#include "blaswrap.h"
/* -- translated by f2c (version 19990503).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Table of constant values */
static doublereal c_b18 = 0.;
static integer c__0 = 0;
static doublereal c_b32 = 1.;
static integer c__4 = 4;
static integer c__6 = 6;
static integer c__1 = 1;
static integer c__2 = 2;
static logical c_false = FALSE_;
static integer c__3 = 3;
static integer c__5 = 5;
static logical c_true = TRUE_;
static integer c__22 = 22;
/* Subroutine */ int ddrvvx_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *niunit,
integer *nounit, doublereal *a, integer *lda, doublereal *h__,
doublereal *wr, doublereal *wi, doublereal *wr1, doublereal *wi1,
doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr,
doublereal *lre, integer *ldlre, doublereal *rcondv, doublereal *
rcndv1, doublereal *rcdvin, doublereal *rconde, doublereal *rcnde1,
doublereal *rcdein, doublereal *scale, doublereal *scale1, doublereal
*result, doublereal *work, integer *nwork, integer *iwork, integer *
info)
{
/* Initialized data */
static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };
static char bal[1*4] = "N" "P" "S" "B";
/* Format strings */
static char fmt_9992[] = "(\002 DDRVVX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9999[] = "(/1x,a3,\002 -- Real Eigenvalue-Eigenvector De"
"composition\002,\002 Expert Driver\002,/\002 Matrix types (see D"
"DRVVX for details): \002)";
static char fmt_9998[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat"
"rix. \002,\002 \002,\002 5=Diagonal: geom"
"etr. spaced entries.\002,/\002 2=Identity matrix. "
" \002,\002 6=Diagona\002,\002l: clustered entries.\002,"
"/\002 3=Transposed Jordan block. \002,\002 \002,\002 "
" 7=Diagonal: large, evenly spaced.\002,/\002 \002,\0024=Diagona"
"l: evenly spaced entries. \002,\002 8=Diagonal: s\002,\002ma"
"ll, evenly spaced.\002)";
static char fmt_9997[] = "(\002 Dense, Non-Symmetric Matrices:\002,/\002"
" 9=Well-cond., ev\002,\002enly spaced eigenvals.\002,\002 14=Il"
"l-cond., geomet. spaced e\002,\002igenals.\002,/\002 10=Well-con"
"d., geom. spaced eigenvals. \002,\002 15=Ill-conditioned, cluste"
"red e.vals.\002,/\002 11=Well-cond\002,\002itioned, clustered e."
"vals. \002,\002 16=Ill-cond., random comp\002,\002lex \002,/\002"
" 12=Well-cond., random complex \002,\002 \002,\002 17=Il"
"l-cond., large rand. complx \002,/\002 13=Ill-condi\002,\002tion"
"ed, evenly spaced. \002,\002 18=Ill-cond., small rand.\002"
",\002 complx \002)";
static char fmt_9996[] = "(\002 19=Matrix with random O(1) entries. "
" \002,\002 21=Matrix \002,\002with small random entries.\002,"
"/\002 20=Matrix with large ran\002,\002dom entries. \002,\002 "
"22=Matrix read from input file\002,/)";
static char fmt_9995[] = "(\002 Tests performed with test threshold ="
"\002,f8.2,//\002 1 = | A VR - VR W | / ( n |A| ulp ) \002,/\002 "
"2 = | transpose(A) VL - VL W | / ( n |A| ulp ) \002,/\002 3 = | "
"|VR(i)| - 1 | / ulp \002,/\002 4 = | |VL(i)| - 1 | / ulp \002,"
"/\002 5 = 0 if W same no matter if VR or VL computed,\002,\002 1"
"/ulp otherwise\002,/\002 6 = 0 if VR same no matter what else co"
"mputed,\002,\002 1/ulp otherwise\002,/\002 7 = 0 if VL same no "
"matter what else computed,\002,\002 1/ulp otherwise\002,/\002 8"
" = 0 if RCONDV same no matter what else computed,\002,\002 1/ul"
"p otherwise\002,/\002 9 = 0 if SCALE, ILO, IHI, ABNRM same no ma"
"tter what else\002,\002 computed, 1/ulp otherwise\002,/\002 10 "
"= | RCONDV - RCONDV(precomputed) | / cond(RCONDV),\002,/\002 11 "
"= | RCONDE - RCONDE(precomputed) | / cond(RCONDE),\002)";
static char fmt_9994[] = "(\002 BALANC='\002,a1,\002',N=\002,i4,\002,I"
"WK=\002,i1,\002, seed=\002,4(i4,\002,\002),\002 type \002,i2,"
"\002, test(\002,i2,\002)=\002,g10.3)";
static char fmt_9993[] = "(\002 N=\002,i5,\002, input example =\002,i3"
",\002, test(\002,i2,\002)=\002,g10.3)";
/* System generated locals */
integer a_dim1, a_offset, h_dim1, h_offset, lre_dim1, lre_offset, vl_dim1,
vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
static integer ibal;
static doublereal cond;
static integer jcol;
static char path[3];
static integer nmax;
static doublereal unfl, ovfl;
static integer i__, j, n;
static logical badnn;
extern /* Subroutine */ int dget23_(logical *, char *, integer *,
doublereal *, integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
integer *);
static integer nfail, imode, iinfo;
static doublereal conds, anorm;
static integer jsize, nerrs, itype, jtype, ntest;
static doublereal rtulp;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
static char balanc[1];
extern doublereal dlamch_(char *);
static char adumma[1*1];
extern /* Subroutine */ int dlatme_(integer *, char *, integer *,
doublereal *, integer *, doublereal *, doublereal *, char *, char
*, char *, char *, doublereal *, integer *, doublereal *, integer
*, integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *);
static integer idumma[1];
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
static integer ioldsd[4];
extern /* Subroutine */ int xerbla_(char *, integer *), dlatmr_(
integer *, integer *, char *, integer *, char *, doublereal *,
integer *, doublereal *, doublereal *, char *, char *, doublereal
*, integer *, doublereal *, doublereal *, integer *, doublereal *,
char *, integer *, integer *, integer *, doublereal *,
doublereal *, char *, doublereal *, integer *, integer *, integer
*), dlatms_(
integer *, integer *, char *, integer *, char *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *, char
*, doublereal *, integer *, doublereal *, integer *), dlasum_(char *, integer *, integer *, integer *);
static integer ntestf, nnwork;
static doublereal rtulpi;
static integer mtypes, ntestt;
static doublereal ulpinv;
static integer iwk;
static doublereal ulp;
/* Fortran I/O blocks */
static cilist io___33 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___46 = { 0, 0, 1, 0, 0 };
static cilist io___48 = { 0, 0, 0, 0, 0 };
static cilist io___49 = { 0, 0, 0, 0, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9993, 0 };
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
DDRVVX checks the nonsymmetric eigenvalue problem expert driver
DGEEVX.
DDRVVX uses both test matrices generated randomly depending on
data supplied in the calling sequence, as well as on data
read from an input file and including precomputed condition
numbers to which it compares the ones it computes.
When DDRVVX is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified in the calling sequence.
For each size ("n") and each type of matrix, one matrix will be
generated and used to test the nonsymmetric eigenroutines. For
each matrix, 9 tests will be performed:
(1) | A * VR - VR * W | / ( n |A| ulp )
Here VR is the matrix of unit right eigenvectors.
W is a block diagonal matrix, with a 1x1 block for each
real eigenvalue and a 2x2 block for each complex conjugate
pair. If eigenvalues j and j+1 are a complex conjugate pair,
so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
2 x 2 block corresponding to the pair will be:
( wr wi )
( -wi wr )
Such a block multiplying an n x 2 matrix ( ur ui ) on the
right will be the same as multiplying ur + i*ui by wr + i*wi.
(2) | A**H * VL - VL * W**H | / ( n |A| ulp )
Here VL is the matrix of unit left eigenvectors, A**H is the
conjugate transpose of A, and W is as above.
(3) | |VR(i)| - 1 | / ulp and largest component real
VR(i) denotes the i-th column of VR.
(4) | |VL(i)| - 1 | / ulp and largest component real
VL(i) denotes the i-th column of VL.
(5) W(full) = W(partial)
W(full) denotes the eigenvalues computed when VR, VL, RCONDV
and RCONDE are also computed, and W(partial) denotes the
eigenvalues computed when only some of VR, VL, RCONDV, and
RCONDE are computed.
(6) VR(full) = VR(partial)
VR(full) denotes the right eigenvectors computed when VL, RCONDV
and RCONDE are computed, and VR(partial) denotes the result
when only some of VL and RCONDV are computed.
(7) VL(full) = VL(partial)
VL(full) denotes the left eigenvectors computed when VR, RCONDV
and RCONDE are computed, and VL(partial) denotes the result
when only some of VR and RCONDV are computed.
(8) 0 if SCALE, ILO, IHI, ABNRM (full) =
SCALE, ILO, IHI, ABNRM (partial)
1/ulp otherwise
SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
(full) is when VR, VL, RCONDE and RCONDV are also computed, and
(partial) is when some are not computed.
(9) RCONDV(full) = RCONDV(partial)
RCONDV(full) denotes the reciprocal condition numbers of the
right eigenvectors computed when VR, VL and RCONDE are also
computed. RCONDV(partial) denotes the reciprocal condition
numbers when only some of VR, VL and RCONDE are computed.
The "sizes" are specified by an array NN(1:NSIZES); the value of
each element NN(j) specifies one size.
The "types" are specified by a logical array DOTYPE( 1:NTYPES );
if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
Currently, the list of possible types is:
(1) The zero matrix.
(2) The identity matrix.
(3) A (transposed) Jordan block, with 1's on the diagonal.
(4) A diagonal matrix with evenly spaced entries
1, ..., ULP and random signs.
(ULP = (first number larger than 1) - 1 )
(5) A diagonal matrix with geometrically spaced entries
1, ..., ULP and random signs.
(6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.
(7) Same as (4), but multiplied by a constant near
the overflow threshold
(8) Same as (4), but multiplied by a constant near
the underflow threshold
(9) A matrix of the form U' T U, where U is orthogonal and
T has evenly spaced entries 1, ..., ULP with random signs
on the diagonal and random O(1) entries in the upper
triangle.
(10) A matrix of the form U' T U, where U is orthogonal and
T has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.
(11) A matrix of the form U' T U, where U is orthogonal and
T has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.
(12) A matrix of the form U' T U, where U is orthogonal and
T has real or complex conjugate paired eigenvalues randomly
chosen from ( ULP, 1 ) and random O(1) entries in the upper
triangle.
(13) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.
(14) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has geometrically spaced entries
1, ..., ULP with random signs on the diagonal and random
O(1) entries in the upper triangle.
(15) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.
(16) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has real or complex conjugate paired
eigenvalues randomly chosen from ( ULP, 1 ) and random
O(1) entries in the upper triangle.
(17) Same as (16), but multiplied by a constant
near the overflow threshold
(18) Same as (16), but multiplied by a constant
near the underflow threshold
(19) Nonsymmetric matrix with random entries chosen from (-1,1).
If N is at least 4, all entries in first two rows and last
row, and first column and last two columns are zero.
(20) Same as (19), but multiplied by a constant
near the overflow threshold
(21) Same as (19), but multiplied by a constant
near the underflow threshold
In addition, an input file will be read from logical unit number
NIUNIT. The file contains matrices along with precomputed
eigenvalues and reciprocal condition numbers for the eigenvalues
and right eigenvectors. For these matrices, in addition to tests
(1) to (9) we will compute the following two tests:
(10) |RCONDV - RCDVIN| / cond(RCONDV)
RCONDV is the reciprocal right eigenvector condition number
computed by DGEEVX and RCDVIN (the precomputed true value)
is supplied as input. cond(RCONDV) is the condition number of
RCONDV, and takes errors in computing RCONDV into account, so
that the resulting quantity should be O(ULP). cond(RCONDV) is
essentially given by norm(A)/RCONDE.
(11) |RCONDE - RCDEIN| / cond(RCONDE)
RCONDE is the reciprocal eigenvalue condition number
computed by DGEEVX and RCDEIN (the precomputed true value)
is supplied as input. cond(RCONDE) is the condition number
of RCONDE, and takes errors in computing RCONDE into account,
so that the resulting quantity should be O(ULP). cond(RCONDE)
is essentially given by norm(A)/RCONDV.
Arguments
==========
NSIZES (input) INTEGER
The number of sizes of matrices to use. NSIZES must be at
least zero. If it is zero, no randomly generated matrices
are tested, but any test matrices read from NIUNIT will be
tested.
NN (input) INTEGER array, dimension (NSIZES)
An array containing the sizes to be used for the matrices.
Zero values will be skipped. The values must be at least
zero.
NTYPES (input) INTEGER
The number of elements in DOTYPE. NTYPES must be at least
zero. If it is zero, no randomly generated test matrices
are tested, but and test matrices read from NIUNIT will be
tested. If it is MAXTYP+1 and NSIZES is 1, then an
additional type, MAXTYP+1 is defined, which is to use
whatever matrix is in A. This is only useful if
DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
DOTYPE (input) LOGICAL array, dimension (NTYPES)
If DOTYPE(j) is .TRUE., then for each size in NN a
matrix of that size and of type j will be generated.
If NTYPES is smaller than the maximum number of types
defined (PARAMETER MAXTYP), then types NTYPES+1 through
MAXTYP will not be generated. If NTYPES is larger
than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
will be ignored.
ISEED (input/output) INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to DDRVVX to continue the same random number
sequence.
THRESH (input) DOUBLE PRECISION
A test will count as "failed" if the "error", computed as
described above, exceeds THRESH. Note that the error
is scaled to be O(1), so THRESH should be a reasonably
small multiple of 1, e.g., 10 or 100. In particular,
it should not depend on the precision (single vs. double)
or the size of the matrix. It must be at least zero.
NIUNIT (input) INTEGER
The FORTRAN unit number for reading in the data file of
problems to solve.
NOUNIT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns INFO not equal to 0.)
A (workspace) DOUBLE PRECISION array, dimension
(LDA, max(NN,12))
Used to hold the matrix whose eigenvalues are to be
computed. On exit, A contains the last matrix actually used.
LDA (input) INTEGER
The leading dimension of the arrays A and H.
LDA >= max(NN,12), since 12 is the dimension of the largest
matrix in the precomputed input file.
H (workspace) DOUBLE PRECISION array, dimension
(LDA, max(NN,12))
Another copy of the test matrix A, modified by DGEEVX.
WR (workspace) DOUBLE PRECISION array, dimension (max(NN))
WI (workspace) DOUBLE PRECISION array, dimension (max(NN))
The real and imaginary parts of the eigenvalues of A.
On exit, WR + WI*i are the eigenvalues of the matrix in A.
WR1 (workspace) DOUBLE PRECISION array, dimension (max(NN,12))
WI1 (workspace) DOUBLE PRECISION array, dimension (max(NN,12))
Like WR, WI, these arrays contain the eigenvalues of A,
but those computed when DGEEVX only computes a partial
eigendecomposition, i.e. not the eigenvalues and left
and right eigenvectors.
VL (workspace) DOUBLE PRECISION array, dimension
(LDVL, max(NN,12))
VL holds the computed left eigenvectors.
LDVL (input) INTEGER
Leading dimension of VL. Must be at least max(1,max(NN,12)).
VR (workspace) DOUBLE PRECISION array, dimension
(LDVR, max(NN,12))
VR holds the computed right eigenvectors.
LDVR (input) INTEGER
Leading dimension of VR. Must be at least max(1,max(NN,12)).
LRE (workspace) DOUBLE PRECISION array, dimension
(LDLRE, max(NN,12))
LRE holds the computed right or left eigenvectors.
LDLRE (input) INTEGER
Leading dimension of LRE. Must be at least max(1,max(NN,12))
RCONDV (workspace) DOUBLE PRECISION array, dimension (N)
RCONDV holds the computed reciprocal condition numbers
for eigenvectors.
RCNDV1 (workspace) DOUBLE PRECISION array, dimension (N)
RCNDV1 holds more computed reciprocal condition numbers
for eigenvectors.
RCDVIN (workspace) DOUBLE PRECISION array, dimension (N)
When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
condition numbers for eigenvectors to be compared with
RCONDV.
RCONDE (workspace) DOUBLE PRECISION array, dimension (N)
RCONDE holds the computed reciprocal condition numbers
for eigenvalues.
RCNDE1 (workspace) DOUBLE PRECISION array, dimension (N)
RCNDE1 holds more computed reciprocal condition numbers
for eigenvalues.
RCDEIN (workspace) DOUBLE PRECISION array, dimension (N)
When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
condition numbers for eigenvalues to be compared with
RCONDE.
RESULT (output) DOUBLE PRECISION array, dimension (11)
The values computed by the seven tests described above.
The values are currently limited to 1/ulp, to avoid overflow.
WORK (workspace) DOUBLE PRECISION array, dimension (NWORK)
NWORK (input) INTEGER
The number of entries in WORK. This must be at least
max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
max( 360 ,6*NN(j)+2*NN(j)**2) for all j.
IWORK (workspace) INTEGER array, dimension (2*max(NN,12))
INFO (output) INTEGER
If 0, then successful exit.
If <0, then input paramter -INFO is incorrect.
If >0, DLATMR, SLATMS, SLATME or DGET23 returned an error
code, and INFO is its absolute value.
-----------------------------------------------------------------------
Some Local Variables and Parameters:
---- ----- --------- --- ----------
ZERO, ONE Real 0 and 1.
MAXTYP The number of types defined.
NMAX Largest value in NN or 12.
NERRS The number of tests which have exceeded THRESH
COND, CONDS,
IMODE Values to be passed to the matrix generators.
ANORM Norm of A; passed to matrix generators.
OVFL, UNFL Overflow and underflow thresholds.
ULP, ULPINV Finest relative precision and its inverse.
RTULP, RTULPI Square roots of the previous 4 values.
The following four arrays decode JTYPE:
KTYPE(j) The general type (1-10) for type "j".
KMODE(j) The MODE value to be passed to the matrix
generator for type "j".
KMAGN(j) The order of magnitude ( O(1),
O(overflow^(1/2) ), O(underflow^(1/2) )
KCONDS(j) Selectw whether CONDS is to be 1 or
1/sqrt(ulp). (0 means irrelevant.)
=====================================================================
Parameter adjustments */
--nn;
--dotype;
--iseed;
h_dim1 = *lda;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--wr;
--wi;
--wr1;
--wi1;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
lre_dim1 = *ldlre;
lre_offset = 1 + lre_dim1 * 1;
lre -= lre_offset;
--rcondv;
--rcndv1;
--rcdvin;
--rconde;
--rcnde1;
--rcdein;
--scale;
--scale1;
--result;
--work;
--iwork;
/* Function Body */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "VX", (ftnlen)2, (ftnlen)2);
/* Check for errors */
ntestt = 0;
ntestf = 0;
*info = 0;
/* Important constants */
badnn = FALSE_;
/* 12 is the largest dimension in the input file of precomputed
problems */
nmax = 12;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda < 1 || *lda < nmax) {
*info = -10;
} else if (*ldvl < 1 || *ldvl < nmax) {
*info = -17;
} else if (*ldvr < 1 || *ldvr < nmax) {
*info = -19;
} else if (*ldlre < 1 || *ldlre < nmax) {
*info = -21;
} else /* if(complicated condition) */ {
/* Computing 2nd power */
i__1 = nmax;
if (nmax * 6 + (i__1 * i__1 << 1) > *nwork) {
*info = -32;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DDRVVX", &i__1);
return 0;
}
/* If nothing to do check on NIUNIT */
if (*nsizes == 0 || *ntypes == 0) {
goto L160;
}
/* More Important constants */
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Precision");
ulpinv = 1. / ulp;
rtulp = sqrt(ulp);
rtulpi = 1. / rtulp;
/* Loop over sizes, types */
nerrs = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
if (*nsizes != 1) {
mtypes = min(21,*ntypes);
} else {
mtypes = min(22,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L140;
}
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Compute "A"
Control parameters:
KMAGN KCONDS KMODE KTYPE
=1 O(1) 1 clustered 1 zero
=2 large large clustered 2 identity
=3 small exponential Jordan
=4 arithmetic diagonal, (w/ eigenvalues)
=5 random log symmetric, w/ eigenvalues
=6 random general, w/ eigenvalues
=7 random diagonal
=8 random symmetric
=9 random general
=10 random triangular */
if (mtypes > 21) {
goto L90;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L30;
case 2: goto L40;
case 3: goto L50;
}
L30:
anorm = 1.;
goto L60;
L40:
anorm = ovfl * ulp;
goto L60;
L50:
anorm = unfl * ulpinv;
goto L60;
L60:
dlaset_("Full", lda, &n, &c_b18, &c_b18, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
/* Special Matrices -- Identity & Jordan block
Zero */
if (itype == 1) {
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
a_ref(jcol, jcol) = anorm;
/* L70: */
}
} else if (itype == 3) {
/* Jordan Block */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
a_ref(jcol, jcol) = anorm;
if (jcol > 1) {
a_ref(jcol, jcol - 1) = 1.;
}
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
dlatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond,
&anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[n
+ 1], &iinfo);
} else if (itype == 5) {
/* Symmetric, eigenvalues specified */
dlatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond,
&anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1],
&iinfo);
} else if (itype == 6) {
/* General, eigenvalues specified */
if (kconds[jtype - 1] == 1) {
conds = 1.;
} else if (kconds[jtype - 1] == 2) {
conds = rtulpi;
} else {
conds = 0.;
}
*(unsigned char *)&adumma[0] = ' ';
dlatme_(&n, "S", &iseed[1], &work[1], &imode, &cond, &c_b32,
adumma, "T", "T", "T", &work[n + 1], &c__4, &conds, &
n, &n, &anorm, &a[a_offset], lda, &work[(n << 1) + 1],
&iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &c__0, &
c__0, &c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 8) {
/* Symmetric, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
if (n >= 4) {
dlaset_("Full", &c__2, &n, &c_b18, &c_b18, &a[a_offset],
lda);
i__3 = n - 3;
dlaset_("Full", &i__3, &c__1, &c_b18, &c_b18, &a_ref(3, 1)
, lda);
i__3 = n - 3;
dlaset_("Full", &i__3, &c__2, &c_b18, &c_b18, &a_ref(3, n
- 1), lda);
dlaset_("Full", &c__1, &n, &c_b18, &c_b18, &a_ref(n, 1),
lda);
}
} else if (itype == 10) {
/* Triangular, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &c__0, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___33.ciunit = *nounit;
s_wsfe(&io___33);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L90:
/* Test for minimal and generous workspace */
for (iwk = 1; iwk <= 3; ++iwk) {
if (iwk == 1) {
nnwork = n * 3;
} else if (iwk == 2) {
/* Computing 2nd power */
i__3 = n;
nnwork = n * 6 + i__3 * i__3;
} else {
/* Computing 2nd power */
i__3 = n;
nnwork = n * 6 + (i__3 * i__3 << 1);
}
nnwork = max(nnwork,1);
/* Test for all balancing options */
for (ibal = 1; ibal <= 4; ++ibal) {
*(unsigned char *)balanc = *(unsigned char *)&bal[ibal -
1];
/* Perform tests */
dget23_(&c_false, balanc, &jtype, thresh, ioldsd, nounit,
&n, &a[a_offset], lda, &h__[h_offset], &wr[1], &
wi[1], &wr1[1], &wi1[1], &vl[vl_offset], ldvl, &
vr[vr_offset], ldvr, &lre[lre_offset], ldlre, &
rcondv[1], &rcndv1[1], &rcdvin[1], &rconde[1], &
rcnde1[1], &rcdein[1], &scale[1], &scale1[1], &
result[1], &work[1], &nnwork, &iwork[1], info);
/* Check for RESULT(j) > THRESH */
ntest = 0;
nfail = 0;
for (j = 1; j <= 9; ++j) {
if (result[j] >= 0.) {
++ntest;
}
if (result[j] >= *thresh) {
++nfail;
}
/* L100: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
io___41.ciunit = *nounit;
s_wsfe(&io___41);
e_wsfe();
io___42.ciunit = *nounit;
s_wsfe(&io___42);
e_wsfe();
io___43.ciunit = *nounit;
s_wsfe(&io___43);
e_wsfe();
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(
doublereal));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 9; ++j) {
if (result[j] >= *thresh) {
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, balanc, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&iwk, (ftnlen)sizeof(
integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
/* L110: */
}
nerrs += nfail;
ntestt += ntest;
/* L120: */
}
/* L130: */
}
L140:
;
}
/* L150: */
}
L160:
/* Read in data from file to check accuracy of condition estimation.
Assume input eigenvalues are sorted lexicographically (increasing
by real part, then decreasing by imaginary part) */
jtype = 0;
L170:
io___46.ciunit = *niunit;
i__1 = s_rsle(&io___46);
if (i__1 != 0) {
goto L220;
}
i__1 = do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L220;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L220;
}
/* Read input data until N=0 */
if (n == 0) {
goto L220;
}
++jtype;
iseed[1] = jtype;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___48.ciunit = *niunit;
s_rsle(&io___48);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__5, &c__1, (char *)&a_ref(i__, j), (ftnlen)sizeof(
doublereal));
}
e_rsle();
/* L180: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___49.ciunit = *niunit;
s_rsle(&io___49);
do_lio(&c__5, &c__1, (char *)&wr1[i__], (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&wi1[i__], (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&rcdein[i__], (ftnlen)sizeof(doublereal))
;
do_lio(&c__5, &c__1, (char *)&rcdvin[i__], (ftnlen)sizeof(doublereal))
;
e_rsle();
/* L190: */
}
/* Computing 2nd power */
i__2 = n;
i__1 = n * 6 + (i__2 * i__2 << 1);
dget23_(&c_true, "N", &c__22, thresh, &iseed[1], nounit, &n, &a[a_offset],
lda, &h__[h_offset], &wr[1], &wi[1], &wr1[1], &wi1[1], &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, &lre[lre_offset], ldlre, &
rcondv[1], &rcndv1[1], &rcdvin[1], &rconde[1], &rcnde1[1], &
rcdein[1], &scale[1], &scale1[1], &result[1], &work[1], &i__1, &
iwork[1], info);
/* Check for RESULT(j) > THRESH */
ntest = 0;
nfail = 0;
for (j = 1; j <= 11; ++j) {
if (result[j] >= 0.) {
++ntest;
}
if (result[j] >= *thresh) {
++nfail;
}
/* L200: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
io___51.ciunit = *nounit;
s_wsfe(&io___51);
e_wsfe();
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
io___53.ciunit = *nounit;
s_wsfe(&io___53);
e_wsfe();
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 11; ++j) {
if (result[j] >= *thresh) {
io___55.ciunit = *nounit;
s_wsfe(&io___55);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(doublereal));
e_wsfe();
}
/* L210: */
}
nerrs += nfail;
ntestt += ntest;
goto L170;
L220:
/* Summary */
dlasum_(path, nounit, &nerrs, &ntestt);
return 0;
/* End of DDRVVX */
} /* ddrvvx_ */
#undef a_ref