 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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) )```
Date
June 2016

Definition at line 417 of file zchkbd.f.

417 *
418 * -- LAPACK test routine (version 3.6.1) --
419 * -- LAPACK is a software package provided by Univ. of Tennessee, --
420 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
421 * June 2016
422 *
423 * .. Scalar Arguments ..
424  INTEGER info, lda, ldpt, ldq, ldx, lwork, nout, nrhs,
425  \$ nsizes, ntypes
426  DOUBLE PRECISION thresh
427 * ..
428 * .. Array Arguments ..
429  LOGICAL dotype( * )
430  INTEGER iseed( 4 ), mval( * ), nval( * )
431  DOUBLE PRECISION bd( * ), be( * ), rwork( * ), s1( * ), s2( * )
432  COMPLEX*16 a( lda, * ), pt( ldpt, * ), q( ldq, * ),
433  \$ u( ldpt, * ), vt( ldpt, * ), work( * ),
434  \$ x( ldx, * ), y( ldx, * ), z( ldx, * )
435 * ..
436 *
437 * ======================================================================
438 *
439 * .. Parameters ..
440  DOUBLE PRECISION zero, one, two, half
441  parameter ( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
442  \$ half = 0.5d0 )
443  COMPLEX*16 czero, cone
444  parameter ( czero = ( 0.0d+0, 0.0d+0 ),
445  \$ cone = ( 1.0d+0, 0.0d+0 ) )
446  INTEGER maxtyp
447  parameter ( maxtyp = 16 )
448 * ..
449 * .. Local Scalars ..
451  CHARACTER uplo
452  CHARACTER*3 path
453  INTEGER i, iinfo, imode, itype, j, jcol, jsize, jtype,
454  \$ log2ui, m, minwrk, mmax, mnmax, mnmin, mq,
455  \$ mtypes, n, nfail, nmax, ntest
456  DOUBLE PRECISION amninv, anorm, cond, ovfl, rtovfl, rtunfl,
457  \$ temp1, temp2, ulp, ulpinv, unfl
458 * ..
459 * .. Local Arrays ..
460  INTEGER ioldsd( 4 ), iwork( 1 ), kmagn( maxtyp ),
461  \$ kmode( maxtyp ), ktype( maxtyp )
462  DOUBLE PRECISION dumma( 1 ), result( 14 )
463 * ..
464 * .. External Functions ..
465  DOUBLE PRECISION dlamch, dlarnd
466  EXTERNAL dlamch, dlarnd
467 * ..
468 * .. External Subroutines ..
469  EXTERNAL alasum, dcopy, dlabad, dlahd2, dsvdch, xerbla,
472 * ..
473 * .. Intrinsic Functions ..
474  INTRINSIC abs, exp, int, log, max, min, sqrt
475 * ..
476 * .. Scalars in Common ..
477  LOGICAL lerr, ok
478  CHARACTER*32 srnamt
479  INTEGER infot, nunit
480 * ..
481 * .. Common blocks ..
482  COMMON / infoc / infot, nunit, ok, lerr
483  COMMON / srnamc / srnamt
484 * ..
485 * .. Data statements ..
486  DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
487  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
488  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
489  \$ 0, 0, 0 /
490 * ..
491 * .. Executable Statements ..
492 *
493 * Check for errors
494 *
495  info = 0
496 *
499  mmax = 1
500  nmax = 1
501  mnmax = 1
502  minwrk = 1
503  DO 10 j = 1, nsizes
504  mmax = max( mmax, mval( j ) )
505  IF( mval( j ).LT.0 )
507  nmax = max( nmax, nval( j ) )
508  IF( nval( j ).LT.0 )
510  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
511  minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
512  \$ mval( j )*( mval( j )+max( mval( j ), nval( j ),
513  \$ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
514  10 CONTINUE
515 *
516 * Check for errors
517 *
518  IF( nsizes.LT.0 ) THEN
519  info = -1
520  ELSE IF( badmm ) THEN
521  info = -2
522  ELSE IF( badnn ) THEN
523  info = -3
524  ELSE IF( ntypes.LT.0 ) THEN
525  info = -4
526  ELSE IF( nrhs.LT.0 ) THEN
527  info = -6
528  ELSE IF( lda.LT.mmax ) THEN
529  info = -11
530  ELSE IF( ldx.LT.mmax ) THEN
531  info = -17
532  ELSE IF( ldq.LT.mmax ) THEN
533  info = -21
534  ELSE IF( ldpt.LT.mnmax ) THEN
535  info = -23
536  ELSE IF( minwrk.GT.lwork ) THEN
537  info = -27
538  END IF
539 *
540  IF( info.NE.0 ) THEN
541  CALL xerbla( 'ZCHKBD', -info )
542  RETURN
543  END IF
544 *
545 * Initialize constants
546 *
547  path( 1: 1 ) = 'Zomplex precision'
548  path( 2: 3 ) = 'BD'
549  nfail = 0
550  ntest = 0
551  unfl = dlamch( 'Safe minimum' )
552  ovfl = dlamch( 'Overflow' )
553  CALL dlabad( unfl, ovfl )
554  ulp = dlamch( 'Precision' )
555  ulpinv = one / ulp
556  log2ui = int( log( ulpinv ) / log( two ) )
557  rtunfl = sqrt( unfl )
558  rtovfl = sqrt( ovfl )
559  infot = 0
560 *
561 * Loop over sizes, types
562 *
563  DO 180 jsize = 1, nsizes
564  m = mval( jsize )
565  n = nval( jsize )
566  mnmin = min( m, n )
567  amninv = one / max( m, n, 1 )
568 *
569  IF( nsizes.NE.1 ) THEN
570  mtypes = min( maxtyp, ntypes )
571  ELSE
572  mtypes = min( maxtyp+1, ntypes )
573  END IF
574 *
575  DO 170 jtype = 1, mtypes
576  IF( .NOT.dotype( jtype ) )
577  \$ GO TO 170
578 *
579  DO 20 j = 1, 4
580  ioldsd( j ) = iseed( j )
581  20 CONTINUE
582 *
583  DO 30 j = 1, 14
584  result( j ) = -one
585  30 CONTINUE
586 *
587  uplo = ' '
588 *
589 * Compute "A"
590 *
591 * Control parameters:
592 *
593 * KMAGN KMODE KTYPE
594 * =1 O(1) clustered 1 zero
595 * =2 large clustered 2 identity
596 * =3 small exponential (none)
597 * =4 arithmetic diagonal, (w/ eigenvalues)
598 * =5 random symmetric, w/ eigenvalues
599 * =6 nonsymmetric, w/ singular values
600 * =7 random diagonal
601 * =8 random symmetric
602 * =9 random nonsymmetric
603 * =10 random bidiagonal (log. distrib.)
604 *
605  IF( mtypes.GT.maxtyp )
606  \$ GO TO 100
607 *
608  itype = ktype( jtype )
609  imode = kmode( jtype )
610 *
611 * Compute norm
612 *
613  GO TO ( 40, 50, 60 )kmagn( jtype )
614 *
615  40 CONTINUE
616  anorm = one
617  GO TO 70
618 *
619  50 CONTINUE
620  anorm = ( rtovfl*ulp )*amninv
621  GO TO 70
622 *
623  60 CONTINUE
624  anorm = rtunfl*max( m, n )*ulpinv
625  GO TO 70
626 *
627  70 CONTINUE
628 *
629  CALL zlaset( 'Full', lda, n, czero, czero, a, lda )
630  iinfo = 0
631  cond = ulpinv
632 *
633  bidiag = .false.
634  IF( itype.EQ.1 ) THEN
635 *
636 * Zero matrix
637 *
638  iinfo = 0
639 *
640  ELSE IF( itype.EQ.2 ) THEN
641 *
642 * Identity
643 *
644  DO 80 jcol = 1, mnmin
645  a( jcol, jcol ) = anorm
646  80 CONTINUE
647 *
648  ELSE IF( itype.EQ.4 ) THEN
649 *
650 * Diagonal Matrix, [Eigen]values Specified
651 *
652  CALL zlatms( mnmin, mnmin, 'S', iseed, 'N', rwork, imode,
653  \$ cond, anorm, 0, 0, 'N', a, lda, work,
654  \$ iinfo )
655 *
656  ELSE IF( itype.EQ.5 ) THEN
657 *
658 * Symmetric, eigenvalues specified
659 *
660  CALL zlatms( mnmin, mnmin, 'S', iseed, 'S', rwork, imode,
661  \$ cond, anorm, m, n, 'N', a, lda, work,
662  \$ iinfo )
663 *
664  ELSE IF( itype.EQ.6 ) THEN
665 *
666 * Nonsymmetric, singular values specified
667 *
668  CALL zlatms( m, n, 'S', iseed, 'N', rwork, imode, cond,
669  \$ anorm, m, n, 'N', a, lda, work, iinfo )
670 *
671  ELSE IF( itype.EQ.7 ) THEN
672 *
673 * Diagonal, random entries
674 *
675  CALL zlatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
676  \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
677  \$ work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
678  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
679 *
680  ELSE IF( itype.EQ.8 ) THEN
681 *
682 * Symmetric, random entries
683 *
684  CALL zlatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
685  \$ cone, 'T', 'N', work( mnmin+1 ), 1, one,
686  \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
687  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
688 *
689  ELSE IF( itype.EQ.9 ) THEN
690 *
691 * Nonsymmetric, random entries
692 *
693  CALL zlatmr( m, n, 'S', iseed, 'N', work, 6, one, cone,
694  \$ 'T', 'N', work( mnmin+1 ), 1, one,
695  \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
696  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
697 *
698  ELSE IF( itype.EQ.10 ) THEN
699 *
700 * Bidiagonal, random entries
701 *
702  temp1 = -two*log( ulp )
703  DO 90 j = 1, mnmin
704  bd( j ) = exp( temp1*dlarnd( 2, iseed ) )
705  IF( j.LT.mnmin )
706  \$ be( j ) = exp( temp1*dlarnd( 2, iseed ) )
707  90 CONTINUE
708 *
709  iinfo = 0
710  bidiag = .true.
711  IF( m.GE.n ) THEN
712  uplo = 'U'
713  ELSE
714  uplo = 'L'
715  END IF
716  ELSE
717  iinfo = 1
718  END IF
719 *
720  IF( iinfo.EQ.0 ) THEN
721 *
722 * Generate Right-Hand Side
723 *
724  IF( bidiag ) THEN
725  CALL zlatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
726  \$ one, cone, 'T', 'N', work( mnmin+1 ), 1,
727  \$ one, work( 2*mnmin+1 ), 1, one, 'N',
728  \$ iwork, mnmin, nrhs, zero, one, 'NO', y,
729  \$ ldx, iwork, iinfo )
730  ELSE
731  CALL zlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
732  \$ cone, 'T', 'N', work( m+1 ), 1, one,
733  \$ work( 2*m+1 ), 1, one, 'N', iwork, m,
734  \$ nrhs, zero, one, 'NO', x, ldx, iwork,
735  \$ iinfo )
736  END IF
737  END IF
738 *
739 * Error Exit
740 *
741  IF( iinfo.NE.0 ) THEN
742  WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
743  \$ jtype, ioldsd
744  info = abs( iinfo )
745  RETURN
746  END IF
747 *
748  100 CONTINUE
749 *
750 * Call ZGEBRD and ZUNGBR to compute B, Q, and P, do tests.
751 *
752  IF( .NOT.bidiag ) THEN
753 *
754 * Compute transformations to reduce A to bidiagonal form:
755 * B := Q' * A * P.
756 *
757  CALL zlacpy( ' ', m, n, a, lda, q, ldq )
758  CALL zgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
759  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
760 *
761 * Check error code from ZGEBRD.
762 *
763  IF( iinfo.NE.0 ) THEN
764  WRITE( nout, fmt = 9998 )'ZGEBRD', iinfo, m, n,
765  \$ jtype, ioldsd
766  info = abs( iinfo )
767  RETURN
768  END IF
769 *
770  CALL zlacpy( ' ', m, n, q, ldq, pt, ldpt )
771  IF( m.GE.n ) THEN
772  uplo = 'U'
773  ELSE
774  uplo = 'L'
775  END IF
776 *
777 * Generate Q
778 *
779  mq = m
780  IF( nrhs.LE.0 )
781  \$ mq = mnmin
782  CALL zungbr( 'Q', m, mq, n, q, ldq, work,
783  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
784 *
785 * Check error code from ZUNGBR.
786 *
787  IF( iinfo.NE.0 ) THEN
788  WRITE( nout, fmt = 9998 )'ZUNGBR(Q)', iinfo, m, n,
789  \$ jtype, ioldsd
790  info = abs( iinfo )
791  RETURN
792  END IF
793 *
794 * Generate P'
795 *
796  CALL zungbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
797  \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
798 *
799 * Check error code from ZUNGBR.
800 *
801  IF( iinfo.NE.0 ) THEN
802  WRITE( nout, fmt = 9998 )'ZUNGBR(P)', iinfo, m, n,
803  \$ jtype, ioldsd
804  info = abs( iinfo )
805  RETURN
806  END IF
807 *
808 * Apply Q' to an M by NRHS matrix X: Y := Q' * X.
809 *
810  CALL zgemm( 'Conjugate transpose', 'No transpose', m,
811  \$ nrhs, m, cone, q, ldq, x, ldx, czero, y,
812  \$ ldx )
813 *
814 * Test 1: Check the decomposition A := Q * B * PT
815 * 2: Check the orthogonality of Q
816 * 3: Check the orthogonality of PT
817 *
818  CALL zbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
819  \$ work, rwork, result( 1 ) )
820  CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
821  \$ rwork, result( 2 ) )
822  CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
823  \$ rwork, result( 3 ) )
824  END IF
825 *
826 * Use ZBDSQR to form the SVD of the bidiagonal matrix B:
827 * B := U * S1 * VT, and compute Z = U' * Y.
828 *
829  CALL dcopy( mnmin, bd, 1, s1, 1 )
830  IF( mnmin.GT.0 )
831  \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
832  CALL zlacpy( ' ', m, nrhs, y, ldx, z, ldx )
833  CALL zlaset( 'Full', mnmin, mnmin, czero, cone, u, ldpt )
834  CALL zlaset( 'Full', mnmin, mnmin, czero, cone, vt, ldpt )
835 *
836  CALL zbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, rwork, vt,
837  \$ ldpt, u, ldpt, z, ldx, rwork( mnmin+1 ),
838  \$ iinfo )
839 *
840 * Check error code from ZBDSQR.
841 *
842  IF( iinfo.NE.0 ) THEN
843  WRITE( nout, fmt = 9998 )'ZBDSQR(vects)', iinfo, m, n,
844  \$ jtype, ioldsd
845  info = abs( iinfo )
846  IF( iinfo.LT.0 ) THEN
847  RETURN
848  ELSE
849  result( 4 ) = ulpinv
850  GO TO 150
851  END IF
852  END IF
853 *
854 * Use ZBDSQR to compute only the singular values of the
855 * bidiagonal matrix B; U, VT, and Z should not be modified.
856 *
857  CALL dcopy( mnmin, bd, 1, s2, 1 )
858  IF( mnmin.GT.0 )
859  \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
860 *
861  CALL zbdsqr( uplo, mnmin, 0, 0, 0, s2, rwork, vt, ldpt, u,
862  \$ ldpt, z, ldx, rwork( mnmin+1 ), iinfo )
863 *
864 * Check error code from ZBDSQR.
865 *
866  IF( iinfo.NE.0 ) THEN
867  WRITE( nout, fmt = 9998 )'ZBDSQR(values)', iinfo, m, n,
868  \$ jtype, ioldsd
869  info = abs( iinfo )
870  IF( iinfo.LT.0 ) THEN
871  RETURN
872  ELSE
873  result( 9 ) = ulpinv
874  GO TO 150
875  END IF
876  END IF
877 *
878 * Test 4: Check the decomposition B := U * S1 * VT
879 * 5: Check the computation Z := U' * Y
880 * 6: Check the orthogonality of U
881 * 7: Check the orthogonality of VT
882 *
883  CALL zbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
884  \$ work, result( 4 ) )
885  CALL zbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
886  \$ rwork, result( 5 ) )
887  CALL zunt01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
888  \$ rwork, result( 6 ) )
889  CALL zunt01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
890  \$ rwork, result( 7 ) )
891 *
892 * Test 8: Check that the singular values are sorted in
893 * non-increasing order and are non-negative
894 *
895  result( 8 ) = zero
896  DO 110 i = 1, mnmin - 1
897  IF( s1( i ).LT.s1( i+1 ) )
898  \$ result( 8 ) = ulpinv
899  IF( s1( i ).LT.zero )
900  \$ result( 8 ) = ulpinv
901  110 CONTINUE
902  IF( mnmin.GE.1 ) THEN
903  IF( s1( mnmin ).LT.zero )
904  \$ result( 8 ) = ulpinv
905  END IF
906 *
907 * Test 9: Compare ZBDSQR with and without singular vectors
908 *
909  temp2 = zero
910 *
911  DO 120 j = 1, mnmin
912  temp1 = abs( s1( j )-s2( j ) ) /
913  \$ max( sqrt( unfl )*max( s1( 1 ), one ),
914  \$ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
915  temp2 = max( temp1, temp2 )
916  120 CONTINUE
917 *
918  result( 9 ) = temp2
919 *
920 * Test 10: Sturm sequence test of singular values
921 * Go up by factors of two until it succeeds
922 *
923  temp1 = thresh*( half-ulp )
924 *
925  DO 130 j = 0, log2ui
926  CALL dsvdch( mnmin, bd, be, s1, temp1, iinfo )
927  IF( iinfo.EQ.0 )
928  \$ GO TO 140
929  temp1 = temp1*two
930  130 CONTINUE
931 *
932  140 CONTINUE
933  result( 10 ) = temp1
934 *
935 * Use ZBDSQR to form the decomposition A := (QU) S (VT PT)
936 * from the bidiagonal form A := Q B PT.
937 *
938  IF( .NOT.bidiag ) THEN
939  CALL dcopy( mnmin, bd, 1, s2, 1 )
940  IF( mnmin.GT.0 )
941  \$ CALL dcopy( mnmin-1, be, 1, rwork, 1 )
942 *
943  CALL zbdsqr( uplo, mnmin, n, m, nrhs, s2, rwork, pt,
944  \$ ldpt, q, ldq, y, ldx, rwork( mnmin+1 ),
945  \$ iinfo )
946 *
947 * Test 11: Check the decomposition A := Q*U * S2 * VT*PT
948 * 12: Check the computation Z := U' * Q' * X
949 * 13: Check the orthogonality of Q*U
950 * 14: Check the orthogonality of VT*PT
951 *
952  CALL zbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
953  \$ ldpt, work, rwork, result( 11 ) )
954  CALL zbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
955  \$ rwork, result( 12 ) )
956  CALL zunt01( 'Columns', m, mq, q, ldq, work, lwork,
957  \$ rwork, result( 13 ) )
958  CALL zunt01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
959  \$ rwork, result( 14 ) )
960  END IF
961 *
962 * End of Loop -- Check for RESULT(j) > THRESH
963 *
964  150 CONTINUE
965  DO 160 j = 1, 14
966  IF( result( j ).GE.thresh ) THEN
967  IF( nfail.EQ.0 )
968  \$ CALL dlahd2( nout, path )
969  WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
970  \$ result( j )
971  nfail = nfail + 1
972  END IF
973  160 CONTINUE
974  IF( .NOT.bidiag ) THEN
975  ntest = ntest + 14
976  ELSE
977  ntest = ntest + 5
978  END IF
979 *
980  170 CONTINUE
981  180 CONTINUE
982 *
983 * Summary
984 *
985  CALL alasum( path, nout, nfail, ntest, 0 )
986 *
987  RETURN
988 *
989 * End of ZCHKBD
990 *
991  9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
992  \$ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
993  9998 FORMAT( ' ZCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
994  \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
995  \$ i5, ')' )
996 *
subroutine dsvdch(N, S, E, SVD, TOL, INFO)
DSVDCH
Definition: dsvdch.f:99
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
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:492
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:53
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zungbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGBR
Definition: zungbr.f:159
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
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:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:128
subroutine zgebrd(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO)
ZGEBRD
Definition: zgebrd.f:207
subroutine zbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
ZBDT01
Definition: zbdt01.f:148
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:75
subroutine zbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RWORK, RESID)
ZBDT02
Definition: zbdt02.f:121
subroutine zbdt03(UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK, RESID)
ZBDT03
Definition: zbdt03.f:137
subroutine zbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
ZBDSQR
Definition: zbdsqr.f:224
subroutine dlahd2(IOUNIT, PATH)
DLAHD2
Definition: dlahd2.f:67
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75

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