 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sdrvvx ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, integer NIUNIT, integer NOUNIT, real, dimension( lda, * ) A, integer LDA, real, dimension( lda, * ) H, real, dimension( * ) WR, real, dimension( * ) WI, real, dimension( * ) WR1, real, dimension( * ) WI1, real, dimension( ldvl, * ) VL, integer LDVL, real, dimension( ldvr, * ) VR, integer LDVR, real, dimension( ldlre, * ) LRE, integer LDLRE, real, dimension( * ) RCONDV, real, dimension( * ) RCNDV1, real, dimension( * ) RCDVIN, real, dimension( * ) RCONDE, real, dimension( * ) RCNDE1, real, dimension( * ) RCDEIN, real, dimension( * ) SCALE, real, dimension( * ) SCALE1, real, dimension( 11 ) RESULT, real, dimension( * ) WORK, integer NWORK, integer, dimension( * ) IWORK, integer INFO )

SDRVVX

Purpose:
```    SDRVVX  checks the nonsymmetric eigenvalue problem expert driver
SGEEVX.

SDRVVX 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 SDRVVX 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 SGEEVX 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 SGEEVX 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.```
Parameters
 [in] NSIZES ``` NSIZES is 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.``` [in] NN ``` NN is 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.``` [in] NTYPES ``` NTYPES is 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. .``` [in] DOTYPE ``` DOTYPE is 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.``` [in,out] ISEED ``` ISEED is 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 SDRVVX to continue the same random number sequence.``` [in] THRESH ``` THRESH is REAL 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.``` [in] NIUNIT ``` NIUNIT is INTEGER The FORTRAN unit number for reading in the data file of problems to solve.``` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)``` [out] A ``` A is REAL 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.``` [in] LDA ``` LDA is 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.``` [out] H ``` H is REAL array, dimension (LDA, max(NN,12)) Another copy of the test matrix A, modified by SGEEVX.``` [out] WR ` WR is REAL array, dimension (max(NN))` [out] WI ``` WI is REAL 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.``` [out] WR1 ` WR1 is REAL array, dimension (max(NN,12))` [out] WI1 ``` WI1 is REAL array, dimension (max(NN,12)) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.``` [out] VL ``` VL is REAL array, dimension (LDVL, max(NN,12)) VL holds the computed left eigenvectors.``` [in] LDVL ``` LDVL is INTEGER Leading dimension of VL. Must be at least max(1,max(NN,12)).``` [out] VR ``` VR is REAL array, dimension (LDVR, max(NN,12)) VR holds the computed right eigenvectors.``` [in] LDVR ``` LDVR is INTEGER Leading dimension of VR. Must be at least max(1,max(NN,12)).``` [out] LRE ``` LRE is REAL array, dimension (LDLRE, max(NN,12)) LRE holds the computed right or left eigenvectors.``` [in] LDLRE ``` LDLRE is INTEGER Leading dimension of LRE. Must be at least max(1,max(NN,12))``` [out] RCONDV ``` RCONDV is REAL array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors.``` [out] RCNDV1 ``` RCNDV1 is REAL array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.``` [out] RCDVIN ``` RCDVIN is REAL array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.``` [out] RCONDE ``` RCONDE is REAL array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues.``` [out] RCNDE1 ``` RCNDE1 is REAL array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.``` [out] RCDEIN ``` RCDEIN is REAL array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.``` [out] SCALE ``` SCALE is REAL array, dimension (N) Holds information describing balancing of matrix.``` [out] SCALE1 ``` SCALE1 is REAL array, dimension (N) Holds information describing balancing of matrix.``` [out] RESULT ``` RESULT is REAL array, dimension (11) The values computed by the seven tests described above. The values are currently limited to 1/ulp, to avoid overflow.``` [out] WORK ` WORK is REAL array, dimension (NWORK)` [in] NWORK ``` NWORK is 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.``` [out] IWORK ` IWORK is INTEGER array, dimension (2*max(NN,12))` [out] INFO ``` INFO is INTEGER If 0, then successful exit. If <0, then input parameter -INFO is incorrect. If >0, SLATMR, SLATMS, SLATME or SGET23 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.)```
Date
June 2016

Definition at line 522 of file sdrvvx.f.

522 *
523 * -- LAPACK test routine (version 3.6.1) --
524 * -- LAPACK is a software package provided by Univ. of Tennessee, --
525 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
526 * June 2016
527 *
528 * .. Scalar Arguments ..
529  INTEGER info, lda, ldlre, ldvl, ldvr, niunit, nounit,
530  \$ nsizes, ntypes, nwork
531  REAL thresh
532 * ..
533 * .. Array Arguments ..
534  LOGICAL dotype( * )
535  INTEGER iseed( 4 ), iwork( * ), nn( * )
536  REAL a( lda, * ), h( lda, * ), lre( ldlre, * ),
537  \$ rcdein( * ), rcdvin( * ), rcnde1( * ),
538  \$ rcndv1( * ), rconde( * ), rcondv( * ),
539  \$ result( 11 ), scale( * ), scale1( * ),
540  \$ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
541  \$ wi1( * ), work( * ), wr( * ), wr1( * )
542 * ..
543 *
544 * =====================================================================
545 *
546 * .. Parameters ..
547  REAL zero, one
548  parameter ( zero = 0.0e0, one = 1.0e0 )
549  INTEGER maxtyp
550  parameter ( maxtyp = 21 )
551 * ..
552 * .. Local Scalars ..
554  CHARACTER balanc
555  CHARACTER*3 path
556  INTEGER i, ibal, iinfo, imode, itype, iwk, j, jcol,
557  \$ jsize, jtype, mtypes, n, nerrs, nfail,
558  \$ nmax, nnwork, ntest, ntestf, ntestt
559  REAL anorm, cond, conds, ovfl, rtulp, rtulpi, ulp,
560  \$ ulpinv, unfl
561 * ..
562 * .. Local Arrays ..
563  CHARACTER adumma( 1 ), bal( 4 )
564  INTEGER idumma( 1 ), ioldsd( 4 ), kconds( maxtyp ),
565  \$ kmagn( maxtyp ), kmode( maxtyp ),
566  \$ ktype( maxtyp )
567 * ..
568 * .. External Functions ..
569  REAL slamch
570  EXTERNAL slamch
571 * ..
572 * .. External Subroutines ..
573  EXTERNAL sget23, slabad, slasum, slatme, slatmr, slatms,
574  \$ slaset, xerbla
575 * ..
576 * .. Intrinsic Functions ..
577  INTRINSIC abs, max, min, sqrt
578 * ..
579 * .. Data statements ..
580  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
581  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
582  \$ 3, 1, 2, 3 /
583  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
584  \$ 1, 5, 5, 5, 4, 3, 1 /
585  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
586  DATA bal / 'N', 'P', 'S', 'B' /
587 * ..
588 * .. Executable Statements ..
589 *
590  path( 1: 1 ) = 'Single precision'
591  path( 2: 3 ) = 'VX'
592 *
593 * Check for errors
594 *
595  ntestt = 0
596  ntestf = 0
597  info = 0
598 *
599 * Important constants
600 *
602 *
603 * 12 is the largest dimension in the input file of precomputed
604 * problems
605 *
606  nmax = 12
607  DO 10 j = 1, nsizes
608  nmax = max( nmax, nn( j ) )
609  IF( nn( j ).LT.0 )
611  10 CONTINUE
612 *
613 * Check for errors
614 *
615  IF( nsizes.LT.0 ) THEN
616  info = -1
617  ELSE IF( badnn ) THEN
618  info = -2
619  ELSE IF( ntypes.LT.0 ) THEN
620  info = -3
621  ELSE IF( thresh.LT.zero ) THEN
622  info = -6
623  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
624  info = -10
625  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
626  info = -17
627  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
628  info = -19
629  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
630  info = -21
631  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
632  info = -32
633  END IF
634 *
635  IF( info.NE.0 ) THEN
636  CALL xerbla( 'SDRVVX', -info )
637  RETURN
638  END IF
639 *
640 * If nothing to do check on NIUNIT
641 *
642  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
643  \$ GO TO 160
644 *
645 * More Important constants
646 *
647  unfl = slamch( 'Safe minimum' )
648  ovfl = one / unfl
649  CALL slabad( unfl, ovfl )
650  ulp = slamch( 'Precision' )
651  ulpinv = one / ulp
652  rtulp = sqrt( ulp )
653  rtulpi = one / rtulp
654 *
655 * Loop over sizes, types
656 *
657  nerrs = 0
658 *
659  DO 150 jsize = 1, nsizes
660  n = nn( jsize )
661  IF( nsizes.NE.1 ) THEN
662  mtypes = min( maxtyp, ntypes )
663  ELSE
664  mtypes = min( maxtyp+1, ntypes )
665  END IF
666 *
667  DO 140 jtype = 1, mtypes
668  IF( .NOT.dotype( jtype ) )
669  \$ GO TO 140
670 *
671 * Save ISEED in case of an error.
672 *
673  DO 20 j = 1, 4
674  ioldsd( j ) = iseed( j )
675  20 CONTINUE
676 *
677 * Compute "A"
678 *
679 * Control parameters:
680 *
681 * KMAGN KCONDS KMODE KTYPE
682 * =1 O(1) 1 clustered 1 zero
683 * =2 large large clustered 2 identity
684 * =3 small exponential Jordan
685 * =4 arithmetic diagonal, (w/ eigenvalues)
686 * =5 random log symmetric, w/ eigenvalues
687 * =6 random general, w/ eigenvalues
688 * =7 random diagonal
689 * =8 random symmetric
690 * =9 random general
691 * =10 random triangular
692 *
693  IF( mtypes.GT.maxtyp )
694  \$ GO TO 90
695 *
696  itype = ktype( jtype )
697  imode = kmode( jtype )
698 *
699 * Compute norm
700 *
701  GO TO ( 30, 40, 50 )kmagn( jtype )
702 *
703  30 CONTINUE
704  anorm = one
705  GO TO 60
706 *
707  40 CONTINUE
708  anorm = ovfl*ulp
709  GO TO 60
710 *
711  50 CONTINUE
712  anorm = unfl*ulpinv
713  GO TO 60
714 *
715  60 CONTINUE
716 *
717  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
718  iinfo = 0
719  cond = ulpinv
720 *
721 * Special Matrices -- Identity & Jordan block
722 *
723 * Zero
724 *
725  IF( itype.EQ.1 ) THEN
726  iinfo = 0
727 *
728  ELSE IF( itype.EQ.2 ) THEN
729 *
730 * Identity
731 *
732  DO 70 jcol = 1, n
733  a( jcol, jcol ) = anorm
734  70 CONTINUE
735 *
736  ELSE IF( itype.EQ.3 ) THEN
737 *
738 * Jordan Block
739 *
740  DO 80 jcol = 1, n
741  a( jcol, jcol ) = anorm
742  IF( jcol.GT.1 )
743  \$ a( jcol, jcol-1 ) = one
744  80 CONTINUE
745 *
746  ELSE IF( itype.EQ.4 ) THEN
747 *
748 * Diagonal Matrix, [Eigen]values Specified
749 *
750  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
751  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
752  \$ iinfo )
753 *
754  ELSE IF( itype.EQ.5 ) THEN
755 *
756 * Symmetric, eigenvalues specified
757 *
758  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
759  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
760  \$ iinfo )
761 *
762  ELSE IF( itype.EQ.6 ) THEN
763 *
764 * General, eigenvalues specified
765 *
766  IF( kconds( jtype ).EQ.1 ) THEN
767  conds = one
768  ELSE IF( kconds( jtype ).EQ.2 ) THEN
769  conds = rtulpi
770  ELSE
771  conds = zero
772  END IF
773 *
774  adumma( 1 ) = ' '
775  CALL slatme( n, 'S', iseed, work, imode, cond, one,
776  \$ adumma, 'T', 'T', 'T', work( n+1 ), 4,
777  \$ conds, n, n, anorm, a, lda, work( 2*n+1 ),
778  \$ iinfo )
779 *
780  ELSE IF( itype.EQ.7 ) THEN
781 *
782 * Diagonal, random eigenvalues
783 *
784  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
785  \$ 'T', 'N', work( n+1 ), 1, one,
786  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
787  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
788 *
789  ELSE IF( itype.EQ.8 ) THEN
790 *
791 * Symmetric, random eigenvalues
792 *
793  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
794  \$ 'T', 'N', work( n+1 ), 1, one,
795  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
796  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
797 *
798  ELSE IF( itype.EQ.9 ) THEN
799 *
800 * General, random eigenvalues
801 *
802  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
803  \$ 'T', 'N', work( n+1 ), 1, one,
804  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
805  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
806  IF( n.GE.4 ) THEN
807  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
808  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
809  \$ lda )
810  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
811  \$ lda )
812  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
813  \$ lda )
814  END IF
815 *
816  ELSE IF( itype.EQ.10 ) THEN
817 *
818 * Triangular, random eigenvalues
819 *
820  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
821  \$ 'T', 'N', work( n+1 ), 1, one,
822  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
823  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
824 *
825  ELSE
826 *
827  iinfo = 1
828  END IF
829 *
830  IF( iinfo.NE.0 ) THEN
831  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
832  \$ ioldsd
833  info = abs( iinfo )
834  RETURN
835  END IF
836 *
837  90 CONTINUE
838 *
839 * Test for minimal and generous workspace
840 *
841  DO 130 iwk = 1, 3
842  IF( iwk.EQ.1 ) THEN
843  nnwork = 3*n
844  ELSE IF( iwk.EQ.2 ) THEN
845  nnwork = 6*n + n**2
846  ELSE
847  nnwork = 6*n + 2*n**2
848  END IF
849  nnwork = max( nnwork, 1 )
850 *
851 * Test for all balancing options
852 *
853  DO 120 ibal = 1, 4
854  balanc = bal( ibal )
855 *
856 * Perform tests
857 *
858  CALL sget23( .false., balanc, jtype, thresh, ioldsd,
859  \$ nounit, n, a, lda, h, wr, wi, wr1, wi1,
860  \$ vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
861  \$ rcndv1, rcdvin, rconde, rcnde1, rcdein,
862  \$ scale, scale1, result, work, nnwork,
863  \$ iwork, info )
864 *
865 * Check for RESULT(j) > THRESH
866 *
867  ntest = 0
868  nfail = 0
869  DO 100 j = 1, 9
870  IF( result( j ).GE.zero )
871  \$ ntest = ntest + 1
872  IF( result( j ).GE.thresh )
873  \$ nfail = nfail + 1
874  100 CONTINUE
875 *
876  IF( nfail.GT.0 )
877  \$ ntestf = ntestf + 1
878  IF( ntestf.EQ.1 ) THEN
879  WRITE( nounit, fmt = 9999 )path
880  WRITE( nounit, fmt = 9998 )
881  WRITE( nounit, fmt = 9997 )
882  WRITE( nounit, fmt = 9996 )
883  WRITE( nounit, fmt = 9995 )thresh
884  ntestf = 2
885  END IF
886 *
887  DO 110 j = 1, 9
888  IF( result( j ).GE.thresh ) THEN
889  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
890  \$ ioldsd, jtype, j, result( j )
891  END IF
892  110 CONTINUE
893 *
894  nerrs = nerrs + nfail
895  ntestt = ntestt + ntest
896 *
897  120 CONTINUE
898  130 CONTINUE
899  140 CONTINUE
900  150 CONTINUE
901 *
902  160 CONTINUE
903 *
904 * Read in data from file to check accuracy of condition estimation.
905 * Assume input eigenvalues are sorted lexicographically (increasing
906 * by real part, then decreasing by imaginary part)
907 *
908  jtype = 0
909  170 CONTINUE
910  READ( niunit, fmt = *, end = 220 )n
911 *
912 * Read input data until N=0
913 *
914  IF( n.EQ.0 )
915  \$ GO TO 220
916  jtype = jtype + 1
917  iseed( 1 ) = jtype
918  DO 180 i = 1, n
919  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
920  180 CONTINUE
921  DO 190 i = 1, n
922  READ( niunit, fmt = * )wr1( i ), wi1( i ), rcdein( i ),
923  \$ rcdvin( i )
924  190 CONTINUE
925  CALL sget23( .true., 'N', 22, thresh, iseed, nounit, n, a, lda, h,
926  \$ wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre,
927  \$ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
928  \$ scale, scale1, result, work, 6*n+2*n**2, iwork,
929  \$ info )
930 *
931 * Check for RESULT(j) > THRESH
932 *
933  ntest = 0
934  nfail = 0
935  DO 200 j = 1, 11
936  IF( result( j ).GE.zero )
937  \$ ntest = ntest + 1
938  IF( result( j ).GE.thresh )
939  \$ nfail = nfail + 1
940  200 CONTINUE
941 *
942  IF( nfail.GT.0 )
943  \$ ntestf = ntestf + 1
944  IF( ntestf.EQ.1 ) THEN
945  WRITE( nounit, fmt = 9999 )path
946  WRITE( nounit, fmt = 9998 )
947  WRITE( nounit, fmt = 9997 )
948  WRITE( nounit, fmt = 9996 )
949  WRITE( nounit, fmt = 9995 )thresh
950  ntestf = 2
951  END IF
952 *
953  DO 210 j = 1, 11
954  IF( result( j ).GE.thresh ) THEN
955  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
956  END IF
957  210 CONTINUE
958 *
959  nerrs = nerrs + nfail
960  ntestt = ntestt + ntest
961  GO TO 170
962  220 CONTINUE
963 *
964 * Summary
965 *
966  CALL slasum( path, nounit, nerrs, ntestt )
967 *
968  9999 FORMAT( / 1x, a3, ' -- Real Eigenvalue-Eigenvector Decomposition',
969  \$ ' Expert Driver', /
970  \$ ' Matrix types (see SDRVVX for details): ' )
971 *
972  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
973  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
974  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
975  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
976  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
977  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
978  \$ 'mall, evenly spaced.' )
979  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
980  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
981  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
982  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
983  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
984  \$ 'lex ', / ' 12=Well-cond., random complex ', ' ',
985  \$ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
986  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
987  \$ ' complx ' )
988  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
989  \$ 'with small random entries.', / ' 20=Matrix with large ran',
990  \$ 'dom entries. ', ' 22=Matrix read from input file', / )
991  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
992  \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
993  \$ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
994  \$ / ' 3 = | |VR(i)| - 1 | / ulp ',
995  \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
996  \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
997  \$ ' 1/ulp otherwise', /
998  \$ ' 6 = 0 if VR same no matter what else computed,',
999  \$ ' 1/ulp otherwise', /
1000  \$ ' 7 = 0 if VL same no matter what else computed,',
1001  \$ ' 1/ulp otherwise', /
1002  \$ ' 8 = 0 if RCONDV same no matter what else computed,',
1003  \$ ' 1/ulp otherwise', /
1004  \$ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
1005  \$ ' computed, 1/ulp otherwise',
1006  \$ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
1007  \$ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
1008  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
1009  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
1010  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
1011  \$ g10.3 )
1012  9992 FORMAT( ' SDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1013  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1014 *
1015  RETURN
1016 *
1017 * End of SDRVVX
1018 *
subroutine sget23(COMP, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, IWORK, INFO)
SGET23
Definition: sget23.f:380
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:473
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:42
subroutine slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:334

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