LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cdrvbd()

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

CDRVBD

Purpose:
``` CDRVBD checks the singular value decomposition (SVD) driver CGESVD,
CGESDD, CGESVJ, CGEJSV, CGESVDX, and CGESVDQ.

CGESVD and CGESDD 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 CDRVBD 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 CGESVD:

(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 CGESDD:

(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 CGESVDQ:

(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 CGESVJ:

(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 CGEJSV:

(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 CGESVDX( 'V', 'V', 'A' )/CGESVDX( '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 CGESVDX( '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 CGESVDX( '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, CDRVBD 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, CDRVBD 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 CDRVBD 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.``` [out] A ``` A is COMPLEX 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 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 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 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 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 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 REAL array, dimension (max(min(MM,NN))) Contains the computed singular values.``` [out] SSAV ``` SSAV is REAL array, dimension (max(min(MM,NN))) Contains another copy of the computed singular values.``` [out] E ``` E is REAL array, dimension (max(min(MM,NN))) Workspace for CGESVD.``` [out] WORK ` WORK is COMPLEX 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 REAL 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) ). -29: LWORK too small. If CLATMS, or CGESVD returns an error code, the absolute value of it is returned.```

Definition at line 397 of file cdrvbd.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  REAL THRESH
412 * ..
413 * .. Array Arguments ..
414  LOGICAL DOTYPE( * )
415  INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
416  REAL E( * ), RWORK( * ), S( * ), SSAV( * )
417  COMPLEX A( LDA, * ), ASAV( LDA, * ), U( LDU, * ),
418  \$ USAV( LDU, * ), VT( LDVT, * ),
419  \$ VTSAV( LDVT, * ), WORK( * )
420 * ..
421 *
422 * =====================================================================
423 *
424 * .. Parameters ..
425  REAL ZERO, ONE, TWO, HALF
426  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
427  \$ half = 0.5e0 )
428  COMPLEX CZERO, CONE
429  parameter( czero = ( 0.0e+0, 0.0e+0 ),
430  \$ cone = ( 1.0e+0, 0.0e+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  REAL ANORM, DIF, DIV, OVFL, RTUNFL, ULP, ULPINV,
443  \$ UNFL, VL, VU
444 * ..
445 * .. Local Scalars for CGESVDQ ..
446  INTEGER LIWORK, NUMRANK
447 * ..
448 * .. Local Arrays ..
449  CHARACTER CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
450  INTEGER IOLDSD( 4 ), ISEED2( 4 )
451  REAL RESULT( 39 )
452 * ..
453 * .. External Functions ..
454  REAL SLAMCH, SLARND
455  EXTERNAL slamch, slarnd
456 * ..
457 * .. External Subroutines ..
458  EXTERNAL alasvm, xerbla, cbdt01, cbdt05, cgesdd,
461 * ..
462 * .. Intrinsic Functions ..
463  INTRINSIC abs, real, 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( 'CDRVBD', -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 = slamch( 'S' )
539  ovfl = one / unfl
540  ulp = slamch( 'E' )
541  ulpinv = one / ulp
542  rtunfl = sqrt( unfl )
543 *
544 * Loop over sizes, types
545 *
546  nerrs = 0
547 *
548  DO 310 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 300 jtype = 1, mtypes
560  IF( .NOT.dotype( jtype ) )
561  \$ GO TO 300
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 claset( '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 claset( '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 clatms( m, n, 'U', iseed, 'N', s, 4, real( 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 clacpy( 'F', m, n, a, lda, asav, lda )
613 *
614 * Do for minimal and adequate (for blocking) workspace
615 *
616  DO 290 iwspc = 1, 4
617 *
618 * Test for CGESVD
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 clacpy( 'F', m, n, asav, lda, a, lda )
635  srnamt = 'CGESVD'
636  CALL cgesvd( '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 cbdt01( 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 cunt01( 'Columns', mnmin, m, usav, ldu, work,
651  \$ lwork, rwork, result( 2 ) )
652  CALL cunt01( '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 clacpy( 'F', m, n, asav, lda, a, lda )
679  srnamt = 'CGESVD'
680  CALL cgesvd( 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 cunt03( '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 cunt03( '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 cunt03( '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 cunt03( '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 cunt03( '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 cunt03( '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( real( mnmin )*ulp*s( 1 ),
727  \$ slamch( '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 CGESDD
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 clacpy( 'F', m, n, asav, lda, a, lda )
751  srnamt = 'CGESDD'
752  CALL cgesdd( '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 cbdt01( 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 cunt01( 'Columns', mnmin, m, usav, ldu, work,
767  \$ lwork, rwork, result( 9 ) )
768  CALL cunt01( '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 clacpy( 'F', m, n, asav, lda, a, lda )
791  srnamt = 'CGESDD'
792  CALL cgesdd( 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 cunt03( 'C', m, mnmin, m, mnmin, usav,
802  \$ ldu, a, lda, work, lwork, rwork,
803  \$ dif, iinfo )
804  ELSE
805  CALL cunt03( '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 cunt03( '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 cunt03( 'R', n, mnmin, n, mnmin, vtsav,
824  \$ ldvt, vt, ldvt, work, lwork,
825  \$ rwork, dif, iinfo )
826  ELSE
827  CALL cunt03( '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 cunt03( '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( real( mnmin )*ulp*s( 1 ),
843  \$ slamch( '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 *
855 * Test CGESVDQ
856 * Note: CGESVDQ only works for M >= N
857 *
858  result( 36 ) = zero
859  result( 37 ) = zero
860  result( 38 ) = zero
861  result( 39 ) = zero
862 *
863  IF( m.GE.n ) THEN
864  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
865  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
866  lswork = min( lswork, lwork )
867  lswork = max( lswork, 1 )
868  IF( iwspc.EQ.4 )
869  \$ lswork = lwork
870 *
871  CALL clacpy( 'F', m, n, asav, lda, a, lda )
872  srnamt = 'CGESVDQ'
873 *
874  lrwork = max(2, m, 5*n)
875  liwork = max( n, 1 )
876  CALL cgesvdq( 'H', 'N', 'N', 'A', 'A',
877  \$ m, n, a, lda, ssav, usav, ldu,
878  \$ vtsav, ldvt, numrank, iwork, liwork,
879  \$ work, lwork, rwork, lrwork, iinfo )
880 *
881  IF( iinfo.NE.0 ) THEN
882  WRITE( nounit, fmt = 9995 )'CGESVDQ', iinfo, m, n,
883  \$ jtype, lswork, ioldsd
884  info = abs( iinfo )
885  RETURN
886  END IF
887 *
888 * Do tests 36--39
889 *
890  CALL cbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
891  \$ vtsav, ldvt, work, rwork, result( 36 ) )
892  IF( m.NE.0 .AND. n.NE.0 ) THEN
893  CALL cunt01( 'Columns', m, m, usav, ldu, work,
894  \$ lwork, rwork, result( 37 ) )
895  CALL cunt01( 'Rows', n, n, vtsav, ldvt, work,
896  \$ lwork, rwork, result( 38 ) )
897  END IF
898  result( 39 ) = zero
899  DO 199 i = 1, mnmin - 1
900  IF( ssav( i ).LT.ssav( i+1 ) )
901  \$ result( 39 ) = ulpinv
902  IF( ssav( i ).LT.zero )
903  \$ result( 39 ) = ulpinv
904  199 CONTINUE
905  IF( mnmin.GE.1 ) THEN
906  IF( ssav( mnmin ).LT.zero )
907  \$ result( 39 ) = ulpinv
908  END IF
909  END IF
910 *
911 * Test CGESVJ
912 * Note: CGESVJ only works for M >= N
913 *
914  result( 15 ) = zero
915  result( 16 ) = zero
916  result( 17 ) = zero
917  result( 18 ) = zero
918 *
919  IF( m.GE.n ) THEN
920  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
921  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
922  lswork = min( lswork, lwork )
923  lswork = max( lswork, 1 )
924  lrwork = max(6,n)
925  IF( iwspc.EQ.4 )
926  \$ lswork = lwork
927 *
928  CALL clacpy( 'F', m, n, asav, lda, usav, lda )
929  srnamt = 'CGESVJ'
930  CALL cgesvj( 'G', 'U', 'V', m, n, usav, lda, ssav,
931  & 0, a, ldvt, work, lwork, rwork,
932  & lrwork, iinfo )
933 *
934 * CGESVJ returns V not VH
935 *
936  DO j=1,n
937  DO i=1,n
938  vtsav(j,i) = conjg(a(i,j))
939  END DO
940  END DO
941 *
942  IF( iinfo.NE.0 ) THEN
943  WRITE( nounit, fmt = 9995 )'GESVJ', iinfo, m, n,
944  \$ jtype, lswork, ioldsd
945  info = abs( iinfo )
946  RETURN
947  END IF
948 *
949 * Do tests 15--18
950 *
951  CALL cbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
952  \$ vtsav, ldvt, work, rwork, result( 15 ) )
953  IF( m.NE.0 .AND. n.NE.0 ) THEN
954  CALL cunt01( 'Columns', m, m, usav, ldu, work,
955  \$ lwork, rwork, result( 16 ) )
956  CALL cunt01( 'Rows', n, n, vtsav, ldvt, work,
957  \$ lwork, rwork, result( 17 ) )
958  END IF
959  result( 18 ) = zero
960  DO 131 i = 1, mnmin - 1
961  IF( ssav( i ).LT.ssav( i+1 ) )
962  \$ result( 18 ) = ulpinv
963  IF( ssav( i ).LT.zero )
964  \$ result( 18 ) = ulpinv
965  131 CONTINUE
966  IF( mnmin.GE.1 ) THEN
967  IF( ssav( mnmin ).LT.zero )
968  \$ result( 18 ) = ulpinv
969  END IF
970  END IF
971 *
972 * Test CGEJSV
973 * Note: CGEJSV only works for M >= N
974 *
975  result( 19 ) = zero
976  result( 20 ) = zero
977  result( 21 ) = zero
978  result( 22 ) = zero
979  IF( m.GE.n ) THEN
980  iwtmp = 2*mnmin*mnmin + 2*mnmin + max( m, n )
981  lswork = iwtmp + ( iwspc-1 )*( lwork-iwtmp ) / 3
982  lswork = min( lswork, lwork )
983  lswork = max( lswork, 1 )
984  IF( iwspc.EQ.4 )
985  \$ lswork = lwork
986  lrwork = max( 7, n + 2*m)
987 *
988  CALL clacpy( 'F', m, n, asav, lda, vtsav, lda )
989  srnamt = 'CGEJSV'
990  CALL cgejsv( 'G', 'U', 'V', 'R', 'N', 'N',
991  & m, n, vtsav, lda, ssav, usav, ldu, a, ldvt,
992  & work, lwork, rwork,
993  & lrwork, iwork, iinfo )
994 *
995 * CGEJSV returns V not VH
996 *
997  DO 133 j=1,n
998  DO 132 i=1,n
999  vtsav(j,i) = conjg(a(i,j))
1000  132 END DO
1001  133 END DO
1002 *
1003  IF( iinfo.NE.0 ) THEN
1004  WRITE( nounit, fmt = 9995 )'GEJSV', iinfo, m, n,
1005  \$ jtype, lswork, ioldsd
1006  info = abs( iinfo )
1007  RETURN
1008  END IF
1009 *
1010 * Do tests 19--22
1011 *
1012  CALL cbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
1013  \$ vtsav, ldvt, work, rwork, result( 19 ) )
1014  IF( m.NE.0 .AND. n.NE.0 ) THEN
1015  CALL cunt01( 'Columns', m, m, usav, ldu, work,
1016  \$ lwork, rwork, result( 20 ) )
1017  CALL cunt01( 'Rows', n, n, vtsav, ldvt, work,
1018  \$ lwork, rwork, result( 21 ) )
1019  END IF
1020  result( 22 ) = zero
1021  DO 134 i = 1, mnmin - 1
1022  IF( ssav( i ).LT.ssav( i+1 ) )
1023  \$ result( 22 ) = ulpinv
1024  IF( ssav( i ).LT.zero )
1025  \$ result( 22 ) = ulpinv
1026  134 CONTINUE
1027  IF( mnmin.GE.1 ) THEN
1028  IF( ssav( mnmin ).LT.zero )
1029  \$ result( 22 ) = ulpinv
1030  END IF
1031  END IF
1032 *
1033 * Test CGESVDX
1034 *
1035 * Factorize A
1036 *
1037  CALL clacpy( 'F', m, n, asav, lda, a, lda )
1038  srnamt = 'CGESVDX'
1039  CALL cgesvdx( 'V', 'V', 'A', m, n, a, lda,
1040  \$ vl, vu, il, iu, ns, ssav, usav, ldu,
1041  \$ vtsav, ldvt, work, lwork, rwork,
1042  \$ iwork, iinfo )
1043  IF( iinfo.NE.0 ) THEN
1044  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1045  \$ jtype, lswork, ioldsd
1046  info = abs( iinfo )
1047  RETURN
1048  END IF
1049 *
1050 * Do tests 1--4
1051 *
1052  result( 23 ) = zero
1053  result( 24 ) = zero
1054  result( 25 ) = zero
1055  CALL cbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
1056  \$ vtsav, ldvt, work, rwork, result( 23 ) )
1057  IF( m.NE.0 .AND. n.NE.0 ) THEN
1058  CALL cunt01( 'Columns', mnmin, m, usav, ldu, work,
1059  \$ lwork, rwork, result( 24 ) )
1060  CALL cunt01( 'Rows', mnmin, n, vtsav, ldvt, work,
1061  \$ lwork, rwork, result( 25 ) )
1062  END IF
1063  result( 26 ) = zero
1064  DO 140 i = 1, mnmin - 1
1065  IF( ssav( i ).LT.ssav( i+1 ) )
1066  \$ result( 26 ) = ulpinv
1067  IF( ssav( i ).LT.zero )
1068  \$ result( 26 ) = ulpinv
1069  140 CONTINUE
1070  IF( mnmin.GE.1 ) THEN
1071  IF( ssav( mnmin ).LT.zero )
1072  \$ result( 26 ) = ulpinv
1073  END IF
1074 *
1075 * Do partial SVDs, comparing to SSAV, USAV, and VTSAV
1076 *
1077  result( 27 ) = zero
1078  result( 28 ) = zero
1079  result( 29 ) = zero
1080  DO 170 iju = 0, 1
1081  DO 160 ijvt = 0, 1
1082  IF( ( iju.EQ.0 .AND. ijvt.EQ.0 ) .OR.
1083  \$ ( iju.EQ.1 .AND. ijvt.EQ.1 ) ) GO TO 160
1084  jobu = cjobv( iju+1 )
1085  jobvt = cjobv( ijvt+1 )
1086  range = cjobr( 1 )
1087  CALL clacpy( 'F', m, n, asav, lda, a, lda )
1088  srnamt = 'CGESVDX'
1089  CALL cgesvdx( jobu, jobvt, 'A', m, n, a, lda,
1090  \$ vl, vu, il, iu, ns, ssav, u, ldu,
1091  \$ vt, ldvt, work, lwork, rwork,
1092  \$ iwork, iinfo )
1093 *
1094 * Compare U
1095 *
1096  dif = zero
1097  IF( m.GT.0 .AND. n.GT.0 ) THEN
1098  IF( iju.EQ.1 ) THEN
1099  CALL cunt03( 'C', m, mnmin, m, mnmin, usav,
1100  \$ ldu, u, ldu, work, lwork, rwork,
1101  \$ dif, iinfo )
1102  END IF
1103  END IF
1104  result( 27 ) = max( result( 27 ), dif )
1105 *
1106 * Compare VT
1107 *
1108  dif = zero
1109  IF( m.GT.0 .AND. n.GT.0 ) THEN
1110  IF( ijvt.EQ.1 ) THEN
1111  CALL cunt03( 'R', n, mnmin, n, mnmin, vtsav,
1112  \$ ldvt, vt, ldvt, work, lwork,
1113  \$ rwork, dif, iinfo )
1114  END IF
1115  END IF
1116  result( 28 ) = max( result( 28 ), dif )
1117 *
1118 * Compare S
1119 *
1120  dif = zero
1121  div = max( real( mnmin )*ulp*s( 1 ),
1122  \$ slamch( 'Safe minimum' ) )
1123  DO 150 i = 1, mnmin - 1
1124  IF( ssav( i ).LT.ssav( i+1 ) )
1125  \$ dif = ulpinv
1126  IF( ssav( i ).LT.zero )
1127  \$ dif = ulpinv
1128  dif = max( dif, abs( ssav( i )-s( i ) ) / div )
1129  150 CONTINUE
1130  result( 29) = max( result( 29 ), dif )
1131  160 CONTINUE
1132  170 CONTINUE
1133 *
1134 * Do tests 8--10
1135 *
1136  DO 180 i = 1, 4
1137  iseed2( i ) = iseed( i )
1138  180 CONTINUE
1139  IF( mnmin.LE.1 ) THEN
1140  il = 1
1141  iu = max( 1, mnmin )
1142  ELSE
1143  il = 1 + int( ( mnmin-1 )*slarnd( 1, iseed2 ) )
1144  iu = 1 + int( ( mnmin-1 )*slarnd( 1, iseed2 ) )
1145  IF( iu.LT.il ) THEN
1146  itemp = iu
1147  iu = il
1148  il = itemp
1149  END IF
1150  END IF
1151  CALL clacpy( 'F', m, n, asav, lda, a, lda )
1152  srnamt = 'CGESVDX'
1153  CALL cgesvdx( 'V', 'V', 'I', m, n, a, lda,
1154  \$ vl, vu, il, iu, nsi, s, u, ldu,
1155  \$ vt, ldvt, work, lwork, rwork,
1156  \$ iwork, iinfo )
1157  IF( iinfo.NE.0 ) THEN
1158  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1159  \$ jtype, lswork, ioldsd
1160  info = abs( iinfo )
1161  RETURN
1162  END IF
1163 *
1164  result( 30 ) = zero
1165  result( 31 ) = zero
1166  result( 32 ) = zero
1167  CALL cbdt05( m, n, asav, lda, s, nsi, u, ldu,
1168  \$ vt, ldvt, work, result( 30 ) )
1169  IF( m.NE.0 .AND. n.NE.0 ) THEN
1170  CALL cunt01( 'Columns', m, nsi, u, ldu, work,
1171  \$ lwork, rwork, result( 31 ) )
1172  CALL cunt01( 'Rows', nsi, n, vt, ldvt, work,
1173  \$ lwork, rwork, result( 32 ) )
1174  END IF
1175 *
1176 * Do tests 11--13
1177 *
1178  IF( mnmin.GT.0 .AND. nsi.GT.1 ) THEN
1179  IF( il.NE.1 ) THEN
1180  vu = ssav( il ) +
1181  \$ max( half*abs( ssav( il )-ssav( il-1 ) ),
1182  \$ ulp*anorm, two*rtunfl )
1183  ELSE
1184  vu = ssav( 1 ) +
1185  \$ max( half*abs( ssav( ns )-ssav( 1 ) ),
1186  \$ ulp*anorm, two*rtunfl )
1187  END IF
1188  IF( iu.NE.ns ) THEN
1189  vl = ssav( iu ) - max( ulp*anorm, two*rtunfl,
1190  \$ half*abs( ssav( iu+1 )-ssav( iu ) ) )
1191  ELSE
1192  vl = ssav( ns ) - max( ulp*anorm, two*rtunfl,
1193  \$ half*abs( ssav( ns )-ssav( 1 ) ) )
1194  END IF
1195  vl = max( vl,zero )
1196  vu = max( vu,zero )
1197  IF( vl.GE.vu ) vu = max( vu*2, vu+vl+half )
1198  ELSE
1199  vl = zero
1200  vu = one
1201  END IF
1202  CALL clacpy( 'F', m, n, asav, lda, a, lda )
1203  srnamt = 'CGESVDX'
1204  CALL cgesvdx( 'V', 'V', 'V', m, n, a, lda,
1205  \$ vl, vu, il, iu, nsv, s, u, ldu,
1206  \$ vt, ldvt, work, lwork, rwork,
1207  \$ iwork, iinfo )
1208  IF( iinfo.NE.0 ) THEN
1209  WRITE( nounit, fmt = 9995 )'GESVDX', iinfo, m, n,
1210  \$ jtype, lswork, ioldsd
1211  info = abs( iinfo )
1212  RETURN
1213  END IF
1214 *
1215  result( 33 ) = zero
1216  result( 34 ) = zero
1217  result( 35 ) = zero
1218  CALL cbdt05( m, n, asav, lda, s, nsv, u, ldu,
1219  \$ vt, ldvt, work, result( 33 ) )
1220  IF( m.NE.0 .AND. n.NE.0 ) THEN
1221  CALL cunt01( 'Columns', m, nsv, u, ldu, work,
1222  \$ lwork, rwork, result( 34 ) )
1223  CALL cunt01( 'Rows', nsv, n, vt, ldvt, work,
1224  \$ lwork, rwork, result( 35 ) )
1225  END IF
1226 *
1227 * End of Loop -- Check for RESULT(j) > THRESH
1228 *
1229  ntest = 0
1230  nfail = 0
1231  DO 190 j = 1, 39
1232  IF( result( j ).GE.zero )
1233  \$ ntest = ntest + 1
1234  IF( result( j ).GE.thresh )
1235  \$ nfail = nfail + 1
1236  190 CONTINUE
1237 *
1238  IF( nfail.GT.0 )
1239  \$ ntestf = ntestf + 1
1240  IF( ntestf.EQ.1 ) THEN
1241  WRITE( nounit, fmt = 9999 )
1242  WRITE( nounit, fmt = 9998 )thresh
1243  ntestf = 2
1244  END IF
1245 *
1246  DO 200 j = 1, 39
1247  IF( result( j ).GE.thresh ) THEN
1248  WRITE( nounit, fmt = 9997 )m, n, jtype, iwspc,
1249  \$ ioldsd, j, result( j )
1250  END IF
1251  200 CONTINUE
1252 *
1253  nerrs = nerrs + nfail
1254  ntestt = ntestt + ntest
1255 *
1256  290 CONTINUE
1257 *
1258  300 CONTINUE
1259  310 CONTINUE
1260 *
1261 * Summary
1262 *
1263  CALL alasvm( 'CBD', nounit, nerrs, ntestt, 0 )
1264 *
1265  9999 FORMAT( ' SVD -- Complex Singular Value Decomposition Driver ',
1266  \$ / ' Matrix types (see CDRVBD for details):',
1267  \$ / / ' 1 = Zero matrix', / ' 2 = Identity matrix',
1268  \$ / ' 3 = Evenly spaced singular values near 1',
1269  \$ / ' 4 = Evenly spaced singular values near underflow',
1270  \$ / ' 5 = Evenly spaced singular values near overflow',
1271  \$ / / ' Tests performed: ( A is dense, U and V are unitary,',
1272  \$ / 19x, ' S is an array, and Upartial, VTpartial, and',
1273  \$ / 19x, ' Spartial are partially computed U, VT and S),', / )
1274  9998 FORMAT( ' Tests performed with Test Threshold = ', f8.2,
1275  \$ / ' CGESVD: ', /
1276  \$ ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1277  \$ / ' 2 = | I - U**T U | / ( M ulp ) ',
1278  \$ / ' 3 = | I - VT VT**T | / ( N ulp ) ',
1279  \$ / ' 4 = 0 if S contains min(M,N) nonnegative values in',
1280  \$ ' decreasing order, else 1/ulp',
1281  \$ / ' 5 = | U - Upartial | / ( M ulp )',
1282  \$ / ' 6 = | VT - VTpartial | / ( N ulp )',
1283  \$ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )',
1284  \$ / ' CGESDD: ', /
1285  \$ ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1286  \$ / ' 9 = | I - U**T U | / ( M ulp ) ',
1287  \$ / '10 = | I - VT VT**T | / ( N ulp ) ',
1288  \$ / '11 = 0 if S contains min(M,N) nonnegative values in',
1289  \$ ' decreasing order, else 1/ulp',
1290  \$ / '12 = | U - Upartial | / ( M ulp )',
1291  \$ / '13 = | VT - VTpartial | / ( N ulp )',
1292  \$ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )',
1293  \$ / ' CGESVJ: ', /
1294  \$ / '15 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1295  \$ / '16 = | I - U**T U | / ( M ulp ) ',
1296  \$ / '17 = | I - VT VT**T | / ( N ulp ) ',
1297  \$ / '18 = 0 if S contains min(M,N) nonnegative values in',
1298  \$ ' decreasing order, else 1/ulp',
1299  \$ / ' CGESJV: ', /
1300  \$ / '19 = | A - U diag(S) VT | / ( |A| max(M,N) ulp )',
1301  \$ / '20 = | I - U**T U | / ( M ulp ) ',
1302  \$ / '21 = | I - VT VT**T | / ( N ulp ) ',
1303  \$ / '22 = 0 if S contains min(M,N) nonnegative values in',
1304  \$ ' decreasing order, else 1/ulp',
1305  \$ / ' CGESVDX(V,V,A): ', /
1306  \$ '23 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1307  \$ / '24 = | I - U**T U | / ( M ulp ) ',
1308  \$ / '25 = | I - VT VT**T | / ( N ulp ) ',
1309  \$ / '26 = 0 if S contains min(M,N) nonnegative values in',
1310  \$ ' decreasing order, else 1/ulp',
1311  \$ / '27 = | U - Upartial | / ( M ulp )',
1312  \$ / '28 = | VT - VTpartial | / ( N ulp )',
1313  \$ / '29 = | S - Spartial | / ( min(M,N) ulp |S| )',
1314  \$ / ' CGESVDX(V,V,I): ',
1315  \$ / '30 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
1316  \$ / '31 = | I - U**T U | / ( M ulp ) ',
1317  \$ / '32 = | I - VT VT**T | / ( N ulp ) ',
1318  \$ / ' CGESVDX(V,V,V) ',
1319  \$ / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp )',
1320  \$ / '34 = | I - U**T U | / ( M ulp ) ',
1321  \$ / '35 = | I - VT VT**T | / ( N ulp ) ',
1322  \$ ' CGESVDQ(H,N,N,A,A',
1323  \$ / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1324  \$ / '37 = | I - U**T U | / ( M ulp ) ',
1325  \$ / '38 = | I - VT VT**T | / ( N ulp ) ',
1326  \$ / '39 = 0 if S contains min(M,N) nonnegative values in',
1327  \$ ' decreasing order, else 1/ulp',
1328  \$ / / )
1329  9997 FORMAT( ' M=', i5, ', N=', i5, ', type ', i1, ', IWS=', i1,
1330  \$ ', seed=', 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
1331  9996 FORMAT( ' CDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1332  \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
1333  \$ i5, ')' )
1334  9995 FORMAT( ' CDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1335  \$ i6, ', N=', i6, ', JTYPE=', i6, ', LSWORK=', i6, / 9x,
1336  \$ 'ISEED=(', 3( i5, ',' ), i5, ')' )
1337 *
1338  RETURN
1339 *
1340 * End of CDRVBD
1341 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine cbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
CBDT01
Definition: cbdt01.f:147
subroutine cunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
CUNT01
Definition: cunt01.f:126
subroutine cunt03(RC, MU, MV, N, K, U, LDU, V, LDV, WORK, LWORK, RWORK, RESULT, INFO)
CUNT03
Definition: cunt03.f:162
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:332
subroutine cgesvj(JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, LDV, CWORK, LWORK, RWORK, LRWORK, INFO)
CGESVJ
Definition: cgesvj.f:351
subroutine cgesvd(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO)
CGESVD computes the singular value decomposition (SVD) for GE matrices
Definition: cgesvd.f:214
subroutine cgejsv(JOBA, JOBU, JOBV, JOBR, JOBT, JOBP, M, N, A, LDA, SVA, U, LDU, V, LDV, CWORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CGEJSV
Definition: cgejsv.f:568
subroutine cgesdd(JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
CGESDD
Definition: cgesdd.f:227
subroutine cgesvdq(JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA, S, U, LDU, V, LDV, NUMRANK, IWORK, LIWORK, CWORK, LCWORK, RWORK, LRWORK, INFO)
CGESVDQ computes the singular value decomposition (SVD) with a QR-Preconditioned QR SVD Method for GE...
Definition: cgesvdq.f:413
subroutine cgesvdx(JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, IL, IU, NS, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)
CGESVDX computes the singular value decomposition (SVD) for GE matrices
Definition: cgesvdx.f:270
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cbdt05(M, N, A, LDA, S, NS, U, LDU, VT, LDVT, WORK, RESID)
CBDT05
Definition: cbdt05.f:125
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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