LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zdrvbd()

 subroutine zdrvbd ( integer NSIZES, integer, dimension( * ) MM, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, double precision THRESH, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldu, * ) U, integer LDU, complex*16, dimension( ldvt, * ) VT, integer LDVT, complex*16, dimension( lda, * ) ASAV, complex*16, dimension( ldu, * ) USAV, complex*16, dimension( ldvt, * ) VTSAV, double precision, dimension( * ) S, double precision, dimension( * ) SSAV, double precision, dimension( * ) E, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUNIT, integer INFO )

ZDRVBD

Purpose:
``` ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD,
ZGESDD, ZGESVJ, ZGEJSV, ZGESVDX, and ZGESVDQ.

ZGESVD and ZGESDD factors A = U diag(S) VT, where U and VT are
unitary and diag(S) is diagonal with the entries of the array S on
its diagonal. The entries of S are the singular values, nonnegative
and stored in decreasing order.  U and VT can be optionally not
computed, overwritten on A, or computed partially.

A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.

When ZDRVBD is called, a number of matrix "sizes" (M's and N's)
and a number of matrix "types" are specified.  For each size (M,N)
and each type of matrix, and for the minimal workspace as well as
workspace adequate to permit blocking, an  M x N  matrix "A" will be
generated and used to test the SVD routines.  For each matrix, A will
be factored as A = U diag(S) VT and the following 12 tests computed:

Test for ZGESVD:

(1)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(2)   | I - U'U | / ( M ulp )

(3)   | I - VT VT' | / ( N ulp )

(4)   S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(5)   | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.

(6)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.

(7)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD

Test for ZGESDD:

(8)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(9)   | I - U'U | / ( M ulp )

(10)  | I - VT VT' | / ( N ulp )

(11)  S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(12)  | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.

(13)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.

(14)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD

Test for ZGESVDQ:

(36)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(37)  | I - U'U | / ( M ulp )

(38)  | I - VT VT' | / ( N ulp )

(39)  S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

Test for ZGESVJ:

(15)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(16)  | I - U'U | / ( M ulp )

(17)  | I - VT VT' | / ( N ulp )

(18)  S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

Test for ZGEJSV:

(19)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(20)  | I - U'U | / ( M ulp )

(21)  | I - VT VT' | / ( N ulp )

(22)  S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

Test for ZGESVDX( 'V', 'V', 'A' )/ZGESVDX( 'N', 'N', 'A' )

(23)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )

(24)  | I - U'U | / ( M ulp )

(25)  | I - VT VT' | / ( N ulp )

(26)  S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(27)  | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.

(28)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.

(29)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD

Test for ZGESVDX( 'V', 'V', 'I' )

(30)  | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )

(31)  | I - U'U | / ( M ulp )

(32)  | I - VT VT' | / ( N ulp )

Test for ZGESVDX( 'V', 'V', 'V' )

(33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )

(34)   | I - U'U | / ( M ulp )

(35)   | I - VT VT' | / ( N ulp )

The "sizes" are specified by the arrays MM(1:NSIZES) and
NN(1:NSIZES); the value of each element pair (MM(j),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 matrix of the form  U D V, where U and V are unitary and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.
(4)  Same as (3), but multiplied by the underflow-threshold / ULP.
(5)  Same as (3), but multiplied by the overflow-threshold * ULP.```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, ZDRVBD does nothing. It must be at least zero.``` [in] MM ``` MM is INTEGER array, dimension (NSIZES) An array containing the matrix "heights" to be used. For each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j) will be ignored. The MM(j) values must be at least zero.``` [in] NN ``` NN is INTEGER array, dimension (NSIZES) An array containing the matrix "widths" to be used. For each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j) will be ignored. The NN(j) values must be at least zero.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, ZDRVBD does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrices are in A and B. 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 (m,n), a matrix 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 ZDRVBD to continue the same random number sequence.``` [in] THRESH ``` THRESH is 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.``` [out] A ``` A is COMPLEX*16 array, dimension (LDA,max(NN)) Used to hold the matrix whose singular values are to be computed. On exit, A contains the last matrix actually used.``` [in] LDA ``` LDA is INTEGER The leading dimension of A. It must be at least 1 and at least max( MM ).``` [out] U ``` U is COMPLEX*16 array, dimension (LDU,max(MM)) Used to hold the computed matrix of right singular vectors. On exit, U contains the last such vectors actually computed.``` [in] LDU ``` LDU is INTEGER The leading dimension of U. It must be at least 1 and at least max( MM ).``` [out] VT ``` VT is COMPLEX*16 array, dimension (LDVT,max(NN)) Used to hold the computed matrix of left singular vectors. On exit, VT contains the last such vectors actually computed.``` [in] LDVT ``` LDVT is INTEGER The leading dimension of VT. It must be at least 1 and at least max( NN ).``` [out] ASAV ``` ASAV is COMPLEX*16 array, dimension (LDA,max(NN)) Used to hold a different copy of the matrix whose singular values are to be computed. On exit, A contains the last matrix actually used.``` [out] USAV ``` USAV is COMPLEX*16 array, dimension (LDU,max(MM)) Used to hold a different copy of the computed matrix of right singular vectors. On exit, USAV contains the last such vectors actually computed.``` [out] VTSAV ``` VTSAV is COMPLEX*16 array, dimension (LDVT,max(NN)) Used to hold a different copy of the computed matrix of left singular vectors. On exit, VTSAV contains the last such vectors actually computed.``` [out] S ``` S is DOUBLE PRECISION array, dimension (max(min(MM,NN))) Contains the computed singular values.``` [out] SSAV ``` SSAV is DOUBLE PRECISION array, dimension (max(min(MM,NN))) Contains another copy of the computed singular values.``` [out] E ``` E is DOUBLE PRECISION array, dimension (max(min(MM,NN))) Workspace for ZGESVD.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all pairs (M,N)=(MM(j),NN(j))``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension ( 5*max(max(MM,NN)) )``` [out] IWORK ` IWORK is INTEGER array, dimension at least 8*min(M,N)` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)``` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some MM(j) < 0 -3: Some NN(j) < 0 -4: NTYPES < 0 -7: THRESH < 0 -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). -12: LDU < 1 or LDU < MMAX. -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ). -21: LWORK too small. If ZLATMS, or ZGESVD returns an error code, the absolute value of it is returned.```

Definition at line 397 of file zdrvbd.f.

401 *
402 * -- LAPACK test routine --
403 * -- LAPACK is a software package provided by Univ. of Tennessee, --
404 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
405 *
406  IMPLICIT NONE
407 *
408 * .. Scalar Arguments ..
409  INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES,
410  \$ NTYPES
411  DOUBLE PRECISION THRESH
412 * ..
413 * .. Array Arguments ..
414  LOGICAL DOTYPE( * )
415  INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
416  DOUBLE PRECISION E( * ), RWORK( * ), S( * ), SSAV( * )
417  COMPLEX*16 A( LDA, * ), ASAV( LDA, * ), U( LDU, * ),
418  \$ USAV( LDU, * ), VT( LDVT, * ),
419  \$ VTSAV( LDVT, * ), WORK( * )
420 * ..
421 *
422 * =====================================================================
423 *
424 * .. Parameters ..
425  DOUBLE PRECISION ZERO, ONE, TWO, HALF
426  parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
427  \$ half = 0.5d0 )
428  COMPLEX*16 CZERO, CONE
429  parameter( czero = ( 0.0d+0, 0.0d+0 ),
430  \$ cone = ( 1.0d+0, 0.0d+0 ) )
431  INTEGER MAXTYP
432  parameter( maxtyp = 5 )
433 * ..
434 * .. Local Scalars ..
436  CHARACTER JOBQ, JOBU, JOBVT, RANGE
437  INTEGER I, IINFO, IJQ, IJU, IJVT, IL, IU, ITEMP,
438  \$ IWSPC, IWTMP, J, JSIZE, JTYPE, LSWORK, M,
439  \$ MINWRK, MMAX, MNMAX, MNMIN, MTYPES, N,
440  \$ NERRS, NFAIL, NMAX, NS, NSI, NSV, NTEST,
441  \$ NTESTF, NTESTT, LRWORK
442  DOUBLE PRECISION ANORM, DIF, DIV, OVFL, RTUNFL, ULP, ULPINV,
443  \$ UNFL, VL, VU
444 * ..
445 * .. Local Scalars for ZGESVDQ ..
446  INTEGER LIWORK, NUMRANK
447 * ..
448 * .. Local Arrays ..
449  CHARACTER CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
450  INTEGER IOLDSD( 4 ), ISEED2( 4 )
451  DOUBLE PRECISION RESULT( 39 )
452 * ..
453 * .. External Functions ..
454  DOUBLE PRECISION DLAMCH, DLARND
455  EXTERNAL dlamch, dlarnd
456 * ..
457 * .. External Subroutines ..
458  EXTERNAL alasvm, xerbla, zbdt01, zbdt05, zgesdd,
461 * ..
462 * .. Intrinsic Functions ..
463  INTRINSIC abs, dble, max, min
464 * ..
465 * .. Scalars in Common ..
466  CHARACTER*32 SRNAMT
467 * ..
468 * .. Common blocks ..
469  COMMON / srnamc / srnamt
470 * ..
471 * .. Data statements ..
472  DATA cjob / 'N', 'O', 'S', 'A' /
473  DATA cjobr / 'A', 'V', 'I' /
474  DATA cjobv / 'N', 'V' /
475 * ..
476 * .. Executable Statements ..
477 *
478 * Check for errors
479 *
480  info = 0
481 *
482 * Important constants
483 *
484  nerrs = 0
485  ntestt = 0
486  ntestf = 0
489  mmax = 1
490  nmax = 1
491  mnmax = 1
492  minwrk = 1
493  DO 10 j = 1, nsizes
494  mmax = max( mmax, mm( j ) )
495  IF( mm( j ).LT.0 )
497  nmax = max( nmax, nn( j ) )
498  IF( nn( j ).LT.0 )
500  mnmax = max( mnmax, min( mm( j ), nn( j ) ) )
501  minwrk = max( minwrk, max( 3*min( mm( j ),
502  \$ nn( j ) )+max( mm( j ), nn( j ) )**2, 5*min( mm( j ),
503  \$ nn( j ) ), 3*max( mm( j ), nn( j ) ) ) )
504  10 CONTINUE
505 *
506 * Check for errors
507 *
508  IF( nsizes.LT.0 ) THEN
509  info = -1
510  ELSE IF( badmm ) THEN
511  info = -2
512  ELSE IF( badnn ) THEN
513  info = -3
514  ELSE IF( ntypes.LT.0 ) THEN
515  info = -4
516  ELSE IF( lda.LT.max( 1, mmax ) ) THEN
517  info = -10
518  ELSE IF( ldu.LT.max( 1, mmax ) ) THEN
519  info = -12
520  ELSE IF( ldvt.LT.max( 1, nmax ) ) THEN
521  info = -14
522  ELSE IF( minwrk.GT.lwork ) THEN
523  info = -21
524  END IF
525 *
526  IF( info.NE.0 ) THEN
527  CALL xerbla( 'ZDRVBD', -info )
528  RETURN
529  END IF
530 *
531 * Quick return if nothing to do
532 *
533  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
534  \$ RETURN
535 *
536 * More Important constants
537 *
538  unfl = dlamch( 'S' )
539  ovfl = one / unfl
540  ulp = dlamch( 'E' )
541  ulpinv = one / ulp
542  rtunfl = sqrt( unfl )
543 *
544 * Loop over sizes, types
545 *
546  nerrs = 0
547 *
548  DO 230 jsize = 1, nsizes
549  m = mm( jsize )
550  n = nn( jsize )
551  mnmin = min( m, n )
552 *
553  IF( nsizes.NE.1 ) THEN
554  mtypes = min( maxtyp, ntypes )
555  ELSE
556  mtypes = min( maxtyp+1, ntypes )
557  END IF
558 *
559  DO 220 jtype = 1, mtypes
560  IF( .NOT.dotype( jtype ) )
561  \$ GO TO 220
562  ntest = 0
563 *
564  DO 20 j = 1, 4
565  ioldsd( j ) = iseed( j )
566  20 CONTINUE
567 *
568 * Compute "A"
569 *
570  IF( mtypes.GT.maxtyp )
571  \$ GO TO 50
572 *
573  IF( jtype.EQ.1 ) THEN
574 *
575 * Zero matrix
576 *
577  CALL zlaset( 'Full', m, n, czero, czero, a, lda )
578  DO 30 i = 1, min( m, n )
579  s( i ) = zero
580  30 CONTINUE
581 *
582  ELSE IF( jtype.EQ.2 ) THEN
583 *
584 * Identity matrix
585 *
586  CALL zlaset( 'Full', m, n, czero, cone, a, lda )
587  DO 40 i = 1, min( m, n )
588  s( i ) = one
589  40 CONTINUE
590 *
591  ELSE
592 *
593 * (Scaled) random matrix
594 *
595  IF( jtype.EQ.3 )
596  \$ anorm = one
597  IF( jtype.EQ.4 )
598  \$ anorm = unfl / ulp
599  IF( jtype.EQ.5 )
600  \$ anorm = ovfl*ulp
601  CALL zlatms( m, n, 'U', iseed, 'N', s, 4, dble( mnmin ),
602  \$ anorm, m-1, n-1, 'N', a, lda, work, iinfo )
603  IF( iinfo.NE.0 ) THEN
604  WRITE( nounit, fmt = 9996 )'Generator', iinfo, m, n,
605  \$ jtype, ioldsd
606  info = abs( iinfo )
607  RETURN
608  END IF
609  END IF
610 *
611  50 CONTINUE
612  CALL zlacpy( 'F', m, n, a, lda, asav, lda )
613 *
614 * Do for minimal and adequate (for blocking) workspace
615 *
616  DO 210 iwspc = 1, 4
617 *
618 * Test for ZGESVD
619 *
620  iwtmp = 2*min( m, n )+max( m, n )
621  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
622  lswork = min( lswork, lwork )
623  lswork = max( lswork, 1 )
624  IF( iwspc.EQ.4 )
625  \$ lswork = lwork
626 *
627  DO 60 j = 1, 35
628  result( j ) = -one
629  60 CONTINUE
630 *
631 * Factorize A
632 *
633  IF( iwspc.GT.1 )
634  \$ CALL zlacpy( 'F', m, n, asav, lda, a, lda )
635  srnamt = 'ZGESVD'
636  CALL zgesvd( 'A', 'A', m, n, a, lda, ssav, usav, ldu,
637  \$ vtsav, ldvt, work, lswork, rwork, iinfo )
638  IF( iinfo.NE.0 ) THEN
639  WRITE( nounit, fmt = 9995 )'GESVD', iinfo, m, n,
640  \$ jtype, lswork, ioldsd
641  info = abs( iinfo )
642  RETURN
643  END IF
644 *
645 * Do tests 1--4
646 *
647  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
648  \$ vtsav, ldvt, work, rwork, result( 1 ) )
649  IF( m.NE.0 .AND. n.NE.0 ) THEN
650  CALL zunt01( 'Columns', mnmin, m, usav, ldu, work,
651  \$ lwork, rwork, result( 2 ) )
652  CALL zunt01( 'Rows', mnmin, n, vtsav, ldvt, work,
653  \$ lwork, rwork, result( 3 ) )
654  END IF
655  result( 4 ) = 0
656  DO 70 i = 1, mnmin - 1
657  IF( ssav( i ).LT.ssav( i+1 ) )
658  \$ result( 4 ) = ulpinv
659  IF( ssav( i ).LT.zero )
660  \$ result( 4 ) = ulpinv
661  70 CONTINUE
662  IF( mnmin.GE.1 ) THEN
663  IF( ssav( mnmin ).LT.zero )
664  \$ result( 4 ) = ulpinv
665  END IF
666 *
667 * Do partial SVDs, comparing to SSAV, USAV, and VTSAV
668 *
669  result( 5 ) = zero
670  result( 6 ) = zero
671  result( 7 ) = zero
672  DO 100 iju = 0, 3
673  DO 90 ijvt = 0, 3
674  IF( ( iju.EQ.3 .AND. ijvt.EQ.3 ) .OR.
675  \$ ( iju.EQ.1 .AND. ijvt.EQ.1 ) )GO TO 90
676  jobu = cjob( iju+1 )
677  jobvt = cjob( ijvt+1 )
678  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
679  srnamt = 'ZGESVD'
680  CALL zgesvd( jobu, jobvt, m, n, a, lda, s, u, ldu,
681  \$ vt, ldvt, work, lswork, rwork, iinfo )
682 *
683 * Compare U
684 *
685  dif = zero
686  IF( m.GT.0 .AND. n.GT.0 ) THEN
687  IF( iju.EQ.1 ) THEN
688  CALL zunt03( 'C', m, mnmin, m, mnmin, usav,
689  \$ ldu, a, lda, work, lwork, rwork,
690  \$ dif, iinfo )
691  ELSE IF( iju.EQ.2 ) THEN
692  CALL zunt03( 'C', m, mnmin, m, mnmin, usav,
693  \$ ldu, u, ldu, work, lwork, rwork,
694  \$ dif, iinfo )
695  ELSE IF( iju.EQ.3 ) THEN
696  CALL zunt03( 'C', m, m, m, mnmin, usav, ldu,
697  \$ u, ldu, work, lwork, rwork, dif,
698  \$ iinfo )
699  END IF
700  END IF
701  result( 5 ) = max( result( 5 ), dif )
702 *
703 * Compare VT
704 *
705  dif = zero
706  IF( m.GT.0 .AND. n.GT.0 ) THEN
707  IF( ijvt.EQ.1 ) THEN
708  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
709  \$ ldvt, a, lda, work, lwork,
710  \$ rwork, dif, iinfo )
711  ELSE IF( ijvt.EQ.2 ) THEN
712  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
713  \$ ldvt, vt, ldvt, work, lwork,
714  \$ rwork, dif, iinfo )
715  ELSE IF( ijvt.EQ.3 ) THEN
716  CALL zunt03( 'R', n, n, n, mnmin, vtsav,
717  \$ ldvt, vt, ldvt, work, lwork,
718  \$ rwork, dif, iinfo )
719  END IF
720  END IF
721  result( 6 ) = max( result( 6 ), dif )
722 *
723 * Compare S
724 *
725  dif = zero
726  div = max( dble( mnmin )*ulp*s( 1 ),
727  \$ dlamch( 'Safe minimum' ) )
728  DO 80 i = 1, mnmin - 1
729  IF( ssav( i ).LT.ssav( i+1 ) )
730  \$ dif = ulpinv
731  IF( ssav( i ).LT.zero )
732  \$ dif = ulpinv
733  dif = max( dif, abs( ssav( i )-s( i ) ) / div )
734  80 CONTINUE
735  result( 7 ) = max( result( 7 ), dif )
736  90 CONTINUE
737  100 CONTINUE
738 *
739 * Test for ZGESDD
740 *
741  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
742  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
743  lswork = min( lswork, lwork )
744  lswork = max( lswork, 1 )
745  IF( iwspc.EQ.4 )
746  \$ lswork = lwork
747 *
748 * Factorize A
749 *
750  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
751  srnamt = 'ZGESDD'
752  CALL zgesdd( 'A', m, n, a, lda, ssav, usav, ldu, vtsav,
753  \$ ldvt, work, lswork, rwork, iwork, iinfo )
754  IF( iinfo.NE.0 ) THEN
755  WRITE( nounit, fmt = 9995 )'GESDD', iinfo, m, n,
756  \$ jtype, lswork, ioldsd
757  info = abs( iinfo )
758  RETURN
759  END IF
760 *
761 * Do tests 1--4
762 *
763  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
764  \$ vtsav, ldvt, work, rwork, result( 8 ) )
765  IF( m.NE.0 .AND. n.NE.0 ) THEN
766  CALL zunt01( 'Columns', mnmin, m, usav, ldu, work,
767  \$ lwork, rwork, result( 9 ) )
768  CALL zunt01( 'Rows', mnmin, n, vtsav, ldvt, work,
769  \$ lwork, rwork, result( 10 ) )
770  END IF
771  result( 11 ) = 0
772  DO 110 i = 1, mnmin - 1
773  IF( ssav( i ).LT.ssav( i+1 ) )
774  \$ result( 11 ) = ulpinv
775  IF( ssav( i ).LT.zero )
776  \$ result( 11 ) = ulpinv
777  110 CONTINUE
778  IF( mnmin.GE.1 ) THEN
779  IF( ssav( mnmin ).LT.zero )
780  \$ result( 11 ) = ulpinv
781  END IF
782 *
783 * Do partial SVDs, comparing to SSAV, USAV, and VTSAV
784 *
785  result( 12 ) = zero
786  result( 13 ) = zero
787  result( 14 ) = zero
788  DO 130 ijq = 0, 2
789  jobq = cjob( ijq+1 )
790  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
791  srnamt = 'ZGESDD'
792  CALL zgesdd( jobq, m, n, a, lda, s, u, ldu, vt, ldvt,
793  \$ work, lswork, rwork, iwork, iinfo )
794 *
795 * Compare U
796 *
797  dif = zero
798  IF( m.GT.0 .AND. n.GT.0 ) THEN
799  IF( ijq.EQ.1 ) THEN
800  IF( m.GE.n ) THEN
801  CALL zunt03( 'C', m, mnmin, m, mnmin, usav,
802  \$ ldu, a, lda, work, lwork, rwork,
803  \$ dif, iinfo )
804  ELSE
805  CALL zunt03( 'C', m, mnmin, m, mnmin, usav,
806  \$ ldu, u, ldu, work, lwork, rwork,
807  \$ dif, iinfo )
808  END IF
809  ELSE IF( ijq.EQ.2 ) THEN
810  CALL zunt03( 'C', m, mnmin, m, mnmin, usav, ldu,
811  \$ u, ldu, work, lwork, rwork, dif,
812  \$ iinfo )
813  END IF
814  END IF
815  result( 12 ) = max( result( 12 ), dif )
816 *
817 * Compare VT
818 *
819  dif = zero
820  IF( m.GT.0 .AND. n.GT.0 ) THEN
821  IF( ijq.EQ.1 ) THEN
822  IF( m.GE.n ) THEN
823  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
824  \$ ldvt, vt, ldvt, work, lwork,
825  \$ rwork, dif, iinfo )
826  ELSE
827  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
828  \$ ldvt, a, lda, work, lwork,
829  \$ rwork, dif, iinfo )
830  END IF
831  ELSE IF( ijq.EQ.2 ) THEN
832  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
833  \$ ldvt, vt, ldvt, work, lwork, rwork,
834  \$ dif, iinfo )
835  END IF
836  END IF
837  result( 13 ) = max( result( 13 ), dif )
838 *
839 * Compare S
840 *
841  dif = zero
842  div = max( dble( mnmin )*ulp*s( 1 ),
843  \$ dlamch( 'Safe minimum' ) )
844  DO 120 i = 1, mnmin - 1
845  IF( ssav( i ).LT.ssav( i+1 ) )
846  \$ dif = ulpinv
847  IF( ssav( i ).LT.zero )
848  \$ dif = ulpinv
849  dif = max( dif, abs( ssav( i )-s( i ) ) / div )
850  120 CONTINUE
851  result( 14 ) = max( result( 14 ), dif )
852  130 CONTINUE
853 *
854 * Test ZGESVDQ
855 * Note: ZGESVDQ only works for M >= N
856 *
857  result( 36 ) = zero
858  result( 37 ) = zero
859  result( 38 ) = zero
860  result( 39 ) = zero
861 *
862  IF( m.GE.n ) THEN
863  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
864  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
865  lswork = min( lswork, lwork )
866  lswork = max( lswork, 1 )
867  IF( iwspc.EQ.4 )
868  \$ lswork = lwork
869 *
870  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
871  srnamt = 'ZGESVDQ'
872 *
873  lrwork = max(2, m, 5*n)
874  liwork = max( n, 1 )
875  CALL zgesvdq( 'H', 'N', 'N', 'A', 'A',
876  \$ m, n, a, lda, ssav, usav, ldu,
877  \$ vtsav, ldvt, numrank, iwork, liwork,
878  \$ work, lwork, rwork, lrwork, iinfo )
879 *
880  IF( iinfo.NE.0 ) THEN
881  WRITE( nounit, fmt = 9995 )'ZGESVDQ', iinfo, m, n,
882  \$ jtype, lswork, ioldsd
883  info = abs( iinfo )
884  RETURN
885  END IF
886 *
887 * Do tests 36--39
888 *
889  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
890  \$ vtsav, ldvt, work, rwork, result( 36 ) )
891  IF( m.NE.0 .AND. n.NE.0 ) THEN
892  CALL zunt01( 'Columns', m, m, usav, ldu, work,
893  \$ lwork, rwork, result( 37 ) )
894  CALL zunt01( 'Rows', n, n, vtsav, ldvt, work,
895  \$ lwork, rwork, result( 38 ) )
896  END IF
897  result( 39 ) = zero
898  DO 199 i = 1, mnmin - 1
899  IF( ssav( i ).LT.ssav( i+1 ) )
900  \$ result( 39 ) = ulpinv
901  IF( ssav( i ).LT.zero )
902  \$ result( 39 ) = ulpinv
903  199 CONTINUE
904  IF( mnmin.GE.1 ) THEN
905  IF( ssav( mnmin ).LT.zero )
906  \$ result( 39 ) = ulpinv
907  END IF
908  END IF
909 *
910 * Test ZGESVJ
911 * Note: ZGESVJ only works for M >= N
912 *
913  result( 15 ) = zero
914  result( 16 ) = zero
915  result( 17 ) = zero
916  result( 18 ) = zero
917 *
918  IF( m.GE.n ) THEN
919  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
920  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
921  lswork = min( lswork, lwork )
922  lswork = max( lswork, 1 )
923  lrwork = max(6,n)
924  IF( iwspc.EQ.4 )
925  \$ lswork = lwork
926 *
927  CALL zlacpy( 'F', m, n, asav, lda, usav, lda )
928  srnamt = 'ZGESVJ'
929  CALL zgesvj( 'G', 'U', 'V', m, n, usav, lda, ssav,
930  & 0, a, ldvt, work, lwork, rwork,
931  & lrwork, iinfo )
932 *
933 * ZGESVJ returns V not VH
934 *
935  DO j=1,n
936  DO i=1,n
937  vtsav(j,i) = conjg(a(i,j))
938  END DO
939  END DO
940 *
941  IF( iinfo.NE.0 ) THEN
942  WRITE( nounit, fmt = 9995 )'GESVJ', iinfo, m, n,
943  \$ jtype, lswork, ioldsd
944  info = abs( iinfo )
945  RETURN
946  END IF
947 *
948 * Do tests 15--18
949 *
950  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
951  \$ vtsav, ldvt, work, rwork, result( 15 ) )
952  IF( m.NE.0 .AND. n.NE.0 ) THEN
953  CALL zunt01( 'Columns', m, m, usav, ldu, work,
954  \$ lwork, rwork, result( 16 ) )
955  CALL zunt01( 'Rows', n, n, vtsav, ldvt, work,
956  \$ lwork, rwork, result( 17 ) )
957  END IF
958  result( 18 ) = zero
959  DO 131 i = 1, mnmin - 1
960  IF( ssav( i ).LT.ssav( i+1 ) )
961  \$ result( 18 ) = ulpinv
962  IF( ssav( i ).LT.zero )
963  \$ result( 18 ) = ulpinv
964  131 CONTINUE
965  IF( mnmin.GE.1 ) THEN
966  IF( ssav( mnmin ).LT.zero )
967  \$ result( 18 ) = ulpinv
968  END IF
969  END IF
970 *
971 * Test ZGEJSV
972 * Note: ZGEJSV only works for M >= N
973 *
974  result( 19 ) = zero
975  result( 20 ) = zero
976  result( 21 ) = zero
977  result( 22 ) = zero
978  IF( m.GE.n ) THEN
979  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
980  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
981  lswork = min( lswork, lwork )
982  lswork = max( lswork, 1 )
983  IF( iwspc.EQ.4 )
984  \$ lswork = lwork
985  lrwork = max( 7, n + 2*m)
986 *
987  CALL zlacpy( 'F', m, n, asav, lda, vtsav, lda )
988  srnamt = 'ZGEJSV'
989  CALL zgejsv( 'G', 'U', 'V', 'R', 'N', 'N',
990  & m, n, vtsav, lda, ssav, usav, ldu, a, ldvt,
991  & work, lwork, rwork,
992  & lrwork, iwork, iinfo )
993 *
994 * ZGEJSV returns V not VH
995 *
996  DO 133 j=1,n
997  DO 132 i=1,n
998  vtsav(j,i) = conjg(a(i,j))
999  132 END DO
1000  133 END DO
1001 *
1002  IF( iinfo.NE.0 ) THEN
1003  WRITE( nounit, fmt = 9995 )'GEJSV', iinfo, m, n,
1004  \$ jtype, lswork, ioldsd
1005  info = abs( iinfo )
1006  RETURN
1007  END IF
1008 *
1009 * Do tests 19--22
1010 *
1011  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
1012  \$ vtsav, ldvt, work, rwork, result( 19 ) )
1013  IF( m.NE.0 .AND. n.NE.0 ) THEN
1014  CALL zunt01( 'Columns', m, m, usav, ldu, work,
1015  \$ lwork, rwork, result( 20 ) )
1016  CALL zunt01( 'Rows', n, n, vtsav, ldvt, work,
1017  \$ lwork, rwork, result( 21 ) )
1018  END IF
1019  result( 22 ) = zero
1020  DO 134 i = 1, mnmin - 1
1021  IF( ssav( i ).LT.ssav( i+1 ) )
1022  \$ result( 22 ) = ulpinv
1023  IF( ssav( i ).LT.zero )
1024  \$ result( 22 ) = ulpinv
1025  134 CONTINUE
1026  IF( mnmin.GE.1 ) THEN
1027  IF( ssav( mnmin ).LT.zero )
1028  \$ result( 22 ) = ulpinv
1029  END IF
1030  END IF
1031 *
1032 * Test ZGESVDX
1033 *
1034 * Factorize A
1035 *
1036  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
1037  srnamt = 'ZGESVDX'
1038  CALL zgesvdx( 'V', 'V', 'A', m, n, a, lda,
1039  \$ vl, vu, il, iu, ns, ssav, usav, ldu,
1040  \$ vtsav, ldvt, work, lwork, rwork,
1041  \$ iwork, iinfo )
1042  IF( iinfo.NE.0 ) THEN
1043  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1044  \$ jtype, lswork, ioldsd
1045  info = abs( iinfo )
1046  RETURN
1047  END IF
1048 *
1049 * Do tests 1--4
1050 *
1051  result( 23 ) = zero
1052  result( 24 ) = zero
1053  result( 25 ) = zero
1054  CALL zbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
1055  \$ vtsav, ldvt, work, rwork, result( 23 ) )
1056  IF( m.NE.0 .AND. n.NE.0 ) THEN
1057  CALL zunt01( 'Columns', mnmin, m, usav, ldu, work,
1058  \$ lwork, rwork, result( 24 ) )
1059  CALL zunt01( 'Rows', mnmin, n, vtsav, ldvt, work,
1060  \$ lwork, rwork, result( 25 ) )
1061  END IF
1062  result( 26 ) = zero
1063  DO 140 i = 1, mnmin - 1
1064  IF( ssav( i ).LT.ssav( i+1 ) )
1065  \$ result( 26 ) = ulpinv
1066  IF( ssav( i ).LT.zero )
1067  \$ result( 26 ) = ulpinv
1068  140 CONTINUE
1069  IF( mnmin.GE.1 ) THEN
1070  IF( ssav( mnmin ).LT.zero )
1071  \$ result( 26 ) = ulpinv
1072  END IF
1073 *
1074 * Do partial SVDs, comparing to SSAV, USAV, and VTSAV
1075 *
1076  result( 27 ) = zero
1077  result( 28 ) = zero
1078  result( 29 ) = zero
1079  DO 170 iju = 0, 1
1080  DO 160 ijvt = 0, 1
1081  IF( ( iju.EQ.0 .AND. ijvt.EQ.0 ) .OR.
1082  \$ ( iju.EQ.1 .AND. ijvt.EQ.1 ) ) GO TO 160
1083  jobu = cjobv( iju+1 )
1084  jobvt = cjobv( ijvt+1 )
1085  range = cjobr( 1 )
1086  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
1087  srnamt = 'ZGESVDX'
1088  CALL zgesvdx( jobu, jobvt, 'A', m, n, a, lda,
1089  \$ vl, vu, il, iu, ns, ssav, u, ldu,
1090  \$ vt, ldvt, work, lwork, rwork,
1091  \$ iwork, iinfo )
1092 *
1093 * Compare U
1094 *
1095  dif = zero
1096  IF( m.GT.0 .AND. n.GT.0 ) THEN
1097  IF( iju.EQ.1 ) THEN
1098  CALL zunt03( 'C', m, mnmin, m, mnmin, usav,
1099  \$ ldu, u, ldu, work, lwork, rwork,
1100  \$ dif, iinfo )
1101  END IF
1102  END IF
1103  result( 27 ) = max( result( 27 ), dif )
1104 *
1105 * Compare VT
1106 *
1107  dif = zero
1108  IF( m.GT.0 .AND. n.GT.0 ) THEN
1109  IF( ijvt.EQ.1 ) THEN
1110  CALL zunt03( 'R', n, mnmin, n, mnmin, vtsav,
1111  \$ ldvt, vt, ldvt, work, lwork,
1112  \$ rwork, dif, iinfo )
1113  END IF
1114  END IF
1115  result( 28 ) = max( result( 28 ), dif )
1116 *
1117 * Compare S
1118 *
1119  dif = zero
1120  div = max( dble( mnmin )*ulp*s( 1 ),
1121  \$ dlamch( 'Safe minimum' ) )
1122  DO 150 i = 1, mnmin - 1
1123  IF( ssav( i ).LT.ssav( i+1 ) )
1124  \$ dif = ulpinv
1125  IF( ssav( i ).LT.zero )
1126  \$ dif = ulpinv
1127  dif = max( dif, abs( ssav( i )-s( i ) ) / div )
1128  150 CONTINUE
1129  result( 29) = max( result( 29 ), dif )
1130  160 CONTINUE
1131  170 CONTINUE
1132 *
1133 * Do tests 8--10
1134 *
1135  DO 180 i = 1, 4
1136  iseed2( i ) = iseed( i )
1137  180 CONTINUE
1138  IF( mnmin.LE.1 ) THEN
1139  il = 1
1140  iu = max( 1, mnmin )
1141  ELSE
1142  il = 1 + int( ( mnmin-1 )*dlarnd( 1, iseed2 ) )
1143  iu = 1 + int( ( mnmin-1 )*dlarnd( 1, iseed2 ) )
1144  IF( iu.LT.il ) THEN
1145  itemp = iu
1146  iu = il
1147  il = itemp
1148  END IF
1149  END IF
1150  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
1151  srnamt = 'ZGESVDX'
1152  CALL zgesvdx( 'V', 'V', 'I', m, n, a, lda,
1153  \$ vl, vu, il, iu, nsi, s, u, ldu,
1154  \$ vt, ldvt, work, lwork, rwork,
1155  \$ iwork, iinfo )
1156  IF( iinfo.NE.0 ) THEN
1157  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1158  \$ jtype, lswork, ioldsd
1159  info = abs( iinfo )
1160  RETURN
1161  END IF
1162 *
1163  result( 30 ) = zero
1164  result( 31 ) = zero
1165  result( 32 ) = zero
1166  CALL zbdt05( m, n, asav, lda, s, nsi, u, ldu,
1167  \$ vt, ldvt, work, result( 30 ) )
1168  IF( m.NE.0 .AND. n.NE.0 ) THEN
1169  CALL zunt01( 'Columns', m, nsi, u, ldu, work,
1170  \$ lwork, rwork, result( 31 ) )
1171  CALL zunt01( 'Rows', nsi, n, vt, ldvt, work,
1172  \$ lwork, rwork, result( 32 ) )
1173  END IF
1174 *
1175 * Do tests 11--13
1176 *
1177  IF( mnmin.GT.0 .AND. nsi.GT.1 ) THEN
1178  IF( il.NE.1 ) THEN
1179  vu = ssav( il ) +
1180  \$ max( half*abs( ssav( il )-ssav( il-1 ) ),
1181  \$ ulp*anorm, two*rtunfl )
1182  ELSE
1183  vu = ssav( 1 ) +
1184  \$ max( half*abs( ssav( ns )-ssav( 1 ) ),
1185  \$ ulp*anorm, two*rtunfl )
1186  END IF
1187  IF( iu.NE.ns ) THEN
1188  vl = ssav( iu ) - max( ulp*anorm, two*rtunfl,
1189  \$ half*abs( ssav( iu+1 )-ssav( iu ) ) )
1190  ELSE
1191  vl = ssav( ns ) - max( ulp*anorm, two*rtunfl,
1192  \$ half*abs( ssav( ns )-ssav( 1 ) ) )
1193  END IF
1194  vl = max( vl,zero )
1195  vu = max( vu,zero )
1196  IF( vl.GE.vu ) vu = max( vu*2, vu+vl+half )
1197  ELSE
1198  vl = zero
1199  vu = one
1200  END IF
1201  CALL zlacpy( 'F', m, n, asav, lda, a, lda )
1202  srnamt = 'ZGESVDX'
1203  CALL zgesvdx( 'V', 'V', 'V', m, n, a, lda,
1204  \$ vl, vu, il, iu, nsv, s, u, ldu,
1205  \$ vt, ldvt, work, lwork, rwork,
1206  \$ iwork, iinfo )
1207  IF( iinfo.NE.0 ) THEN
1208  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1209  \$ jtype, lswork, ioldsd
1210  info = abs( iinfo )
1211  RETURN
1212  END IF
1213 *
1214  result( 33 ) = zero
1215  result( 34 ) = zero
1216  result( 35 ) = zero
1217  CALL zbdt05( m, n, asav, lda, s, nsv, u, ldu,
1218  \$ vt, ldvt, work, result( 33 ) )
1219  IF( m.NE.0 .AND. n.NE.0 ) THEN
1220  CALL zunt01( 'Columns', m, nsv, u, ldu, work,
1221  \$ lwork, rwork, result( 34 ) )
1222  CALL zunt01( 'Rows', nsv, n, vt, ldvt, work,
1223  \$ lwork, rwork, result( 35 ) )
1224  END IF
1225 *
1226 * End of Loop -- Check for RESULT(j) > THRESH
1227 *
1228  ntest = 0
1229  nfail = 0
1230  DO 190 j = 1, 39
1231  IF( result( j ).GE.zero )
1232  \$ ntest = ntest + 1
1233  IF( result( j ).GE.thresh )
1234  \$ nfail = nfail + 1
1235  190 CONTINUE
1236 *
1237  IF( nfail.GT.0 )
1238  \$ ntestf = ntestf + 1
1239  IF( ntestf.EQ.1 ) THEN
1240  WRITE( nounit, fmt = 9999 )
1241  WRITE( nounit, fmt = 9998 )thresh
1242  ntestf = 2
1243  END IF
1244 *
1245  DO 200 j = 1, 39
1246  IF( result( j ).GE.thresh ) THEN
1247  WRITE( nounit, fmt = 9997 )m, n, jtype, iwspc,
1248  \$ ioldsd, j, result( j )
1249  END IF
1250  200 CONTINUE
1251 *
1252  nerrs = nerrs + nfail
1253  ntestt = ntestt + ntest
1254 *
1255  210 CONTINUE
1256 *
1257  220 CONTINUE
1258  230 CONTINUE
1259 *
1260 * Summary
1261 *
1262  CALL alasvm( 'ZBD', nounit, nerrs, ntestt, 0 )
1263 *
1264  9999 FORMAT( ' SVD -- Complex Singular Value Decomposition Driver ',
1265  \$ / ' Matrix types (see ZDRVBD for details):',
1266  \$ / / ' 1 = Zero matrix', / ' 2 = Identity matrix',
1267  \$ / ' 3 = Evenly spaced singular values near 1',
1268  \$ / ' 4 = Evenly spaced singular values near underflow',
1269  \$ / ' 5 = Evenly spaced singular values near overflow',
1270  \$ / / ' Tests performed: ( A is dense, U and V are unitary,',
1271  \$ / 19x, ' S is an array, and Upartial, VTpartial, and',
1272  \$ / 19x, ' Spartial are partially computed U, VT and S),', / )
1273  9998 FORMAT( ' Tests performed with Test Threshold = ', f8.2,
1274  \$ / ' ZGESVD: ', /
1275  \$ ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1276  \$ / ' 2 = | I - U**T U | / ( M ulp ) ',
1277  \$ / ' 3 = | I - VT VT**T | / ( N ulp ) ',
1278  \$ / ' 4 = 0 if S contains min(M,N) nonnegative values in',
1279  \$ ' decreasing order, else 1/ulp',
1280  \$ / ' 5 = | U - Upartial | / ( M ulp )',
1281  \$ / ' 6 = | VT - VTpartial | / ( N ulp )',
1282  \$ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )',
1283  \$ / ' ZGESDD: ', /
1284  \$ ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1285  \$ / ' 9 = | I - U**T U | / ( M ulp ) ',
1286  \$ / '10 = | I - VT VT**T | / ( N ulp ) ',
1287  \$ / '11 = 0 if S contains min(M,N) nonnegative values in',
1288  \$ ' decreasing order, else 1/ulp',
1289  \$ / '12 = | U - Upartial | / ( M ulp )',
1290  \$ / '13 = | VT - VTpartial | / ( N ulp )',
1291  \$ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )',
1292  \$ / ' ZGESVJ: ', /
1293  \$ / '15 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1294  \$ / '16 = | I - U**T U | / ( M ulp ) ',
1295  \$ / '17 = | I - VT VT**T | / ( N ulp ) ',
1296  \$ / '18 = 0 if S contains min(M,N) nonnegative values in',
1297  \$ ' decreasing order, else 1/ulp',
1298  \$ / ' ZGESJV: ', /
1299  \$ / '19 = | A - U diag(S) VT | / ( |A| max(M,N) ulp )',
1300  \$ / '20 = | I - U**T U | / ( M ulp ) ',
1301  \$ / '21 = | I - VT VT**T | / ( N ulp ) ',
1302  \$ / '22 = 0 if S contains min(M,N) nonnegative values in',
1303  \$ ' decreasing order, else 1/ulp',
1304  \$ / ' ZGESVDX(V,V,A): ', /
1305  \$ '23 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1306  \$ / '24 = | I - U**T U | / ( M ulp ) ',
1307  \$ / '25 = | I - VT VT**T | / ( N ulp ) ',
1308  \$ / '26 = 0 if S contains min(M,N) nonnegative values in',
1309  \$ ' decreasing order, else 1/ulp',
1310  \$ / '27 = | U - Upartial | / ( M ulp )',
1311  \$ / '28 = | VT - VTpartial | / ( N ulp )',
1312  \$ / '29 = | S - Spartial | / ( min(M,N) ulp |S| )',
1313  \$ / ' ZGESVDX(V,V,I): ',
1314  \$ / '30 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
1315  \$ / '31 = | I - U**T U | / ( M ulp ) ',
1316  \$ / '32 = | I - VT VT**T | / ( N ulp ) ',
1317  \$ / ' ZGESVDX(V,V,V) ',
1318  \$ / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
1319  \$ / '34 = | I - U**T U | / ( M ulp ) ',
1320  \$ / '35 = | I - VT VT**T | / ( N ulp ) ',
1321  \$ ' ZGESVDQ(H,N,N,A,A',
1322  \$ / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1323  \$ / '37 = | I - U**T U | / ( M ulp ) ',
1324  \$ / '38 = | I - VT VT**T | / ( N ulp ) ',
1325  \$ / '39 = 0 if S contains min(M,N) nonnegative values in',
1326  \$ ' decreasing order, else 1/ulp',
1327  \$ / / )
1328  9997 FORMAT( ' M=', i5, ', N=', i5, ', type ', i1, ', IWS=', i1,
1329  \$ ', seed=', 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
1330  9996 FORMAT( ' ZDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1331  \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
1332  \$ i5, ')' )
1333  9995 FORMAT( ' ZDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1334  \$ i6, ', N=', i6, ', JTYPE=', i6, ', LSWORK=', i6, / 9x,
1335  \$ 'ISEED=(', 3( i5, ',' ), i5, ')' )
1336 *
1337  RETURN
1338 *
1339 * End of ZDRVBD
1340 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine zbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
ZBDT01
Definition: zbdt01.f:147
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:126
subroutine zunt03(RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK, RWORK, RESULT, INFO)
ZUNT03
Definition: zunt03.f:162
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
subroutine zgesvj(JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, LDV, CWORK, LWORK, RWORK, LRWORK, INFO)
ZGESVJ
Definition: zgesvj.f:351
subroutine zgejsv(JOBA, JOBU, JOBV, JOBR, JOBT, JOBP, M, N, A, LDA, SVA, U, LDU, V, LDV, CWORK, LWORK, RWORK, LRWORK, IWORK, INFO)
ZGEJSV
Definition: zgejsv.f:569
subroutine zgesvdx(JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, IL, IU, NS, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
ZGESVDX computes the singular value decomposition (SVD) for GE matrices
Definition: zgesvdx.f:270
subroutine zgesvdq(JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA, S, U, LDU, V, LDV, NUMRANK, IWORK, LIWORK, CWORK, LCWORK, RWORK, LRWORK, INFO)
ZGESVDQ computes the singular value decomposition (SVD) with a QR-Preconditioned QR SVD Method for GE...
Definition: zgesvdq.f:413
subroutine zgesdd(JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
ZGESDD
Definition: zgesdd.f:227
subroutine zgesvd(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO)
ZGESVD computes the singular value decomposition (SVD) for GE matrices
Definition: zgesvd.f:214
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zbdt05(M, N, A, LDA, S, NS, U, LDU, VT, LDVT, WORK, RESID)
ZBDT05
Definition: zbdt05.f:125
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
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