LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ sdrvbd()

 subroutine sdrvbd ( integer nsizes, integer, dimension( * ) mm, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, real, dimension( lda, * ) a, integer lda, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( lda, * ) asav, real, dimension( ldu, * ) usav, real, dimension( ldvt, * ) vtsav, real, dimension( * ) s, real, dimension( * ) ssav, real, dimension( * ) e, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer nout, integer info )

SDRVBD

Purpose:
``` SDRVBD checks the singular value decomposition (SVD) drivers
SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.

Both SGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
orthogonal 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 SDRVBD 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 SGESVD:

(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 SGESDD:

(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 SGESVDQ:

(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 SGESVJ:

(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 SGEJSV:

(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 SGESVDX( 'V', 'V', 'A' )/SGESVDX( '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 SGESVDX( '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 SGESVDX( '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 orthogonal 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 matrix sizes (M,N) contained in the vectors MM and NN.``` [in] MM ``` MM is INTEGER array, dimension (NSIZES) The values of the matrix row dimension M.``` [in] NN ``` NN is INTEGER array, dimension (NSIZES) The values of the matrix column dimension N.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, SDRVBD 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, 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. On exit, ISEED is changed and can be used in the next call to SDRVBD to continue the same random number sequence.``` [in] THRESH ``` THRESH is REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. The test ratios are scaled to be O(1), so THRESH should be a small multiple of 1, e.g., 10 or 100. To have every test ratio printed, use THRESH = 0.``` [out] A ``` A is REAL array, dimension (LDA,NMAX) where NMAX is the maximum value of N in NN.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,MMAX), where MMAX is the maximum value of M in MM.``` [out] U ` U is REAL array, dimension (LDU,MMAX)` [in] LDU ``` LDU is INTEGER The leading dimension of the array U. LDU >= max(1,MMAX).``` [out] VT ` VT is REAL array, dimension (LDVT,NMAX)` [in] LDVT ``` LDVT is INTEGER The leading dimension of the array VT. LDVT >= max(1,NMAX).``` [out] ASAV ` ASAV is REAL array, dimension (LDA,NMAX)` [out] USAV ` USAV is REAL array, dimension (LDU,MMAX)` [out] VTSAV ` VTSAV is REAL array, dimension (LDVT,NMAX)` [out] S ``` S is REAL array, dimension (max(min(MM,NN)))``` [out] SSAV ``` SSAV is REAL array, dimension (max(min(MM,NN)))``` [out] E ``` E is REAL array, dimension (max(min(MM,NN)))``` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )``` [out] IWORK ` IWORK is INTEGER array, dimension at least 8*min(M,N)` [in] NOUT ``` NOUT 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 SLATMS, or SGESVD returns an error code, the absolute value of it is returned.```

Definition at line 363 of file sdrvbd.f.

366*
367* -- LAPACK test routine --
368* -- LAPACK is a software package provided by Univ. of Tennessee, --
369* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
370*
371 IMPLICIT NONE
372*
373* .. Scalar Arguments ..
374 INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
375 \$ NTYPES
376 REAL THRESH
377* ..
378* .. Array Arguments ..
379 LOGICAL DOTYPE( * )
380 INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
381 REAL A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
382 \$ SSAV( * ), U( LDU, * ), USAV( LDU, * ),
383 \$ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
384* ..
385*
386* =====================================================================
387*
388* .. Parameters ..
389 REAL ZERO, ONE, TWO, HALF
390 parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
391 \$ half = 0.5e0 )
392 INTEGER MAXTYP
393 parameter( maxtyp = 5 )
394* ..
395* .. Local Scalars ..
397 CHARACTER JOBQ, JOBU, JOBVT, RANGE
398 CHARACTER*3 PATH
399 INTEGER I, IINFO, IJQ, IJU, IJVT, IL,IU, IWS, IWTMP,
400 \$ ITEMP, J, JSIZE, JTYPE, LSWORK, M, MINWRK,
401 \$ MMAX, MNMAX, MNMIN, MTYPES, N, NFAIL,
402 \$ NMAX, NS, NSI, NSV, NTEST
403 REAL ANORM, DIF, DIV, OVFL, RTUNFL, ULP,
404 \$ ULPINV, UNFL, VL, VU
405* ..
406* .. Local Scalars for DGESVDQ ..
407 INTEGER LIWORK, LRWORK, NUMRANK
408* ..
409* .. Local Arrays for DGESVDQ ..
410 REAL RWORK( 2 )
411* ..
412* .. Local Arrays ..
413 CHARACTER CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
414 INTEGER IOLDSD( 4 ), ISEED2( 4 )
415 REAL RESULT( 39 )
416* ..
417* .. External Functions ..
418 REAL SLAMCH, SLARND
419 EXTERNAL slamch, slarnd
420* ..
421* .. External Subroutines ..
422 EXTERNAL alasvm, sbdt01, sgejsv, sgesdd, sgesvd,
425* ..
426* .. Intrinsic Functions ..
427 INTRINSIC abs, real, int, max, min
428* ..
429* .. Scalars in Common ..
430 LOGICAL LERR, OK
431 CHARACTER*32 SRNAMT
432 INTEGER INFOT, NUNIT
433* ..
434* .. Common blocks ..
435 COMMON / infoc / infot, nunit, ok, lerr
436 COMMON / srnamc / srnamt
437* ..
438* .. Data statements ..
439 DATA cjob / 'N', 'O', 'S', 'A' /
440 DATA cjobr / 'A', 'V', 'I' /
441 DATA cjobv / 'N', 'V' /
442* ..
443* .. Executable Statements ..
444*
445* Check for errors
446*
447 info = 0
448 badmm = .false.
449 badnn = .false.
450 mmax = 1
451 nmax = 1
452 mnmax = 1
453 minwrk = 1
454 DO 10 j = 1, nsizes
455 mmax = max( mmax, mm( j ) )
456 IF( mm( j ).LT.0 )
457 \$ badmm = .true.
458 nmax = max( nmax, nn( j ) )
459 IF( nn( j ).LT.0 )
460 \$ badnn = .true.
461 mnmax = max( mnmax, min( mm( j ), nn( j ) ) )
462 minwrk = max( minwrk, max( 3*min( mm( j ),
463 \$ nn( j ) )+max( mm( j ), nn( j ) ), 5*min( mm( j ),
464 \$ nn( j )-4 ) )+2*min( mm( j ), nn( j ) )**2 )
465 10 CONTINUE
466*
467* Check for errors
468*
469 IF( nsizes.LT.0 ) THEN
470 info = -1
471 ELSE IF( badmm ) THEN
472 info = -2
473 ELSE IF( badnn ) THEN
474 info = -3
475 ELSE IF( ntypes.LT.0 ) THEN
476 info = -4
477 ELSE IF( lda.LT.max( 1, mmax ) ) THEN
478 info = -10
479 ELSE IF( ldu.LT.max( 1, mmax ) ) THEN
480 info = -12
481 ELSE IF( ldvt.LT.max( 1, nmax ) ) THEN
482 info = -14
483 ELSE IF( minwrk.GT.lwork ) THEN
484 info = -21
485 END IF
486*
487 IF( info.NE.0 ) THEN
488 CALL xerbla( 'SDRVBD', -info )
489 RETURN
490 END IF
491*
492* Initialize constants
493*
494 path( 1: 1 ) = 'Single precision'
495 path( 2: 3 ) = 'BD'
496 nfail = 0
497 ntest = 0
498 unfl = slamch( 'Safe minimum' )
499 ovfl = one / unfl
500 ulp = slamch( 'Precision' )
501 rtunfl = sqrt( unfl )
502 ulpinv = one / ulp
503 infot = 0
504*
505* Loop over sizes, types
506*
507 DO 240 jsize = 1, nsizes
508 m = mm( jsize )
509 n = nn( jsize )
510 mnmin = min( m, n )
511*
512 IF( nsizes.NE.1 ) THEN
513 mtypes = min( maxtyp, ntypes )
514 ELSE
515 mtypes = min( maxtyp+1, ntypes )
516 END IF
517*
518 DO 230 jtype = 1, mtypes
519 IF( .NOT.dotype( jtype ) )
520 \$ GO TO 230
521*
522 DO 20 j = 1, 4
523 ioldsd( j ) = iseed( j )
524 20 CONTINUE
525*
526* Compute "A"
527*
528 IF( mtypes.GT.maxtyp )
529 \$ GO TO 30
530*
531 IF( jtype.EQ.1 ) THEN
532*
533* Zero matrix
534*
535 CALL slaset( 'Full', m, n, zero, zero, a, lda )
536*
537 ELSE IF( jtype.EQ.2 ) THEN
538*
539* Identity matrix
540*
541 CALL slaset( 'Full', m, n, zero, one, a, lda )
542*
543 ELSE
544*
545* (Scaled) random matrix
546*
547 IF( jtype.EQ.3 )
548 \$ anorm = one
549 IF( jtype.EQ.4 )
550 \$ anorm = unfl / ulp
551 IF( jtype.EQ.5 )
552 \$ anorm = ovfl*ulp
553 CALL slatms( m, n, 'U', iseed, 'N', s, 4, real( mnmin ),
554 \$ anorm, m-1, n-1, 'N', a, lda, work, iinfo )
555 IF( iinfo.NE.0 ) THEN
556 WRITE( nout, fmt = 9996 )'Generator', iinfo, m, n,
557 \$ jtype, ioldsd
558 info = abs( iinfo )
559 RETURN
560 END IF
561 END IF
562*
563 30 CONTINUE
564 CALL slacpy( 'F', m, n, a, lda, asav, lda )
565*
566* Do for minimal and adequate (for blocking) workspace
567*
568 DO 220 iws = 1, 4
569*
570 DO 40 j = 1, 32
571 result( j ) = -one
572 40 CONTINUE
573*
574* Test SGESVD: Factorize A
575*
576 iwtmp = max( 3*min( m, n )+max( m, n ), 5*min( m, n ) )
577 lswork = iwtmp + ( iws-1 )*( lwork-iwtmp ) / 3
578 lswork = min( lswork, lwork )
579 lswork = max( lswork, 1 )
580 IF( iws.EQ.4 )
581 \$ lswork = lwork
582*
583 IF( iws.GT.1 )
584 \$ CALL slacpy( 'F', m, n, asav, lda, a, lda )
585 srnamt = 'SGESVD'
586 CALL sgesvd( 'A', 'A', m, n, a, lda, ssav, usav, ldu,
587 \$ vtsav, ldvt, work, lswork, iinfo )
588 IF( iinfo.NE.0 ) THEN
589 WRITE( nout, fmt = 9995 )'GESVD', iinfo, m, n, jtype,
590 \$ lswork, ioldsd
591 info = abs( iinfo )
592 RETURN
593 END IF
594*
595* Do tests 1--4
596*
597 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
598 \$ vtsav, ldvt, work, result( 1 ) )
599 IF( m.NE.0 .AND. n.NE.0 ) THEN
600 CALL sort01( 'Columns', m, m, usav, ldu, work, lwork,
601 \$ result( 2 ) )
602 CALL sort01( 'Rows', n, n, vtsav, ldvt, work, lwork,
603 \$ result( 3 ) )
604 END IF
605 result( 4 ) = zero
606 DO 50 i = 1, mnmin - 1
607 IF( ssav( i ).LT.ssav( i+1 ) )
608 \$ result( 4 ) = ulpinv
609 IF( ssav( i ).LT.zero )
610 \$ result( 4 ) = ulpinv
611 50 CONTINUE
612 IF( mnmin.GE.1 ) THEN
613 IF( ssav( mnmin ).LT.zero )
614 \$ result( 4 ) = ulpinv
615 END IF
616*
617* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
618*
619 result( 5 ) = zero
620 result( 6 ) = zero
621 result( 7 ) = zero
622 DO 80 iju = 0, 3
623 DO 70 ijvt = 0, 3
624 IF( ( iju.EQ.3 .AND. ijvt.EQ.3 ) .OR.
625 \$ ( iju.EQ.1 .AND. ijvt.EQ.1 ) )GO TO 70
626 jobu = cjob( iju+1 )
627 jobvt = cjob( ijvt+1 )
628 CALL slacpy( 'F', m, n, asav, lda, a, lda )
629 srnamt = 'SGESVD'
630 CALL sgesvd( jobu, jobvt, m, n, a, lda, s, u, ldu,
631 \$ vt, ldvt, work, lswork, iinfo )
632*
633* Compare U
634*
635 dif = zero
636 IF( m.GT.0 .AND. n.GT.0 ) THEN
637 IF( iju.EQ.1 ) THEN
638 CALL sort03( 'C', m, mnmin, m, mnmin, usav,
639 \$ ldu, a, lda, work, lwork, dif,
640 \$ iinfo )
641 ELSE IF( iju.EQ.2 ) THEN
642 CALL sort03( 'C', m, mnmin, m, mnmin, usav,
643 \$ ldu, u, ldu, work, lwork, dif,
644 \$ iinfo )
645 ELSE IF( iju.EQ.3 ) THEN
646 CALL sort03( 'C', m, m, m, mnmin, usav, ldu,
647 \$ u, ldu, work, lwork, dif,
648 \$ iinfo )
649 END IF
650 END IF
651 result( 5 ) = max( result( 5 ), dif )
652*
653* Compare VT
654*
655 dif = zero
656 IF( m.GT.0 .AND. n.GT.0 ) THEN
657 IF( ijvt.EQ.1 ) THEN
658 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
659 \$ ldvt, a, lda, work, lwork, dif,
660 \$ iinfo )
661 ELSE IF( ijvt.EQ.2 ) THEN
662 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
663 \$ ldvt, vt, ldvt, work, lwork,
664 \$ dif, iinfo )
665 ELSE IF( ijvt.EQ.3 ) THEN
666 CALL sort03( 'R', n, n, n, mnmin, vtsav,
667 \$ ldvt, vt, ldvt, work, lwork,
668 \$ dif, iinfo )
669 END IF
670 END IF
671 result( 6 ) = max( result( 6 ), dif )
672*
673* Compare S
674*
675 dif = zero
676 div = max( mnmin*ulp*s( 1 ), unfl )
677 DO 60 i = 1, mnmin - 1
678 IF( ssav( i ).LT.ssav( i+1 ) )
679 \$ dif = ulpinv
680 IF( ssav( i ).LT.zero )
681 \$ dif = ulpinv
682 dif = max( dif, abs( ssav( i )-s( i ) ) / div )
683 60 CONTINUE
684 result( 7 ) = max( result( 7 ), dif )
685 70 CONTINUE
686 80 CONTINUE
687*
688* Test SGESDD: Factorize A
689*
690 iwtmp = 5*mnmin*mnmin + 9*mnmin + max( m, n )
691 lswork = iwtmp + ( iws-1 )*( lwork-iwtmp ) / 3
692 lswork = min( lswork, lwork )
693 lswork = max( lswork, 1 )
694 IF( iws.EQ.4 )
695 \$ lswork = lwork
696*
697 CALL slacpy( 'F', m, n, asav, lda, a, lda )
698 srnamt = 'SGESDD'
699 CALL sgesdd( 'A', m, n, a, lda, ssav, usav, ldu, vtsav,
700 \$ ldvt, work, lswork, iwork, iinfo )
701 IF( iinfo.NE.0 ) THEN
702 WRITE( nout, fmt = 9995 )'GESDD', iinfo, m, n, jtype,
703 \$ lswork, ioldsd
704 info = abs( iinfo )
705 RETURN
706 END IF
707*
708* Do tests 8--11
709*
710 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
711 \$ vtsav, ldvt, work, result( 8 ) )
712 IF( m.NE.0 .AND. n.NE.0 ) THEN
713 CALL sort01( 'Columns', m, m, usav, ldu, work, lwork,
714 \$ result( 9 ) )
715 CALL sort01( 'Rows', n, n, vtsav, ldvt, work, lwork,
716 \$ result( 10 ) )
717 END IF
718 result( 11 ) = zero
719 DO 90 i = 1, mnmin - 1
720 IF( ssav( i ).LT.ssav( i+1 ) )
721 \$ result( 11 ) = ulpinv
722 IF( ssav( i ).LT.zero )
723 \$ result( 11 ) = ulpinv
724 90 CONTINUE
725 IF( mnmin.GE.1 ) THEN
726 IF( ssav( mnmin ).LT.zero )
727 \$ result( 11 ) = ulpinv
728 END IF
729*
730* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
731*
732 result( 12 ) = zero
733 result( 13 ) = zero
734 result( 14 ) = zero
735 DO 110 ijq = 0, 2
736 jobq = cjob( ijq+1 )
737 CALL slacpy( 'F', m, n, asav, lda, a, lda )
738 srnamt = 'SGESDD'
739 CALL sgesdd( jobq, m, n, a, lda, s, u, ldu, vt, ldvt,
740 \$ work, lswork, iwork, iinfo )
741*
742* Compare U
743*
744 dif = zero
745 IF( m.GT.0 .AND. n.GT.0 ) THEN
746 IF( ijq.EQ.1 ) THEN
747 IF( m.GE.n ) THEN
748 CALL sort03( 'C', m, mnmin, m, mnmin, usav,
749 \$ ldu, a, lda, work, lwork, dif,
750 \$ info )
751 ELSE
752 CALL sort03( 'C', m, mnmin, m, mnmin, usav,
753 \$ ldu, u, ldu, work, lwork, dif,
754 \$ info )
755 END IF
756 ELSE IF( ijq.EQ.2 ) THEN
757 CALL sort03( 'C', m, mnmin, m, mnmin, usav, ldu,
758 \$ u, ldu, work, lwork, dif, info )
759 END IF
760 END IF
761 result( 12 ) = max( result( 12 ), dif )
762*
763* Compare VT
764*
765 dif = zero
766 IF( m.GT.0 .AND. n.GT.0 ) THEN
767 IF( ijq.EQ.1 ) THEN
768 IF( m.GE.n ) THEN
769 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
770 \$ ldvt, vt, ldvt, work, lwork,
771 \$ dif, info )
772 ELSE
773 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
774 \$ ldvt, a, lda, work, lwork, dif,
775 \$ info )
776 END IF
777 ELSE IF( ijq.EQ.2 ) THEN
778 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
779 \$ ldvt, vt, ldvt, work, lwork, dif,
780 \$ info )
781 END IF
782 END IF
783 result( 13 ) = max( result( 13 ), dif )
784*
785* Compare S
786*
787 dif = zero
788 div = max( mnmin*ulp*s( 1 ), unfl )
789 DO 100 i = 1, mnmin - 1
790 IF( ssav( i ).LT.ssav( i+1 ) )
791 \$ dif = ulpinv
792 IF( ssav( i ).LT.zero )
793 \$ dif = ulpinv
794 dif = max( dif, abs( ssav( i )-s( i ) ) / div )
795 100 CONTINUE
796 result( 14 ) = max( result( 14 ), dif )
797 110 CONTINUE
798*
799* Test SGESVDQ
800* Note: SGESVDQ only works for M >= N
801*
802 result( 36 ) = zero
803 result( 37 ) = zero
804 result( 38 ) = zero
805 result( 39 ) = zero
806*
807 IF( m.GE.n ) THEN
808 iwtmp = 5*mnmin*mnmin + 9*mnmin + max( m, n )
809 lswork = iwtmp + ( iws-1 )*( lwork-iwtmp ) / 3
810 lswork = min( lswork, lwork )
811 lswork = max( lswork, 1 )
812 IF( iws.EQ.4 )
813 \$ lswork = lwork
814*
815 CALL slacpy( 'F', m, n, asav, lda, a, lda )
816 srnamt = 'SGESVDQ'
817*
818 lrwork = 2
819 liwork = max( n, 1 )
820 CALL sgesvdq( 'H', 'N', 'N', 'A', 'A',
821 \$ m, n, a, lda, ssav, usav, ldu,
822 \$ vtsav, ldvt, numrank, iwork, liwork,
823 \$ work, lwork, rwork, lrwork, iinfo )
824*
825 IF( iinfo.NE.0 ) THEN
826 WRITE( nout, fmt = 9995 )'SGESVDQ', iinfo, m, n,
827 \$ jtype, lswork, ioldsd
828 info = abs( iinfo )
829 RETURN
830 END IF
831*
832* Do tests 36--39
833*
834 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
835 \$ vtsav, ldvt, work, result( 36 ) )
836 IF( m.NE.0 .AND. n.NE.0 ) THEN
837 CALL sort01( 'Columns', m, m, usav, ldu, work,
838 \$ lwork, result( 37 ) )
839 CALL sort01( 'Rows', n, n, vtsav, ldvt, work,
840 \$ lwork, result( 38 ) )
841 END IF
842 result( 39 ) = zero
843 DO 199 i = 1, mnmin - 1
844 IF( ssav( i ).LT.ssav( i+1 ) )
845 \$ result( 39 ) = ulpinv
846 IF( ssav( i ).LT.zero )
847 \$ result( 39 ) = ulpinv
848 199 CONTINUE
849 IF( mnmin.GE.1 ) THEN
850 IF( ssav( mnmin ).LT.zero )
851 \$ result( 39 ) = ulpinv
852 END IF
853 END IF
854*
855* Test SGESVJ
856* Note: SGESVJ only works for M >= N
857*
858 result( 15 ) = zero
859 result( 16 ) = zero
860 result( 17 ) = zero
861 result( 18 ) = zero
862*
863 IF( m.GE.n ) THEN
864 iwtmp = 5*mnmin*mnmin + 9*mnmin + max( m, n )
865 lswork = iwtmp + ( iws-1 )*( lwork-iwtmp ) / 3
866 lswork = min( lswork, lwork )
867 lswork = max( lswork, 1 )
868 IF( iws.EQ.4 )
869 \$ lswork = lwork
870*
871 CALL slacpy( 'F', m, n, asav, lda, usav, lda )
872 srnamt = 'SGESVJ'
873 CALL sgesvj( 'G', 'U', 'V', m, n, usav, lda, ssav,
874 & 0, a, ldvt, work, lwork, info )
875*
876* SGESVJ returns V not VT
877*
878 DO j=1,n
879 DO i=1,n
880 vtsav(j,i) = a(i,j)
881 END DO
882 END DO
883*
884 IF( iinfo.NE.0 ) THEN
885 WRITE( nout, fmt = 9995 )'GESVJ', iinfo, m, n,
886 \$ jtype, lswork, ioldsd
887 info = abs( iinfo )
888 RETURN
889 END IF
890*
891* Do tests 15--18
892*
893 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
894 \$ vtsav, ldvt, work, result( 15 ) )
895 IF( m.NE.0 .AND. n.NE.0 ) THEN
896 CALL sort01( 'Columns', m, m, usav, ldu, work,
897 \$ lwork, result( 16 ) )
898 CALL sort01( 'Rows', n, n, vtsav, ldvt, work,
899 \$ lwork, result( 17 ) )
900 END IF
901 result( 18 ) = zero
902 DO 120 i = 1, mnmin - 1
903 IF( ssav( i ).LT.ssav( i+1 ) )
904 \$ result( 18 ) = ulpinv
905 IF( ssav( i ).LT.zero )
906 \$ result( 18 ) = ulpinv
907 120 CONTINUE
908 IF( mnmin.GE.1 ) THEN
909 IF( ssav( mnmin ).LT.zero )
910 \$ result( 18 ) = ulpinv
911 END IF
912 END IF
913*
914* Test SGEJSV
915* Note: SGEJSV only works for M >= N
916*
917 result( 19 ) = zero
918 result( 20 ) = zero
919 result( 21 ) = zero
920 result( 22 ) = zero
921 IF( m.GE.n ) THEN
922 iwtmp = 5*mnmin*mnmin + 9*mnmin + max( m, n )
923 lswork = iwtmp + ( iws-1 )*( lwork-iwtmp ) / 3
924 lswork = min( lswork, lwork )
925 lswork = max( lswork, 1 )
926 IF( iws.EQ.4 )
927 \$ lswork = lwork
928*
929 CALL slacpy( 'F', m, n, asav, lda, vtsav, lda )
930 srnamt = 'SGEJSV'
931 CALL sgejsv( 'G', 'U', 'V', 'R', 'N', 'N',
932 & m, n, vtsav, lda, ssav, usav, ldu, a, ldvt,
933 & work, lwork, iwork, info )
934*
935* SGEJSV returns V not VT
936*
937 DO 140 j=1,n
938 DO 130 i=1,n
939 vtsav(j,i) = a(i,j)
940 130 END DO
941 140 END DO
942*
943 IF( iinfo.NE.0 ) THEN
944 WRITE( nout, fmt = 9995 )'GEJSV', iinfo, m, n,
945 \$ jtype, lswork, ioldsd
946 info = abs( iinfo )
947 RETURN
948 END IF
949*
950* Do tests 19--22
951*
952 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
953 \$ vtsav, ldvt, work, result( 19 ) )
954 IF( m.NE.0 .AND. n.NE.0 ) THEN
955 CALL sort01( 'Columns', m, m, usav, ldu, work,
956 \$ lwork, result( 20 ) )
957 CALL sort01( 'Rows', n, n, vtsav, ldvt, work,
958 \$ lwork, result( 21 ) )
959 END IF
960 result( 22 ) = zero
961 DO 150 i = 1, mnmin - 1
962 IF( ssav( i ).LT.ssav( i+1 ) )
963 \$ result( 22 ) = ulpinv
964 IF( ssav( i ).LT.zero )
965 \$ result( 22 ) = ulpinv
966 150 CONTINUE
967 IF( mnmin.GE.1 ) THEN
968 IF( ssav( mnmin ).LT.zero )
969 \$ result( 22 ) = ulpinv
970 END IF
971 END IF
972*
973* Test SGESVDX
974*
975 CALL slacpy( 'F', m, n, asav, lda, a, lda )
976 CALL sgesvdx( 'V', 'V', 'A', m, n, a, lda,
977 \$ vl, vu, il, iu, ns, ssav, usav, ldu,
978 \$ vtsav, ldvt, work, lwork, iwork,
979 \$ iinfo )
980 IF( iinfo.NE.0 ) THEN
981 WRITE( nout, fmt = 9995 )'GESVDX', iinfo, m, n,
982 \$ jtype, lswork, ioldsd
983 info = abs( iinfo )
984 RETURN
985 END IF
986*
987* Do tests 23--29
988*
989 result( 23 ) = zero
990 result( 24 ) = zero
991 result( 25 ) = zero
992 CALL sbdt01( m, n, 0, asav, lda, usav, ldu, ssav, e,
993 \$ vtsav, ldvt, work, result( 23 ) )
994 IF( m.NE.0 .AND. n.NE.0 ) THEN
995 CALL sort01( 'Columns', m, m, usav, ldu, work, lwork,
996 \$ result( 24 ) )
997 CALL sort01( 'Rows', n, n, vtsav, ldvt, work, lwork,
998 \$ result( 25 ) )
999 END IF
1000 result( 26 ) = zero
1001 DO 160 i = 1, mnmin - 1
1002 IF( ssav( i ).LT.ssav( i+1 ) )
1003 \$ result( 26 ) = ulpinv
1004 IF( ssav( i ).LT.zero )
1005 \$ result( 26 ) = ulpinv
1006 160 CONTINUE
1007 IF( mnmin.GE.1 ) THEN
1008 IF( ssav( mnmin ).LT.zero )
1009 \$ result( 26 ) = ulpinv
1010 END IF
1011*
1012* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
1013*
1014 result( 27 ) = zero
1015 result( 28 ) = zero
1016 result( 29 ) = zero
1017 DO 180 iju = 0, 1
1018 DO 170 ijvt = 0, 1
1019 IF( ( iju.EQ.0 .AND. ijvt.EQ.0 ) .OR.
1020 \$ ( iju.EQ.1 .AND. ijvt.EQ.1 ) )GO TO 170
1021 jobu = cjobv( iju+1 )
1022 jobvt = cjobv( ijvt+1 )
1023 range = cjobr( 1 )
1024 CALL slacpy( 'F', m, n, asav, lda, a, lda )
1025 CALL sgesvdx( jobu, jobvt, range, m, n, a, lda,
1026 \$ vl, vu, il, iu, ns, s, u, ldu,
1027 \$ vt, ldvt, work, lwork, iwork,
1028 \$ iinfo )
1029*
1030* Compare U
1031*
1032 dif = zero
1033 IF( m.GT.0 .AND. n.GT.0 ) THEN
1034 IF( iju.EQ.1 ) THEN
1035 CALL sort03( 'C', m, mnmin, m, mnmin, usav,
1036 \$ ldu, u, ldu, work, lwork, dif,
1037 \$ iinfo )
1038 END IF
1039 END IF
1040 result( 27 ) = max( result( 27 ), dif )
1041*
1042* Compare VT
1043*
1044 dif = zero
1045 IF( m.GT.0 .AND. n.GT.0 ) THEN
1046 IF( ijvt.EQ.1 ) THEN
1047 CALL sort03( 'R', n, mnmin, n, mnmin, vtsav,
1048 \$ ldvt, vt, ldvt, work, lwork,
1049 \$ dif, iinfo )
1050 END IF
1051 END IF
1052 result( 28 ) = max( result( 28 ), dif )
1053*
1054* Compare S
1055*
1056 dif = zero
1057 div = max( mnmin*ulp*s( 1 ), unfl )
1058 DO 190 i = 1, mnmin - 1
1059 IF( ssav( i ).LT.ssav( i+1 ) )
1060 \$ dif = ulpinv
1061 IF( ssav( i ).LT.zero )
1062 \$ dif = ulpinv
1063 dif = max( dif, abs( ssav( i )-s( i ) ) / div )
1064 190 CONTINUE
1065 result( 29 ) = max( result( 29 ), dif )
1066 170 CONTINUE
1067 180 CONTINUE
1068*
1069* Do tests 30--32: SGESVDX( 'V', 'V', 'I' )
1070*
1071 DO 200 i = 1, 4
1072 iseed2( i ) = iseed( i )
1073 200 CONTINUE
1074 IF( mnmin.LE.1 ) THEN
1075 il = 1
1076 iu = max( 1, mnmin )
1077 ELSE
1078 il = 1 + int( ( mnmin-1 )*slarnd( 1, iseed2 ) )
1079 iu = 1 + int( ( mnmin-1 )*slarnd( 1, iseed2 ) )
1080 IF( iu.LT.il ) THEN
1081 itemp = iu
1082 iu = il
1083 il = itemp
1084 END IF
1085 END IF
1086 CALL slacpy( 'F', m, n, asav, lda, a, lda )
1087 CALL sgesvdx( 'V', 'V', 'I', m, n, a, lda,
1088 \$ vl, vu, il, iu, nsi, s, u, ldu,
1089 \$ vt, ldvt, work, lwork, iwork,
1090 \$ iinfo )
1091 IF( iinfo.NE.0 ) THEN
1092 WRITE( nout, fmt = 9995 )'GESVDX', iinfo, m, n,
1093 \$ jtype, lswork, ioldsd
1094 info = abs( iinfo )
1095 RETURN
1096 END IF
1097*
1098 result( 30 ) = zero
1099 result( 31 ) = zero
1100 result( 32 ) = zero
1101 CALL sbdt05( m, n, asav, lda, s, nsi, u, ldu,
1102 \$ vt, ldvt, work, result( 30 ) )
1103 CALL sort01( 'Columns', m, nsi, u, ldu, work, lwork,
1104 \$ result( 31 ) )
1105 CALL sort01( 'Rows', nsi, n, vt, ldvt, work, lwork,
1106 \$ result( 32 ) )
1107*
1108* Do tests 33--35: SGESVDX( 'V', 'V', 'V' )
1109*
1110 IF( mnmin.GT.0 .AND. nsi.GT.1 ) THEN
1111 IF( il.NE.1 ) THEN
1112 vu = ssav( il ) +
1113 \$ max( half*abs( ssav( il )-ssav( il-1 ) ),
1114 \$ ulp*anorm, two*rtunfl )
1115 ELSE
1116 vu = ssav( 1 ) +
1117 \$ max( half*abs( ssav( ns )-ssav( 1 ) ),
1118 \$ ulp*anorm, two*rtunfl )
1119 END IF
1120 IF( iu.NE.ns ) THEN
1121 vl = ssav( iu ) - max( ulp*anorm, two*rtunfl,
1122 \$ half*abs( ssav( iu+1 )-ssav( iu ) ) )
1123 ELSE
1124 vl = ssav( ns ) - max( ulp*anorm, two*rtunfl,
1125 \$ half*abs( ssav( ns )-ssav( 1 ) ) )
1126 END IF
1127 vl = max( vl,zero )
1128 vu = max( vu,zero )
1129 IF( vl.GE.vu ) vu = max( vu*2, vu+vl+half )
1130 ELSE
1131 vl = zero
1132 vu = one
1133 END IF
1134 CALL slacpy( 'F', m, n, asav, lda, a, lda )
1135 CALL sgesvdx( 'V', 'V', 'V', m, n, a, lda,
1136 \$ vl, vu, il, iu, nsv, s, u, ldu,
1137 \$ vt, ldvt, work, lwork, iwork,
1138 \$ iinfo )
1139 IF( iinfo.NE.0 ) THEN
1140 WRITE( nout, fmt = 9995 )'GESVDX', iinfo, m, n,
1141 \$ jtype, lswork, ioldsd
1142 info = abs( iinfo )
1143 RETURN
1144 END IF
1145*
1146 result( 33 ) = zero
1147 result( 34 ) = zero
1148 result( 35 ) = zero
1149 CALL sbdt05( m, n, asav, lda, s, nsv, u, ldu,
1150 \$ vt, ldvt, work, result( 33 ) )
1151 CALL sort01( 'Columns', m, nsv, u, ldu, work, lwork,
1152 \$ result( 34 ) )
1153 CALL sort01( 'Rows', nsv, n, vt, ldvt, work, lwork,
1154 \$ result( 35 ) )
1155*
1156* End of Loop -- Check for RESULT(j) > THRESH
1157*
1158 DO 210 j = 1, 39
1159 IF( result( j ).GE.thresh ) THEN
1160 IF( nfail.EQ.0 ) THEN
1161 WRITE( nout, fmt = 9999 )
1162 WRITE( nout, fmt = 9998 )
1163 END IF
1164 WRITE( nout, fmt = 9997 )m, n, jtype, iws, ioldsd,
1165 \$ j, result( j )
1166 nfail = nfail + 1
1167 END IF
1168 210 CONTINUE
1169 ntest = ntest + 39
1170 220 CONTINUE
1171 230 CONTINUE
1172 240 CONTINUE
1173*
1174* Summary
1175*
1176 CALL alasvm( path, nout, nfail, ntest, 0 )
1177*
1178 9999 FORMAT( ' SVD -- Real Singular Value Decomposition Driver ',
1179 \$ / ' Matrix types (see SDRVBD for details):',
1180 \$ / / ' 1 = Zero matrix', / ' 2 = Identity matrix',
1181 \$ / ' 3 = Evenly spaced singular values near 1',
1182 \$ / ' 4 = Evenly spaced singular values near underflow',
1183 \$ / ' 5 = Evenly spaced singular values near overflow', / /
1184 \$ ' Tests performed: ( A is dense, U and V are orthogonal,',
1185 \$ / 19x, ' S is an array, and Upartial, VTpartial, and',
1186 \$ / 19x, ' Spartial are partially computed U, VT and S),', / )
1187 9998 FORMAT( ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1188 \$ / ' 2 = | I - U**T U | / ( M ulp ) ',
1189 \$ / ' 3 = | I - VT VT**T | / ( N ulp ) ',
1190 \$ / ' 4 = 0 if S contains min(M,N) nonnegative values in',
1191 \$ ' decreasing order, else 1/ulp',
1192 \$ / ' 5 = | U - Upartial | / ( M ulp )',
1193 \$ / ' 6 = | VT - VTpartial | / ( N ulp )',
1194 \$ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )',
1195 \$ / ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1196 \$ / ' 9 = | I - U**T U | / ( M ulp ) ',
1197 \$ / '10 = | I - VT VT**T | / ( N ulp ) ',
1198 \$ / '11 = 0 if S contains min(M,N) nonnegative values in',
1199 \$ ' decreasing order, else 1/ulp',
1200 \$ / '12 = | U - Upartial | / ( M ulp )',
1201 \$ / '13 = | VT - VTpartial | / ( N ulp )',
1202 \$ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )',
1203 \$ / '15 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1204 \$ / '16 = | I - U**T U | / ( M ulp ) ',
1205 \$ / '17 = | I - VT VT**T | / ( N ulp ) ',
1206 \$ / '18 = 0 if S contains min(M,N) nonnegative values in',
1207 \$ ' decreasing order, else 1/ulp',
1208 \$ / '19 = | U - Upartial | / ( M ulp )',
1209 \$ / '20 = | VT - VTpartial | / ( N ulp )',
1210 \$ / '21 = | S - Spartial | / ( min(M,N) ulp |S| )',
1211 \$ / '22 = 0 if S contains min(M,N) nonnegative values in',
1212 \$ ' decreasing order, else 1/ulp',
1213 \$ ' SGESVDX(V,V,A) ',
1214 \$ / '23 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ),'
1215 \$ / '24 = | I - U**T U | / ( M ulp ) ',
1216 \$ / '25 = | I - VT VT**T | / ( N ulp ) ',
1217 \$ / '26 = 0 if S contains min(M,N) nonnegative values in',
1218 \$ ' decreasing order, else 1/ulp',
1219 \$ / '27 = | U - Upartial | / ( M ulp )',
1220 \$ / '28 = | VT - VTpartial | / ( N ulp )',
1221 \$ / '29 = | S - Spartial | / ( min(M,N) ulp |S| )',
1222 \$ / '30 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp ),',
1223 \$ ' SGESVDX(V,V,I) ',
1224 \$ / '31 = | I - U**T U | / ( M ulp ) ',
1225 \$ / '32 = | I - VT VT**T | / ( N ulp ) ',
1226 \$ / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp ),',
1227 \$ ' SGESVDX(V,V,V) ',
1228 \$ / '34 = | I - U**T U | / ( M ulp ) ',
1229 \$ / '35 = | I - VT VT**T | / ( N ulp ) ',
1230 \$ ' SGESVDQ(H,N,N,A,A',
1231 \$ / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
1232 \$ / '37 = | I - U**T U | / ( M ulp ) ',
1233 \$ / '38 = | I - VT VT**T | / ( N ulp ) ',
1234 \$ / '39 = 0 if S contains min(M,N) nonnegative values in',
1235 \$ ' decreasing order, else 1/ulp',
1236 \$ / / )
1237 9997 FORMAT( ' M=', i5, ', N=', i5, ', type ', i1, ', IWS=', i1,
1238 \$ ', seed=', 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
1239 9996 FORMAT( ' SDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1240 \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
1241 \$ i5, ')' )
1242 9995 FORMAT( ' SDRVBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1243 \$ i6, ', N=', i6, ', JTYPE=', i6, ', LSWORK=', i6, / 9x,
1244 \$ 'ISEED=(', 3( i5, ',' ), i5, ')' )
1245*
1246 RETURN
1247*
1248* End of SDRVBD
1249*
subroutine alasvm(type, nout, nfail, nrun, nerrs)
ALASVM
Definition alasvm.f:73
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine sgejsv(joba, jobu, jobv, jobr, jobt, jobp, m, n, a, lda, sva, u, ldu, v, ldv, work, lwork, iwork, info)
SGEJSV
Definition sgejsv.f:476
subroutine sgesdd(jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
SGESDD
Definition sgesdd.f:213
subroutine sgesvd(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, info)
SGESVD computes the singular value decomposition (SVD) for GE matrices
Definition sgesvd.f:211
subroutine sgesvdq(joba, jobp, jobr, jobu, jobv, m, n, a, lda, s, u, ldu, v, ldv, numrank, iwork, liwork, work, lwork, rwork, lrwork, info)
SGESVDQ computes the singular value decomposition (SVD) with a QR-Preconditioned QR SVD Method for GE...
Definition sgesvdq.f:415
subroutine sgesvdx(jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
SGESVDX computes the singular value decomposition (SVD) for GE matrices
Definition sgesvdx.f:263
subroutine sgesvj(joba, jobu, jobv, m, n, a, lda, sva, mv, v, ldv, work, lwork, info)
SGESVJ
Definition sgesvj.f:323
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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:110
subroutine sbdt01(m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid)
SBDT01
Definition sbdt01.f:141
subroutine sbdt05(m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)
SBDT05
Definition sbdt05.f:127
real function slarnd(idist, iseed)
SLARND
Definition slarnd.f:73
subroutine slatms(m, n, dist, iseed, sym, d, mode, cond, dmax, kl, ku, pack, a, lda, work, info)
SLATMS
Definition slatms.f:321
subroutine sort01(rowcol, m, n, u, ldu, work, lwork, resid)
SORT01
Definition sort01.f:116
subroutine sort03(rc, mu, mv, n, k, u, ldu, v, ldv, work, lwork, result, info)
SORT03
Definition sort03.f:156
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