 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zchkbd()

 subroutine zchkbd ( integer NSIZES, integer, dimension( * ) MVAL, integer, dimension( * ) NVAL, integer NTYPES, logical, dimension( * ) DOTYPE, integer NRHS, integer, dimension( 4 ) ISEED, double precision THRESH, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) BD, double precision, dimension( * ) BE, double precision, dimension( * ) S1, double precision, dimension( * ) S2, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldx, * ) Y, complex*16, dimension( ldx, * ) Z, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( ldpt, * ) PT, integer LDPT, complex*16, dimension( ldpt, * ) U, complex*16, dimension( ldpt, * ) VT, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer NOUT, integer INFO )

ZCHKBD

Purpose:
``` ZCHKBD checks the singular value decomposition (SVD) routines.

ZGEBRD reduces a complex general m by n matrix A to real upper or
lower bidiagonal form by an orthogonal transformation: Q' * A * P = B
(or A = Q * B * P').  The matrix B is upper bidiagonal if m >= n
and lower bidiagonal if m < n.

ZUNGBR generates the orthogonal matrices Q and P' from ZGEBRD.
Note that Q and P are not necessarily square.

ZBDSQR computes the singular value decomposition of the bidiagonal
matrix B as B = U S V'.  It is called three times to compute
1)  B = U S1 V', where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B.
2)  Same as 1), but the singular values are stored in S2 and the
singular vectors are not computed.
3)  A = (UQ) S (P'V'), the SVD of the original matrix A.
In addition, ZBDSQR has an option to apply the left orthogonal matrix
U to a matrix X, useful in least squares applications.

For each pair of matrix dimensions (M,N) and each selected matrix
type, an M by N matrix A and an M by NRHS matrix X are generated.
The problem dimensions are as follows
A:          M x N
Q:          M x min(M,N) (but M x M if NRHS > 0)
P:          min(M,N) x N
B:          min(M,N) x min(M,N)
U, V:       min(M,N) x min(M,N)
S1, S2      diagonal, order min(M,N)
X:          M x NRHS

For each generated matrix, 14 tests are performed:

Test ZGEBRD and ZUNGBR

(1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'

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

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

Test ZBDSQR on bidiagonal matrix B

(4)   | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'

(5)   | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
and   Z = U' Y.
(6)   | I - U' U | / ( min(M,N) ulp )

(7)   | I - VT VT' | / ( min(M,N) ulp )

(8)   S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(9)   0 if the true singular values of B are within THRESH of
those in S1.  2*THRESH if they are not.  (Tested using
DSVDCH)

(10)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.

Test ZBDSQR on matrix A

(11)  | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )

(12)  | X - (QU) Z | / ( |X| max(M,k) ulp )

(13)  | I - (QU)'(QU) | / ( M ulp )

(14)  | I - (VT PT) (PT'VT') | / ( N ulp )

The possible matrix types are

(1)  The zero matrix.
(2)  The identity matrix.

(3)  A diagonal matrix with evenly spaced entries
1, ..., ULP  and random signs.
(ULP = (first number larger than 1) - 1 )
(4)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random signs.
(5)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.

(6)  Same as (3), but multiplied by SQRT( overflow threshold )
(7)  Same as (3), but multiplied by SQRT( underflow threshold )

(8)  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.

(9)  A matrix of the form  U D V, where U and V are orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.

(10) A matrix of the form  U D V, where U and V are orthogonal and
D has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal.

(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )

(13) Rectangular matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )

Special case:
(16) A bidiagonal matrix with random entries chosen from a
logarithmic distribution on [ulp^2,ulp^(-2)]  (I.e., each
entry is  e^x, where x is chosen uniformly on
[ 2 log(ulp), -2 log(ulp) ] .)  For *this* type:
(a) ZGEBRD is not called to reduce it to bidiagonal form.
(b) the bidiagonal is  min(M,N) x min(M,N); if M<N, the
matrix will be lower bidiagonal, otherwise upper.
(c) only tests 5--8 and 14 are performed.

A subset of the full set of matrix types may be selected through
the logical array DOTYPE.```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of values of M and N contained in the vectors MVAL and NVAL. The matrix sizes are used in pairs (M,N).``` [in] MVAL ``` MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NM) The values of the matrix column dimension N.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, ZCHKBD 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] NRHS ``` NRHS is INTEGER The number of columns in the "right-hand side" matrices X, Y, and Z, used in testing ZBDSQR. If NRHS = 0, then the operations on the right-hand side will not be tested. NRHS must be at least 0.``` [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 values of ISEED are changed on exit, and can be used in the next call to ZCHKBD to continue the same random number sequence.``` [in] THRESH ``` THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. Note that the expected value of the test ratios is O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100.``` [out] A ``` A is COMPLEX*16 array, dimension (LDA,NMAX) where NMAX is the maximum value of N in NVAL.``` [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 MVAL.``` [out] BD ``` BD is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] BE ``` BE is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] S1 ``` S1 is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] S2 ``` S2 is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] X ` X is COMPLEX*16 array, dimension (LDX,NRHS)` [in] LDX ``` LDX is INTEGER The leading dimension of the arrays X, Y, and Z. LDX >= max(1,MMAX).``` [out] Y ` Y is COMPLEX*16 array, dimension (LDX,NRHS)` [out] Z ` Z is COMPLEX*16 array, dimension (LDX,NRHS)` [out] Q ` Q is COMPLEX*16 array, dimension (LDQ,MMAX)` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,MMAX).``` [out] PT ` PT is COMPLEX*16 array, dimension (LDPT,NMAX)` [in] LDPT ``` LDPT is INTEGER The leading dimension of the arrays PT, U, and V. LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).``` [out] U ``` U is COMPLEX*16 array, dimension (LDPT,max(min(MVAL(j),NVAL(j))))``` [out] VT ``` VT is COMPLEX*16 array, dimension (LDPT,max(min(MVAL(j),NVAL(j))))``` [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 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all pairs (M,N)=(MM(j),NN(j))``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (5*max(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 -6: NRHS < 0 -8: THRESH < 0 -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). -17: LDB < 1 or LDB < MMAX. -21: LDQ < 1 or LDQ < MMAX. -23: LDP < 1 or LDP < MNMAX. -27: LWORK too small. If ZLATMR, CLATMS, ZGEBRD, ZUNGBR, or ZBDSQR, returns an error code, the absolute value of it is returned. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NTEST The number of tests performed, or which can be performed so far, for the current matrix. MMAX Largest value in NN. NMAX Largest value in NN. MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal matrix.) MNMAX The maximum value of MNMIN for j=1,...,NSIZES. NFAIL The number of tests which have exceeded THRESH COND, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. RTOVFL, RTUNFL Square roots of the previous 2 values. ULP, ULPINV Finest relative precision and its inverse. The following four arrays decode JTYPE: KTYPE(j) The general type (1-10) for type "j". KMODE(j) The MODE value to be passed to the matrix generator for type "j". KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )```

Definition at line 411 of file zchkbd.f.

415*
416* -- LAPACK test routine --
417* -- LAPACK is a software package provided by Univ. of Tennessee, --
418* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
419*
420* .. Scalar Arguments ..
421 INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
422 \$ NSIZES, NTYPES
423 DOUBLE PRECISION THRESH
424* ..
425* .. Array Arguments ..
426 LOGICAL DOTYPE( * )
427 INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
428 DOUBLE PRECISION BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
429 COMPLEX*16 A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
430 \$ U( LDPT, * ), VT( LDPT, * ), WORK( * ),
431 \$ X( LDX, * ), Y( LDX, * ), Z( LDX, * )
432* ..
433*
434* ======================================================================
435*
436* .. Parameters ..
437 DOUBLE PRECISION ZERO, ONE, TWO, HALF
438 parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
439 \$ half = 0.5d0 )
440 COMPLEX*16 CZERO, CONE
441 parameter( czero = ( 0.0d+0, 0.0d+0 ),
442 \$ cone = ( 1.0d+0, 0.0d+0 ) )
443 INTEGER MAXTYP
444 parameter( maxtyp = 16 )
445* ..
446* .. Local Scalars ..
448 CHARACTER UPLO
449 CHARACTER*3 PATH
450 INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
451 \$ LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN, MQ,
452 \$ MTYPES, N, NFAIL, NMAX, NTEST
453 DOUBLE PRECISION AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
454 \$ TEMP1, TEMP2, ULP, ULPINV, UNFL
455* ..
456* .. Local Arrays ..
457 INTEGER IOLDSD( 4 ), IWORK( 1 ), KMAGN( MAXTYP ),
458 \$ KMODE( MAXTYP ), KTYPE( MAXTYP )
459 DOUBLE PRECISION DUMMA( 1 ), RESULT( 14 )
460* ..
461* .. External Functions ..
462 DOUBLE PRECISION DLAMCH, DLARND
463 EXTERNAL dlamch, dlarnd
464* ..
465* .. External Subroutines ..
466 EXTERNAL alasum, dcopy, dlabad, dlahd2, dsvdch, xerbla,
469* ..
470* .. Intrinsic Functions ..
471 INTRINSIC abs, exp, int, log, max, min, sqrt
472* ..
473* .. Scalars in Common ..
474 LOGICAL LERR, OK
475 CHARACTER*32 SRNAMT
476 INTEGER INFOT, NUNIT
477* ..
478* .. Common blocks ..
479 COMMON / infoc / infot, nunit, ok, lerr
480 COMMON / srnamc / srnamt
481* ..
482* .. Data statements ..
483 DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
484 DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
485 DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
486 \$ 0, 0, 0 /
487* ..
488* .. Executable Statements ..
489*
490* Check for errors
491*
492 info = 0
493*
496 mmax = 1
497 nmax = 1
498 mnmax = 1
499 minwrk = 1
500 DO 10 j = 1, nsizes
501 mmax = max( mmax, mval( j ) )
502 IF( mval( j ).LT.0 )
504 nmax = max( nmax, nval( j ) )
505 IF( nval( j ).LT.0 )
507 mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
508 minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
509 \$ mval( j )*( mval( j )+max( mval( j ), nval( j ),
510 \$ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
511 10 CONTINUE
512*
513* Check for errors
514*
515 IF( nsizes.LT.0 ) THEN
516 info = -1
517 ELSE IF( badmm ) THEN
518 info = -2
519 ELSE IF( badnn ) THEN
520 info = -3
521 ELSE IF( ntypes.LT.0 ) THEN
522 info = -4
523 ELSE IF( nrhs.LT.0 ) THEN
524 info = -6
525 ELSE IF( lda.LT.mmax ) THEN
526 info = -11
527 ELSE IF( ldx.LT.mmax ) THEN
528 info = -17
529 ELSE IF( ldq.LT.mmax ) THEN
530 info = -21
531 ELSE IF( ldpt.LT.mnmax ) THEN
532 info = -23
533 ELSE IF( minwrk.GT.lwork ) THEN
534 info = -27
535 END IF
536*
537 IF( info.NE.0 ) THEN
538 CALL xerbla( 'ZCHKBD', -info )
539 RETURN
540 END IF
541*
542* Initialize constants
543*
544 path( 1: 1 ) = 'Zomplex precision'
545 path( 2: 3 ) = 'BD'
546 nfail = 0
547 ntest = 0
548 unfl = dlamch( 'Safe minimum' )
549 ovfl = dlamch( 'Overflow' )
550 CALL dlabad( unfl, ovfl )
551 ulp = dlamch( 'Precision' )
552 ulpinv = one / ulp
553 log2ui = int( log( ulpinv ) / log( two ) )
554 rtunfl = sqrt( unfl )
555 rtovfl = sqrt( ovfl )
556 infot = 0
557*
558* Loop over sizes, types
559*
560 DO 180 jsize = 1, nsizes
561 m = mval( jsize )
562 n = nval( jsize )
563 mnmin = min( m, n )
564 amninv = one / max( m, n, 1 )
565*
566 IF( nsizes.NE.1 ) THEN
567 mtypes = min( maxtyp, ntypes )
568 ELSE
569 mtypes = min( maxtyp+1, ntypes )
570 END IF
571*
572 DO 170 jtype = 1, mtypes
573 IF( .NOT.dotype( jtype ) )
574 \$ GO TO 170
575*
576 DO 20 j = 1, 4
577 ioldsd( j ) = iseed( j )
578 20 CONTINUE
579*
580 DO 30 j = 1, 14
581 result( j ) = -one
582 30 CONTINUE
583*
584 uplo = ' '
585*
586* Compute "A"
587*
588* Control parameters:
589*
590* KMAGN KMODE KTYPE
591* =1 O(1) clustered 1 zero
592* =2 large clustered 2 identity
593* =3 small exponential (none)
594* =4 arithmetic diagonal, (w/ eigenvalues)
595* =5 random symmetric, w/ eigenvalues
596* =6 nonsymmetric, w/ singular values
597* =7 random diagonal
598* =8 random symmetric
599* =9 random nonsymmetric
600* =10 random bidiagonal (log. distrib.)
601*
602 IF( mtypes.GT.maxtyp )
603 \$ GO TO 100
604*
605 itype = ktype( jtype )
606 imode = kmode( jtype )
607*
608* Compute norm
609*
610 GO TO ( 40, 50, 60 )kmagn( jtype )
611*
612 40 CONTINUE
613 anorm = one
614 GO TO 70
615*
616 50 CONTINUE
617 anorm = ( rtovfl*ulp )*amninv
618 GO TO 70
619*
620 60 CONTINUE
621 anorm = rtunfl*max( m, n )*ulpinv
622 GO TO 70
623*
624 70 CONTINUE
625*
626 CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
627 iinfo = 0
628 cond = ulpinv
629*
630 bidiag = .false.
631 IF( itype.EQ.1 ) THEN
632*
633* Zero matrix
634*
635 iinfo = 0
636*
637 ELSE IF( itype.EQ.2 ) THEN
638*
639* Identity
640*
641 DO 80 jcol = 1, mnmin
642 a( jcol, jcol ) = anorm
643 80 CONTINUE
644*
645 ELSE IF( itype.EQ.4 ) THEN
646*
647* Diagonal Matrix, [Eigen]values Specified
648*
649 CALL zlatms( mnmin, mnmin, 'S', iseed, 'N', rwork, imode,
650 \$ cond, anorm, 0, 0, 'N', a, lda, work,
651 \$ iinfo )
652*
653 ELSE IF( itype.EQ.5 ) THEN
654*
655* Symmetric, eigenvalues specified
656*
657 CALL zlatms( mnmin, mnmin, 'S', iseed, 'S', rwork, imode,
658 \$ cond, anorm, m, n, 'N', a, lda, work,
659 \$ iinfo )
660*
661 ELSE IF( itype.EQ.6 ) THEN
662*
663* Nonsymmetric, singular values specified
664*
665 CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode, cond,
666 \$ anorm, m, n, 'N', a, lda, work, iinfo )
667*
668 ELSE IF( itype.EQ.7 ) THEN
669*
670* Diagonal, random entries
671*
672 CALL zlatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
673 \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
674 \$ work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
675 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
676*
677 ELSE IF( itype.EQ.8 ) THEN
678*
679* Symmetric, random entries
680*
681 CALL zlatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
682 \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
683 \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
684 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
685*
686 ELSE IF( itype.EQ.9 ) THEN
687*
688* Nonsymmetric, random entries
689*
690 CALL zlatmr( m, n, 'S', iseed, 'N', work, 6, one, cone,
691 \$ 'T', 'N', work( mnmin+1 ), 1, one,
692 \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
693 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
694*
695 ELSE IF( itype.EQ.10 ) THEN
696*
697* Bidiagonal, random entries
698*
699 temp1 = -two*log( ulp )
700 DO 90 j = 1, mnmin
701 bd( j ) = exp( temp1*dlarnd( 2, iseed ) )
702 IF( j.LT.mnmin )
703 \$ be( j ) = exp( temp1*dlarnd( 2, iseed ) )
704 90 CONTINUE
705*
706 iinfo = 0
707 bidiag = .true.
708 IF( m.GE.n ) THEN
709 uplo = 'U'
710 ELSE
711 uplo = 'L'
712 END IF
713 ELSE
714 iinfo = 1
715 END IF
716*
717 IF( iinfo.EQ.0 ) THEN
718*
719* Generate Right-Hand Side
720*
721 IF( bidiag ) THEN
722 CALL zlatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
723 \$ one, cone, 'T', 'N', work( mnmin+1 ), 1,
724 \$ one, work( 2*mnmin+1 ), 1, one, 'N',
725 \$ iwork, mnmin, nrhs, zero, one, 'NO', y,
726 \$ ldx, iwork, iinfo )
727 ELSE
728 CALL zlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
729 \$ cone, 'T', 'N', work( m+1 ), 1, one,
730 \$ work( 2*m+1 ), 1, one, 'N', iwork, m,
731 \$ nrhs, zero, one, 'NO', x, ldx, iwork,
732 \$ iinfo )
733 END IF
734 END IF
735*
736* Error Exit
737*
738 IF( iinfo.NE.0 ) THEN
739 WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
740 \$ jtype, ioldsd
741 info = abs( iinfo )
742 RETURN
743 END IF
744*
745 100 CONTINUE
746*
747* Call ZGEBRD and ZUNGBR to compute B, Q, and P, do tests.
748*
749 IF( .NOT.bidiag ) THEN
750*
751* Compute transformations to reduce A to bidiagonal form:
752* B := Q' * A * P.
753*
754 CALL zlacpy( ' ', m, n, a, lda, q, ldq )
755 CALL zgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
756 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
757*
758* Check error code from ZGEBRD.
759*
760 IF( iinfo.NE.0 ) THEN
761 WRITE( nout, fmt = 9998 )'ZGEBRD', iinfo, m, n,
762 \$ jtype, ioldsd
763 info = abs( iinfo )
764 RETURN
765 END IF
766*
767 CALL zlacpy( ' ', m, n, q, ldq, pt, ldpt )
768 IF( m.GE.n ) THEN
769 uplo = 'U'
770 ELSE
771 uplo = 'L'
772 END IF
773*
774* Generate Q
775*
776 mq = m
777 IF( nrhs.LE.0 )
778 \$ mq = mnmin
779 CALL zungbr( 'Q', m, mq, n, q, ldq, work,
780 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
781*
782* Check error code from ZUNGBR.
783*
784 IF( iinfo.NE.0 ) THEN
785 WRITE( nout, fmt = 9998 )'ZUNGBR(Q)', iinfo, m, n,
786 \$ jtype, ioldsd
787 info = abs( iinfo )
788 RETURN
789 END IF
790*
791* Generate P'
792*
793 CALL zungbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
794 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
795*
796* Check error code from ZUNGBR.
797*
798 IF( iinfo.NE.0 ) THEN
799 WRITE( nout, fmt = 9998 )'ZUNGBR(P)', iinfo, m, n,
800 \$ jtype, ioldsd
801 info = abs( iinfo )
802 RETURN
803 END IF
804*
805* Apply Q' to an M by NRHS matrix X: Y := Q' * X.
806*
807 CALL zgemm( 'Conjugate transpose', 'No transpose', m,
808 \$ nrhs, m, cone, q, ldq, x, ldx, czero, y,
809 \$ ldx )
810*
811* Test 1: Check the decomposition A := Q * B * PT
812* 2: Check the orthogonality of Q
813* 3: Check the orthogonality of PT
814*
815 CALL zbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
816 \$ work, rwork, result( 1 ) )
817 CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
818 \$ rwork, result( 2 ) )
819 CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
820 \$ rwork, result( 3 ) )
821 END IF
822*
823* Use ZBDSQR to form the SVD of the bidiagonal matrix B:
824* B := U * S1 * VT, and compute Z = U' * Y.
825*
826 CALL dcopy( mnmin, bd, 1, s1, 1 )
827 IF( mnmin.GT.0 )
828 \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
829 CALL zlacpy( ' ', m, nrhs, y, ldx, z, ldx )
830 CALL zlaset( 'Full', mnmin, mnmin, czero, cone, u, ldpt )
831 CALL zlaset( 'Full', mnmin, mnmin, czero, cone, vt, ldpt )
832*
833 CALL zbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, rwork, vt,
834 \$ ldpt, u, ldpt, z, ldx, rwork( mnmin+1 ),
835 \$ iinfo )
836*
837* Check error code from ZBDSQR.
838*
839 IF( iinfo.NE.0 ) THEN
840 WRITE( nout, fmt = 9998 )'ZBDSQR(vects)', iinfo, m, n,
841 \$ jtype, ioldsd
842 info = abs( iinfo )
843 IF( iinfo.LT.0 ) THEN
844 RETURN
845 ELSE
846 result( 4 ) = ulpinv
847 GO TO 150
848 END IF
849 END IF
850*
851* Use ZBDSQR to compute only the singular values of the
852* bidiagonal matrix B; U, VT, and Z should not be modified.
853*
854 CALL dcopy( mnmin, bd, 1, s2, 1 )
855 IF( mnmin.GT.0 )
856 \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
857*
858 CALL zbdsqr( uplo, mnmin, 0, 0, 0, s2, rwork, vt, ldpt, u,
859 \$ ldpt, z, ldx, rwork( mnmin+1 ), iinfo )
860*
861* Check error code from ZBDSQR.
862*
863 IF( iinfo.NE.0 ) THEN
864 WRITE( nout, fmt = 9998 )'ZBDSQR(values)', iinfo, m, n,
865 \$ jtype, ioldsd
866 info = abs( iinfo )
867 IF( iinfo.LT.0 ) THEN
868 RETURN
869 ELSE
870 result( 9 ) = ulpinv
871 GO TO 150
872 END IF
873 END IF
874*
875* Test 4: Check the decomposition B := U * S1 * VT
876* 5: Check the computation Z := U' * Y
877* 6: Check the orthogonality of U
878* 7: Check the orthogonality of VT
879*
880 CALL zbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
881 \$ work, result( 4 ) )
882 CALL zbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
883 \$ rwork, result( 5 ) )
884 CALL zunt01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
885 \$ rwork, result( 6 ) )
886 CALL zunt01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
887 \$ rwork, result( 7 ) )
888*
889* Test 8: Check that the singular values are sorted in
890* non-increasing order and are non-negative
891*
892 result( 8 ) = zero
893 DO 110 i = 1, mnmin - 1
894 IF( s1( i ).LT.s1( i+1 ) )
895 \$ result( 8 ) = ulpinv
896 IF( s1( i ).LT.zero )
897 \$ result( 8 ) = ulpinv
898 110 CONTINUE
899 IF( mnmin.GE.1 ) THEN
900 IF( s1( mnmin ).LT.zero )
901 \$ result( 8 ) = ulpinv
902 END IF
903*
904* Test 9: Compare ZBDSQR with and without singular vectors
905*
906 temp2 = zero
907*
908 DO 120 j = 1, mnmin
909 temp1 = abs( s1( j )-s2( j ) ) /
910 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
911 \$ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
912 temp2 = max( temp1, temp2 )
913 120 CONTINUE
914*
915 result( 9 ) = temp2
916*
917* Test 10: Sturm sequence test of singular values
918* Go up by factors of two until it succeeds
919*
920 temp1 = thresh*( half-ulp )
921*
922 DO 130 j = 0, log2ui
923 CALL dsvdch( mnmin, bd, be, s1, temp1, iinfo )
924 IF( iinfo.EQ.0 )
925 \$ GO TO 140
926 temp1 = temp1*two
927 130 CONTINUE
928*
929 140 CONTINUE
930 result( 10 ) = temp1
931*
932* Use ZBDSQR to form the decomposition A := (QU) S (VT PT)
933* from the bidiagonal form A := Q B PT.
934*
935 IF( .NOT.bidiag ) THEN
936 CALL dcopy( mnmin, bd, 1, s2, 1 )
937 IF( mnmin.GT.0 )
938 \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
939*
940 CALL zbdsqr( uplo, mnmin, n, m, nrhs, s2, rwork, pt,
941 \$ ldpt, q, ldq, y, ldx, rwork( mnmin+1 ),
942 \$ iinfo )
943*
944* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
945* 12: Check the computation Z := U' * Q' * X
946* 13: Check the orthogonality of Q*U
947* 14: Check the orthogonality of VT*PT
948*
949 CALL zbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
950 \$ ldpt, work, rwork, result( 11 ) )
951 CALL zbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
952 \$ rwork, result( 12 ) )
953 CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
954 \$ rwork, result( 13 ) )
955 CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
956 \$ rwork, result( 14 ) )
957 END IF
958*
959* End of Loop -- Check for RESULT(j) > THRESH
960*
961 150 CONTINUE
962 DO 160 j = 1, 14
963 IF( result( j ).GE.thresh ) THEN
964 IF( nfail.EQ.0 )
965 \$ CALL dlahd2( nout, path )
966 WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
967 \$ result( j )
968 nfail = nfail + 1
969 END IF
970 160 CONTINUE
971 IF( .NOT.bidiag ) THEN
972 ntest = ntest + 14
973 ELSE
974 ntest = ntest + 5
975 END IF
976*
977 170 CONTINUE
978 180 CONTINUE
979*
980* Summary
981*
982 CALL alasum( path, nout, nfail, ntest, 0 )
983*
984 RETURN
985*
986* End of ZCHKBD
987*
988 9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
989 \$ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
990 9998 FORMAT( ' ZCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
991 \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
992 \$ i5, ')' )
993*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
ZBDT01
Definition: zbdt01.f:147
subroutine zbdt03(UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK, RESID)
ZBDT03
Definition: zbdt03.f:135
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:126
subroutine zbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
ZBDT02
Definition: zbdt02.f:120
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
subroutine zlatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
ZLATMR
Definition: zlatmr.f:490
subroutine zungbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGBR
Definition: zungbr.f:157
subroutine zgebrd(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO)
ZGEBRD
Definition: zgebrd.f:205
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 zbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
ZBDSQR
Definition: zbdsqr.f:222
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dsvdch(N, S, E, SVD, TOL, INFO)
DSVDCH
Definition: dsvdch.f:97
subroutine dlahd2(IOUNIT, PATH)
DLAHD2
Definition: dlahd2.f:65
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
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