 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cchkbb()

 subroutine cchkbb ( integer NSIZES, integer, dimension( * ) MVAL, integer, dimension( * ) NVAL, integer NWDTHS, integer, dimension( * ) KK, integer NTYPES, logical, dimension( * ) DOTYPE, integer NRHS, integer, dimension( 4 ) ISEED, real THRESH, integer NOUNIT, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) BD, real, dimension( * ) BE, complex, dimension( ldq, * ) Q, integer LDQ, complex, dimension( ldp, * ) P, integer LDP, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( ldc, * ) CC, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT, integer INFO )

CCHKBB

Purpose:
``` CCHKBB tests the reduction of a general complex rectangular band
matrix to real bidiagonal form.

CGBBRD factors a general band matrix A as  Q B P* , where * means
conjugate transpose, B is upper bidiagonal, and Q and P are unitary;
CGBBRD can also overwrite a given matrix C with Q* C .

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 C are generated.
The problem dimensions are as follows
A:          M x N
Q:          M x M
P:          N x N
B:          min(M,N) x min(M,N)
C:          M x NRHS

For each generated matrix, 4 tests are performed:

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

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

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

(4)   | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.

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:

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 )```
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). If NSIZES is zero, CCHKBB does nothing. NSIZES must be at least zero.``` [in] MVAL ``` MVAL is INTEGER array, dimension (NSIZES) The values of the matrix row dimension M.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NSIZES) The values of the matrix column dimension N.``` [in] NWDTHS ``` NWDTHS is INTEGER The number of bandwidths to use. If it is zero, CCHKBB does nothing. It must be at least zero.``` [in] KK ``` KK is INTEGER array, dimension (NWDTHS) An array containing the bandwidths to be used for the band matrices. The values must be at least zero.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, CCHKBB 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 matrix is in A. 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 in NN a matrix of that size and 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" matrix C. 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 random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to CCHKBB to continue the same random number sequence.``` [in] THRESH ``` THRESH is REAL A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.``` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)``` [in,out] A ``` A is REAL array, dimension (LDA, max(NN)) Used to hold the matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of A. It must be at least 1 and at least max( NN ).``` [out] AB ``` AB is REAL array, dimension (LDAB, max(NN)) Used to hold A in band storage format.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of AB. It must be at least 2 (not 1!) and at least max( KK )+1.``` [out] BD ``` BD is REAL array, dimension (max(NN)) Used to hold the diagonal of the bidiagonal matrix computed by CGBBRD.``` [out] BE ``` BE is REAL array, dimension (max(NN)) Used to hold the off-diagonal of the bidiagonal matrix computed by CGBBRD.``` [out] Q ``` Q is COMPLEX array, dimension (LDQ, max(NN)) Used to hold the unitary matrix Q computed by CGBBRD.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of Q. It must be at least 1 and at least max( NN ).``` [out] P ``` P is COMPLEX array, dimension (LDP, max(NN)) Used to hold the unitary matrix P computed by CGBBRD.``` [in] LDP ``` LDP is INTEGER The leading dimension of P. It must be at least 1 and at least max( NN ).``` [out] C ``` C is COMPLEX array, dimension (LDC, max(NN)) Used to hold the matrix C updated by CGBBRD.``` [in] LDC ``` LDC is INTEGER The leading dimension of U. It must be at least 1 and at least max( NN ).``` [out] CC ``` CC is COMPLEX array, dimension (LDC, max(NN)) Used to hold a copy of the matrix C.``` [out] WORK ` WORK is COMPLEX array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least max( LDA+1, max(NN)+1 )*max(NN).``` [out] RWORK ` RWORK is REAL array, dimension (max(NN))` [out] RESULT ``` RESULT is REAL array, dimension (4) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.``` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. ----------------------------------------------------------------------- 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. NTESTT The total number of tests performed so far. NMAX Largest value in NN. NMATS The number of matrices generated so far. NERRS The number of tests which have exceeded THRESH so far. COND, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. ULP, ULPINV Finest relative precision and its inverse. RTOVFL, RTUNFL Square roots of the previous 2 values. 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 357 of file cchkbb.f.

361 *
362 * -- LAPACK test routine (input) --
363 * -- LAPACK is a software package provided by Univ. of Tennessee, --
364 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
365 *
366 * .. Scalar Arguments ..
367  INTEGER INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
368  \$ NRHS, NSIZES, NTYPES, NWDTHS
369  REAL THRESH
370 * ..
371 * .. Array Arguments ..
372  LOGICAL DOTYPE( * )
373  INTEGER ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
374  REAL BD( * ), BE( * ), RESULT( * ), RWORK( * )
375  COMPLEX A( LDA, * ), AB( LDAB, * ), C( LDC, * ),
376  \$ CC( LDC, * ), P( LDP, * ), Q( LDQ, * ),
377  \$ WORK( * )
378 * ..
379 *
380 * =====================================================================
381 *
382 * .. Parameters ..
383  COMPLEX CZERO, CONE
384  parameter( czero = ( 0.0e+0, 0.0e+0 ),
385  \$ cone = ( 1.0e+0, 0.0e+0 ) )
386  REAL ZERO, ONE
387  parameter( zero = 0.0e+0, one = 1.0e+0 )
388  INTEGER MAXTYP
389  parameter( maxtyp = 15 )
390 * ..
391 * .. Local Scalars ..
393  INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JR, JSIZE,
394  \$ JTYPE, JWIDTH, K, KL, KMAX, KU, M, MMAX, MNMAX,
395  \$ MNMIN, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
396  \$ NTESTT
397  REAL AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, ULP,
398  \$ ULPINV, UNFL
399 * ..
400 * .. Local Arrays ..
401  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
402  \$ KMODE( MAXTYP ), KTYPE( MAXTYP )
403 * ..
404 * .. External Functions ..
405  REAL SLAMCH
406  EXTERNAL slamch
407 * ..
408 * .. External Subroutines ..
409  EXTERNAL cbdt01, cbdt02, cgbbrd, clacpy, claset, clatmr,
411 * ..
412 * .. Intrinsic Functions ..
413  INTRINSIC abs, max, min, real, sqrt
414 * ..
415 * .. Data statements ..
416  DATA ktype / 1, 2, 5*4, 5*6, 3*9 /
417  DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3 /
418  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
419  \$ 0, 0 /
420 * ..
421 * .. Executable Statements ..
422 *
423 * Check for errors
424 *
425  ntestt = 0
426  info = 0
427 *
428 * Important constants
429 *
432  mmax = 1
433  nmax = 1
434  mnmax = 1
435  DO 10 j = 1, nsizes
436  mmax = max( mmax, mval( j ) )
437  IF( mval( j ).LT.0 )
439  nmax = max( nmax, nval( j ) )
440  IF( nval( j ).LT.0 )
442  mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
443  10 CONTINUE
444 *
446  kmax = 0
447  DO 20 j = 1, nwdths
448  kmax = max( kmax, kk( j ) )
449  IF( kk( j ).LT.0 )
451  20 CONTINUE
452 *
453 * Check for errors
454 *
455  IF( nsizes.LT.0 ) THEN
456  info = -1
457  ELSE IF( badmm ) THEN
458  info = -2
459  ELSE IF( badnn ) THEN
460  info = -3
461  ELSE IF( nwdths.LT.0 ) THEN
462  info = -4
463  ELSE IF( badnnb ) THEN
464  info = -5
465  ELSE IF( ntypes.LT.0 ) THEN
466  info = -6
467  ELSE IF( nrhs.LT.0 ) THEN
468  info = -8
469  ELSE IF( lda.LT.nmax ) THEN
470  info = -13
471  ELSE IF( ldab.LT.2*kmax+1 ) THEN
472  info = -15
473  ELSE IF( ldq.LT.nmax ) THEN
474  info = -19
475  ELSE IF( ldp.LT.nmax ) THEN
476  info = -21
477  ELSE IF( ldc.LT.nmax ) THEN
478  info = -23
479  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
480  info = -26
481  END IF
482 *
483  IF( info.NE.0 ) THEN
484  CALL xerbla( 'CCHKBB', -info )
485  RETURN
486  END IF
487 *
488 * Quick return if possible
489 *
490  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
491  \$ RETURN
492 *
493 * More Important constants
494 *
495  unfl = slamch( 'Safe minimum' )
496  ovfl = one / unfl
497  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
498  ulpinv = one / ulp
499  rtunfl = sqrt( unfl )
500  rtovfl = sqrt( ovfl )
501 *
502 * Loop over sizes, widths, types
503 *
504  nerrs = 0
505  nmats = 0
506 *
507  DO 160 jsize = 1, nsizes
508  m = mval( jsize )
509  n = nval( jsize )
510  mnmin = min( m, n )
511  amninv = one / real( max( 1, m, n ) )
512 *
513  DO 150 jwidth = 1, nwdths
514  k = kk( jwidth )
515  IF( k.GE.m .AND. k.GE.n )
516  \$ GO TO 150
517  kl = max( 0, min( m-1, k ) )
518  ku = max( 0, min( n-1, k ) )
519 *
520  IF( nsizes.NE.1 ) THEN
521  mtypes = min( maxtyp, ntypes )
522  ELSE
523  mtypes = min( maxtyp+1, ntypes )
524  END IF
525 *
526  DO 140 jtype = 1, mtypes
527  IF( .NOT.dotype( jtype ) )
528  \$ GO TO 140
529  nmats = nmats + 1
530  ntest = 0
531 *
532  DO 30 j = 1, 4
533  ioldsd( j ) = iseed( j )
534  30 CONTINUE
535 *
536 * Compute "A".
537 *
538 * Control parameters:
539 *
540 * KMAGN KMODE KTYPE
541 * =1 O(1) clustered 1 zero
542 * =2 large clustered 2 identity
543 * =3 small exponential (none)
544 * =4 arithmetic diagonal, (w/ singular values)
545 * =5 random log (none)
546 * =6 random nonhermitian, w/ singular values
547 * =7 (none)
548 * =8 (none)
549 * =9 random nonhermitian
550 *
551  IF( mtypes.GT.maxtyp )
552  \$ GO TO 90
553 *
554  itype = ktype( jtype )
555  imode = kmode( jtype )
556 *
557 * Compute norm
558 *
559  GO TO ( 40, 50, 60 )kmagn( jtype )
560 *
561  40 CONTINUE
562  anorm = one
563  GO TO 70
564 *
565  50 CONTINUE
566  anorm = ( rtovfl*ulp )*amninv
567  GO TO 70
568 *
569  60 CONTINUE
570  anorm = rtunfl*max( m, n )*ulpinv
571  GO TO 70
572 *
573  70 CONTINUE
574 *
575  CALL claset( 'Full', lda, n, czero, czero, a, lda )
576  CALL claset( 'Full', ldab, n, czero, czero, ab, ldab )
577  iinfo = 0
578  cond = ulpinv
579 *
580 * Special Matrices -- Identity & Jordan block
581 *
582 * Zero
583 *
584  IF( itype.EQ.1 ) THEN
585  iinfo = 0
586 *
587  ELSE IF( itype.EQ.2 ) THEN
588 *
589 * Identity
590 *
591  DO 80 jcol = 1, n
592  a( jcol, jcol ) = anorm
593  80 CONTINUE
594 *
595  ELSE IF( itype.EQ.4 ) THEN
596 *
597 * Diagonal Matrix, singular values specified
598 *
599  CALL clatms( m, n, 'S', iseed, 'N', rwork, imode,
600  \$ cond, anorm, 0, 0, 'N', a, lda, work,
601  \$ iinfo )
602 *
603  ELSE IF( itype.EQ.6 ) THEN
604 *
605 * Nonhermitian, singular values specified
606 *
607  CALL clatms( m, n, 'S', iseed, 'N', rwork, imode,
608  \$ cond, anorm, kl, ku, 'N', a, lda, work,
609  \$ iinfo )
610 *
611  ELSE IF( itype.EQ.9 ) THEN
612 *
613 * Nonhermitian, random entries
614 *
615  CALL clatmr( m, n, 'S', iseed, 'N', work, 6, one,
616  \$ cone, 'T', 'N', work( n+1 ), 1, one,
617  \$ work( 2*n+1 ), 1, one, 'N', idumma, kl,
618  \$ ku, zero, anorm, 'N', a, lda, idumma,
619  \$ iinfo )
620 *
621  ELSE
622 *
623  iinfo = 1
624  END IF
625 *
626 * Generate Right-Hand Side
627 *
628  CALL clatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
629  \$ cone, 'T', 'N', work( m+1 ), 1, one,
630  \$ work( 2*m+1 ), 1, one, 'N', idumma, m, nrhs,
631  \$ zero, one, 'NO', c, ldc, idumma, iinfo )
632 *
633  IF( iinfo.NE.0 ) THEN
634  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
635  \$ jtype, ioldsd
636  info = abs( iinfo )
637  RETURN
638  END IF
639 *
640  90 CONTINUE
641 *
642 * Copy A to band storage.
643 *
644  DO 110 j = 1, n
645  DO 100 i = max( 1, j-ku ), min( m, j+kl )
646  ab( ku+1+i-j, j ) = a( i, j )
647  100 CONTINUE
648  110 CONTINUE
649 *
650 * Copy C
651 *
652  CALL clacpy( 'Full', m, nrhs, c, ldc, cc, ldc )
653 *
654 * Call CGBBRD to compute B, Q and P, and to update C.
655 *
656  CALL cgbbrd( 'B', m, n, nrhs, kl, ku, ab, ldab, bd, be,
657  \$ q, ldq, p, ldp, cc, ldc, work, rwork,
658  \$ iinfo )
659 *
660  IF( iinfo.NE.0 ) THEN
661  WRITE( nounit, fmt = 9999 )'CGBBRD', iinfo, n, jtype,
662  \$ ioldsd
663  info = abs( iinfo )
664  IF( iinfo.LT.0 ) THEN
665  RETURN
666  ELSE
667  result( 1 ) = ulpinv
668  GO TO 120
669  END IF
670  END IF
671 *
672 * Test 1: Check the decomposition A := Q * B * P'
673 * 2: Check the orthogonality of Q
674 * 3: Check the orthogonality of P
675 * 4: Check the computation of Q' * C
676 *
677  CALL cbdt01( m, n, -1, a, lda, q, ldq, bd, be, p, ldp,
678  \$ work, rwork, result( 1 ) )
679  CALL cunt01( 'Columns', m, m, q, ldq, work, lwork, rwork,
680  \$ result( 2 ) )
681  CALL cunt01( 'Rows', n, n, p, ldp, work, lwork, rwork,
682  \$ result( 3 ) )
683  CALL cbdt02( m, nrhs, c, ldc, cc, ldc, q, ldq, work,
684  \$ rwork, result( 4 ) )
685 *
686 * End of Loop -- Check for RESULT(j) > THRESH
687 *
688  ntest = 4
689  120 CONTINUE
690  ntestt = ntestt + ntest
691 *
692 * Print out tests which fail.
693 *
694  DO 130 jr = 1, ntest
695  IF( result( jr ).GE.thresh ) THEN
696  IF( nerrs.EQ.0 )
697  \$ CALL slahd2( nounit, 'CBB' )
698  nerrs = nerrs + 1
699  WRITE( nounit, fmt = 9998 )m, n, k, ioldsd, jtype,
700  \$ jr, result( jr )
701  END IF
702  130 CONTINUE
703 *
704  140 CONTINUE
705  150 CONTINUE
706  160 CONTINUE
707 *
708 * Summary
709 *
710  CALL slasum( 'CBB', nounit, nerrs, ntestt )
711  RETURN
712 *
713  9999 FORMAT( ' CCHKBB: ', a, ' returned INFO=', i5, '.', / 9x, 'M=',
714  \$ i5, ' N=', i5, ' K=', i5, ', JTYPE=', i5, ', ISEED=(',
715  \$ 3( i5, ',' ), i5, ')' )
716  9998 FORMAT( ' M =', i4, ' N=', i4, ', K=', i3, ', seed=',
717  \$ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
718 *
719 * End of CCHKBB
720 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 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 cgbbrd(VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, RWORK, INFO)
CGBBRD
Definition: cgbbrd.f:193
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 slahd2(IOUNIT, PATH)
SLAHD2
Definition: slahd2.f:65
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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