * A22 - S * A21
*
*                --- ... apply it to columns i and i+1, ... ---
*
              DO 3020 Q = I+2, MIN( I+D, N )
                TMP = C * A( Q-I, I+1 ) - S * A( Q-I+1, I )
                A( Q-I+1, I ) = C * A( Q-I+1, I ) + S * A( Q-I, I+1 )
                A( Q-I, I+1 ) = TMP
 3020         CONTINUE
              IF ( ( I+D+1 ) .LE. N ) THEN
                FILL = S * A( D+1, I+1 )
                A( D+1, I+1 ) = C * A( D+1, I+1 )
              ENDIF
*
*                --- ... and chase the fill-in element down the band ---
*
              DO 3200 K = I+D, N-1, D
*
                CALL SLARTG( A( D+1, K-D ), FILL, C, S, TMP )
                A( D+1, K-D ) = TMP
*
                DO 3110 Q = K-D+1, K-1
                  TMP = C * A( K-Q+2, Q ) - S * A( K-Q+1, Q )
                  A( K-Q+1, Q ) = C * A( K-Q+1, Q ) + S * A( K-Q+2, Q )
                  A( K-Q+2, Q ) = TMP
 3110           CONTINUE
*
                A11 = C * A( 1, K ) + S * A( 2, K )
                A21 = C * A( 2, K ) - S * A( 1, K )
                A12 = C * A( 2, K ) + S * A( 1, K+1 )
                A22 = C * A( 1, K+1 ) - S * A( 2, K )
                A( 1, K ) = C * A11 + S * A12
                A( 2, K ) = C * A21 + S * A22
                A( 1, K+1 ) = C * A22 - S * A21
*
                DO 3120 Q = K+2, MIN( K+D, N )
                  TMP = C * A( Q-K, K+1 ) - S * A( Q-K+1, K )
                  A( Q-K+1, K ) = C * A( Q-K+1, K ) + S * A( Q-K, K+1 )
                  A( Q-K, K+1 ) = TMP
 3120           CONTINUE
                IF ( ( K+D+1 ) .LE. N ) THEN
                  FILL = S * A( D+1, K+1 )
                  A( D+1, K+1 ) = C * A( D+1, K+1 )
                ENDIF
 3200         CONTINUE
*
 3300       CONTINUE
*
*              --- mark the last d entries of the row "not used" ---
*
            DO 3410 I = N-D+1, N
              A( D+1, I ) = NOTUSD
 3410       CONTINUE
*
 3500     CONTINUE
*
* - - - - - - - - end : first initialize in lower packed storage - - - -
*
          IF ( UPPER ) THEN
*
*              --- convert from lower to upper banded storage ---
*
            DO 3700 I = 0, B/2
              CALL SCOPY( N-B+I, A( B+1-I, 1 ), LDA, WORK, 1 )
              DO 3610 J = 1, N-I
                A( B+1-I, I+J ) = A( I+1, J )
 3610         CONTINUE
              DO 3620 K = 1, I
                A( B+1-I, K ) = NOTUSD
 3620         CONTINUE
              CALL SCOPY( N-B+I, WORK, 1, A( I+1, B+1-I ), LDA )
              DO 3630 K = 1, B-I
                A( I+1, K ) = NOTUSD
 3630         CONTINUE
 3700       CONTINUE
          ENDIF
*
* - - - - - - - - end : initialize matrix in banded storage - - - - - -
*
        ENDIF
*
*          --- generate identity matrix in U ---
*
        IF ( NEEDU ) THEN
          CALL SLASET( 'All', N, N, ZERO, ONE, U, LDU )
        ENDIF
*
 9999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYNCK( EVLS, FRMT1, UPLO1, N, B1, A1, LDA1, SZA1,
     >                     FRMT2, B2, A2, LDA2, D, E,
     >                     JOBU, U, LDU,
     >                     ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                     NOTUSD, WORK, SZWORK, INFO )
*
* Description:
*
*   This routine performs numerical tests after an orthogonal
*   transformation
*                 T
*      A --> B = U  * A * U.
*   A is rebuilt by calling ssyini, B may be given in banded or
*   tridiagonal format.
*   Depending on whether U was build explicitly during the reduction,
*   either
*                           T
*      the orthogonality   U  * U - I      of U
*      and the residual    U * B - A * U
*   or
*      the difference between A's and B's eigenvalues
*   is checked.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           FRMT1, UPLO1, FRMT2, JOBU
        INTEGER               N, B1, LDA1, SZA1, B2, LDA2, LDU,
     >                        SZWORK, INFO
        REAL                  ORTHU, SORTHU, RES, SRES, DEVLS, SDEVLS,
     >                        NOTUSD
        REAL                  EVLS( * ), A1( LDA1, * ), A2( LDA2, * ),
     >                        D( * ), E( * ), U( LDU, * ), WORK( * )
*
*   evls    (in) real array, dimension ( n )
*           The eigenvalues of the matrix A, as returned from ssyini.
*
*   frmt1   (in) character*1
*           The storage format of the original matrix A.
*           frmt1 = 'F' : (Symmetric) full storage.
*                 = 'B' : (Symmetric) banded storage.
*
*   uplo1   (in) character*1
*           Which triangle of the matrix A (and B) is used?
*           uplo1 = 'U' : Use the upper triangle.
*                 = 'L' : Use the lower triangle.
*           In banded storage (frmt1 = 'B'), uplo1 also determines
*           whether the upper or lower banded storage scheme is used.
*
*   n       (in) integer
*           The dimension of the matrix.
*           n >= 0.
*
*   b1      (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           original matrix A.
*           0 <= b1 <= max( n-1, 0 ).
*
*   a1      (out) real array, dimension ( lda1, n )
*           a1 is used to build a copy of the original n-by-n symmetric
*           matrix A with semibandwidth b1.
*           If frmt = 'F' then A is returned in the leading n-by-n
*           subarray - that is, matrix element A( i, j ) is stored at
*           array position a1( i, j ) -, with the strict lower
*           (uplo = 'U') or the strictly upper (uplo = 'L') triangle set
*           to some large value (NOT_USED).
*           If frmt = 'B' then A is returned in banded format in the
*           leading (b1+1)-times-n subarray - that is, matrix element
*           A( i, j ) is stored at array position a1( b1+1+i-j, j ) if
*           uplo = 'U', and at position a1( 1+i-j, j ) if uplo = 'L'.
*
*   lda1    (in) integer
*           The leading dimension of the array a1.
*           lda >= n,    if frmt1 = 'F'
*               >= b1+1, if frmt1 = 'B'.
*
*   sza1    (in) integer
*           The total size (in elements) of the array (not matrix!) a1.
*           sza1 >= lda1 * n.
*
*   frmt2   (in) character*1
*           The storage format of the reduced matrix B.
*           frmt1 = 'B' : (Symmetric) banded storage.
*                 = 'T' : (Symmetric) tridiagonal in arrays d and e.
*
*   b2      (in) integer
*           The semibandwidth (i.e., the number of subdiagonals) of the
*           reduced matrix B.
*           0 <= b2 <= max( n-1, 0 ).
*
*   a2      (in) real array, dimension ( lda2, n )
*           If frmt2 = 'B' then the leading (b2+1)-times-n subarray of
*           a2 holds the reduced symmetric matrix B with semibandwidth
*           b2 in banded format - that is, matrix element A( i, j ) is
*           stored at array position a2( b2+1+i-j, j ) if uplo = 'U',
*           and at position a2( 1+i-j, j ) if uplo = 'L'.
*           If frmt2 = 'T' then a2 is not referenced.
*
*   lda2    (in) integer
*           The leading dimension of the array a2.
*           lda2 >= b2+1.
*
*   d       (in) real array, dimension ( n )
*           If frmt2 = 'T' then the first n elements of d hold the
*           main diagonal of the tridiagonal matrix B.
*           If frmt2 = 'B' then d is not referenced.
*
*   e       (in) real array, dimension ( n-1 )
*           If frmt2 = 'T' then the first n-1 elements of e hold the
*           subdiagonal (superdiagonal) of the tridiagonal matrix B.
*           If frmt2 = 'B' then e is not referenced.
*
*   jobu    (in) character*1
*           Does U contain the accumulated transformations ?
*           jobu = 'U' : Yes.
*                = 'N' : No.
*
*   u       (in) real array, dimension ( ldu, n )
*           If jobu = 'U' then the leading n-by-n subarray contains
*           the accumulated transformations from the reduction (an
*           orthogonal matrix).
*           If jobu = 'N' then u is not accessed.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= n.
*
*   orthu   (out) real
*           The orthogonality error : F-norm( U''*U - I ).
*           If jobu = 'N' then orthu is set to 0.
*
*   sorthu  (out) real
*           The scaled orthogonality error : orthu / ( n * macheps).
*           If jobu = 'N' then sorthu is set to 0.
*
*   res     (out) real
*           The residual : F-norm( U*B - A*U ).
*           If jobu = 'N' then res is set to 0.
*
*   sres    (out) real
*           The scaled residual : res / ( n * macheps * F-norm( A ) ).
*           If jobu = 'N' then sres is set to 0.
*
*   devls   (out) real
*           The change of the eigenvalues :
*              2-norm( sort(evls) - sort(spec(B)) ).
*           If jobu = 'U' then devls is set to 0.
*
*   sdevls  (out) real
*           The scaled eigenvalue changes :
*              devls / ( n * macheps * F-norm( A ) ).
*           If jobu = 'U' then sdevls is set to 0.
*
*   notusd  (in) real
*           Value for marking elements that should not be used.
*           Typically a rather large number.
*
*   work    (workspace) real array, dimension ( szwork )
*
*   szwork  (in) integer
*           The length of the array work.
*           szwork >= max( 3*n-2, 2*n ).
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           =   0 : All arguments are OK.
*           =  -2 : frmt1 is none of 'F', 'B' (upper/lower case).
*           =  -3 : uplo1 is none of 'U', 'L' (upper/lower case).
*           =  -4 : n is out of range ( < 0 ).
*           =  -5 : b1 is out of range ( < 0 or > max( n-1, 0 ) ).
*           =  -7 : lda1 too small ( < n, if full, < b1+1, if banded).
*           =  -8 : sza1 is too small ( < n * lda1 ).
*           =  -9 : frmt2 is none of 'B', 'T' (upper/lower case).
*           = -10 : b2 is out of range ( < 0 or > max( n-1, 0 ),
*                   or > 1 if frmt2 = 'T' ).
*           = -12 : lda2 is too small ( < b2+1 ).
*           = -15 : jobu is none of 'U', 'N' (upper/lower case).
*           = -17 : ldu is too small ( < n ).
*           = -26 : szwork is too small (see above).
*
* ----------------------------------------------------------------------
*
* Local constants and variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        LOGICAL               FULL1, UPPER, TRI2, HAVEU
        REAL                  EPS, NORMA
        INTEGER               NCOLS, COLS, J0, J, IX
*
*   full1   build A in full storage ?
*   upper   use upper triangle ?
*   tri2    is B given in tridiagonal storage ?
*   haveu   is the accumulated matrix U available ?
*   eps     machine epsilon
*   norma   the Frobenius norm of the matrix A
*   ncols   maximum width of a block column that fits into workspace
*   cols    width of current block column
*   j0      first column of the current block column
*   j       current column
*   ix      points to the position of the current column in workspace
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        REAL                  R1MACH, SLANGE, SNRM2
        EXTERNAL              SAXPY, SCOPY, SGEMM, SGEMV, R1MACH,
     >                        SLANGE, SLASRT, SNRM2, SSBEV, SSBMV,
     >                        SSCAL, SSTEV, SSYINI, SSYMM
*
*   saxpy   add multiple of a vector to another one (BLAS)
*   scopy   vector copy (BLAS)
*   sgemm   matrix-matrix product (BLAS)
*   sgemv   matrix-vector product (BLAS)
*   slamch  determine machine parameters (LAPACK)
*   slange  matrix norm (LAPACK)
*   slasrt  sort a vector (LAPACK)
*   snrm2   2-norm of a vector (BLAS)
*   ssbev   compute eigensystem of symmetric banded matrix (LAPACK)
*   ssbmv   banded symmetri matrix-vector product (BLAS)
*   sscal   scale a vector (BLAS)
*   sstev   compute eigensystem of symmetric tridiagonal matrix (LAPACK)
*   ssyini  initialize symmetric matrix (this file)
*   ssymm   symmetric matrix-matrix product (BLAS)
*
        INTRINSIC             MAX, MIN, SQRT
*
* ----------------------------------------------------------------------
*
*          --- sanity check for the arguments ---
*
        FULL1 = LSAME( FRMT1, 'Full' )
        UPPER = LSAME( UPLO1, 'Upper' )
        TRI2 = LSAME( FRMT2, 'Tridiagonal' )
        HAVEU = LSAME( JOBU, 'U' )
*
        IF ( .NOT. ( FULL1 .OR. LSAME( FRMT1, 'Banded' ) ) ) THEN
          INFO = -2
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO1, 'Lower' ) ) ) THEN
          INFO = -3
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -4
        ELSEIF ( ( B1 .LT. 0 ) .OR. ( B1 .GT. MAX( N-1, 0 ) ) ) THEN
          INFO = -5
        ELSEIF ( ( FULL1 .AND. ( LDA1 .LT. N ) ) .OR.
     >           ( LDA1 .LT. B1+1 ) ) THEN
          INFO = -7
        ELSEIF ( SZA1 .LT. N*LDA1 ) THEN
          INFO = -8
        ELSEIF ( .NOT. ( TRI2 .OR. LSAME( FRMT2, 'Banded' ) ) ) THEN
          INFO = -9
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND.
     >             ( ( B2 .GT. N-1 ) .OR.
     >               ( TRI2 .AND. ( B2 .GT. 1 ) ) ) ) ) THEN
          INFO = -10
        ELSEIF ( LDA2 .LT. B2+1 ) THEN
          INFO = -12
        ELSEIF ( .NOT. ( HAVEU .OR. LSAME( JOBU, 'NoU' ) ) ) THEN
          INFO = -15
        ELSEIF ( LDU .LT. N ) THEN
          INFO = -17
        ELSEIF ( SZWORK .LT. MAX( 3*N-2, 2*N ) ) THEN
          INFO = -26
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .NE. 0 )     GOTO 9999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 9999
*
*          --- determine machine precision ---
*
        EPS = R1MACH(4)
*                                                     T
*  - - - - - - compute orthogonality error = F-Norm( U  * U - I ) - - -
*
        IF ( LSAME( JOBU, 'Update' ) ) THEN
          ORTHU = ZERO
*                                     T
*            --- how many columns of U  * U - I fit into workspace ? ---
*
          NCOLS = SZWORK / N
          DO 1100 J0 = 1, N, NCOLS
            COLS = MIN( NCOLS, N-J0+1 )
*                                                     T
*              --- compute n-by-cols block column of U  * U ---
*
            CALL SGEMM( 'Transpose', 'NoTranspose', N, COLS, N,
     >                  ONE, U, LDU, U( 1, J0 ), LDU, ZERO, WORK, N )
*
*              --- subtract corresponding parts of I ---
*
            DO 1010 J = J0, J0+COLS-1
              WORK( (J-J0)*N+J ) = WORK( (J-J0)*N+J ) - ONE
 1010       CONTINUE
            ORTHU = ORTHU + SLANGE( 'Frobenius', N, COLS, WORK, N,
     >                              WORK )**2
 1100     CONTINUE
          ORTHU = SQRT( ORTHU )
          SORTHU = ORTHU / ( N * EPS )
        ELSE
*
*            --- no orthogonality information available ---
*
          ORTHU = - ONE
          SORTHU = - ONE
        ENDIF
*                                                           T
*  - - - - - - end : compute orthogonality error = F-Norm( U  * U - I )
*
        NORMA = SNRM2( N, EVLS, 1 )
*
        IF ( LSAME( JOBU, 'Update' ) ) THEN
*
*            --- do not compute changes in eigenvalues ---
*
          DEVLS = - ONE
          SDEVLS = - ONE
*
*  - - - - - - - compute residual error = F-Norm( U * B - A * U ) - - -
*
*            --- build another copy of the original matrix A ---
*
          CALL SSYINI( 'Spectrum', EVLS, N, ZERO,
     >                 FRMT1, UPLO1, N, B1, A1, LDA1, SZA1,
     >                 'NoU', WORK, N, 0,
     >                 NOTUSD, WORK, SZWORK, INFO )
*
          RES = ZERO
*
*            --- how many cols of U * B - A * U fit into workspace ? ---
*
          NCOLS = SZWORK / N
*
          DO 2000 J0 = 1, N, NCOLS
            COLS = MIN( NCOLS, N-J0+1 )
*
*              --- build the next cols columns of U * B ---
*
            IF ( LSAME( FRMT2, 'Tridiagonal' ) ) THEN
              DO 2010 J = J0, J0+COLS-1
                IX = ( J - J0 ) * N + 1
                CALL SCOPY( N, U( 1, J ), 1, WORK( IX ), 1 )
                CALL SSCAL( N, D( J ), WORK( IX ), 1 )
                IF ( J .GT. 1 ) THEN
                  CALL SAXPY( N, E( J-1 ), U( 1, J-1 ), 1,
     >                        WORK( IX ), 1 )
                ENDIF
                IF ( J .LT. N ) THEN
                  CALL SAXPY( N, E( J ), U( 1, J+1 ), 1, WORK( IX ), 1 )
                ENDIF
 2010         CONTINUE
            ELSE
              DO 2020 J = J0, J0+COLS-1
                IX = ( J - J0 ) * N + 1
                CALL SGEMV( 'NoTranspose', N, MIN( B2+1, N-J+1 ),
     >                      ONE, U( 1, J ), LDU, A2( 1, J ), 1,
     >                      ZERO, WORK( IX ), 1 )
                IF ( B2 .GT. 0 ) THEN
                  IF ( J .GT. B2 ) THEN
                    CALL SGEMV( 'NoTranspose', N, B2,
     >                          ONE, U( 1, J-B2 ), LDU,
     >                          A2( B2+1, J-B2 ), LDA2 - 1,
     >                          ONE, WORK( IX ), 1 )
                  ELSEIF ( J .GT. 1 ) THEN
                    CALL SGEMV( 'NoTranspose', N, J - 1,
     >                          ONE, U( 1, 1 ), LDU,
     >                          A2( J, 1 ), LDA2 - 1,
     >                          ONE, WORK( IX ), 1 )
                  ENDIF
                ENDIF
 2020         CONTINUE
            ENDIF
*
*              --- subtract corresponding columns of A * U ---
*
            IF ( LSAME( FRMT1, 'Full' ) ) THEN
              CALL SSYMM( 'Left', UPLO1, N, COLS,
     >                   -ONE, A1, LDA1, U( 1, J0 ), LDU,
     >                   ONE, WORK, N )
            ELSE
              DO 2110 J = J0, J0+COLS-1
                CALL SSBMV( UPLO1, N, B1, -ONE, A1, LDA1, U( 1, J ), 1,
     >                      ONE, WORK( (J-J0)*N+1 ), 1 )
 2110         CONTINUE
            ENDIF
*
            RES = RES + SLANGE( 'Frobenius', N, COLS, WORK, N, WORK )**2
 2000     CONTINUE
*
          RES = SQRT( RES )
          SRES = RES / ( N * NORMA * EPS )
*
*  - - - - - - - end : compute residual error = F-Norm( U * B - A * U )
*
        ELSE
*
*            --- no residual information available ---
*
          RES = - ONE
          SRES = - ONE
*
*  - - - - - - - check if eigenvalues have changed - - - - - - - - - - -
*
*            --- compute eigenvalues of the tridiagonal or banded
*                matrix                                           ---
*
          IF ( LSAME( FRMT2, 'Tridiagonal' ) ) THEN
            CALL SSTEV( 'NoEigenvectors', N, D, E, WORK, N, WORK, INFO )
          ELSE
            CALL SSBEV( 'NoEigenvectors', 'Lower', N, B2, A2, LDA2,
     >                  D, WORK, N, WORK, INFO )
          ENDIF
*
*            --- compare with (sorted) original eigenvalues ---
*
          IF ( INFO .EQ. 0 ) THEN
            CALL SLASRT( 'Increasing', N, EVLS, INFO )
            CALL SAXPY( N, -ONE, EVLS, 1, D, 1 )
            DEVLS = SNRM2( N, D, 1 )
            SDEVLS = DEVLS / ( N * NORMA * EPS )
          ELSE
            DEVLS = - ONE
            SDEVLS = - ONE
          ENDIF
*
*  - - - - - - - end : check if eigenvalues have changed - - - - - - - -
*
        ENDIF
*
 9999   RETURN
        END
*
* **********************************************************************
*
        LOGICAL FUNCTION LXSAME( S1, S2 )
*
* Description:
*
*   Checks if two strings agree (ignoring case).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*( * )       S1, S2
*
*   s1      (in) character*( * )
*           The first string.
*
*   s2      (in) character*( * )
*           The second string.
*
* Local constants and variables:
*
        INTEGER               I
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             LEN
*
* ----------------------------------------------------------------------
*
        LXSAME = ( LEN( S1 ) .EQ. LEN( S2 ) )
        IF ( LXSAME ) THEN
          DO 100 I = 1, LEN( S1 )
            LXSAME = LXSAME .AND. LSAME( S1( I:I ), S2( I:I ) )
  100     CONTINUE
        ENDIF
*
        RETURN
        END
*
SHAR_EOF
fi # end of overwriting check
cd ..
if test ! -d 'Src'
then
	mkdir 'Src'
fi
cd 'Src'
if test -f 'src.f'
then
	echo shar: will not over-write existing file "'src.f'"
else
cat << "SHAR_EOF" > 'src.f'
* **********************************************************************
*
        INTEGER FUNCTION NBDFLT( ALGO, PREC, REQEST, N, B1, B2, NEEDU )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Determine an appropriate default blocking factor or crossover point
*   or intermediate bandwidth for the reduction routine specified in
*   algo.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*5           ALGO
        CHARACTER*1           PREC, REQEST
        INTEGER               N, B1, B2
        LOGICAL               NEEDU
*
*   algo    (in) character*5
*           For which SBR routine do we need a control parameter ?
*           algo = 'SYRDB' : Reduction full -> banded.
*                = 'SBRDB' : Reduction banded -> banded.
*                = 'SBRDT' : Reduction banded -> tridiagonal.
*                = 'SYRDD' : Driver for reducing full matrices.
*                = 'SBRDD' : Driver for reducing banded matrices.
*
*   prec    (in) character*1
*           Is it the single or double precision routine ?
*           prec = 'D' : Double precision.
*                = 'S' : Single precision.
*
*   reqest  (in) character*1
*           Which control parameter is required ?
*           reqest = 'B' : Blocking factor or intermediate bandwidth.
*                  = 'C' : Crossover point to LAPACK code.
*
*   n       (in) integer
*           The size of the matrix to reduce.
*           n >= 0.
*
*   b1      (in) integer
*           The bandwidth of the matrix before the reduction.
*           0 <= b1 < n.
*
*   b2      (in) integer
*           The bandwidth of the matrix after the reduction.
*           1 <= b2 <= b1 or b1 = b2 = 0.
*
*   needu   (in) logical
*           Do we update the transformation matrix ?
*           needu = .true.  : Yes.
*                 = .false. : No.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               SINGLE
        INTEGER               DELTAB
*
*   single  single or double precision routine ?
*   deltab  number of diagonals to reduce
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
* ----------------------------------------------------------------------
*
        SINGLE = LSAME( PREC, 'SinglePrecision' )
        DELTAB = B1 - B2
*
        IF ( ( ALGO .EQ. 'SYRDB' ) .AND.
     >       ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for reduction from full to banded ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDB' ) .AND.
     >           ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for bandwidth reduction ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ELSE
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ELSE
              NBDFLT = ( ( DELTAB + 7 ) / 8 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ENDIF
          IF ( NBDFLT .LT. 1 )     NBDFLT = 1
*
        ELSEIF ( ( ALGO .EQ. 'SBRDT' ) .AND.
     >           ( LSAME( REQEST, 'BlockingFactor' ) ) ) THEN
*
*            --- block size for reduction to tridiagonal form ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = ( ( B1 + 5 ) / 6 ) * 2
            ELSE
              NBDFLT = ( ( B1 + 5 ) / 6 ) * 2
            ENDIF
            IF ( NBDFLT .LT. 4 )     NBDFLT = 4
            IF ( NBDFLT .GT. DELTAB )     NBDFLT = DELTAB
          ELSE
            NBDFLT = 1
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SYRDD' ) .AND.
     >           ( LSAME( REQEST, 'Bandwidth' ) ) ) THEN
*
*            --- intermediate bandwidth in the reduction driver ---
*
          IF ( NEEDU ) THEN
            NBDFLT = 1
          ELSE
            IF ( ( N .GE. 300 ) .OR. ( B2 .GT. 1 ) ) THEN
              IF ( SINGLE ) THEN
                NBDFLT = 32
              ELSE
                NBDFLT = 32
              ENDIF
            ELSE
              NBDFLT = 1
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDD' ) .AND.
     >           ( LSAME( REQEST, 'Bandwidth' ) ) ) THEN
*
*            --- intermediate bandwidth in the reduction driver ---
*
          IF ( NEEDU ) THEN
            NBDFLT = 1
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 32
            ELSE
              NBDFLT = 32
            ENDIF
          ENDIF
*
        ELSEIF ( ( ALGO .EQ. 'SBRDD' ) .AND.
     >           ( LSAME( REQEST, 'CrossoverPoint' ) ) ) THEN
*
*            --- crossover point from SBRDT to SBTRD ---
*
          IF ( NEEDU ) THEN
            IF ( SINGLE ) THEN
              NBDFLT = 8
            ELSE
              NBDFLT = 8
            ENDIF
          ELSE
            IF ( SINGLE ) THEN
              NBDFLT = 16
            ELSE
              NBDFLT = 16
            ENDIF
          ENDIF
*
        ELSE
          NBDFLT = 1
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYRDB( UPLO, JOB, N, B, A, LDA, DRPTOL,
     >                     U, LDU, NB, TAU,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-times-n matrix A with either its lower or upper
*   triangle explicitly stored, ssyrdb reduces A to a symmetric banded
*   matrix B with b sub(super)diagonals by using a sequence of
*   orthogonal similarity transformations. If desired, the same
*   transformations are also applied from the right to the matrix U.
*   That is, if initially U was the identity, then the resulting banded
*   matrix B and the updated U fulfill the equation
*
*       T
*      U  * A * U   =   B  .
*
*   A must be given in full storage (with either its lower or upper
*   triangle explicitly stored) and will be overwritten with B and
*   the "mantissae" of the Householder vectors used for the reduction.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO, JOB
        INTEGER               N, B, LDA, LDU, NB, LWORK, INFO
        REAL                  DRPTOL
        REAL                  A( LDA, * ), U( LDU, * ), TAU( * ),
     >                        WORK( * )
*
*   uplo    (in) character*1
*           Reduce the upper or lower triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   job     (in) character*1
*           Specifies if U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of the reduced matrix B.
*           1 <= b < n, if n > 1.
*           b = 0     , if n <= 1.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A with
*           either its lower (uplo = 'L') or upper (uplo = 'U') triangle
*           stored.
*           On exit, the main diagonal and the first b sub-(super-)
*           diagonals contain the banded matrix B, and the Householder
*           vectors that were used in the reduction are stored in the
*           remaining parts of the lower (upper) triangle.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   drptol  (in) real
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   u       (in/out) real array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce A to banded form.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor, as suggested by the user, for the
*           reduction and the update of U.
*           0 <= nb <= b.
*           nb = 0 : User does not know how many Householder transforms
*                    should be blocked for reasonable performance.
*                    Let the routine figure it out (depending on the
*                    workspace available).
*           nb = 1 : Do not block.
*           nb > 1 : Try to block nb Housholder transforms
*                    (if the workspace is not sufficient then a smaller
*                    blocking factor will be used).
*
*   tau     (out) real array, dimension ( n )
*           The scaling factors for the Householder transforms used in
*           the reduction.
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= 3 * n - 2 * b.
*
*           Workspace that small prevents blocking and may degrade
*           performance. For using nb-blocked transformations, provide
*           lwork >= nb * ( 3 * n - 2 * b ).
*           As a rule, lwork >= 50 * n should be fine.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : uplo is none of 'U', 'L' (upper/lower case).
*                = - 2 : job is none of 'U', 'N' (upper/lower case).
*                = - 3 : n is out of range (negative).
*                = - 4 : b is out of range ( < 0, or = 0 while n > 1,
*                        or >= n ).
*                = - 6 : lda is out of range ( < n or < 1 ).
*                = - 7 : drptol is out of range (negative).
*                = - 9 : ldu is out of range ( < n or < 1 ).
*                = -10 : nb is out of range (negative).
*                = -13 : lwork is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the reduction and in the
*                        update of U.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO
        PARAMETER             ( ZERO = 0.0E0 )
*
        LOGICAL               UPPER, NEEDU
        INTEGER               NB0, NB1, NB2, J, J0,
     >                        LEN, IW, IY, IWORK
*
*   upper   reduce the upper triangle of A ?
*   needu   update U ?
*   nb0     the final blocking factor for "full" block columns
*   nb1     width of the current block column to reduce (= nb0, except
*           for the last block column)
*   nb2     number of nonzero Householder vectors in the current
*           WY transform
*   j       first column of the current block column
*   j0      last column of the current block column
*   len     length of the current block column
*   iw      points to the portion of the workspace where the block
*           transform W is stored
*   iy      points to the location of Y in the workspace
*   iwork   points to the portion of work that is used as workspace for
*           other routines
*
* The workspace is used as follows:
*
*   - The first nb1 * len <= nb0 * ( n - b ) elements hold the block W
*     of the current block WY transform.
*     Here, nb1 <= nb0 denotes the width of the current block column and
*     len <= n - b denotes its height; nb0 is the final blocking factor.
*   - The next nb1 * len elements hold the block Y.
*   - Another ( len + nb1 ) * nb1 <= n * nb0 elements are used as
*     workspace in the routines sgeqrl, sgewyg, sgewy, and ssywy.
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor (SBR)
*
        EXTERNAL              SGEQRL, SGEWY, SGEWYG, SSYWY
*
*   sgeqrl  QR or QL factorization (SBR)
*   sgewy   apply WY transform from one side (SBR)
*   sgewyg  generate WY factors (SBRtoolbox)
*   ssywy   apply two-sided WY transform to a symmetric matrix (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        UPPER = LSAME( UPLO, 'U' )
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
          INFO = - 1
        ELSEIF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = - 2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 3
        ELSEIF ( ( ( N .LE. 1 ) .AND. ( B .NE. 0 ) ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B .LT. 1 ) .OR. ( B .GE. N ) ) ) ) THEN
          INFO = - 4
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = - 6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = - 7
        ELSEIF ( LDU .LT. MAX( N, 1 ) ) THEN
          INFO = - 9
        ELSEIF ( NB .LT. 0 ) THEN
          INFO = -10
        ELSEIF ( LWORK .LT. ( 3*N-2*B ) ) THEN
          INFO = -13
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( ( N .LE. 1 ) .OR. ( B .EQ. ( N-1 ) ) )      GOTO 999
*
*          --- compute the maximum blocking factor for the
*                given workspace                             ---
*
        NB0 = LWORK / ( 3 * N - 2 * B )
*
*          --- adjust to the user-supplied or default value ---
*
        IF ( NB .GT. 0 ) THEN
          NB0 = MIN( NB, B, NB0 )
        ELSE
          NB0 = MIN( NBDFLT( 'SYRDB', 'SinglePrec', 'BlockingFactor',
     >                       N, N-1, B, NEEDU ),
     >               B, NB0 )
        ENDIF
*
* ......................................................................
*
        IW = 1
*
        IF ( UPPER ) THEN
*
*            --- reduce the upper triangle ---
*
          DO 100 J0 = N, B+2, - NB0
*
            LEN = J0 - B
            NB1 = MIN( NB0, LEN-1 )
            J = J0 - NB1 + 1
            IY = IW + NB1 * LEN
            IWORK = IY + NB1 * LEN
*
            CALL SGEQRL( 'L', LEN, NB1, A( 1, J ), LDA, DRPTOL,
     >                   TAU( J ), WORK( IWORK ) )
            CALL SGEWYG( 'Upper', LEN, NB1, A( 1, J ), LDA, TAU( J ),
     >                   WORK( IW ), LEN, WORK( IY ), LEN, NB2,
     >                   WORK( IWORK ) )
            CALL SGEWY( 'Left', LEN, B - NB1, NB2, A( 1, LEN+1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
            CALL SSYWY( 'Upper', LEN, NB2, A( 1, 1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
*
            IF ( NEEDU ) THEN
              CALL SGEWY( 'Right', N, LEN, NB2, U( 1, 1 ), LDU,
     >                    WORK( IW ), LEN, WORK( IY ), LEN,
     >                    WORK( IWORK ) )
            ENDIF
*
  100     CONTINUE
*
          TAU( B+1 ) = ZERO
*
        ELSE
*
*            --- reduce the lower triangle ---
*
          DO 200 J = 1, N-B-1, NB0
*
            LEN = N - ( J + B ) + 1
            NB1 = MIN( NB0, LEN - 1 )
            IY = IW + NB1 * LEN
            IWORK = IY + NB1 * LEN
*
            CALL SGEQRL( 'R', LEN, NB1, A( J+B, J ), LDA, DRPTOL,
     >                   TAU( J ), WORK( IWORK ) )
            CALL SGEWYG( 'Lower', LEN, NB1, A( J+B, J ), LDA, TAU( J ),
     >                   WORK( IW ), LEN, WORK( IY ), LEN, NB2,
     >                   WORK( IWORK ) )
            CALL SGEWY( 'Left', LEN, B - NB1, NB2, A( J+B, J+NB1 ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
            CALL SSYWY( 'Lower', LEN, NB2, A( J+B, J+B ), LDA,
     >                  WORK( IW ), LEN, WORK( IY ), LEN,
     >                  WORK( IWORK ) )
*
            IF ( NEEDU ) THEN
              CALL SGEWY( 'Right', N, LEN, NB2, U( 1, J+B ), LDU,
     >                    WORK( IW ), LEN, WORK( IY ), LEN,
     >                    WORK( IWORK ) )
            ENDIF
     >
  200     CONTINUE
*
          TAU( N-B ) = ZERO
*
        ENDIF
*
*          --- return the blocking factor ---
*
        INFO = NB0
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYGTR( UPLO, N, B, A, LDA, TAU, WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   ssygtr generates a real orthogonal matrix U of size n, defined as
*   the product of n - b Householder transformations, as returned by
*   ssyrdb.
*
*   If uplo = 'U' then
*
*      U  =  H( n ) * ... * H( b + 2 ),
*
*   where the "mantissa" of the length-( k - b ) Householder
*   transformation H( k ) is stored in a( 1:k-b-1, k ) and its scaling
*   factor is stored in tau( k ),
*
*   if uplo = 'L' then
*
*      U  =  H( 1 ) * ... * H( n - b - 1 ),
*
*   where the "mantiassa" of the length-(n - b - k - 1) Householder
*   transformation H( k ) is stored in a( b+k+1:n, k ) and its scaling
*   factor is stored in tau( k ).
*
*   On exit, a is overwritten with the orthogonal matrix U.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDA, LWORK, INFO
        REAL                  A( LDA, * ), TAU( * ), WORK( * )
*
*   uplo    (in) character*1
*           Are the Householder vectors stored in the upper or lower
*           triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The dimension of the reduced matrix A (and of the requested
*           orthogonal matrix).
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of the reduced matrix.
*           1 <= b < n, if n > 1.
*           b = 0     , if n <= 1.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the columns of a hold the "mantissae" of the
*           Householder transformations, as returned from ssyrdb.
*           On exit, a is overwritten with the orthogonal matrix U.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   tau     (in) real array, dimension ( n ).
*           The scaling factors for the Householder transformations, as
*           returned by ssyrdb.
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= n - b.
*
*           Workspace that small prevents blocking and may degrade
*           performance. For using nb-blocked transformations, provide
*           lwork >= nb * ( n - b ).
*           As a rule, lwork >= 20 * n should be fine.
*
*   info    (out) integer
*           On exit, info indocates the consistence of the arguments.
*           info =  1 : All arguments were OK.
*           info = -1 : uplo is none of 'U', 'L' (upper/lower case).
*                = -2 : n is out of range (negative).
*                = -3 : b is out of range ( < 0, or = 0 while n > 1,
*                       or >= n ).
*                = -5 : lda is out of range ( < n or < 1 ).
*                = -8 : lwork is out of range ( < n - b ).
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        LOGICAL               UPPER
        INTEGER               B1, J
*
*   upper   are the Householder vectors stored in the upper triangle ?
*   b1      = b + 1
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              SCOPY, SLASET, SORGQL, SORGQR
*
*   scopy   vector copy (BLAS)
*   slaset  initialize matrix (LAPACK)
*   sorgql  build orthogonal matrix after QL factorization (LAPACK)
*   sorgqr  build orthogonal matrix after QR factorization (LAPACK)
*
        INTRINSIC             MAX
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the input ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( ( N .LE. 1 ) .AND. ( B .NE. 0 ) ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B .LT. 1 ) .OR. ( B .GE. N ) ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LWORK .LT. ( N-B ) ) THEN
          INFO = - 8
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( B1 .GE. N ) THEN
          CALL SLASET( 'All', N, N, ZERO, ONE, A, LDA )
          GOTO 999
        ENDIF
*
* ......................................................................
*
        IF ( UPPER ) THEN
*
*            --- move the Householder vectors by b columns to
*                the left                                     ---
*
          DO 100 J = B+2, N
            CALL SCOPY( J-B1, A( 1, J ), 1, A( 1, J-B ), 1 )
  100     CONTINUE
*
*            --- set the last b columns and rows to identity ---
*
          CALL SLASET( 'All', B, N-B, ZERO, ZERO, A( N-B+1, 1 ), LDA )
          CALL SLASET( 'All', N-B, B, ZERO, ZERO, A( 1, N-B+1 ), LDA )
          CALL SLASET( 'All', B, B, ZERO, ONE, A( N-B+1, N-B+1 ), LDA )
*
*            --- generate the leading ( n-b )-by-( n-b )
*                orthogonal matrix                       ---
*
          CALL SORGQL( N-B, N-B, N-B, A, LDA, TAU( B+1 ),
     >                 WORK, LWORK, INFO )
*
        ELSE
*
*            --- move the Householder vectors by b columns to
*                the right                                    ---
*
          DO 200 J = N-1, B1, -1
            CALL SCOPY( N-J, A( J+1, J-B ), 1, A( J+1, J ), 1 )
  200     CONTINUE
*
*            --- set the first b columns and rows to identity ---
*
          CALL SLASET( 'All', N, B, ZERO, ONE, A, LDA )
          CALL SLASET( 'All', B, N-B, ZERO, ZERO, A( 1, B1 ), LDA )
*
*            --- generate the trailing ( n-b )-by-( n-b )
*                orthogonal matrix                        ---
*
          CALL SORGQR( N-B, N-B, N-B, A( B1, B1 ), LDA, TAU,
     >                 WORK, LWORK, INFO )
*
        ENDIF
*
        IF ( INFO .EQ. 0 )     INFO = 1
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSBRDB( JOB, N, B1, B2, A, LDA, DRPTOL,
     >                     U, LDU, NB,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-times-n matrix A with b1 sub(or super-)
*   diagonals, ssbrdb reduces A to a narrower band with b2 sub(super)
*   diagonals by using a sequence of orthogonal similarity
*   transformations. If desired, the same transformations are also
*   applied from the right to the matrix U. That is, if initially U was
*   the identity, then the resulting banded matrix B and the updated U
*   fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK packed storage scheme for lower
*   triangular banded matrices and will be overwritten with B.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOB
        INTEGER               N, B1, B2, LDA, LDU, NB, LWORK, INFO
        REAL                  DRPTOL
        REAL                  A( LDA, * ), U( LDU, * ), WORK( * )
*
*   job     (in) character*1
*           Specifies whether U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix.
*           n >= 0.
*
*   b1      (in) integer
*           The number of sub(super-)diagonals of A.
*           b1 >= 0 and b1 < n (if n > 0).
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 <= b1 or b2 = b1 = 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A. The
*           leading ( b1+1 )-by-n part of a contains the lower triangle
*           of A with A( i, j ) stored in a( 1+i-j, j ), and the
*           strictly upper triangle is not referenced.
*           On exit, for i = 1, ..., b2+1, the first n - i + 1 elements
*           in the i-th row of a contain the reduced matrix B,
*           for i = b2 + 2, ..., b1+1, the first n - i + 1 elements in
*           the i-th row of a are zeroed, and
*           for i = b1 + 2, ..., min( b1+(b1-b2)+nb, n, lda ), the first
*           n - i + 1 elements in the i-th row of a are destroyed.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( b1 + 1, n ).
*
*           To avoid unnecessary copying and therefore improve the
*           performance in the blocked case, we recommend
*           lda >= nb + b1 + ( b1 - b2 ).
*
*   drptol  (in) real
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   u       (in/out) real array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied by all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor nb, as suggested by the user, for the
*           reduction of A and the update of U.
*           0 <= nb <= b2.
*           nb = 0 : User does not know how many Householder transforms
*                    should be blocked for reasonable performance. Let
*                    the routine figure it out (depending on the
*                    workspace available).
*              = 1 : Do not block
*              > 1 : Try to block nb Householder transforms (if the
*                    workspace is not sufficient then a smaller blocking
*                    factor will be used).
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           lwork >= 3 * b1 + b2,    if U is not required, and
*                 >= n + 2 * b1 + 1, if U is required.
*
*           Workspace that small enforces non-blocked transforms.
*           For using nb-blocked transforms, we need
*           lwork >= ( 3 * b1 + b2 ) * nb,    if U is not required, and
*                 >= ( n + 2 * b1 + 1 ) * nb, if U is required.
*
*           If lda < b1 + ( b1 - b2 ) + nb, then ADDITIONAL workspace
*           is needed to buffer some of the intermediate fill-in during
*           the reduction. More precisely, we need
*           another ndiag * ( ndiag+1 ) / 2 elements to buffer one
*              ndiag-by-ndiag triangle of each diagonal block, where
*              ndiag = min( b1+(b1-b2)+nb, n ) - lda, and
*           another ( n / b1 ) * nsub * ( nsub+1 ) / 2  elements to
*              buffer an nsub-by-nsub triangle from each of the n / b1
*              subdiagonal blocks, where
*              nsub = min( b1+(b1-b2), n ) - lda
*           Note that roughly n * ( b1 + (b1-b2) - lda ) / 2 elements
*           are sufficient, and that no buffer space is required if
*           lda >= b1 + ( b1 - b2 ) + nb.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : job is none of 'U', 'N' (upper/lower case).
*                = - 2 : n is out of range (negative).
*                = - 3 : b1 is out of range (negative or >= n ).
*                = - 4 : b2 is out of range ( < 0, or = 0 while b1 >= 1,
*                        or > b1 ).
*                = - 6 : lda is out of range ( < b1 + ( b1 - b2 ) + 1
*                        and < n ).
*                = - 7 : drptol is out of range ( < 0.0 ).
*                = - 9 : ldu is out of range ( < n ).
*                = -10 : nb is out of range (negative).
*                = -12 : lwork is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the reduction and in the
*                        update of U.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
*            --- constants ---
*
        REAL                  ZERO
        PARAMETER             ( ZERO = 0.0E0 )
*
*            --- for the reduction part ---
*
        LOGICAL               NEEDU
        INTEGER               DELTAB, NB0, LDH, PREW, K,
     >                        L, NBLK, NB1, LDWY
*
*   needu   is U required ?
*   deltab  = b1 - b2, the number of diagonals to remove
*   nb0     blocking factor that is ultimately used in the reduction
*           and in the update
*   ldh     = min( deltab + nb0, n - b2 ), the size of the blocks
*           affected by each block transform
*   prew    = b2 - nb0, the width of the block to be premultiplied
*   k       numbers the "elimination steps"
*   l       numbers the bulge chasing operations associated with each
*           elimination step
*   nblk    number of the current block column
*   nb1     number of nonzero Householder vectors in the current block
*           transform
*   ldwy    leading dimension of the arrays containing W and Y
*
*          --- workspace management ---
*
        INTEGER               NSUB, SZSUB, LSUB, NSUB1, NDIAG, LDIAG,
     >                        NDIAG1, ISUB, IDIAG, IC, ID, ID1, IX,
     >                        IW, IY, IWORK, J
*
*   nsub    the dimension of the triangles from the subdiagonal blocks
*           that must be buffered in the workspace
*           (nsub <= b1 + ( b1 - b2 ) - lda)
*   szsub   = nsub * ( nsub+1 ) / 2, the size of each such triangle
*   lsub    = ( n / b ) * szsub, the total size of all these triangles
*   nsub1   the dimension of the current triangle, plus 1
*   ndiag   the dimension of the triangle from the main diagonal block
*           that must be buffered in the workspace
*           (ndiag <= b1 + ( b1 - b2 ) + nb0 - lda )
*   ldiag   = ndiag * ( ndiag+1 ) / 2, the size of this triangle
*   ndiag1  the dimension of the current triangle, plus 1
*   isub    points to the portion of the workspace that will hold the
*           triangles from all the subdiagonal blocks
*   idiag   points to the portion of the workspace that will hold the
*           triangle from the current diagonal block
*   ic      column position of the next element to be buffered
*   id      diagonal position of the next element to be buffered
*   id1     = id + 1
*   ix      position in the workspace for this element
*   iw      points to the portion of work that will hold the block
*           W of the WY tranform
*   iy      points to the portion of work that will hold Y
*   iwork   points to the portion of work that is used as workspace
*           in the routines sqrupd, ssywy, and sgewy
*
* The workspace is used as follows:
*
*   - The first ( n / b1 ) * nsub * ( nsub+1 ) / 2 elements are used to
*     buffer nsub-by-nsub triangles of fill-in from the subdiagonal
*     blocks (see the discussion on lwork).
*     Here, nsub = min( b1+(b1-b2), n ) - lda <= b1 - b2 - 1.
*     These elements are needed only if nsub > 0.
*   - The next ndiag * ( ndiag+1 ) / 2 elements are used to buffer one
*     ndiag-by-ndiag triangle from the current diagonal block.
*     Here, ndiag = min( b1+(b1-b2)+nb0, n ) - lda <= b1 - 1.
*     These elements are needed only if ndiag > 0.
*   - The following ldh * nb0 elements hold the block W of the block WY
*     transform.
*     Here, ldh = min( b1-b2+nb0, n-b2 ) <= b1 - b2 + nb0 <= b1.
*   - The following ldh * nb0 elements hold the block Y.
*   - The remaining workspace is alternatively used by the routines
*     sqrupd (which needs ( n+1 )*nb0 elements if U is required and
*     ( ldh+1 )*nb0 elements otherwise), ssywy (( b1+1 )*nb0 elements),
*     and sgewy (b1*nb0 elements).
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor
*
        EXTERNAL              SGEWY, SQRUPD, SSYWY
*
*   sgewy   apply WY block transform (SBR)
*   sqrupd  QR decomposition of a block of A, update of U, and premulti-
*           plication of another block of A (SBR)
*   ssywy   apply two-sided block transform to a symmetric matrix (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B1 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B1 .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( B1 .GE. 1 ) .AND. ( B2 .EQ. 0 ) ) .OR.
     >           ( B2 .GT. B1 ) ) THEN
          INFO = - 4
        ELSEIF ( LDA .LT. MIN( B1+1, N ) ) THEN
          INFO = - 6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = - 7
        ELSEIF ( NEEDU .AND. ( LDU .LT. MAX( N, 1 ) ) ) THEN
          INFO = - 9
        ELSEIF ( NB .LT. 0 ) THEN
          INFO = - 10
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( ( N .EQ. 0 ) .OR. ( B2 .EQ. B1 ) )     GOTO 999
*
*          --- determine blocking factor ---
*
        IF ( NB .GT. 0 ) THEN
          NB0 = NB
        ELSE
          NB0 = NBDFLT( 'SBRDB', 'PrecString', 'BlockingFactor',
     >                  N, B1, B2, NEEDU )
        ENDIF
        NB0 = MIN( NB0, B2 )
*
*          --- how many diagonals are eliminated, and how many must
*              be buffered ?                                        ---
*
        DELTAB = B1 - B2
        NSUB = MAX( MIN( B1+DELTAB, N ) - LDA, 0 )
        SZSUB = ( NSUB * ( NSUB + 1 ) ) / 2
        LSUB = ( N / B1 ) * SZSUB
*
*          --- reduce nb0 until workspace is sufficient ---
*
   10   CONTINUE
*
*            --- how much of the diagonal blocks must be buffered ? ---
*
          NDIAG = MAX( MIN( B1+DELTAB+NB0, N ) - LDA, 0 )
          LDIAG = ( NDIAG * ( NDIAG + 1 ) ) / 2
          IF ( NEEDU ) THEN
            IWORK = ( N + 2 * B1 + 1 ) * NB0
          ELSE
            IWORK = ( 3 * B1 + B2 ) * NB0
          ENDIF
          IF ( LWORK .LT. ( LSUB+LDIAG+IWORK ) ) THEN
            IF ( NB0 .GT. 1 ) THEN
              NB0 = NB0 - 1
              GOTO 10
            ELSE
              INFO = -12
              GOTO 999
            ENDIF
          ENDIF
*
*          --- OK, now that we have nb0, set other constants ---
*
        LDH = MIN( DELTAB+NB0, N-B2 )
        PREW = MAX( B2-NB0, 0 )
*
*          --- set up pointers to the submatrices stored in work
*              (the data layout is pointed out above)            ---
*
        ISUB = 1
        IDIAG = ISUB + LSUB
        IW = IDIAG + LDIAG
        IY = IW + LDH * NB0
        IWORK = IY + LDH * NB0
*
*          --- make sure that the "bulge buffer" is empty ---
*
        DO 30 K = B1+2, MIN( B1+NB0+DELTAB, LDA, N )
          DO 20 J = 1, N-K+1
            A( K, J ) = ZERO
   20     CONTINUE
   30   CONTINUE
*
        DO 40 K = ISUB, IDIAG+LDIAG-1
          WORK( K ) = ZERO
   40   CONTINUE
*
* ......................................................................
*
        DO 400 K = 1, N - B2 - 1, NB0
*
*            --- QR decomposition to eliminate the leading nb0
*                columns of the band                           ---
*
          CALL SQRUPD( MIN( LDH, N-K-B2+1 ), NB0, DELTAB,
     >                 A( B2+1, K ), LDA - 1, DRPTOL,
     >                 NEEDU, N, U( 1, K+B2 ), LDU,
     >                 PREW, A( PREW+1, K+NB0 ),
     >                 NB1, WORK( IY ), WORK( IW ), LDWY,
     >                 WORK( IWORK ) )
*
*              --- bulge chasing ---
*
          DO 300 L = K + B2, N - 1, B1
*
            NBLK = 1 + ( L - K - B2 ) / B1
            IF ( NB1 .GT. 0 ) THEN
*
*                --- symmetric update of diagonal block ---
*
              CALL SSYWY( 'Lower', MIN( LDH, N-L+1 ), NB1,
     >                    A( 1, L ), LDA - 1,
     >                    WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                    WORK( IWORK ) )
            ENDIF
*
*              --- if lda < b1 + ( b1 - b2 ) + nb0, then before
*                  transforming the subdiagonal block, an
*                  ndiag-by-ndiag triangle of the diagonal block
*                  must be copied into the workspace ...         ---
*
            NDIAG = MIN( B1+LDH, N-L+1 ) - LDA
            NDIAG1 = NDIAG + 1
            IX = IDIAG
            DO 120 J = 1, NDIAG
              IC = L + J
              DO 110 ID = 1, NDIAG1-J
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  110         CONTINUE
  120       CONTINUE
*
*              --- ... the bottommost rows of the subdiagonal block
*                  must be set to zero                              ---
*
            NSUB = MIN( MAX( N-L+1-LDA, 0 ), B1+(B1-B2)-LDA )
            NSUB1 = NSUB + 1
            DO 140 ID = NSUB1, NDIAG
              ID1 = ID + 1
              DO 130 J = 1, ID
                A( ID1-J, L+J ) = ZERO
  130         CONTINUE
  140       CONTINUE
*
*              --- ... and an nsub-by-nsub triangle of the
*                  subdiagonal block must be restored from workspace ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 160 J = 1, NSUB
              IC = L + J
              DO 150 ID = 1, NSUB1-J
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  150         CONTINUE
  160       CONTINUE
*
            IF ( NB1 .GT. 0 ) THEN
*
*                  --- postmultiply ---
*
              IF ( N .GE. ( L+LDH ) ) THEN
                CALL SGEWY( 'Right', MIN( B1, N-L-LDH+1 ),
     >                      LDH, NB1, A( LDH+1, L ), LDA - 1,
     >                      WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                      WORK( IWORK ) )
              ENDIF
            ENDIF
*
            IF ( N .GT. ( L+B1 ) ) THEN
*
*                --- QR decomposition to eliminate the leading
*                    nb0 columns of the bulge                  ---
*
              CALL SQRUPD( MIN( LDH, N-L-B1+1 ), NB0, DELTAB,
     >                     A( B1+1, L ), LDA - 1, DRPTOL,
     >                     NEEDU, N, U( 1, L+B1 ), LDU,
     >                     B1 - NB0, A( B1-NB0+1, L+NB0 ),
     >                     NB1, WORK( IY ), WORK( IW ), LDWY,
     >                     WORK( IWORK ) )
            ENDIF
*
*              --- if lda < b1 + ( b1 - b2 ) + nb0, then an
*                  nsub-by-nsub triangle of the subdiagonal block
*                  must be copied into the workspace ...          ---
*
            NSUB = MIN( MAX( N-L-NB0+1-LDA, 0 ), B1+(B1-B2)-LDA )
            NSUB1 = NSUB + 1
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 220 J = 1, NSUB
              IC = L + J + NB0
              DO 210 ID = 1, NSUB1-J
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  210         CONTINUE
  220       CONTINUE
*
*              --- ... and the ndiag-by-ndiag triangle of the
*                  diagonal block must be restored from workspace ---
*
            IX = IDIAG
            DO 240 J = 1, NDIAG
              IC = L + J
              DO 230 ID = 1, NDIAG1-J
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  230         CONTINUE
  240       CONTINUE
*
  300     CONTINUE
*
  400   CONTINUE
*
        INFO = NB0
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSBRDT( JOB, N, B, A, LDA, DRPTOL,
     >                     D, E,
     >                     U, LDU, NB,
     >                     WORK, LWORK, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a symmetric n-by-n matrix A with b sub(or super-) diagonals,
*   ssbrdt reduces A to tridiagonal form using a sequence of orthogonal
*   similarity transformations. If desired, the same transformations are
*   also applied from the right to the matrix U. That is, if initially U
*   was the identity, then the resulting tridiagonal matrix T and the
*   updated U fulfill the equation
*
*       T
*      U  * A * U = T  .
*
*   A must be given in the LAPACK packed storage scheme for lower
*   triangular banded matrices.
*
* Author: Bruno Lang
*         Aachen University of technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOB
        INTEGER               N, B, LDA, LDU, NB, LWORK, INFO
        REAL                  DRPTOL
        REAL                  A( LDA, * ), D( * ), E( * ), U( LDU, * ),
     >                        WORK( * )
*
*   job     (in) character*1
*           Specifies whether U is required or not.
*           job = 'U' : Update U.
*               = 'N' : Do not update U.
*
*   n       (in) integer
*           The order of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The number of sub(super-)diagonals of A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, this array contains the symmetric matrix A. The
*           leading ( b+1 )-by-n part of a contains the lower triangle
*           of A with A( i, j ) stored in a( 1+i-j, j ), and the
*           strictly upper triangle is not referenced.
*           On exit, for i = 1, ..., min( 2*b, n, lda ), the first
*           n - i + 1 elements in the i-th row of a are destroyed.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= b+1.
*           For optimum performance, we recommend lda >= 2*b.
*
*   drptol  (in) real
*           The threshold for dropping Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   d       (out) real array, dimension ( n )
*           On exit, d( 1 .. n ) contains the main diagonal of the
*           reduced tridiagonal matrix.
*
*   e       (out) real array, dimension ( n-1 )
*           On exit, e( 1 .. n-1 ) contains the sub(super-)diagonal of
*           the reduced tridiagonal matrix.
*
*   u       (in/out) real array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nb      (in) integer
*           The blocking factor nb, as suggested by the user, for the
*           update of U (nb is accessed only if U is required).
*           nb >= 0.
*               = 0 : User does not know how many Householder transforms
*                     should be blocked for reasonable performance. Let
*                     the routine figure it out (depending on the
*                     workspace available).
*               = 1 : Do not block the update of U.
*               > 1 : Try to block nb Householder transforms (if the
*                     workspace is not sufficient then a smaller
*                     blocking factor will be used).
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The size of the workspace (must be provided on entry).
*           If lda >= 2*b, then
*             lwork >= 2 * b, if U is not required.
*             lwork >= b + n, if U is required and is updated with
*                             non-blocked Householder transforms.
*             lwork >= 2 * nb * ( n + b + nb - 1 ), if U is updated
*                             with nb-blocked transforms.
*           If lda < 2*b, then ADDITIONAL ( n/b + 1 )*szsub + nsave
*                         elements of workspace are needed to buffer
*                         intermediate elements. Here, nsave = 2*b-lda,
*                         and szsub = (nsave*(nsave-1))/2.
*                         Note that this is roughly n*(2*b-lda)/2
*                         elements.
*
*   info    (out) integer
*           On exit, info indicates the consistence of the arguments.
*           info = - 1 : job is none of 'U', 'N' (upper/lower case).
*                = - 2 : n is out of range (negative).
*                = - 3 : b is out of range (negative or
*                        >= n, while n > 0 ).
*                = - 5 : lda is too small ( < min( b+1, n ) ).
*                = - 6 : drptol is out of range (negative).
*                = -10 : ldu is too small ( < n or < 1 ).
*                = -11 : nb is out of range (negative).
*                = -13 : workspace is too small (see above).
*           info >=  1 : All arguments are OK.
*                        In this case, info returns the blocking factor
*                        that was used in the update of U (if job='U'),
*                        or info = 1 (if job='N').
*
* ----------------------------------------------------------------------
*
* Local variables:
*
*          --- constants ---
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
*          --- for the reduction part ---
*
        INTEGER               NSAVE, NSAVE1, IDIAG, ISUB, SZSUB, ID, IC,
     >                        IX, NBLK, HEIGHT, WIDTH, K, J, I, J0
        REAL                  TAU
*
*   nsave   the number of diagonals that must be saved
*   nsave1  = nsave + 1
*   idiag   points to the portion of the workspace that holds the part
*           of the current diagonal block of the band
*   isub    points to the portion of the workspace that holds the part
*           of the subdiagonal blocks of the band
*   szsub   number of elements that must be saved from each subdiagonal
*           block
*   id      diagonal position of the element to save
*   ic      column position of the element to save
*   ix      position in the workspace for saving the element
*   nblk    number of the block to process next
*   height  height of the block to process next
*   width   width of the subdiagonal block
*   k       numbers the columns to be eliminated
*   j       counter for the "progress" of the bulge chasing
*   tau     scaling factor of the current Householder transform
*
*          --- for updating U ---
*
        LOGICAL               NEEDU, BLOCK, ONFLY
        INTEGER               NB0, IV, IY, IW, ITAU, IWORK, LDWY0,
     >                        K0, IFIRST, NB1, LDWY, NB2, V
        DOUBLE PRECISION      BETA
*
*   needu   is U needed ?
*   block   is U needed, and is there enough workspace for blocking the
*           updates ?
*   onfly   is U needed, and is blocking prohibited by small workspace ?
*   nb0     blocking factor that is ultimately used in the update
*   iv      points to the portion of work that will hold the Householder
*           vectors for nb consecutive "eliminate & chase" sweeps
*           (required size for this buffer : n * nb0)
*   iy      points to the portion of work that will hold the block
*           transform Y in the WY representation (required size for this
*           buffer : ( b + nb0 - 1 ) * nb0)
*   iw      points to the portion of work that will hold the block
*           transform W in the WY representation (required size for this
*           buffer : ( b + nb0 - 1 ) * nb0)
*   itau    points to the portion of work that will hold the scaling
*           factors (required size for this buffer: nb0)
*   iwork   points to the protion of work that may be used as working
*           space by the routines slarfx, ssyrf, and sgewy.
*           (required size for this buffer : n * nb0, if U is needed,
*           b otherwise)
*   ldwy0   = b + nb0 - 1, the leading dimension of "full" block
*           Householder reflectors W and Y, resp.
*   k0      number of the first sweep that contributed to the the
*           current block transform
*   ifirst  first row affected by the current block transform
*   nb1     number of transforms in the current block update (usually
*           = nb0, except for the one at the bottom or the last sweeps)
*   ldwy    size of the current block transform (usually = ldwy0,
*           except for the last block transform of the sweep)
*   nb2     number of nonzero transforms in the current block update
*           (usually = nb1, except for special matrices)
*   v       points to the portion of work that holds the current
*           Householder vector
*   beta    coefficient in the quadratic equation for determining the
*           maximum possible blocking factor
*
* The workspace is used as follows:
*
*   If lda < 2 * b then some of the intermediate fill-in is held in the
*   workspace. More precisely, nsave = 2 * b - lda is the size of the
*   (triangular) blocks that extend beyond the array a. Then
*   nsave-by-nsave blocks of the band must be swapped between the array
*   a and the workspace. Note that actually only (nsave-1)-by-(nsave-1)
*   blocks of size szsub = ( ( nsave - 1 ) * nsave ) / 2 must be saved
*   as the remaining nsave elements are made zero by the algorithm.
*   - The first szsub + nsave elements of the workspace are used to
*     buffer a triangular portion of the current diagonal block, and
*   - the next ( n / b ) * szsub elements hold n / b triangular
*     (nsave-1)-by-(nsave-1) portions of the subdiagonal blocks.
*   If lda >= 2 * b then the whole fill-in fits into the array a, and
*   the above-mentioned buffers are not needed.
*
*   If U is not needed (or U is needed, but its update is non-blocked)
*   then the next b places of work hold the current Householder vector
*   and the following b (or n, resp.) places are used as workspace for
*   applying the transformation.
*
*   If U is updated via blocked Householder transforms (comprising nb0
*   Householder transforms)
*                                                  T
*      (affected part of)   U  =  U  *  ( I + W * Y  )
*   then in the current implementation
*   - the next n * nb0 places hold the Householder vectors for
*     nb0 successive "eliminate & chase" sweeps down the band,
*   - the next ( b + nb0 - 1 ) * nb0 places hold the block Y,
*   - the next ( b + nb0 - 1 ) * nb0 places hold W,
*   - the next n * nb0 places are alternatively used as workspace for
*     the routines ssyrf (b elements), slarfx (b elements), and sgewyr
*     (n * nb0 elements), and
*   - the buffer for nb0 scaling factors is overlapped with the first
*     nb0 elements of the "multiuse" workspace.
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default blocking factor
*
        EXTERNAL              SCOPY, SGBWYG, SGEWY, SLARFX, SLBRFG,
     >                        SSYRF
*
*   scopy   vector copy (BLAS)
*   sgbwyg  generate WY block reflector (SBR)
*   sgewy   apply WY block reflector (SBR)
*   slbrfg  determine Householder vector (SBR)
*   ssyrf   apply two-sided transform to a symmetric matrix (SBR)
*   slarfx  apply Householder transform (LAPACK)
*
        INTRINSIC             DBLE, INT, MAX, MIN, MOD, SQRT
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOB, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOB, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -2
        ELSEIF ( ( B .LT. 0 ) .OR. ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) )
     >  THEN
          INFO = -3
        ELSEIF ( LDA .LT. ( B+1 ) ) THEN
          INFO = -5
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -6
        ELSEIF ( LDU .LT. MAX( N, 1 ) ) THEN
          INFO = -10
        ELSEIF ( NEEDU .AND. ( NB .LT. 0 ) ) THEN
          INFO = -11
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 ) THEN
          GOTO 999
        ELSEIF ( B .EQ. 0 ) THEN
          CALL SCOPY( N, A( 1, 1 ), LDA, D, 1 )
          DO 10 J = 1, N-1
            E( J ) = ZERO
   10     CONTINUE
          GOTO 999
        ELSEIF ( B .EQ. 1 ) THEN
          CALL SCOPY( N, A( 1, 1 ), LDA, D, 1 )
          CALL SCOPY( N-1, A( 2, 1 ), LDA, E, 1 )
          GOTO 999
        ENDIF
*
*          --- check if workspace is sufficient ---
*
        NSAVE = 2 * B - LDA
        IF ( NSAVE .GT. 0 ) THEN
          SZSUB = ( ( NSAVE - 1 ) * NSAVE ) / 2
          IX = SZSUB + NSAVE + ( N / B ) * SZSUB
        ELSE
          SZSUB = 0
          IX = 0
        ENDIF
        IF ( ( LWORK .LT. ( IX+2*B ) ) .OR.
     >       ( NEEDU .AND. ( LWORK .LT. ( IX+B+N ) ) ) ) THEN
          INFO = -13
          GOTO 999
        ENDIF
*
*          --- compute the final blocking factor for updating U ---
*
        IF ( NEEDU ) THEN
*
*            --- first determine the maximum possible value nb0
*                (for blocking nb0 updates, we need
*                2 * nb0 * ( n + b + nb0 - 1 ) workspace).      ---
*
          BETA = DBLE( N + B - 1 )
          NB0 = INT( ( SQRT( BETA**2 + 2.0D0*( LWORK-IX ) ) - BETA )
     >               / 2.0D0 )
*
*            --- adjust to the user-supplied or default value ---
*
          IF ( NB .GT. 0 ) THEN
            NB0 = MIN( NB, NB0, N-2 )
          ELSE
            NB0 = MIN( NBDFLT( 'SBRDT', 'SinglePrec', 'BlockingFactor',
     >                         N, B, 1, .TRUE. ),
     >                 NB0 )
          ENDIF
*
          IF ( NB0 .LT. 1 )     NB0 = 1
*
*            --- OK, now we are done ---
*
          BLOCK = ( NB0 .GT. 1 )
          ONFLY = ( .NOT. BLOCK )
          INFO = NB0
        ELSE
          NB0 = 1
          BLOCK = .FALSE.
          ONFLY = .FALSE.
        ENDIF
*
*          --- set up pointers to the submatrices stored in work
*              (the data layout is pointed out above)            ---
*
        IF ( NSAVE .GT. 0 ) THEN
          IDIAG = 1
          ISUB = IDIAG + ( SZSUB + NSAVE )
          IV = ISUB + ( N / B ) * SZSUB
        ELSE
          IDIAG = -1
          ISUB = -1
          IV = 1
        ENDIF
*
        LDWY0 = B + NB0 - 1
        IF ( BLOCK ) THEN
          IY = IV + N * NB0
          IW = IY + LDWY0 * NB0
          IWORK = IW + LDWY0 * NB0
          ITAU = IWORK
        ELSE
          IY = -1
          IW = -1
          IWORK = IV + B
          ITAU = -1
        ENDIF
        V = IV
*
*          --- make sure that the "bulge buffer" is empty ---
*
        DO 30 J = 2, N-B
          DO 20 K = B+2, MIN( 2*B, LDA, N-J+1 )
            A( K, J ) = ZERO
   20     CONTINUE
   30   CONTINUE
*
        DO 40 IX = 1, IV-1
          WORK( IX ) = ZERO
   40   CONTINUE
*
* ......................................................................
*
        K0 = 1
*
*          --- in the k-th pass of the following main loop,
*              the k-th column of the band is zeroed and the
*              resulting bulge is chased down the band       ---
*
        DO 700 K = 1, N-2
*
*            --- determine the length of the column and the
*                Householder vector                         ---
*
          HEIGHT = MIN( B, N-K )
          CALL SLBRFG( HEIGHT, A( 2, K ), A( 3, K ), 1, TAU, DRPTOL )
*
*            --- save the vector and zero column of A ---
*
          IF ( BLOCK ) THEN
            V = IV + ( K - K0 ) * ( N - K0 + 1 )
          ENDIF
          WORK( V ) = ONE
          CALL SCOPY( HEIGHT-1, A( 3, K ), 1, WORK( V+1 ), 1 )
          DO 110 I = 3, HEIGHT+1
            A( I, K ) = ZERO
  110     CONTINUE
*
*            --- save the new tridiagonal elements ---
*
          D( K ) = A( 1, K )
          E( K ) = A( 2, K )
*
          IF ( TAU .NE. ZERO ) THEN
*
*              --- apply the Householder transform to both sides
*                  of the first diagonal block                   ---
*
            CALL SSYRF( 'Lower', HEIGHT, WORK( V ), 1, TAU,
     >                  A( 1, K+1 ), LDA - 1, WORK( IWORK ) )
*
*              --- if the transformations of U are not blocked
*                  then apply them as they are generated       ---
*
            IF ( ONFLY ) THEN
              CALL SLARFX( 'Right', N, HEIGHT, WORK( V ), TAU,
     >                     U( 1, K+1 ), LDU, WORK( IWORK ) )
            ENDIF
          ENDIF
*
*            --- start the bulge chasing ---
*
          DO 500 J = K+1, N-B, B
            NBLK = 1 + ( J - K - 1 ) / B
*
*              --- determine the size of the subdiagonal block ---
*
            WIDTH = HEIGHT
            HEIGHT = MIN( B, N-J-(B-1) )
*
*              --- if lda is too small then parts of the diagonal
*                  block must be saved ...                        ---
*
            NSAVE = B + HEIGHT - LDA
            NSAVE1 = NSAVE + 1
            IX = IDIAG
            DO 220 J0 = 1, NSAVE
              IC = J + J0
              DO 210 ID = 1, NSAVE1-J0
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  210         CONTINUE
  220       CONTINUE
*
*              --- ... and the subdiagonal block must be restored ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            IF ( HEIGHT .EQ. B ) THEN
              DO 230 J0 = 1, NSAVE
                A( NSAVE1-J0, J+J0 ) = ZERO
  230         CONTINUE
              DO 250 J0 = 2, NSAVE
                IC = J + J0 - 1
                DO 240 ID = 1, NSAVE1-J0
                  A( ID, IC ) = WORK( IX )
                  IX = IX + 1
  240           CONTINUE
  250         CONTINUE
            ELSE
              DO 270 J0 = 1, NSAVE
                IC = J + J0
                DO 260 ID = 1, NSAVE1-J0
                  A( ID, IC ) = WORK( IX )
                  IX = IX + 1
  260           CONTINUE
  270         CONTINUE
            ENDIF
*
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the previous Householder transform
*                    to the subdiagonal block (from the right) ---
*
              CALL SLARFX( 'Right', HEIGHT, WIDTH, WORK( V ), TAU,
     >                     A( B+1, J ), LDA-1, WORK( IWORK ) )
            ENDIF
*
*              --- save the previous scaling factor ---
*
            WORK( V ) = TAU
*
*              --- generate a new Householder transform to
*                  zero the first column of the subdiagonal block ---
*
            CALL SLBRFG( HEIGHT, A( B+1, J ), A( B+2, J ), 1,
     >                   TAU, DRPTOL )
*
            IF ( BLOCK ) THEN
              V = IV + ( K - K0 ) * ( N - K0 + 1 ) + NBLK * B
            ENDIF
            WORK( V ) = ONE
            CALL SCOPY( HEIGHT-1, A( B+2, J ), 1, WORK( V+1 ), 1 )
            DO 310 I = B+2, B+HEIGHT
              A( I, J ) = ZERO
  310       CONTINUE
*
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the transform to the subdiagonal block
*                    (from the left)                              ---
*
              CALL SLARFX( 'Left', HEIGHT, WIDTH-1, WORK( V ), TAU,
     >                     A( B, J+1 ), LDA-1, WORK( IWORK ) )
            ENDIF
*
*              --- if lda is too small then the subdiagonal block
*                  must be saved ...                              ---
*
            IX = ISUB + ( NBLK - 1 ) * SZSUB
            DO 420 J0 = 2, NSAVE
              IC = J + J0
              DO 410 ID = 1, NSAVE1-J0
                WORK( IX ) = A( ID, IC )
                IX = IX + 1
  410         CONTINUE
  420       CONTINUE
*
*              --- ... and the diagonal block must be restored ---
*
            IX = IDIAG
            DO 440 J0 = 1, NSAVE
              IC = J + J0
              DO 430 ID = 1, NSAVE1-J0
                A( ID, IC ) = WORK( IX )
                IX = IX + 1
  430         CONTINUE
  440       CONTINUE
            IF ( TAU .NE. ZERO ) THEN
*
*                --- apply the transform to the diagonal block
*                    (two-sided)                               ---
*
              CALL SSYRF( 'Lower', HEIGHT, WORK( V ), 1, TAU,
     >                    A( 1, J+B ), LDA-1, WORK( IWORK ) )
*
*                --- if the transformations of U are not blocked
*                    then apply them as they are generated       ---
*
              IF ( ONFLY ) THEN
                CALL SLARFX( 'Right', N, HEIGHT, WORK( V ), TAU,
     >                      U( 1, J+B ), LDU, WORK( IWORK ) )
              ENDIF
            ENDIF
*
  500     CONTINUE
*
*            --- save the last scaling factor ---
*
          WORK( V ) = TAU
*
* ......................................................................
*
          IF ( BLOCK ) THEN
*
*              --- (delayed) update of the transformation matrix U.
*                  To allow blocked operations, the update is only
*                  done in every nb0-th pass through the k loop     ---
*
            IF ( ( MOD( K, NB0 ) .EQ. 0 ) .OR. ( K .EQ. ( N-2 ) ) )
     >      THEN
*
*                --- the following loop applies block transforms
*                    reversely to their generation, e.g., starting
*                    at the bottom and working up.
*                      First, determine which columns ifirst ...
*                    are affected by the block transform and
*                    how many (nb1) transforms it contains         ---
*
              DO 600 IFIRST = N-MOD( N-K0-1, B ), K0+1, -B
*
*                  --- how many Householder transforms contribute
*                      to the current block transform ?           ---
*
                NB1 = MIN( K-K0+1, N-IFIRST+1 )
                LDWY = MIN( LDWY0, N-IFIRST+1 )
*
*                  --- determine the block Householder reflector
*                      corresponding to these nb1 vectors        ---
*
                V = IFIRST - K0 - 1 + IV
                CALL SCOPY( NB1, WORK( V ), N-K0+1, WORK( ITAU ), 1 )
                CALL SGBWYG( LDWY, NB1, B-1,
     >                       WORK( V ), N-K0, WORK( ITAU ),
     >                       WORK( IW ), LDWY, WORK( IY ), LDWY, NB2 )
*
*                  --- update U by postmultiplying ---
*
                CALL SGEWY( 'Right', N, LDWY, NB2,
     >                      U( 1, IFIRST ), LDU,
     >                      WORK( IW ), LDWY, WORK( IY ), LDWY,
     >                      WORK( IWORK ) )
*
  600         CONTINUE
*
              K0 = K0 + NB0
*
            ENDIF
          ENDIF
*
* ......................................................................
*
  700   CONTINUE
*
*          --- end of the main loop: cleanup for the very tail
*              of the band                                     ---
*
        D( N-1 ) = A( 1, N-1 )
        E( N-1 ) = A( 2, N-1 )
*
        D( N ) = A( 1, N )
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSY2BC( UPLO, N, B, AFULL, LDFULL, ABAND, LDBAND,
     >                     INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   ssy2bc copies a symmetric banded A matrix from (upper or lower)
*   symmetric (full) storage to lower banded storage.
*
*   Note that afull and aband must refer to different memory locations,
*   i.e., A may NOT be repacked within the same array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDFULL, LDBAND, INFO
        REAL                  AFULL( LDFULL, * ), ABAND( LDBAND, * )
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of the
*           array afull ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   afull   (in) real array, dimension ( ldfull, n )
*           The symmetric banded matrix A in upper or lower symmetric
*           storage.
*
*   ldfull  (in) integer
*           The leading dimension of the array afull.
*           ldfull >= max( n, 1 ).
*
*   aband   (out) real array, dimension ( ldband, n )
*           The symmetric banded matrix A in lower banded storage (upper
*           banded storage is not supported).
*
*   ldband  (in)
*           The leading dimension of the array aband.
*           ldband >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldfull was out of range ( < n or < 1 ).
*                = -7 : ldband was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               J, I
*
*   upper   is A given in upper symmetric storage ?
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDFULL .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LDBAND .LT. ( B+1 ) ) THEN
          INFO = - 7
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower" ---
*
          DO 110 J = 1, N
            DO 100 I = MAX( J-B, 1 ), J
              ABAND( 1+J-I, I ) = AFULL( I, J )
  100       CONTINUE
  110     CONTINUE
        ELSE
*
*            --- "lower to lower" ---
*
          DO 210 J = 1, N
            DO 200 I = J, MIN( J+B, N )
              ABAND( 1+I-J, J ) = AFULL( I, J )
  200       CONTINUE
  210     CONTINUE
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSY2BI( UPLO, N, B, A, LDFULL, LDBAND, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   ssy2bi copies a symmetric banded A matrix from (upper or lower)
*   symmetric (full) storage to lower banded storage within the same
*   array a (i.e., in-place).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDFULL, LDBAND, INFO
        REAL                  A( * )
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of the
*           array a ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   a       (in/out) real array,
*           dimension ( max( ldfull, ldband), n )
*           On entry, the symmetric banded matrix A in upper or lower
*           symmetric storage.
*           On exit, the symmetric banded matrix A in lower banded
*           storage (upper banded storage is not supported).
*           Note that this routine treats a as a one-dimensional array.
*
*   ldfull  (in) integer
*           The leading dimension of the array a (in full storage).
*           ldfull >= max( n, 1 ).
*
*   ldband  (in)
*           The leading dimension of the array a (in banded storage).
*           ldband >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldfull was out of range ( < n or < 1 ).
*                = -6 : ldband was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, IBAND, IFULL, J, I
*
*   upper   is A given in upper symmetric storage ?
*   b1      = b + 1
*   iband   iband + i points to the next entry in a (banded storage)
*   ifull   ifull + i points to the next entry in a (full storage)
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              SSB2BI
*
*   ssb2bi  in-place repacking from banded to banded storage (SBR)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDFULL .LT. MAX( N, 1 ) ) THEN
          INFO = - 5
        ELSEIF ( LDBAND .LT. B1 ) THEN
          INFO = - 6
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower"; avoid overwriting by first
*                packing the band as tight as possible (i.e.,
*                leading dimension b + 1) and then "stretching"
*                to leading dimension ldband                    ---
*
          DO 110 J = 1, N
              IBAND = ( J - 1 ) * B1 + 1 - J
              DO 100 I = J, MIN( J+B, N )
                A( IBAND+I ) = A( (I-1)*LDFULL+J )
  100         CONTINUE
  110     CONTINUE
*
          IF ( LDBAND .GT. B1 ) THEN
            CALL SSB2BI( 'Lower', N, B, A, B1, LDBAND, INFO )
          ENDIF
*
        ELSE
*
*            --- "lower to lower"; avoid overwriting by
*                 copying the columns in the "safe" order ---
*
          IF ( LDBAND .LE. ( LDFULL+1 ) ) THEN
            DO 210 J = 1, N
              IBAND = ( J - 1 ) * LDBAND + 1 - J
              IFULL = ( J - 1 ) * LDFULL
              DO 200 I = J, MIN( J+B, N )
                A( IBAND+I ) = A( IFULL+I )
  200         CONTINUE
  210       CONTINUE
          ELSE
            DO 310 J = N, 1, -1
              IBAND = ( J - 1 ) * LDBAND + 1 - J
              IFULL = ( J - 1 ) * LDFULL
              DO 300 I = MIN( J+B, N ), J, -1
                A( IBAND+I ) = A( IFULL+I )
  300         CONTINUE
  310       CONTINUE
          ENDIF
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSB2BC( UPLO, N, B, ASRC, LDSRC, ADST, LDDST, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   ssb2bc copies a symmetric banded A matrix from upper or lower
*   banded storage to lower banded storage. It may be used to pack the
*   matrix tightly by setting lddst accordingly.
*
*   Note that asrc and adst must refer to different memory locations,
*   i.e., A may NOT be repacked within the same array.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDSRC, LDDST, INFO
        REAL                  ASRC( LDSRC, * ), ADST( LDDST, * )
*
*   uplo    (in) character*1
*           Is the matrix A given in upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n, if n >= 1.
*           b = 0     , if n = 0.
*
*   asrc    (in) real array, dimension ( ldsrc, n )
*           The symmetric banded matrix A in upper or lower banded
*           storage.
*
*   ldsrc   (in) integer
*           The leading dimension of the array asrc.
*           ldsrc >= b + 1.
*
*   adst    (out) real array, dimension ( lddst, n )
*           The symmetric banded matrix A in lower banded storage.
*
*   lddst   (in) integer
*           The leading dimension of the array adst.
*           lddst >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldsrc was out of range ( < b + 1 ).
*                = -7 : lddst was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, J, I
*
*   upper   is A given in upper banded storage ?
*   b1      = b + 1
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDSRC .LT. B1 ) THEN
          INFO = - 5
        ELSEIF ( LDDST .LT. B1 ) THEN
          INFO = - 7
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*              --- "upper to lower" ---
*
          DO 110 J = 1, N
            DO 100 I = 1, MIN( B1, N-J+1 )
              ADST( I, J ) = ASRC( B+2-I, J+I-1 )
  100       CONTINUE
  110     CONTINUE
        ELSE
*
*            --- "lower to lower" ---
*
          DO 210 J = 1, N
            DO 200 I = 1, MIN( B1, N-J+1 )
              ADST( I, J ) = ASRC( I, J )
  200       CONTINUE
  210     CONTINUE
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSB2BI( UPLO, N, B, A, LDSRC, LDDST, INFO )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   ssb2bi copies a symmetric banded A matrix from upper or lower banded
*   storage to lower banded storage within the same array a (i.e.,
*   in-place). It may be used to pack the matrix tightly by setting
*   lddst accordingly.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, B, LDSRC, LDDST, INFO
        REAL                  A( * )
*
*   uplo    (in) character*1
*           Is the matrix A given in the upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b       (in) integer
*           The (semi-)bandwidth of the matrix A.
*           0 <= b < n.
*
*   a       (in/out) real array,
*           dimension ( max( ldsrc, lddst ), n )
*           On entry, the symmetric banded matrix A in upper or lower
*           banded storage.
*           On exit, the symmetric banded matrix A in lower banded
*           storage (upper banded storage is not supported).
*           Note that this routine treats a as a one-dimensional array.
*
*   ldsrc   (in) integer
*           The leading dimension of the array a (input storage scheme).
*           ldsrc >= b + 1.
*
*   lddst   (in) integer
*           The leading dimension of the array a (output storage
*           scheme).
*           lddst >= b + 1.
*
*   info    (out) integer
*           On exit, info indicates the consistency of the arguments.
*           info = -1 : uplo was none of 'U', 'L' (upper/lower case).
*                = -2 : n was out of range (negative).
*                = -3 : b was out of range (negative or >= n ).
*                = -5 : ldsrc was out of range ( < b + 1 ).
*                = -6 : lddst was out of range ( < b + 1 ).
*           info =  1 : All arguments were ok.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        LOGICAL               UPPER
        INTEGER               B1, LDSRC1, ISRC, IDST, J, I
*
*   upper   is A given in upper banded storage ?
*   b1      = b + 1
*   ldsrc1  leading dimension of the current source, minus 1
*   isrc    isrc + i points to the next source element in a
*   idst    idst + something points to the next destination element in a
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in the parameters ---
*
        UPPER = LSAME( UPLO, 'U' )
        B1 = B + 1
*
        IF ( .NOT. ( UPPER .OR. ( LSAME( UPLO, 'L' ) ) ) ) THEN
          INFO = - 1
        ELSEIF ( N .LT. 0 ) THEN
          INFO = - 2
        ELSEIF ( ( B .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B .GE. N ) ) ) THEN
          INFO = - 3
        ELSEIF ( LDSRC .LT. B1 ) THEN
          INFO = - 5
        ELSEIF ( LDDST .LT. B1 ) THEN
          INFO = - 6
        ELSE
          INFO = 1
        ENDIF
*
        IF ( INFO .NE. 1 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
*          --- non-trivial case ---
*
        IF ( UPPER ) THEN
*
*            --- "upper to lower" ---
*
          IF ( LDDST .LE. LDSRC ) THEN
*
*              --- no danger of overwriting ---
*
            LDSRC1 = LDSRC - 1
            DO 110 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 2 ) * LDSRC + B + 2
              DO 100 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I*LDSRC1 )
  100         CONTINUE
  110       CONTINUE
          ELSE
*
*              --- first copy to upper storage, then transpose ---
*
            DO 210 J = N, 1, -1
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 200 I = B1, MAX( B1-J+1, 1 ), -1
                A( IDST+I ) = A( ISRC+I )
  200         CONTINUE
  210       CONTINUE
*
            LDSRC1 = LDDST - 1
            DO 230 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 2 ) * LDDST + B + 2
              DO 220 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I*LDSRC1 )
  220         CONTINUE
  230       CONTINUE
          ENDIF
*
        ELSE
*
*            --- "lower to lower"; avoid overwriting by
*                 copying the columns in the "safe" order ---
*
          IF ( LDDST .LE. LDSRC )
     >    THEN
            DO 310 J = 1, N
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 300 I = 1, MIN( B1, N-J+1 )
                A( IDST+I ) = A( ISRC+I )
  300         CONTINUE
  310       CONTINUE
          ELSE
            DO 410 J = N, 1, -1
              IDST = ( J - 1 ) * LDDST
              ISRC = ( J - 1 ) * LDSRC
              DO 400 I = MIN( B1, N-J+1 ), 1, -1
                A( IDST+I ) = A( ISRC+I )
  400         CONTINUE
  410       CONTINUE
          ENDIF
*
        ENDIF
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSBRDD( JOBU, UPLO, N, B1, B2, A, LDA, DRPTOL, D, E,
     >                     U, LDU, NSTEPS, B, NB,
     >                     WORK, LWORK, STEP, INFO )
*
* Description:
*
*   Driver routine for the multi-step reduction of symmetric banded
*   matrices to narrower banded form.
*   Given a symmetric n-by-n matrix A with b1 sub(or super-) diagonals,
*   ssbrdd reduces A to a symmetric banded matrix B with b2 sub(or
*   super-) diagonals using a sequence of orthogonal transformations.
*   If desired, the same transformations are also applied from the right
*   to the matrix U. That is, if initially U was the identity, then the
*   resulting banded matrix B and the updated U fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK packed storage scheme for upper or
*   lower banded matrices and is returned in lower banded storage (upper
*   banded is not supported for output).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOBU, UPLO
        INTEGER               N, B1, B2, LDA, LDU, NSTEPS, LWORK, STEP,
     >                        INFO
        INTEGER               B( * ), NB( * )
        REAL                  DRPTOL
        REAL                  A( LDA, * ), D( * ), E( * ), U( LDU, * ),
     >                        WORK( * )
*
*   jobu    (in) character*1
*           Specifies whether U is required or not.
*           jobu = 'U' : Update U.
*                = 'N' : Do not update U.
*
*   uplo    (in) character*1
*           Is the matrix A given in the upper or lower banded storage ?
*           uplo = 'U' : Upper banded storage.
*                = 'L' : Lower banded storage.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b1      (in) integer
*           The number of sub(super-)diagonals of A.
*           0 <= b1 < n, if n > 0.
*           b1 = 0,      if n = 0.
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 <= b1 or b2 = b1 = 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the leading (b1+1)-by-n portion of a contains the
*           symmetric banded matrix A in upper or lower banded storage.
*           If uplo='U' then for i = 1, ..., n, the matrix elements
*           A( i, j ), j = i, ..., min( i+b1, n ), are stored at
*           position a( b1+1+i-j, j ), whereas for uplo='L', the matrix
*           elements A( i, j ), j = max( i-b, 1 ), ..., i, are stored at
*           position a( 1+i-j, j ).
*           On exit, the leading (b2+1)-by-n portion of a contains the
*           reduced matrix B in lower (!) banded storage.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( b1+1, n ) and lda > 0.
*
*   drptol  (in) real
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   d       (out) real array, dimension ( n )
*           If b2 = 1 then, on exit, d( 1 .. n ) contains the main
*           diagonal of the resulting tridiagonal matrix B.
*
*   e       (out) real array, dimension ( n-1 )
*           If b2 = 1 then, on exit, e( 1 .. n-1 ) contains the
*           subdiagonal of the resulting tridiagonal matrix B.
*
*   u       (in/out) real array, dimension ( ldu, n )
*           On entry, u contains some n-by-n matrix U.
*           On exit, U is postmultiplied with all orthogonal transforms
*           that were used to reduce the bandwidth of A.
*           Accessed only if the update of U is required.
*
*   ldu     (in) integer
*           The leading dimension of the array u.
*           ldu >= max( n, 1 ).
*
*   nsteps  (in) integer
*           The number of reduction steps.
*           nsteps >= 0.
*
*           If nsteps > 0 then the reduction from b1 to b2 is done in
*           exactly nsteps steps with user-specified intermediate
*           bandwidths and blocking factors (see paramaters b and nb,
*           below).
*           If nsteps = 0 then the routine tries to determine these
*           parameters on its own.
*           If you do not know or if you do not care, use 0.
*
*   b       (in) integer array, dimension ( nsteps-1 )
*           The sequence of intermediate bandwidths. The nsteps
*           bandwidth reduction steps are
*              b1 --> b( 1 ),
*              b( 1 ) --> b( 2 ),
*              ...
*              b( nsteps-1 ) --> b2.
*           This array is accessed only if nsteps > 1.
*
*   nb      (in) integer array, dimension ( nsteps )
*           The blocking factors nb, as suggested by the user, for the
*           reduction and/or the accumulation of the transformations
*           in each of the nb reduction steps.
*           Note that the automatic selection of suitable blocking
*           factors is enabled by setting nb( i ) = 0 for some steps i.
*           This array is accessed only if nsteps > 0.
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The length of the workspace array.
*           The exact amount of workspace required depends on the
*           sequence of intermediate bandwidths (i.e., b), on the
*           leading dimension of the array a (i.e., lda), and on the
*           blocking factors for the reduction steps (i.e., nb).
*           lwork >= maximum workspace requirement for any of the
*                    reduction steps.
*           As a rule, lwork >= b1 * n should work fine.
*
*   step    (out) integer
*           On exit, step returns the number of the last reduction step
*           that was performed (or tried).
*
*   info    (out) integer
*           On exit, info indicates the status of the reduction.
*           info =   1 : All arguments were OK, and the reduction went
*                        without problems.
*                =  -1 : jobu is none of 'U', 'N' (upper/lower case).
*                =  -2 : uplo is none of 'U', 'L' (upper/lower case).
*                =  -3 : n is out of range (negative).
*                =  -4 : b1 is out of range ( < 0 or >= n ).
*                =  -5 : b2 is out of range ( < 0, or = 0 while b1 >= 1,
*                        or > b1 ).
*                =  -7 : lda is too small (see above).
*                =  -8 : drptol is out of range (negative).
*                = -12 : ldu is out of range ( < n ).
*                = -13 : nsteps is out of range (negative).
*                = -14 : the sequence of bandwidths b1, b( 1 ), b( 2 ),
*                        ..., b( nsteps-1 ), b2 is not monotonically
*                        decreasing
*                = -15 : nb contains negative entries
*                = -17 : lwork is too small (see above).
*           If info < 0 and step > 0 then the parameter for the step-th
*           reduction step was not OK.
*
* Local constants and variables:
*
        REAL                  ZERO
        PARAMETER             ( ZERO = 0.0E0 )
*
        LOGICAL               NEEDU, UPPER
        INTEGER               BCURR, LDCURR, NBCURR, BNEXT, LDNEXT, NX
        CHARACTER*1           ULCURR
*
*   needu   is U needed ?
*   upper   is A given in upper or lower banded storage ?
*   bcurr   current bandwidth
*   ldcurr  current leading dimension of the band
*   nbcurr  blocking factor for the current step
*   bnext   bandwidth after the next reduction step
*   ldnext  leading dimension of the band after repacking
*   nx      cross-over point from LAPACK to SBR code, and block size
*   ulcurr  is the current band in upper or lower storage ?
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine default crossover point from LAPACK to SBR code
*           or default intermediate bandwidth (SBR)
*
        EXTERNAL              SSB2BI, SSBRDB, SSBRDT, SSBTRD
*
*   ssb2bi  in-place repacking of banded matrices (SBR)
*   ssbrdb  one-step reduction banded -> banded (SBR)
*   ssbrdt  one-step reduction banded -> tridiagonal (SBR)
*   ssbtrd  one-step reduction banded -> tridiagonal (LAPACK)
*
        INTRINSIC             MAX, MIN
*
* ----------------------------------------------------------------------
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOBU, 'U' )
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -3
        ELSEIF ( ( B1 .LT. 0 ) .OR.
     >           ( ( N .GT. 0 ) .AND. ( B1 .GE. N ) ) ) THEN
          INFO = -4
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( B2 .EQ. 0 ) .AND. ( B1 .GE. 1 ) ) .OR.
     >           ( B2 .GT. B1 ) ) THEN
          INFO = -5
        ELSEIF ( LDA .LT. ( B1+1 ) ) THEN
          INFO = -7
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -8
        ELSEIF ( NEEDU .AND. ( LDU .LT. MAX( N, 1 ) ) ) THEN
          INFO = -12
        ELSEIF ( NSTEPS .LT. 0 ) THEN
          INFO = -13
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 1 ) THEN
          IF ( ( B( 1 ) .GT. B1 ) .OR. ( B2 .GT. B( NSTEPS-1 ) ) ) THEN
            INFO = -14
          ELSE
            DO 10 STEP = 1, NSTEPS-2
              IF ( B( STEP+1 ) .GT. B( STEP ) )     INFO = -14
   10       CONTINUE
          ENDIF
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 0 ) THEN
          DO 20 STEP = 1, NSTEPS
            IF ( NB( STEP ) .LT. 0 )     INFO = -15
   20     CONTINUE
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
*          --- set current bandwidth, leading dimension, etc. ---
*
        ULCURR = UPLO
        BCURR = B1
        LDCURR = LDA
        STEP = 0
*
*          --- while bandwidth is too large do next reduction step ---
*
  100   IF ( BCURR .GT. B2 ) THEN
          STEP = STEP + 1
*
*            --- determine target bandwidth and blocking factor
*                for the next reduction step                    ---
*
          IF ( STEP .LT. NSTEPS ) THEN
            BNEXT = B( STEP )
            NBCURR = NB( STEP )
          ELSEIF ( STEP .EQ. NSTEPS ) THEN
            BNEXT = B2
            NBCURR = NB( STEP )
          ELSE
*
*              --- automatic bandwidth selection ---
*
            BNEXT = NBDFLT( 'SBRDD', 'SinglePrec', 'Bandwidth',
     >                      N, BCURR, B2, NEEDU )
*
*              --- if the proposed intermediate bandwidth is out
*                  of range then do a one-step reduction         ---
*
            IF ( ( BNEXT .GE. BCURR ) .OR. ( BNEXT .LT. B2 ) ) THEN
              BNEXT = B2
            ENDIF
            NBCURR = 0
          ENDIF
*
          IF ( BNEXT .EQ. 1 ) THEN
*
*              --- reduction to tridiagonal form;
*                  use SBR or LAPACK code ?       ---
*
            NX = NBDFLT( 'SBRDD', 'SinglePrec', 'CrossoverPoint',
     >                   N, BCURR, B2, NEEDU )
            IF ( BCURR .LT. NX ) THEN
*
*                --- LAPACK tridiagonalization; first repack the
*                    band to improve performance                 ---
*
              LDNEXT = BCURR + 1
              IF ( LDCURR .NE. LDNEXT ) THEN
                CALL SSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
                LDCURR = LDNEXT
                ULCURR = 'Lower'
              ENDIF
*
              IF ( LWORK .LT. N ) THEN
                INFO = -17
              ELSE
                CALL SSBTRD( JOBU, ULCURR, N, BCURR, A, LDCURR, D, E,
     >                       U, LDU, WORK, INFO )
              ENDIF
            ELSE
*
*                --- SBR tridiagonalization; first repack the band
*                    to improve performance                        ---
*
              LDNEXT = MIN( 2*BCURR, LDA )
              IF ( ( LDCURR .NE. LDNEXT ) .OR.
     >             LSAME( ULCURR, 'Upper' ) ) THEN
                CALL SSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
                LDCURR = LDNEXT
                ULCURR = 'Lower'
              ENDIF
*
              CALL SSBRDT( JOBU, N, BCURR, A, LDCURR, DRPTOL, D, E,
     >                     U, LDU, NBCURR, WORK, LWORK, INFO )
              IF ( INFO .EQ. -13 )     INFO = -17
            ENDIF
*
          ELSE
*
*              --- SBR reduction to narrower banded form; first
*                  repack the band to improve performance (optimum
*                  leading dimension depends on the blocking
*                  factor - so determine that one first)           ---
*
            IF ( NBCURR .EQ. 0 ) THEN
              NX = NBDFLT( 'SBRDB', 'SinglePrec', 'BlockingFactor',
     >                     N, BCURR, BNEXT, NEEDU )
            ELSE
              NX = NBCURR
            ENDIF
            IF ( NX .GT. BNEXT )     NX = BNEXT
            IF ( NX .LT. 1 )     NX = 1
            LDNEXT = MIN( BCURR+(BCURR-BNEXT)+NX, LDA )
            IF ( ( LDCURR .NE. LDNEXT ) .OR.
     >           LSAME( ULCURR, 'Upper' ) ) THEN
              CALL SSB2BI( ULCURR, N, BCURR, A, LDCURR, LDNEXT, INFO )
              LDCURR = LDNEXT
              ULCURR = 'Lower'
            ENDIF
*
            CALL SSBRDB( JOBU, N, BCURR, BNEXT, A, LDCURR, DRPTOL,
     >                   U, LDU, NBCURR, WORK, LWORK, INFO )
            IF ( INFO .EQ. -12 )     INFO = -17
          ENDIF
*
          BCURR = BNEXT
          IF ( INFO .GE. 0 )     GOTO 100
*
        ENDIF
*
*          --- after the reduction, repack the band to leading
*              dimension lda and lower banded storage scheme   ---
*
        IF ( ( INFO .GE. 0 ) .AND.
     >       ( ( LDCURR .NE. LDA ) .OR. LSAME( ULCURR, 'Upper' ) ) )
     >  THEN
          CALL SSB2BI( ULCURR, N, BCURR, A, LDCURR, LDA, INFO )
        ENDIF
*
        IF ( INFO .GE. 0 )     INFO = 1
*
  999   RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYRDD( JOBU, UPLO, N, B2, A, LDA, DRPTOL,
     >                     ABAND, LDBAND, D, E, NSTEPS, B, NB,
     >                     WORK, LWORK, STEP, INFO )
*
* Description:
*
*   Driver routine for the multi-step reduction of symmetric matrices to
*   banded form.
*   Given a symmetric n-by-n matrix A, ssyrdd reduces A to a symmetric
*   banded matrix B with b2 sub(or super-) diagonals using a sequence of
*   orthogonal transformations.
*   If desired, the same transformations are also accumulated in an
*   orthogonal matrix U. That is, the resulting banded matrix B and the
*   accumulated matrix U fulfill the equation
*
*       T
*      U  * A * U  =  B  .
*
*   A must be given in the LAPACK symmetric storage scheme with either
*   the upper or lower triangle stored explicitly, and B is returned in
*   lower banded storage (upper banded is not supported for output).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Parameters:
*
        CHARACTER*1           JOBU, UPLO
        INTEGER               N, B2, LDA, LDBAND, NSTEPS, LWORK, STEP,
     >                        INFO
        INTEGER               B( * ), NB( * )
        REAL                  DRPTOL
        REAL                  A( LDA, * ), ABAND( LDBAND, * ),
     >                        D( * ), E( * ), WORK( * )
*
*   jobu    (in) character*1
*           Specifies whether U is required or not.
*           jobu = 'U' : Build U.
*                = 'N' : Do not build U.
*
*   uplo    (in) character*1
*           Is the matrix A stored in the upper or lower triangle of a ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the matrix A.
*           n >= 0.
*
*   b2      (in) integer
*           The number of sub(super-)diagonals of B.
*           1 <= b2 < n, if n > 1.
*           b2 = 0     , if n <= 1.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the leading n-by-n portion of a contains the
*           symmetric matrix A in upper or lower symmetric storage.
*           If uplo='U' then the upper triangle of A is stored in
*           the upper triangle of the leading n-by-n portion of a;
*           if uplo='L' then the lower triangle of A is stored in
*           the lower triangle of the leading n-by-n portion of a.
*           On exit, A is destroyed.
*           If jobu='U' then the leading n-by-n portion of a holds
*           the orthogonal matrix U.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   drptol  (in) real
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
*   aband   (out) real array, dimension ( ldband, n )
*           On exit, the leading (b2+1)-by-n portion of aband holds the
*           symmetric banded matrix B in lower banded storage (i.e., for
*           j = 1, ..., n and i = j, ..., min( j+b2, n ), the matrix
*           element B( i, j ) is stored in location aband( i-j+1, j ).
*
*   ldband  (in) integer
*           The leading dimension of the array aband.
*           ldband >= b( 1 ) + 1, if nsteps > 1.
*                  >= b2 + 1    , otherwise.
*           For reasonable performance, set ldband >= 2 * b( 1 ) if
*           nsteps > 1, and ldband >= 50 if nsteps = 0.
*
*   d       (out) real array, dimension ( n )
*           If b2 = 1 then, on exit, d( 1 .. n ) contains the main
*           diagonal of the resulting tridiagonal matrix B.
*
*   e       (out) real array, dimension ( n-1 )
*           If b2 = 1 then, on exit, e( 1 .. n-1 ) contains the
*           subdiagonal of the resulting tridiagonal matrix B.
*
*   nsteps  (in) integer
*           The number of reduction steps.
*           nsteps >= 0.
*
*           If nsteps > 0 then the reduction from full to b2 diagonals
*           is done in exactly nsteps steps with user-specified
*           intermediate bandwidths and blocking factors (see paramaters
*           b and nb, below).
*           If nsteps = 0 then the routine tries to determine these
*           parameters on its own.
*           If you do not know or if you do not care, use 0.
*
*   b       (in) integer array, dimension ( nsteps-1 )
*           The sequence of intermediate bandwidths. The nsteps
*           bandwidth reduction steps are
*              n-1 --> b( 1 ),
*              b( 1 ) --> b( 2 ),
*              ...
*              b( nsteps-1 ) --> b2.
*           This array is accessed only if nsteps > 1.
*
*   nb      (in) integer array, dimension ( nsteps )
*           The blocking factors nb, as suggested by the user, for the
*           reduction and/or the accumulation of the transformations
*           in each of the nb reduction steps.
*           Note that the automatic selection of suitable blocking
*           factors is enabled by setting nb( i ) = 0 for some steps i.
*           This array is accessed only if nsteps > 0.
*
*   work    (workspace) real array, dimension ( lwork )
*
*   lwork   (in) integer
*           The length of the workspace array.
*           The exact amount of workspace required depends on the
*           sequence of intermediate bandwidths (i.e., b), on the
*           leading dimension of the array a (i.e., lda), and on the
*           blocking factors for the reduction steps (i.e., nb).
*           lwork >= maximum workspace requirement for any of the
*                    reduction steps.
*           Minimum requirement is 4 * n, but setting lwork this low may
*           severely degrade performance.
*           As a rule, lwork >= 50 * n should work fine; if you can
*           spare it, use lwork >= 100 * n.
*
*   step    (out) integer
*           On exit, step returns the number of the last reduction step
*           that was performed (or tried).
*
*   info    (out) integer
*           On exit, info indicates the status of the reduction.
*           info =   1 : All arguments were OK, and the reduction went
*                        without problems.
*                =  -1 : jobu is none of 'U', 'N' (upper/lower case).
*                =  -2 : uplo is none of 'U', 'L' (upper/lower case).
*                =  -3 : n is out of range (negative).
*                =  -4 : b2 is out of range ( < 0,
*                        or < 1 or >= n while n > 1 ).
*                =  -6 : lda is too small (see above).
*                =  -7 : drptol is out of range (negative).
*                =  -9 : ldband is out of range ( < b(1)+1 ).
*                = -12 : nsteps is out of range (negative).
*                = -13 : the sequence of bandwidths n-1, b( 1 ), b( 2 ),
*                        ..., b( nsteps-1 ), b2 is not monotonically
*                        decreasing
*                = -14 : nb contains negative entries
*                = -16 : lwork is too small (see above).
*           If info < 0 and step > 0 then the parameter for the step-th
*           reduction step was not OK.
*
* Local constants and variables:
*
        REAL                  ZERO
        PARAMETER             ( ZERO = 0.0E0 )
*
        LOGICAL               NEEDU, UPPER
        INTEGER               BNEXT, NBCURR
*
*   needu   is U needed ?
*   upper   is the upper triangle of A stored ?
*   nbcurr  blocking factor for the current step
*   bnext   bandwidth after the next reduction step
*
* Routines called:
*
        LOGICAL               LSAME
        INTEGER               NBDFLT
        EXTERNAL              LSAME, NBDFLT
*
*   lsame   case-insensitive character matching (BLAS)
*   nbdflt  determine intermediate bandwidth (SBR)
*
        EXTERNAL              SORGTR, SSBRDD, SSY2BC, SSYGTR, SSYRDB,
     >                        SSYTRD
*
*   sorgtr  accumulation of the transformations (LAPACK)
*   ssbrdd  bandwidth reduction for banded matrices (SBR)
*   ssy2bc  repacking from full to banded storage (SBR)
*   ssygtr  accumulation of the transformations (SBR)
*   ssyrdb  reduction full -> banded (SBR)
*   ssytrd  one-step reduction full -> tridiagonal (LAPACK)
*
        INTRINSIC             MAX
*
* ----------------------------------------------------------------------
*
        STEP = 1
*
*          --- check for errors in input ---
*
        NEEDU = LSAME( JOBU, 'U' )
        UPPER = LSAME( UPLO, 'U' )
*
        IF ( .NOT. ( NEEDU .OR. LSAME( JOBU, 'N' ) ) ) THEN
          INFO = -1
        ELSEIF ( .NOT. ( UPPER .OR. LSAME( UPLO, 'Lower' ) ) ) THEN
          INFO = -2
        ELSEIF ( N .LT. 0 ) THEN
          INFO = -3
        ELSEIF ( ( B2 .LT. 0 ) .OR.
     >           ( ( N .GT. 1 ) .AND.
     >             ( ( B2 .LT. 1 ) .OR. ( B2 .GT. N-1 ) ) ) ) THEN
          INFO = -4
        ELSEIF ( LDA .LT. MAX( N, 1 ) ) THEN
          INFO = -6
        ELSEIF ( DRPTOL .LT. ZERO ) THEN
          INFO = -7
        ELSEIF ( ( LDBAND .LE. B2 ) .OR.
     >           ( ( NSTEPS .GT. 1 ) .AND. ( LDBAND .LE. B( 1 ) ) ) )
     >  THEN
          INFO = -9
        ELSEIF ( NSTEPS .LT. 0 ) THEN
          INFO = -12
        ELSEIF ( LWORK .LT. 4*N ) THEN
          INFO = -16
        ELSE
          INFO = 0
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 1 ) THEN
          IF ( ( B( 1 ) .GT. ( N-1 ) ) .OR.
     >         ( B2 .GT. B( NSTEPS-1 ) ) ) THEN
            INFO = -13
          ELSE
            DO 10 STEP = 1, NSTEPS-2
              IF ( B( STEP+1 ) .GT. B( STEP ) )     INFO = -13
   10       CONTINUE
          ENDIF
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
        IF ( NSTEPS .GT. 0 ) THEN
          DO 20 STEP = 1, NSTEPS
            IF ( NB( STEP ) .LT. 0 )     INFO = -14
   20     CONTINUE
        ENDIF
        IF ( INFO .LT. 0 )     GOTO 999
*
*          --- check for quick return ---
*
        IF ( N .EQ. 0 )     GOTO 999
*
        STEP = 1
*
*          --- determine first intermediate bandwidth and blocking
*              factor                                              ---
*
        IF ( NSTEPS .GT. 0 ) THEN
          IF ( NSTEPS .EQ. 1 ) THEN
            BNEXT = B2
          ELSE
            BNEXT = B( 1 )
          ENDIF
          NBCURR = NB( 1 )
        ELSE
*
*            --- automatic bandwidth selection ---
*
          BNEXT = NBDFLT( 'SYRDD', 'SinglePrec', 'Bandwidth',
     >                    N, N - 1, B2, NEEDU )
*
*              --- if the proposed intermediate bandwidth is out
*                  of range then do a one-step reduction         ---
*
          IF ( ( BNEXT .GT. N-1 ) .OR. ( BNEXT .LT. B2 ) .OR.
     >         ( LDBAND .LT. 2*BNEXT ) ) THEN
            BNEXT = B2
          ENDIF
          NBCURR = 0
        ENDIF
*
        IF ( BNEXT .EQ. 1 ) THEN
*
*            --- use LAPACK code for direct tridiagonalization ---
*
          CALL SSYTRD( UPLO, N, A, LDA, D, E, WORK( 1 ),
     >                 WORK( N ), LWORK-N+1, INFO )
          IF ( NEEDU ) THEN
            CALL SORGTR( UPLO, N, A, LDA, WORK( 1 ),
     >                   WORK( N ), LWORK-N+1, INFO )
          ENDIF
        ELSE
*
*            --- reduction to bandwidth > 1 width ssyrdb ---
*
          CALL SSYRDB( UPLO, 'NoU', N, BNEXT, A, LDA, DRPTOL,
     >                 WORK( 1 ), N, NBCURR, WORK( 1 ),
     >                 WORK( N+1 ), LWORK-N, INFO )
*
*            --- repack the reduced matrix to banded storage ---
*
          CALL SSY2BC( UPLO, N, BNEXT, A, LDA, ABAND, LDBAND, INFO )
*
*            --- accumulation of the transformations, if required ---
*
          IF ( NEEDU ) THEN
            CALL SSYGTR( UPLO, N, BNEXT, A, LDA, WORK( 1 ),
     >                   WORK( N+1 ), LWORK-N, INFO )
          ENDIF
*
*            --- further reduce the banded matrix, if required ---
*
          IF ( ( BNEXT .GT. B2 ) .AND. ( INFO .GE. 0 ) ) THEN
            IF ( NSTEPS .EQ. 0 ) THEN
              CALL SSBRDD( JOBU, 'Lower', N, BNEXT, B2, ABAND, LDBAND,
     >                     DRPTOL, D, E, A, LDA, 0, B, NB,
     >                     WORK, LWORK, STEP, INFO )
            ELSE
              CALL SSBRDD( JOBU, 'Lower', N, BNEXT, B2, ABAND, LDBAND,
     >                     DRPTOL, D, E, A, LDA, NSTEPS-1, B( 2 ),
     >                     NB( 2 ), WORK, LWORK, STEP, INFO )
            ENDIF
            STEP = STEP + 1
          ENDIF
        ENDIF
*
  999   IF ( INFO .GE. 0 )     INFO = 1
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SLBRFG( N, ALPHA, X, INCX, TAU, DRPTOL )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   slbrfg generates an elementary reflector H of order n, such that
*
*                                    T
*      H * ( alpha ) = ( beta ) ,   H  * H = I ,
*          (   x   )   (   0  )
*
*   where alpha and beta are scalars, and x is an ( n - 1 )-element
*   vector. H is represented in the form
*
*                                 T
*      H = I - tau * ( 1 ) * ( 1 v  ) ,
*                    ( v )
*
*   where tau is a scalar and v is an ( n - 1 )-element vector.
*
*   If the elements of x are all zero, or the 2-norm of x does not
*   exceed drptol, then x is simply zeroed out, tau is set to 0,
*   indicating that H is the identity matrix. In this case, the
*   transformation is effectively skipped.
*
*   Otherwise  1 <= tau <= 2.
*
*   This routine is a modified version of slbrfg by Bischof/Sun which
*   in turn is a modified version of the LAPACK routine slarfg.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               N, INCX
        REAL                  ALPHA, TAU, DRPTOL
        REAL                  X( * )
*
*   n       (in) integer
*           The order of the elementary reflector.
*           n >= 0.
*
*   alpha   (in/out) real
*           On entry, the value alpha.
*           On exit, it is overwritten with the value beta.
*
*   x       (in/out) real array, dimension ( 1+(n-2)*incx )
*           On entry, the vector x.
*           On exit, the "x elements" are overwritten with the vector v.
*
*   incx    (in) integer
*           The increment between elements of x.
*           incx > 0.
*
*   tau     (out) real
*           The scaling factor tau.
*
*   drptol  (in) real
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to eliminate is already <= drptol
*           then the transform is skipped.
*           drptol >= 0.0.
*           If you do not know, use 0.0.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        REAL                  XNORM, BETA, SAFMIN, RSAFMN
        INTEGER               CNT, J
*
*   xnorm   2-norm of x
*   beta    the computed value beta
*   safmin  safe minimum (such that relative accuracy can be guaranteed)
*   rsafmn  1 / safmin
*   cnt     counts the rescaling steps
*
* Routines called:
*
        REAL                  SLAMCH, SLAPY2, SNRM2
        EXTERNAL              SLAMCH, SLAPY2, SNRM2, SSCAL
*
*   slamch        determine machine parameters (LAPACK)
*   slapy2        stable 2-norm of 2-vector (LAPACK)
*   snrm2         2-norm of a vector (BLAS)
*   sscal         vector scaling (BLAS)
*
        INTRINSIC             SIGN, ABS
*
* ----------------------------------------------------------------------
*
*            --- check for quick exit ---
*
        IF ( N .LE. 1 ) THEN
          TAU = ZERO
        ELSE
*
          XNORM = SNRM2( N-1, X, INCX )
*
          IF ( XNORM .LE. DRPTOL ) THEN
*
*              --- H = I ---
*
            TAU = ZERO
            DO 10 J = 1, N-1
              X( 1+(J-1)*INCX ) = ZERO
   10       CONTINUE
*
          ELSE
*
*              --- general case ---
*
            BETA = - SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )
            SAFMIN = SLAMCH( 'S' ) / SLAMCH( 'E' )
*
            IF ( ABS( BETA ) .LT. SAFMIN ) THEN
*
*                --- xnorm, beta may be inaccurate; scale x
*                    and recompute them                     ---
*
              RSAFMN = ONE / SAFMIN
              CNT = 0
*
  100         CONTINUE
                CNT = CNT + 1
                ALPHA = ALPHA * RSAFMN
                CALL SSCAL( N-1, RSAFMN, X, INCX )
                BETA = BETA * RSAFMN
              IF ( ABS( BETA ) .LT. SAFMIN )     GOTO 100
*
*                --- now abs( beta ) is at least safmin ---
*
              XNORM = SNRM2( N-1, X, INCX )
              BETA = - SIGN( SLAPY2( ALPHA, XNORM ), ALPHA )
              TAU = ( BETA - ALPHA ) / BETA
              CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
*
*                --- if alpha is subnormal, it may lose
*                    relative accuracy                  ---
*
              ALPHA = BETA
*
              DO 110 J = 1, CNT
                ALPHA = ALPHA * SAFMIN
  110         CONTINUE
*
            ELSE
*
              TAU = ( BETA - ALPHA ) / BETA
              CALL SSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
              ALPHA = BETA
*
            ENDIF
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYRF( UPLO, N, V, INCV, TAU,
     >                    A, LDA, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*                                                      T
*   Apply the Householder transform H = I - tau * v * v  from both
*   sides to the symmetric matrix A, i.e., update
*
*                            T
*      A := H * A * H   ( = H  * A * H )  .
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* ----------------------------------------------------------------------
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, INCV, LDA
        REAL                  TAU
        REAL                  V( * ), A( LDA, * ), WORK( * )
*
*  uplo     (in) character*1
*           Is the upper or lower triangle of A stored ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*  n        (in) integer
*           The dimension of the matrix A.
*           n >= 0.
*
*  v        (in) real array, dimension ( 1+(n-1)*incv )
*           The Householder vector associated with H.
*           Usually, v( 1 ) = 1, and v( 2:n ) contains the "mantissa" of
*           the transform.
*
*  incv     (in) integer
*           The increment between the elements of v.
*           incv > 0.
*
*  tau      (in) real
*           The scaling factor for the transform.
*
*  a        (in/out) real array, dimension ( lda, n )
*           On entry, an n-by-n symmetric matrix A with either the lower
*           or the upper triangle stored.
*           On exit, the leading A is overwritten with H * A * H.
*
*  lda      (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*  work     (workspace) real array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        REAL                  ALPHA
*
*   alpha   auxiliary factor
*
* Routines called:
*
        REAL                  SDOT
        EXTERNAL              SAXPY, SDOT, SSYMV, SSYR2
*
*   saxpy   add multiple of a vector to another vector (BLAS)
*   sdot    dot product of two vectors (BLAS)
*   ssymv   symmetric matrix-vector product (BLAS)
*   ssyr2   symmetric rank-2 update (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( N .GT. 0 ) .AND. ( TAU .NE. ZERO ) ) THEN
*
*              --- work( 1:n ) := x = tau * A * v ---
*
          CALL SSYMV( UPLO, N, TAU, A, LDA, V, INCV, ZERO, WORK, 1 )
*
*                                                        T
*              --- work( 1:n ) := w = x - 1/2 * tau * ( x  * v ) * v ---
*
          ALPHA = -0.5E0 * TAU * SDOT( N, WORK, 1, V, INCV )
          CALL SAXPY( N, ALPHA, V, INCV, WORK, 1 )
*
*                                T        T
*              --- A := A - v * w  - w * v  ---
*
          CALL SSYR2( UPLO, N, -ONE, V, INCV, WORK, 1, A, LDA )
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SGBQR2( M, N, D, A, LDA, TAU, DRPTOL, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given an m-by-n matrix A with d subdiagonals, sgeqr2 computes
*   a QR factorization of A.
*
*   The matrix Q is represented as a product of elementary reflectors
*
*      Q  =  H( 1 ) * ... * H( k )   ,   where k = min( m, n ).
*
*   Each H( j ) has the form
*
*                                  T
*      H( j )  =  I  -  tau * v * v
*
*   where tau is a scalar, and v is a vector of length m with
*   v( 1:j-1 ) = 0   and   v( j ) = 1.
*   On exit, v( j+1:m ) is stored in a( j+1:m, j ) and tau in tau( j ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               M, N, D, LDA
        REAL                  DRPTOL
        REAL                  A( LDA, * ), TAU( * ), WORK( * )
*
*   m       (in) integer
*           The number of rows in the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns in the matrix A.
*           n >= 0.
*
*   d       (in) integer
*           The number of subdiagonals of the matrix A.
*           0 <= d <= m - 1, if m > 0.
*           d = 0          , if m = 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the m-by-n matrix A with lower bandwidth b.
*           On exit, the elements on and above the diagonal contain the
*           min( m, n )-by-n upper trapezoidal matrix R (R is upper
*           triangular if m >= n); the elements below the diagonal,
*           together with the array tau, represent the orthogonal
*           matrix Q as a product of Householder transformations.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( m, 1 ).
*
*   tau     (out) real array, dimension ( min( m-1, n ) )
*           The scaling factors of the Householder transformations.
*
*   drptol  (in) real
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to be zeroed is already less than
*           drptol then the transform is skipped.
*           drptol >= 0.0.
*
*   work    (workspace) real array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        INTEGER               J, LEN
        REAL                  AJJ
*
*   len     length of the current transform
*   ajj     temporary buffer for the element a( j, j )
*
* Routines called:
*
        EXTERNAL              SLARFX, SLBRFG
*
*   slarfx  apply Householder transformation (LAPACK)
*   slbrfg  generate Householder vector (SBR)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        DO 100 J = 1, MIN( M-1, N )
*
          LEN = MIN( D+1, M-J+1 )
*
*            --- generate Householder reflector H( j ) to zero
*                A( j+1:j+d, j )                               ---
*
          CALL SLBRFG( LEN, A( J, J ), A( J+1, J ), 1,
     >                 TAU( J ), DRPTOL )
*
*            --- apply the transform ---
*
          IF ( TAU( J ) .NE. ZERO ) THEN
*
            AJJ = A( J, J )
            A( J, J ) = ONE
            CALL SLARFX( 'Left', LEN, N-J, A( J, J ), TAU( J ),
     >                  A( J, J+1 ), LDA, WORK )
            A( J, J ) = AJJ
*
          ENDIF
*
  100   CONTINUE
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SGEQRL( DECOMP, M, N, A, LDA, DRPTOL,
     >                     TAU, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Compute the QR or QL factorization of the m-by-n matrix A,
*   where m >= n.
*
*   The matrix Q is represented as a product of elementary reflectors
*
*      Q  =  H( 1 ) * ... * H( n )        (QR decomposition)
*
*   or
*
*      Q  =  H( n ) * ... * H( 1 )        (QL decomposition).
*
*   Each H( j ) has the form
*
*                                  T
*      H( j )  =  I  -  tau * v * v
*
*   where tau is a scalar, and v is a vector of length m.
*
*   In the QR case,
*     v( 1:j-1 ) = 0   and   v( j ) = 1   and, on exit, v( j+1:m ) is
*     stored in a( j+1:m, j ) and tau in tau( j ).
*
*   In the QL case,
*     v( m-n+j+1:m ) = 0   and   v( m-n+j ) = 1   and, on exit,
*     v( 1:m-n+j-1 ) is stored in a( 1:m-n+j-1, j ) and tau in tau( j ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           DECOMP
        INTEGER               M, N, LDA
        REAL                  DRPTOL
        REAL                  A( LDA, * ), TAU( * ), WORK( * )
*
*   decomp  (in) character*1
*           Which decomposition is required ?
*           decomp = 'L' : QL decomposition.
*                  = 'R' : QR decomposition.
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           0 <= n <= m.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the m-by-n matrix A.
*           If decomp = 'R' then, on exit, the elements on and above the
*           diagonal contain the n-by-n upper triangular matrix R; the
*           elements below the diagonal, together with the array tau,
*           represent the orthogonal matrix Q as a product of
*           Householder transformations.
*           If decomp = 'L' then, on exit, the n-by-n matrix L is stored
*           in the lower triangle at the "bottom" of A, and the
*           Householder vectors are stored in the remaining trapezoid.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= min( m, 1 ).
*
*   tau     (out) real array, dimension ( n )
*           The scaling factors of the Householder transformations.
*
*   drptol  (in) real
*           Threshold for dropping Householder transforms.
*           If the norm of the vector to be zeroed is already less than
*           drptol then the transform is skipped.
*           drptol >= 0.0.
*
*   work    (workspace) real array, dimension ( n )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ONE
        PARAMETER             ( ONE = 1.0E0 )
*
        INTEGER               I, J
        REAL                  TMP
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              SLARFX, SLBRFG
*
*   slarfx  apply Householder transform (LAPACK)
*   slbrfg  generate Householder vector (SBR)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        IF ( N .GT. 0 ) THEN
*
          IF ( LSAME( DECOMP, 'L' ) ) THEN
*
*              --- QL factorization ---
*
            DO 100 J = N, 1, -1
*
*                --- generate Householder vector to zero out
*                    A( 1:m-n+j, j)                          ---
*
              I = M - N + J
              CALL SLBRFG( I, A( I, J ), A( 1, J ), 1, TAU( J ),
     >                     DRPTOL )
*
*                --- apply transformation from the left ---
*
              TMP = A( I, J )
              A( I, J ) = ONE
              CALL SLARFX( 'Left', I, J-1, A( 1, J ), TAU( J ),
     >                     A, LDA, WORK )
              A( I, J ) = TMP
*
  100       CONTINUE
*
          ELSE
*
*              --- QR factorization ---
*
            DO 200 J = 1, N
*
*                --- generate Householder vector to zero out
*                    A( j+1:m, j )                           ---
*
              CALL SLBRFG( M-J+1, A( J, J ),
     >                     A( MIN( J+1, M ), J ), 1, TAU( J ),
     >                     DRPTOL )
*
*                --- apply transformation from the left ---
*
              TMP = A( J, J )
              A( J, J ) = ONE
              CALL SLARFX( 'Left', M-J+1, N-J, A( J, J ), TAU( J ),
     >                     A( J, J+1 ), LDA, WORK )
              A( J, J ) = TMP
*
  200       CONTINUE
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SGBWYG( M, N, D, A, LDA, TAU,
     >                     W, LDW, Y, LDY, K )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a set of Householder vectors as returned by sgbqr2, this
*   routine returns W and Y such that
*
*                       T
*      Q  =  I  +  W * Y
*
*   where Q is the product of the Householder matrices.
*
*   Each Householder transformation is represented by a vector vj and
*   a scalar tau( j ) such that
*                                         T  T          T
*      H( j )  =  I  -  tau( j ) * ( 1, vj  )  * ( 1, vj  )  .
*
*   The matrix Q is accumulated as
*                                                  T
*      Q( j + 1 )  =  I  +  W( j + 1 ) * Y( j + 1 )   =  Q( j ) * H( j )
*
*   where
*                                            T          T
*      Y( j + 1 )  =  [ Y( j ), y ]   with  y  = [ 0, vj  ]   and
*
*      W( j + 1 )  =  [ W( j ), w ]   with  w = - tau( j ) * Q( j ) * y.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        INTEGER               M, N, D, LDA, LDW, LDY, K
        REAL                  A( LDA, * ), TAU( * ),
     >                        W( LDW, * ), Y( LDY, * )
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           n >= 0.
*
*   d       (in) integer
*           The number of subdiagonals of the matrix A (as the vectors
*           vj are stored in these subdiagonals, d is the length of
*           these transforms, minus 1).
*           0 <= d <= m - 1, if m > 0.
*           d = 0          , if m = 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the d subdiagonals of the m-by-n matrix A contain
*           the Householder vectors vj.
*           On exit, A is zero below the main diagonal.
*
*   lda     (in) integer
*           The leading dimension of the array A.
*           lda >= max( m, 1 ).
*
*   tau     (in/out) real array, dimension ( n )
*           On entry, tau contains the scaling factors for the
*           Householder transforms.
*           On exit, tau is destroyed.
*
*   w       (out) real array, dimension ( ldw, n )
*           On exit, the first k columns of w contain the block
*           reflector W (zero below the d-th subdiagonal).
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ).
*
*   y       (out) real array, dimension ( ldy, n )
*           On exit, the first k columns of y contain the block
*           reflector Y (zero above the main diagonal and below the d-th
*           subdiagonal).
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ).
*
*   k       (out) integer
*           On exit, k is the "active blocksize"
*           = the number of valid columns in W and Y
*           = the number of nontrivial Householder transforms contained
*             in W and Y
*           = the number of nonzero tau entries in the input.
*           0 <= k <= n.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        INTEGER               I, J, LEN
*
*   len     length of the vector v( j )
*
* Routines called:
*
        EXTERNAL              SGEMV, SSWAP
*
*   sgemv   matrix-vector product (BLAS)
*   sswap   swap two vectors (BLAS)
*
        INTRINSIC             MIN
*
* ----------------------------------------------------------------------
*
        K = 0
*
        DO 200 J = 1, MIN( M-1, N )
*
          IF ( TAU( J ) .NE. ZERO ) THEN
*
*              --- W and Y grow ---
*
            K = K + 1
            LEN = MIN( M-J, D )
*
*              --- copy vj to Y( :, k ) and zero A( j+1:j+d, j ) ---
*
            DO 110 I = 1, M
              Y( I, K ) = ZERO
  110       CONTINUE
            Y( J, K ) = ONE
            CALL SSWAP( LEN, A( J+1, J ), 1, Y( J+1, K ), 1 )
*
*                --- W( :, k ) = - tau( j ) * Y( :, k ) ---
*
            DO 120 I = 1, J-1
              W( I, K ) = ZERO
  120       CONTINUE
            DO 130 I = J, J+LEN
              W( I, K ) = -TAU( J ) * Y( I, K )
  130       CONTINUE
            DO 140 I = J+LEN+1, M
              W( I, K ) = ZERO
  140       CONTINUE
*
*              --- W( :, k ) = - tau( j ) * Q( j-1 ) * y( j )
*                                                    T
*                         = ( I + W( j-1 ) * Y( k-1 )  ) * W( :, k ) ---
*
            CALL SGEMV( 'Transpose', LEN+J, K-1,
     >                  ONE, Y, LDY, W( 1, K ), 1, ZERO, TAU, 1 )
            CALL SGEMV( 'NoTranspose', LEN+J, K-1,
     >                  ONE, W, LDW, TAU, 1, ONE, W( 1, K ), 1 )
*
          ENDIF
*
  200   CONTINUE
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SGEWYG( UPLO, M, N, A, LDA, TAU,
     >                     W, LDW, Y, LDY, K,
     >                     WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Given a set of Householder vectors as returned by sgeqrl, this
*   routine returns W and Y such that
*
*                       T
*      Q  =  I  +  W * Y
*
*   where Q is the product of the Householder matrices.
*
*   Each Householder transformation is represented by a vector vj and
*   a scalar tau( j ) such that
*                                         T  T          T
*      H( j )  =  I  -  tau( j ) * ( 1, vj  )  * ( 1, vj  )  .
*
*   The matrix Q is accumulated as
*                                                  T
*      Q( j + 1 )  =  I  +  W( j + 1 ) * Y( j + 1 )   =  Q( j ) * H( j )
*
*   where
*                                            T          T
*      Y( j + 1 )  =  [ Y( j ), y ]   with  y  = [ 0, vj  ]   and
*
*      W( j + 1 )  =  [ W( j ), w ]   with  w = - tau( j ) * Q( j ) * y.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               M, N, LDA, LDW, LDY, K
        REAL                  A( LDA, * ), TAU( * ),
     >                        W( LDW, * ), Y( LDY, * ), WORK( * )
*
*   uplo    (in) character*1
*           Are the Housholder vectors stored in the upper or lower
*           triangle of A ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   m       (in) integer
*           The row dimension of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The column dimension of A.
*           0 <= n <= m.
*
*   a       (in) real array, dimension ( lda, n )
*           The matrix containing the Householder vectors.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( m, 1 ).
*
*   tau     (in) real array, dimension ( n )
*           The scaling factors for the Householder transformations.
*
*   w       (out) real array, dimension ( ldw, n )
*           On exit, the first k columns of w contain the block
*           reflector W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ).
*
*   y       (out) real array, dimension ( ldy, n )
*           On exit, the first k columns of y contain the block
*           reflector Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ).
*
*   k       (out) integer
*           On exit, k is the "active blocksize"
*           = the number of valid columns in W and Y
*           = the number of nontrivial Householder transforms contained
*             in W and Y
*           = the number of nonzero tau entries in the input.
*           0 <= k <= n.
*
*   work    (workspace) real array, dimension ( n-1 )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
        INTEGER               J, I
        REAL                  TMP
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              SCOPY, SGEMV
*
*   scopy   BLAS
*   sgemv   BLAS
*
* ----------------------------------------------------------------------
*
        K = 0
*
        IF ( ( M .GT. 0 ) .AND. ( N .GT. 0 ) ) THEN
*
          IF ( LSAME( UPLO, 'Lower' ) ) THEN
*
*              --- vectors come from a QR decomposition ---
*
            DO 200 J = 1, N
*
              TMP = - TAU( J )
*
              IF ( TMP .NE. ZERO ) THEN
                K = K + 1
*
*                  --- Y( :, k ) := vj ---
*
                DO 110 I = 1, J-1
                  Y( I, K ) = ZERO
  110           CONTINUE
                Y( J, K ) = ONE
                CALL SCOPY( M-J, A( J+1, J ), 1, Y( J+1, K ), 1 )
*
*                  --- W( :, k ) := - tau( j ) * vj ---
*
                DO 120 I = 1, J-1
                  W( I, K ) = ZERO
  120           CONTINUE
                DO 130 I = J, M
                  W( I, K ) = TMP * Y( I, K )
  130           CONTINUE
*
*                     --- apply previous transformations ---
*
                IF ( K .GT. 1 ) THEN
                  CALL SGEMV( 'Transpose', M, K-1,
     >                        ONE, Y, LDY, W( 1, K ), 1, ZERO, WORK, 1 )
                  CALL SGEMV( 'NoTranspose', M, K-1,
     >                        ONE, W, LDW, WORK, 1, ONE, W( 1, K ), 1 )
                ENDIF
              ENDIF
*
  200       CONTINUE
*
          ELSE
*
*                --- vectors come from a QL decomposition ---
*
            DO 400 J = N, 1, -1
*
              TMP = - TAU( J )
*
              IF ( TMP .NE. ZERO ) THEN
                K = K + 1
*
*                    --- Y( :, k ) := vj ---
*
                DO 310 I = M-N+J+1, M
                  Y( I, K ) = ZERO
  310           CONTINUE
                Y( M-N+J, K ) = ONE
                CALL SCOPY( M-N+J-1, A( 1, J ), 1, Y( 1, K ), 1 )
*
*                    --- W( :, k ) := - tau( j ) * vj ---
*
                DO 320 I = M-N+J+1, M
                  W( I, K ) = ZERO
  320           CONTINUE
                DO 330 I = 1, M-N+J
                  W( I, K ) = TMP * Y( I, K )
  330           CONTINUE
*
*                     --- apply previous transformations ---
*
                IF ( K .GT. 1 ) THEN
                  CALL SGEMV( 'Transpose', M, K-1,
     >                        ONE, Y, LDY, W( 1, K ), 1, ZERO, WORK, 1 )
                  CALL SGEMV( 'NoTranspose', M, K-1,
     >                        ONE, W, LDW, WORK, 1, ONE, W( 1, K ), 1 )
                ENDIF
              ENDIF
*
  400       CONTINUE
*
          ENDIF
*
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SGEWY( SIDE, M, N, K, A, LDA,
     >                    W, LDW, Y, LDY,
     >                    WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Apply a WY block transform to the matrix A (from the left or from
*   the right), i.e., update A as
*
*                        T  T
*      A  :=  ( I + W * Y  )  * A   , or
*
*                            T
*      A  :=  A * ( I + W * Y  )    , resp.
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           SIDE
        INTEGER               M, N, K, LDA, LDW, LDY
        REAL                  A( LDA, * ), W( LDW, * ), Y( LDY, * ),
     >                        WORK( * )
*
*   side    (in) character*1
*           Apply the transforms from the left or from the right ?
*           side = 'L' : From the left.
*                = 'R' : From the right.
*
*   m       (in) integer
*           The number of rows of the matrix A.
*           m >= 0.
*
*   n       (in) integer
*           The number of columns of the matrix A.
*           n >= 0.
*
*   k       (in) integer
*           The number of columns of the matrices W and Y.
*           k >= 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the matrix A.
*                               T  T
*           On exit, ( I + W * Y  )  * A, if side = 'L', or
*                                   T
*                    A * ( I + W * Y  ),  if side = 'R'.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( m, 1 ).
*
*   w       (in) real array, dimension ( ldw, k )
*           The matrix W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( m, 1 ), if side = 'L'.
*               >= max( n, 1 ), if side = 'R'.
*           (W has row dimension m or n, resp.)
*
*   y       (in) real array, dimension ( ldy, k )
*           The matrix Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( m, 1 ), if side = 'L'.
*               >= max( n, 1 ), if side = 'R'.
*           (Y has row dimension m or n, resp.)
*
*   work    (workspace) real array,
*           dimension ( n*k ), if side = 'L'.
*                     ( m*k ), if side = 'R'.
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
* Routines called:
*
        LOGICAL               LSAME
        EXTERNAL              LSAME
*
*   lsame   case-insensitive character matching (BLAS)
*
        EXTERNAL              SGEMM
*
*   sgemm   matrix-matrix product (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( K .GT. 0 ) .AND. ( M .GT. 0 ) .AND. ( N .GT. 0 ) ) THEN
*
          IF ( LSAME( SIDE, 'L' ) ) THEN
*
*                            T
*                --- work = W  * A ---
*
            CALL SGEMM( 'Transpose', 'NoTranspose', K, N, M,
     >                  ONE, W, LDW, A, LDA, ZERO, WORK, K )
*
*                --- A = Y * work + A ---
*
            CALL SGEMM( 'NoTranspose', 'NoTranspose', M, N, K,
     >                  ONE, Y, LDY, WORK, K, ONE, A, LDA )
*
          ELSE
*
*                --- work = A * W ---
*
            CALL SGEMM( 'NoTranspose', 'NoTranspose', M, K, N,
     >                  ONE, A, LDA, W, LDW, ZERO, WORK, M )
*
*                                    T
*                --- A = A + work * Y  ---
*
            CALL SGEMM( 'NoTranspose', 'Transpose', M, N, K,
     >                  ONE, WORK, M, Y, LDY, ONE, A, LDA )
*
          ENDIF
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SQRUPD( M, N, B, A, LDA, DRPTOL,
     >                     NEEDA1, M1, A1, LDA1, N2, A2,
     >                     NB, Y, W, LDWY, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   sqrupd forms the QR factorization
*
*      A  =  Q * R
*
*   of the m-by-n block A and overwrites A by R.
*   In addition, the matrices W and Y in the block representation
*
*                     T
*      Q  =  I + W * Y
*
*   are built from the Householder transforms that were used in the
*   QR decomposition, a matrix A1 may be updated via
*
*      A1 := A1 * Q  ,
*
*   and another matrix A2 is updated via
*
*             T
*      A2 := Q  * A2  .
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
* Parameters:
*
        INTEGER               M, N, B, LDA, M1, LDA1, N2, NB, LDWY
        REAL                  DRPTOL
        LOGICAL               NEEDA1
        REAL                  A( LDA, * ), A1( LDA1, * ), A2( LDA, * ),
     >                        Y( * ), W( * ), WORK( * )
*
*   m       (in) integer
*           The number of rows in the block A, for which a QR
*           decomposition is sought.
*           m > 0.
*
*   n       (in) integer
*           The number of columns in that block.
*           n > 0.
*
*   b       (in) integer
*           The number of nonzero subdiagonals in the block (the
*           subdiagonals below the b-th are supposed to be zero and are
*           not accessed.)
*           b > 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, A is a m-by-n matrix with lower bandwidth <= b.
*           Because of the banded storage scheme used in the calling
*           routine, the zero elements below the b-th subdiagonal may
*           not be explicitly stored. Therefore, they are not accessed
*           in this routine.
*           On exit, the subdiagonals 1, ..., b of A are zeroed out, and
*           the upper triangle of A is overwritten with the matrix R of
*           the factorization A = Q * R.
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= m.
*
*   drptol  (in) real
*           Threshold for dropping the Householder transformations: if
*           the norm of the vector to be eliminated is already smaller
*           than drptol then the transformation is skipped.
*           drptol >= 0.0.
*
*   needa1  (in) logical
*           Is A1 required or not ?
*           needa1 = .true.  : Update A1.
*                  = .false. : Do not update A1.
*
*   m1      (in) integer
*           The number of rows of the matrix A1 (the number of columns
*           must be m). Accessed only if A1 is required.
*           m1 >= 0.
*
*   a1      (in/out) real array, dimension ( lda1, m )
*           On entry, the m1-by-m matrix A1.
*           On exit, A1 may be overwritten with A1 * Q.
*
*   lda1    (in) integer
*           The leading dimension of the array a1. Accessed only if A1
*           is required.
*           lda1 >= max( m1, 1 ).
*
*   n2      (in) integer
*           The number of columns in the block A2.
*           0 <= n2 <= lda.
*
*   a2      (in/out) real array, dimension ( lda, n2 )
*           On entry, the m-by-n2 matrix A2.
*                                            T
*           On exit, A2 is overwritten with Q  * A2.
*
*   nb      (out) integer
*           The number of non-zero Householder vectors contributing to
*           Q.
*           0 <= nb <= min( m-1, n ).
*
*   y       (out) real array, dimension ( ldwy, n )           T
*           The m-by-nb matrix Y in the representation Q = I + W * Y .
*
*   w       (out) real array, dimension ( ldwy, n )           T
*           The m-by-nb matrix W in the representation Q = I + W * Y .
*
*   ldwy    (out) integer
*           The leading dimension of the arrays w and y.
*           ldwy = m.
*
*   work    (workspace) real array,
*           dimension ( max( m1, m )*n + n ),   if A1 is required.
*                     ( m*n + n )           ,   otherwise.
*
* ----------------------------------------------------------------------
*
* Local variables :
*
        INTEGER               ITAU, IWORK
*
*  itau     points to the portion of work that will hold the scaling
*           values tau for the blocked transforms (required size for
*           this buffer : n elements)
*  iwork    points to the portion of work that will be used as workspace
*           for the routines sgbqr2 (n elements) and sgewy
*           ( max( m1, m ) * nb elements).
*
* Routines called:
*
        EXTERNAL              SGBQR2, SGBWYG, SGEWY
*
*   sgbqr2  QR factorization of a banded matrix (SBR)
*   sgbwyg  generate WY factors (SBR)
*   sgewy   apply WY transform (SBR)
*
* ----------------------------------------------------------------------
*
*            --- set pointers to subdivide workspace ---
*
        ITAU = 1
        IWORK = ITAU + N
*
*            --- factorize A = Q * R ---
*
        CALL SGBQR2( M, N, B, A, LDA, WORK( ITAU ), DRPTOL,
     >               WORK( IWORK ) )
*
*            --- build W and Y factors ---
*
        LDWY = M
        CALL SGBWYG( M, N, B, A, LDA, WORK( ITAU ),
     >               W, LDWY, Y, LDWY, NB )
*
        IF ( NB .GT. 0 ) THEN
*
*              --- update A1 ---
*
          IF ( NEEDA1 ) THEN
            CALL SGEWY( 'Right', M1, M, NB, A1, LDA1,
     >                  W, LDWY, Y, LDWY, WORK( IWORK ) )
          ENDIF
*
*              --- premultiply A2 ---
*
          IF ( N2 .GT. 0 ) THEN
            CALL SGEWY( 'Left', M, N2, NB, A2, LDA,
     >                  W, LDWY, Y, LDWY, WORK( IWORK ) )
          ENDIF
        ENDIF
*
        RETURN
        END
*
* **********************************************************************
*
        SUBROUTINE SSYWY( UPLO, N, K, A, LDA, W, LDW, Y, LDY, WORK )
*
* ----------------------------------------------------------------------
*
* Description:
*
*   Apply a two-sided WY block transform to the symmetric matrix A,
*                                   T  T                  T
*   i.e., replace A with ( I + W * Y  )  * A * ( I + W * Y  ).
*
* Author: Bruno Lang
*         Aachen University of Technology
*         na.blang@na-net.ornl.gov
* Date: May 17, 2000
* Version: SBR Toolbox, Rev. 1.4.1
*
* Note: >>> This routine performs no sanity checks on its arguments. <<<
*
* Parameters:
*
        CHARACTER*1           UPLO
        INTEGER               N, K, LDA, LDW, LDY
        REAL                  A( LDA, * ), W( LDW, * ), Y( LDY, * ),
     >                        WORK( * )
*
*   uplo    (in) character*1
*           Is the upper or lower triangle of A stored ?
*           uplo = 'U' : Upper triangle.
*                = 'L' : Lower triangle.
*
*   n       (in) integer
*           The size of the block to transform.
*           n >= 0.
*
*   k       (in) integer
*           The number of nontrivial Householder transforms in the
*           block WY transform.
*           k >= 0.
*
*   a       (in/out) real array, dimension ( lda, n )
*           On entry, the n-by-n symmetric matrix A.
*                                                T  T             T
*           On exit, A is overwritten with ( I+WY  )  * A * ( I+WY  ).
*
*   lda     (in) integer
*           The leading dimension of the array a.
*           lda >= max( n, 1 ).
*
*   w       (in) real array, dimension ( ldw, k )
*           Contains the block reflector W.
*
*   ldw     (in) integer
*           The leading dimension of the array w.
*           ldw >= max( n, 1 ).
*
*   y       (in) real array, dimension ( ldy, k )
*           Contains the block reflector Y.
*
*   ldy     (in) integer
*           The leading dimension of the array y.
*           ldy >= max( n, 1 ).
*
*   work    (workspace) real array, dimension ( (n+k)*k )
*
* ----------------------------------------------------------------------
*
* Local variables:
*
        REAL                  ZERO, ONE
        PARAMETER             ( ZERO = 0.0E0, ONE = 1.0E0 )
*
* Routines called:
*
        EXTERNAL              SGEMM, SSYMM, SSYR2K
*
*   sgemm   matrix-matrix product (BLAS)
*   ssymm   symmetric matrix-matrix product (BLAS)
*   ssyr2k  symmetric rank-2 update (BLAS)
*
* ----------------------------------------------------------------------
*
        IF ( ( N .GT. 0 ) .AND. ( K .GT. 0 ) ) THEN
*
*              --- work( 1 .. n*k ) := X1 = A * W ---
*
          CALL SSYMM( 'Left', UPLO, N, K,
     >                ONE, A, LDA, W, LDW, ZERO, WORK, N )
*
*                                                           T
*              --- work( n*k+1 .. n*k+k*k ) := X2 = 1/2 * X1  * W ---
*
          CALL SGEMM( 'Transpose', 'NoTranspose', K, K, N,
     >                0.5E0, WORK, N, W, LDW, ZERO, WORK( N*K+1 ), K )
*
*              --- work( 1 .. n*k ) := X3 = X1 + Y * X2 ---
*
          CALL SGEMM( 'NoTranspose', 'NoTranspose', N, K, K,
     >                ONE, Y, LDY, WORK( N*K+1 ), K, ONE, WORK, N )
*
*                                 T        T
*              --- A := A + X3 * Y + Y * X3  ---
*
          CALL SSYR2K( UPLO, 'NoTranspose', N, K,
     >                 ONE, WORK, N, Y, LDY, ONE, A, LDA )
*
        ENDIF
*
        RETURN
        END
SHAR_EOF
fi # end of overwriting check
cd ..
cd ..
cd ..
#       End of shell archive
exit 0