 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ cchkbd()

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

CCHKBD

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

CGEBRD 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.

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

CBDSQR 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, CBDSQR 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 CGEBRD and CUNGBR

(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 CBDSQR 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
SSVDCH)

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

Test CBDSQR 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) CGEBRD 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, CCHKBD 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 CBDSQR. 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 CCHKBD 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. 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 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 REAL array, dimension (max(min(MVAL(j),NVAL(j)))) [out] BE BE is REAL array, dimension (max(min(MVAL(j),NVAL(j)))) [out] S1 S1 is REAL array, dimension (max(min(MVAL(j),NVAL(j)))) [out] S2 S2 is REAL array, dimension (max(min(MVAL(j),NVAL(j)))) [out] X X is COMPLEX 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 array, dimension (LDX,NRHS) [out] Z Z is COMPLEX array, dimension (LDX,NRHS) [out] Q Q is COMPLEX 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 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 array, dimension (LDPT,max(min(MVAL(j),NVAL(j)))) [out] VT VT is COMPLEX array, dimension (LDPT,max(min(MVAL(j),NVAL(j)))) [out] WORK WORK is COMPLEX 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 REAL 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 CLATMR, CLATMS, CGEBRD, CUNGBR, or CBDSQR, 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 cchkbd.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  REAL THRESH
424 * ..
425 * .. Array Arguments ..
426  LOGICAL DOTYPE( * )
427  INTEGER ISEED( 4 ), MVAL( * ), NVAL( * )
428  REAL BD( * ), BE( * ), RWORK( * ), S1( * ), S2( * )
429  COMPLEX 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  REAL ZERO, ONE, TWO, HALF
438  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
439  \$ half = 0.5e0 )
440  COMPLEX CZERO, CONE
441  parameter( czero = ( 0.0e+0, 0.0e+0 ),
442  \$ cone = ( 1.0e+0, 0.0e+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  REAL 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  REAL DUMMA( 1 ), RESULT( 14 )
460 * ..
461 * .. External Functions ..
462  REAL SLAMCH, SLARND
463  EXTERNAL slamch, slarnd
464 * ..
465 * .. External Subroutines ..
466  EXTERNAL alasum, cbdsqr, cbdt01, cbdt02, cbdt03,
469  \$ slahd2, ssvdch, xerbla
470 * ..
471 * .. Intrinsic Functions ..
472  INTRINSIC abs, exp, int, log, max, min, sqrt
473 * ..
474 * .. Scalars in Common ..
475  LOGICAL LERR, OK
476  CHARACTER*32 SRNAMT
477  INTEGER INFOT, NUNIT
478 * ..
479 * .. Common blocks ..
480  COMMON / infoc / infot, nunit, ok, lerr
481  COMMON / srnamc / srnamt
482 * ..
483 * .. Data statements ..
484  DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
485  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
486  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
487  \$ 0, 0, 0 /
488 * ..
489 * .. Executable Statements ..
490 *
491 * Check for errors
492 *
493  info = 0
494 *
497  mmax = 1
498  nmax = 1
499  mnmax = 1
500  minwrk = 1
501  DO 10 j = 1, nsizes
502  mmax = max( mmax, mval( j ) )
503  IF( mval( j ).LT.0 )
505  nmax = max( nmax, nval( j ) )
506  IF( nval( j ).LT.0 )
508  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
509  minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
510  \$ mval( j )*( mval( j )+max( mval( j ), nval( j ),
511  \$ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
512  10 CONTINUE
513 *
514 * Check for errors
515 *
516  IF( nsizes.LT.0 ) THEN
517  info = -1
518  ELSE IF( badmm ) THEN
519  info = -2
520  ELSE IF( badnn ) THEN
521  info = -3
522  ELSE IF( ntypes.LT.0 ) THEN
523  info = -4
524  ELSE IF( nrhs.LT.0 ) THEN
525  info = -6
526  ELSE IF( lda.LT.mmax ) THEN
527  info = -11
528  ELSE IF( ldx.LT.mmax ) THEN
529  info = -17
530  ELSE IF( ldq.LT.mmax ) THEN
531  info = -21
532  ELSE IF( ldpt.LT.mnmax ) THEN
533  info = -23
534  ELSE IF( minwrk.GT.lwork ) THEN
535  info = -27
536  END IF
537 *
538  IF( info.NE.0 ) THEN
539  CALL xerbla( 'CCHKBD', -info )
540  RETURN
541  END IF
542 *
543 * Initialize constants
544 *
545  path( 1: 1 ) = 'Complex precision'
546  path( 2: 3 ) = 'BD'
547  nfail = 0
548  ntest = 0
549  unfl = slamch( 'Safe minimum' )
550  ovfl = slamch( 'Overflow' )
551  CALL slabad( unfl, ovfl )
552  ulp = slamch( 'Precision' )
553  ulpinv = one / ulp
554  log2ui = int( log( ulpinv ) / log( two ) )
555  rtunfl = sqrt( unfl )
556  rtovfl = sqrt( ovfl )
557  infot = 0
558 *
559 * Loop over sizes, types
560 *
561  DO 180 jsize = 1, nsizes
562  m = mval( jsize )
563  n = nval( jsize )
564  mnmin = min( m, n )
565  amninv = one / max( m, n, 1 )
566 *
567  IF( nsizes.NE.1 ) THEN
568  mtypes = min( maxtyp, ntypes )
569  ELSE
570  mtypes = min( maxtyp+1, ntypes )
571  END IF
572 *
573  DO 170 jtype = 1, mtypes
574  IF( .NOT.dotype( jtype ) )
575  \$ GO TO 170
576 *
577  DO 20 j = 1, 4
578  ioldsd( j ) = iseed( j )
579  20 CONTINUE
580 *
581  DO 30 j = 1, 14
582  result( j ) = -one
583  30 CONTINUE
584 *
585  uplo = ' '
586 *
587 * Compute "A"
588 *
589 * Control parameters:
590 *
591 * KMAGN KMODE KTYPE
592 * =1 O(1) clustered 1 zero
593 * =2 large clustered 2 identity
594 * =3 small exponential (none)
595 * =4 arithmetic diagonal, (w/ eigenvalues)
596 * =5 random symmetric, w/ eigenvalues
597 * =6 nonsymmetric, w/ singular values
598 * =7 random diagonal
599 * =8 random symmetric
600 * =9 random nonsymmetric
601 * =10 random bidiagonal (log. distrib.)
602 *
603  IF( mtypes.GT.maxtyp )
604  \$ GO TO 100
605 *
606  itype = ktype( jtype )
607  imode = kmode( jtype )
608 *
609 * Compute norm
610 *
611  GO TO ( 40, 50, 60 )kmagn( jtype )
612 *
613  40 CONTINUE
614  anorm = one
615  GO TO 70
616 *
617  50 CONTINUE
618  anorm = ( rtovfl*ulp )*amninv
619  GO TO 70
620 *
621  60 CONTINUE
622  anorm = rtunfl*max( m, n )*ulpinv
623  GO TO 70
624 *
625  70 CONTINUE
626 *
627  CALL claset( 'Full', lda, n, czero, czero, a, lda )
628  iinfo = 0
629  cond = ulpinv
630 *
631  bidiag = .false.
632  IF( itype.EQ.1 ) THEN
633 *
634 * Zero matrix
635 *
636  iinfo = 0
637 *
638  ELSE IF( itype.EQ.2 ) THEN
639 *
640 * Identity
641 *
642  DO 80 jcol = 1, mnmin
643  a( jcol, jcol ) = anorm
644  80 CONTINUE
645 *
646  ELSE IF( itype.EQ.4 ) THEN
647 *
648 * Diagonal Matrix, [Eigen]values Specified
649 *
650  CALL clatms( mnmin, mnmin, 'S', iseed, 'N', rwork, imode,
651  \$ cond, anorm, 0, 0, 'N', a, lda, work,
652  \$ iinfo )
653 *
654  ELSE IF( itype.EQ.5 ) THEN
655 *
656 * Symmetric, eigenvalues specified
657 *
658  CALL clatms( mnmin, mnmin, 'S', iseed, 'S', rwork, imode,
659  \$ cond, anorm, m, n, 'N', a, lda, work,
660  \$ iinfo )
661 *
662  ELSE IF( itype.EQ.6 ) THEN
663 *
664 * Nonsymmetric, singular values specified
665 *
666  CALL clatms( m, n, 'S', iseed, 'N', rwork, imode, cond,
667  \$ anorm, m, n, 'N', a, lda, work, iinfo )
668 *
669  ELSE IF( itype.EQ.7 ) THEN
670 *
671 * Diagonal, random entries
672 *
673  CALL clatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
674  \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
675  \$ work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
676  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
677 *
678  ELSE IF( itype.EQ.8 ) THEN
679 *
680 * Symmetric, random entries
681 *
682  CALL clatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
683  \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
684  \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
685  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
686 *
687  ELSE IF( itype.EQ.9 ) THEN
688 *
689 * Nonsymmetric, random entries
690 *
691  CALL clatmr( m, n, 'S', iseed, 'N', work, 6, one, cone,
692  \$ 'T', 'N', work( mnmin+1 ), 1, one,
693  \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
694  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
695 *
696  ELSE IF( itype.EQ.10 ) THEN
697 *
698 * Bidiagonal, random entries
699 *
700  temp1 = -two*log( ulp )
701  DO 90 j = 1, mnmin
702  bd( j ) = exp( temp1*slarnd( 2, iseed ) )
703  IF( j.LT.mnmin )
704  \$ be( j ) = exp( temp1*slarnd( 2, iseed ) )
705  90 CONTINUE
706 *
707  iinfo = 0
708  bidiag = .true.
709  IF( m.GE.n ) THEN
710  uplo = 'U'
711  ELSE
712  uplo = 'L'
713  END IF
714  ELSE
715  iinfo = 1
716  END IF
717 *
718  IF( iinfo.EQ.0 ) THEN
719 *
720 * Generate Right-Hand Side
721 *
722  IF( bidiag ) THEN
723  CALL clatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
724  \$ one, cone, 'T', 'N', work( mnmin+1 ), 1,
725  \$ one, work( 2*mnmin+1 ), 1, one, 'N',
726  \$ iwork, mnmin, nrhs, zero, one, 'NO', y,
727  \$ ldx, iwork, iinfo )
728  ELSE
729  CALL clatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
730  \$ cone, 'T', 'N', work( m+1 ), 1, one,
731  \$ work( 2*m+1 ), 1, one, 'N', iwork, m,
732  \$ nrhs, zero, one, 'NO', x, ldx, iwork,
733  \$ iinfo )
734  END IF
735  END IF
736 *
737 * Error Exit
738 *
739  IF( iinfo.NE.0 ) THEN
740  WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
741  \$ jtype, ioldsd
742  info = abs( iinfo )
743  RETURN
744  END IF
745 *
746  100 CONTINUE
747 *
748 * Call CGEBRD and CUNGBR to compute B, Q, and P, do tests.
749 *
750  IF( .NOT.bidiag ) THEN
751 *
752 * Compute transformations to reduce A to bidiagonal form:
753 * B := Q' * A * P.
754 *
755  CALL clacpy( ' ', m, n, a, lda, q, ldq )
756  CALL cgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
757  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
758 *
759 * Check error code from CGEBRD.
760 *
761  IF( iinfo.NE.0 ) THEN
762  WRITE( nout, fmt = 9998 )'CGEBRD', iinfo, m, n,
763  \$ jtype, ioldsd
764  info = abs( iinfo )
765  RETURN
766  END IF
767 *
768  CALL clacpy( ' ', m, n, q, ldq, pt, ldpt )
769  IF( m.GE.n ) THEN
770  uplo = 'U'
771  ELSE
772  uplo = 'L'
773  END IF
774 *
775 * Generate Q
776 *
777  mq = m
778  IF( nrhs.LE.0 )
779  \$ mq = mnmin
780  CALL cungbr( 'Q', m, mq, n, q, ldq, work,
781  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
782 *
783 * Check error code from CUNGBR.
784 *
785  IF( iinfo.NE.0 ) THEN
786  WRITE( nout, fmt = 9998 )'CUNGBR(Q)', iinfo, m, n,
787  \$ jtype, ioldsd
788  info = abs( iinfo )
789  RETURN
790  END IF
791 *
792 * Generate P'
793 *
794  CALL cungbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
795  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
796 *
797 * Check error code from CUNGBR.
798 *
799  IF( iinfo.NE.0 ) THEN
800  WRITE( nout, fmt = 9998 )'CUNGBR(P)', iinfo, m, n,
801  \$ jtype, ioldsd
802  info = abs( iinfo )
803  RETURN
804  END IF
805 *
806 * Apply Q' to an M by NRHS matrix X: Y := Q' * X.
807 *
808  CALL cgemm( 'Conjugate transpose', 'No transpose', m,
809  \$ nrhs, m, cone, q, ldq, x, ldx, czero, y,
810  \$ ldx )
811 *
812 * Test 1: Check the decomposition A := Q * B * PT
813 * 2: Check the orthogonality of Q
814 * 3: Check the orthogonality of PT
815 *
816  CALL cbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
817  \$ work, rwork, result( 1 ) )
818  CALL cunt01( 'Columns', m, mq, q, ldq, work, lwork,
819  \$ rwork, result( 2 ) )
820  CALL cunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
821  \$ rwork, result( 3 ) )
822  END IF
823 *
824 * Use CBDSQR to form the SVD of the bidiagonal matrix B:
825 * B := U * S1 * VT, and compute Z = U' * Y.
826 *
827  CALL scopy( mnmin, bd, 1, s1, 1 )
828  IF( mnmin.GT.0 )
829  \$ CALL scopy( mnmin-1, be, 1, rwork, 1 )
830  CALL clacpy( ' ', m, nrhs, y, ldx, z, ldx )
831  CALL claset( 'Full', mnmin, mnmin, czero, cone, u, ldpt )
832  CALL claset( 'Full', mnmin, mnmin, czero, cone, vt, ldpt )
833 *
834  CALL cbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, rwork, vt,
835  \$ ldpt, u, ldpt, z, ldx, rwork( mnmin+1 ),
836  \$ iinfo )
837 *
838 * Check error code from CBDSQR.
839 *
840  IF( iinfo.NE.0 ) THEN
841  WRITE( nout, fmt = 9998 )'CBDSQR(vects)', iinfo, m, n,
842  \$ jtype, ioldsd
843  info = abs( iinfo )
844  IF( iinfo.LT.0 ) THEN
845  RETURN
846  ELSE
847  result( 4 ) = ulpinv
848  GO TO 150
849  END IF
850  END IF
851 *
852 * Use CBDSQR to compute only the singular values of the
853 * bidiagonal matrix B; U, VT, and Z should not be modified.
854 *
855  CALL scopy( mnmin, bd, 1, s2, 1 )
856  IF( mnmin.GT.0 )
857  \$ CALL scopy( mnmin-1, be, 1, rwork, 1 )
858 *
859  CALL cbdsqr( uplo, mnmin, 0, 0, 0, s2, rwork, vt, ldpt, u,
860  \$ ldpt, z, ldx, rwork( mnmin+1 ), iinfo )
861 *
862 * Check error code from CBDSQR.
863 *
864  IF( iinfo.NE.0 ) THEN
865  WRITE( nout, fmt = 9998 )'CBDSQR(values)', iinfo, m, n,
866  \$ jtype, ioldsd
867  info = abs( iinfo )
868  IF( iinfo.LT.0 ) THEN
869  RETURN
870  ELSE
871  result( 9 ) = ulpinv
872  GO TO 150
873  END IF
874  END IF
875 *
876 * Test 4: Check the decomposition B := U * S1 * VT
877 * 5: Check the computation Z := U' * Y
878 * 6: Check the orthogonality of U
879 * 7: Check the orthogonality of VT
880 *
881  CALL cbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
882  \$ work, result( 4 ) )
883  CALL cbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
884  \$ rwork, result( 5 ) )
885  CALL cunt01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
886  \$ rwork, result( 6 ) )
887  CALL cunt01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
888  \$ rwork, result( 7 ) )
889 *
890 * Test 8: Check that the singular values are sorted in
891 * non-increasing order and are non-negative
892 *
893  result( 8 ) = zero
894  DO 110 i = 1, mnmin - 1
895  IF( s1( i ).LT.s1( i+1 ) )
896  \$ result( 8 ) = ulpinv
897  IF( s1( i ).LT.zero )
898  \$ result( 8 ) = ulpinv
899  110 CONTINUE
900  IF( mnmin.GE.1 ) THEN
901  IF( s1( mnmin ).LT.zero )
902  \$ result( 8 ) = ulpinv
903  END IF
904 *
905 * Test 9: Compare CBDSQR with and without singular vectors
906 *
907  temp2 = zero
908 *
909  DO 120 j = 1, mnmin
910  temp1 = abs( s1( j )-s2( j ) ) /
911  \$ max( sqrt( unfl )*max( s1( 1 ), one ),
912  \$ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
913  temp2 = max( temp1, temp2 )
914  120 CONTINUE
915 *
916  result( 9 ) = temp2
917 *
918 * Test 10: Sturm sequence test of singular values
919 * Go up by factors of two until it succeeds
920 *
921  temp1 = thresh*( half-ulp )
922 *
923  DO 130 j = 0, log2ui
924  CALL ssvdch( mnmin, bd, be, s1, temp1, iinfo )
925  IF( iinfo.EQ.0 )
926  \$ GO TO 140
927  temp1 = temp1*two
928  130 CONTINUE
929 *
930  140 CONTINUE
931  result( 10 ) = temp1
932 *
933 * Use CBDSQR to form the decomposition A := (QU) S (VT PT)
934 * from the bidiagonal form A := Q B PT.
935 *
936  IF( .NOT.bidiag ) THEN
937  CALL scopy( mnmin, bd, 1, s2, 1 )
938  IF( mnmin.GT.0 )
939  \$ CALL scopy( mnmin-1, be, 1, rwork, 1 )
940 *
941  CALL cbdsqr( uplo, mnmin, n, m, nrhs, s2, rwork, pt,
942  \$ ldpt, q, ldq, y, ldx, rwork( mnmin+1 ),
943  \$ iinfo )
944 *
945 * Test 11: Check the decomposition A := Q*U * S2 * VT*PT
946 * 12: Check the computation Z := U' * Q' * X
947 * 13: Check the orthogonality of Q*U
948 * 14: Check the orthogonality of VT*PT
949 *
950  CALL cbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
951  \$ ldpt, work, rwork, result( 11 ) )
952  CALL cbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
953  \$ rwork, result( 12 ) )
954  CALL cunt01( 'Columns', m, mq, q, ldq, work, lwork,
955  \$ rwork, result( 13 ) )
956  CALL cunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
957  \$ rwork, result( 14 ) )
958  END IF
959 *
960 * End of Loop -- Check for RESULT(j) > THRESH
961 *
962  150 CONTINUE
963  DO 160 j = 1, 14
964  IF( result( j ).GE.thresh ) THEN
965  IF( nfail.EQ.0 )
966  \$ CALL slahd2( nout, path )
967  WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
968  \$ result( j )
969  nfail = nfail + 1
970  END IF
971  160 CONTINUE
972  IF( .NOT.bidiag ) THEN
973  ntest = ntest + 14
974  ELSE
975  ntest = ntest + 5
976  END IF
977 *
978  170 CONTINUE
979  180 CONTINUE
980 *
981 * Summary
982 *
983  CALL alasum( path, nout, nfail, ntest, 0 )
984 *
985  RETURN
986 *
987 * End of CCHKBD
988 *
989  9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
990  \$ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
991  9998 FORMAT( ' CCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
992  \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
993  \$ i5, ')' )
994 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
CBDT02
Definition: cbdt02.f:120
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 cbdt03(UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK, RESID)
CBDT03
Definition: cbdt03.f:135
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:332
subroutine clatmr(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)
CLATMR
Definition: clatmr.f:490
subroutine cungbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGBR
Definition: cungbr.f:157
subroutine cgebrd(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO)
CGEBRD
Definition: cgebrd.f:206
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 cbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
CBDSQR
Definition: cbdsqr.f:222
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine ssvdch(N, S, E, SVD, TOL, INFO)
SSVDCH
Definition: ssvdch.f:97
subroutine slahd2(IOUNIT, PATH)
SLAHD2
Definition: slahd2.f:65
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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