LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cchkhb()

subroutine cchkhb ( integer  NSIZES,
integer, dimension( * )  NN,
integer  NWDTHS,
integer, dimension( * )  KK,
integer  NTYPES,
logical, dimension( * )  DOTYPE,
integer, dimension( 4 )  ISEED,
real  THRESH,
integer  NOUNIT,
complex, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  SD,
real, dimension( * )  SE,
complex, dimension( ldu, * )  U,
integer  LDU,
complex, dimension( * )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( * )  RESULT,
integer  INFO 
)

CCHKHB

Purpose:
 CCHKHB tests the reduction of a Hermitian band matrix to tridiagonal
 from, used with the Hermitian eigenvalue problem.

 CHBTRD factors a Hermitian band matrix A as  U S U* , where * means
 conjugate transpose, S is symmetric tridiagonal, and U is unitary.
 CHBTRD can use either just the lower or just the upper triangle
 of A; CCHKHB checks both cases.

 When CCHKHB is called, a number of matrix "sizes" ("n's"), a number
 of bandwidths ("k's"), and a number of matrix "types" are
 specified.  For each size ("n"), each bandwidth ("k") less than or
 equal to "n", and each type of matrix, one matrix will be generated
 and used to test the hermitian banded reduction routine.  For each
 matrix, a number of tests will be performed:

 (1)     | A - V S V* | / ( |A| n ulp )  computed by CHBTRD with
                                         UPLO='U'

 (2)     | I - UU* | / ( n ulp )

 (3)     | A - V S V* | / ( |A| n ulp )  computed by CHBTRD with
                                         UPLO='L'

 (4)     | I - UU* | / ( n ulp )

 The "sizes" are specified by an array NN(1:NSIZES); the value of
 each element NN(j) specifies one size.
 The "types" are specified by a logical array DOTYPE( 1:NTYPES );
 if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
 Currently, the list of possible types is:

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

 (3)  A 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 (4), but multiplied by SQRT( overflow threshold )
 (7)  Same as (4), but multiplied by SQRT( underflow threshold )

 (8)  A matrix of the form  U* D U, where U is unitary and
      D has evenly spaced entries 1, ..., ULP with random signs
      on the diagonal.

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

 (10) A matrix of the form  U* D U, where U is unitary 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) Hermitian 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 sizes of matrices to use.  If it is zero,
          CCHKHB does nothing.  It must be at least zero.
[in]NN
          NN is INTEGER array, dimension (NSIZES)
          An array containing the sizes to be used for the matrices.
          Zero values will be skipped.  The values must be at least
          zero.
[in]NWDTHS
          NWDTHS is INTEGER
          The number of bandwidths to use.  If it is zero,
          CCHKHB 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, CCHKHB
          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,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 CCHKHB 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 COMPLEX array, dimension
                            (LDA, max(NN))
          Used to hold the matrix whose eigenvalues are to be
          computed.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 2 (not 1!)
          and at least max( KK )+1.
[out]SD
          SD is REAL array, dimension (max(NN))
          Used to hold the diagonal of the tridiagonal matrix computed
          by CHBTRD.
[out]SE
          SE is REAL array, dimension (max(NN))
          Used to hold the off-diagonal of the tridiagonal matrix
          computed by CHBTRD.
[out]U
          U is COMPLEX array, dimension (LDU, max(NN))
          Used to hold the unitary matrix computed by CHBTRD.
[in]LDU
          LDU is INTEGER
          The leading dimension of U.  It must be at least 1
          and at least max( NN ).
[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
[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) )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 295 of file cchkhb.f.

298 *
299 * -- LAPACK test routine --
300 * -- LAPACK is a software package provided by Univ. of Tennessee, --
301 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
302 *
303 * .. Scalar Arguments ..
304  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
305  $ NWDTHS
306  REAL THRESH
307 * ..
308 * .. Array Arguments ..
309  LOGICAL DOTYPE( * )
310  INTEGER ISEED( 4 ), KK( * ), NN( * )
311  REAL RESULT( * ), RWORK( * ), SD( * ), SE( * )
312  COMPLEX A( LDA, * ), U( LDU, * ), WORK( * )
313 * ..
314 *
315 * =====================================================================
316 *
317 * .. Parameters ..
318  COMPLEX CZERO, CONE
319  parameter( czero = ( 0.0e+0, 0.0e+0 ),
320  $ cone = ( 1.0e+0, 0.0e+0 ) )
321  REAL ZERO, ONE, TWO, TEN
322  parameter( zero = 0.0e+0, one = 1.0e+0, two = 2.0e+0,
323  $ ten = 10.0e+0 )
324  REAL HALF
325  parameter( half = one / two )
326  INTEGER MAXTYP
327  parameter( maxtyp = 15 )
328 * ..
329 * .. Local Scalars ..
330  LOGICAL BADNN, BADNNB
331  INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
332  $ JTYPE, JWIDTH, K, KMAX, MTYPES, N, NERRS,
333  $ NMATS, NMAX, NTEST, NTESTT
334  REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
335  $ TEMP1, ULP, ULPINV, UNFL
336 * ..
337 * .. Local Arrays ..
338  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
339  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
340 * ..
341 * .. External Functions ..
342  REAL SLAMCH
343  EXTERNAL slamch
344 * ..
345 * .. External Subroutines ..
346  EXTERNAL chbt21, chbtrd, clacpy, clatmr, clatms, claset,
347  $ slasum, xerbla
348 * ..
349 * .. Intrinsic Functions ..
350  INTRINSIC abs, conjg, max, min, real, sqrt
351 * ..
352 * .. Data statements ..
353  DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
354  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
355  $ 2, 3 /
356  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
357  $ 0, 0 /
358 * ..
359 * .. Executable Statements ..
360 *
361 * Check for errors
362 *
363  ntestt = 0
364  info = 0
365 *
366 * Important constants
367 *
368  badnn = .false.
369  nmax = 1
370  DO 10 j = 1, nsizes
371  nmax = max( nmax, nn( j ) )
372  IF( nn( j ).LT.0 )
373  $ badnn = .true.
374  10 CONTINUE
375 *
376  badnnb = .false.
377  kmax = 0
378  DO 20 j = 1, nsizes
379  kmax = max( kmax, kk( j ) )
380  IF( kk( j ).LT.0 )
381  $ badnnb = .true.
382  20 CONTINUE
383  kmax = min( nmax-1, kmax )
384 *
385 * Check for errors
386 *
387  IF( nsizes.LT.0 ) THEN
388  info = -1
389  ELSE IF( badnn ) THEN
390  info = -2
391  ELSE IF( nwdths.LT.0 ) THEN
392  info = -3
393  ELSE IF( badnnb ) THEN
394  info = -4
395  ELSE IF( ntypes.LT.0 ) THEN
396  info = -5
397  ELSE IF( lda.LT.kmax+1 ) THEN
398  info = -11
399  ELSE IF( ldu.LT.nmax ) THEN
400  info = -15
401  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
402  info = -17
403  END IF
404 *
405  IF( info.NE.0 ) THEN
406  CALL xerbla( 'CCHKHB', -info )
407  RETURN
408  END IF
409 *
410 * Quick return if possible
411 *
412  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
413  $ RETURN
414 *
415 * More Important constants
416 *
417  unfl = slamch( 'Safe minimum' )
418  ovfl = one / unfl
419  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
420  ulpinv = one / ulp
421  rtunfl = sqrt( unfl )
422  rtovfl = sqrt( ovfl )
423 *
424 * Loop over sizes, types
425 *
426  nerrs = 0
427  nmats = 0
428 *
429  DO 190 jsize = 1, nsizes
430  n = nn( jsize )
431  aninv = one / real( max( 1, n ) )
432 *
433  DO 180 jwidth = 1, nwdths
434  k = kk( jwidth )
435  IF( k.GT.n )
436  $ GO TO 180
437  k = max( 0, min( n-1, k ) )
438 *
439  IF( nsizes.NE.1 ) THEN
440  mtypes = min( maxtyp, ntypes )
441  ELSE
442  mtypes = min( maxtyp+1, ntypes )
443  END IF
444 *
445  DO 170 jtype = 1, mtypes
446  IF( .NOT.dotype( jtype ) )
447  $ GO TO 170
448  nmats = nmats + 1
449  ntest = 0
450 *
451  DO 30 j = 1, 4
452  ioldsd( j ) = iseed( j )
453  30 CONTINUE
454 *
455 * Compute "A".
456 * Store as "Upper"; later, we will copy to other format.
457 *
458 * Control parameters:
459 *
460 * KMAGN KMODE KTYPE
461 * =1 O(1) clustered 1 zero
462 * =2 large clustered 2 identity
463 * =3 small exponential (none)
464 * =4 arithmetic diagonal, (w/ eigenvalues)
465 * =5 random log hermitian, w/ eigenvalues
466 * =6 random (none)
467 * =7 random diagonal
468 * =8 random hermitian
469 * =9 positive definite
470 * =10 diagonally dominant tridiagonal
471 *
472  IF( mtypes.GT.maxtyp )
473  $ GO TO 100
474 *
475  itype = ktype( jtype )
476  imode = kmode( jtype )
477 *
478 * Compute norm
479 *
480  GO TO ( 40, 50, 60 )kmagn( jtype )
481 *
482  40 CONTINUE
483  anorm = one
484  GO TO 70
485 *
486  50 CONTINUE
487  anorm = ( rtovfl*ulp )*aninv
488  GO TO 70
489 *
490  60 CONTINUE
491  anorm = rtunfl*n*ulpinv
492  GO TO 70
493 *
494  70 CONTINUE
495 *
496  CALL claset( 'Full', lda, n, czero, czero, a, lda )
497  iinfo = 0
498  IF( jtype.LE.15 ) THEN
499  cond = ulpinv
500  ELSE
501  cond = ulpinv*aninv / ten
502  END IF
503 *
504 * Special Matrices -- Identity & Jordan block
505 *
506 * Zero
507 *
508  IF( itype.EQ.1 ) THEN
509  iinfo = 0
510 *
511  ELSE IF( itype.EQ.2 ) THEN
512 *
513 * Identity
514 *
515  DO 80 jcol = 1, n
516  a( k+1, jcol ) = anorm
517  80 CONTINUE
518 *
519  ELSE IF( itype.EQ.4 ) THEN
520 *
521 * Diagonal Matrix, [Eigen]values Specified
522 *
523  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode,
524  $ cond, anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
525  $ work, iinfo )
526 *
527  ELSE IF( itype.EQ.5 ) THEN
528 *
529 * Hermitian, eigenvalues specified
530 *
531  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode,
532  $ cond, anorm, k, k, 'Q', a, lda, work,
533  $ iinfo )
534 *
535  ELSE IF( itype.EQ.7 ) THEN
536 *
537 * Diagonal, random eigenvalues
538 *
539  CALL clatmr( n, n, 'S', iseed, 'H', work, 6, one,
540  $ cone, 'T', 'N', work( n+1 ), 1, one,
541  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
542  $ zero, anorm, 'Q', a( k+1, 1 ), lda,
543  $ idumma, iinfo )
544 *
545  ELSE IF( itype.EQ.8 ) THEN
546 *
547 * Hermitian, random eigenvalues
548 *
549  CALL clatmr( n, n, 'S', iseed, 'H', work, 6, one,
550  $ cone, 'T', 'N', work( n+1 ), 1, one,
551  $ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
552  $ zero, anorm, 'Q', a, lda, idumma, iinfo )
553 *
554  ELSE IF( itype.EQ.9 ) THEN
555 *
556 * Positive definite, eigenvalues specified.
557 *
558  CALL clatms( n, n, 'S', iseed, 'P', rwork, imode,
559  $ cond, anorm, k, k, 'Q', a, lda,
560  $ work( n+1 ), iinfo )
561 *
562  ELSE IF( itype.EQ.10 ) THEN
563 *
564 * Positive definite tridiagonal, eigenvalues specified.
565 *
566  IF( n.GT.1 )
567  $ k = max( 1, k )
568  CALL clatms( n, n, 'S', iseed, 'P', rwork, imode,
569  $ cond, anorm, 1, 1, 'Q', a( k, 1 ), lda,
570  $ work, iinfo )
571  DO 90 i = 2, n
572  temp1 = abs( a( k, i ) ) /
573  $ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
574  IF( temp1.GT.half ) THEN
575  a( k, i ) = half*sqrt( abs( a( k+1,
576  $ i-1 )*a( k+1, i ) ) )
577  END IF
578  90 CONTINUE
579 *
580  ELSE
581 *
582  iinfo = 1
583  END IF
584 *
585  IF( iinfo.NE.0 ) THEN
586  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
587  $ jtype, ioldsd
588  info = abs( iinfo )
589  RETURN
590  END IF
591 *
592  100 CONTINUE
593 *
594 * Call CHBTRD to compute S and U from upper triangle.
595 *
596  CALL clacpy( ' ', k+1, n, a, lda, work, lda )
597 *
598  ntest = 1
599  CALL chbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
600  $ work( lda*n+1 ), iinfo )
601 *
602  IF( iinfo.NE.0 ) THEN
603  WRITE( nounit, fmt = 9999 )'CHBTRD(U)', iinfo, n,
604  $ jtype, ioldsd
605  info = abs( iinfo )
606  IF( iinfo.LT.0 ) THEN
607  RETURN
608  ELSE
609  result( 1 ) = ulpinv
610  GO TO 150
611  END IF
612  END IF
613 *
614 * Do tests 1 and 2
615 *
616  CALL chbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
617  $ work, rwork, result( 1 ) )
618 *
619 * Convert A from Upper-Triangle-Only storage to
620 * Lower-Triangle-Only storage.
621 *
622  DO 120 jc = 1, n
623  DO 110 jr = 0, min( k, n-jc )
624  a( jr+1, jc ) = conjg( a( k+1-jr, jc+jr ) )
625  110 CONTINUE
626  120 CONTINUE
627  DO 140 jc = n + 1 - k, n
628  DO 130 jr = min( k, n-jc ) + 1, k
629  a( jr+1, jc ) = zero
630  130 CONTINUE
631  140 CONTINUE
632 *
633 * Call CHBTRD to compute S and U from lower triangle
634 *
635  CALL clacpy( ' ', k+1, n, a, lda, work, lda )
636 *
637  ntest = 3
638  CALL chbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
639  $ work( lda*n+1 ), iinfo )
640 *
641  IF( iinfo.NE.0 ) THEN
642  WRITE( nounit, fmt = 9999 )'CHBTRD(L)', iinfo, n,
643  $ jtype, ioldsd
644  info = abs( iinfo )
645  IF( iinfo.LT.0 ) THEN
646  RETURN
647  ELSE
648  result( 3 ) = ulpinv
649  GO TO 150
650  END IF
651  END IF
652  ntest = 4
653 *
654 * Do tests 3 and 4
655 *
656  CALL chbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
657  $ work, rwork, result( 3 ) )
658 *
659 * End of Loop -- Check for RESULT(j) > THRESH
660 *
661  150 CONTINUE
662  ntestt = ntestt + ntest
663 *
664 * Print out tests which fail.
665 *
666  DO 160 jr = 1, ntest
667  IF( result( jr ).GE.thresh ) THEN
668 *
669 * If this is the first test to fail,
670 * print a header to the data file.
671 *
672  IF( nerrs.EQ.0 ) THEN
673  WRITE( nounit, fmt = 9998 )'CHB'
674  WRITE( nounit, fmt = 9997 )
675  WRITE( nounit, fmt = 9996 )
676  WRITE( nounit, fmt = 9995 )'Hermitian'
677  WRITE( nounit, fmt = 9994 )'unitary', '*',
678  $ 'conjugate transpose', ( '*', j = 1, 4 )
679  END IF
680  nerrs = nerrs + 1
681  WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
682  $ jr, result( jr )
683  END IF
684  160 CONTINUE
685 *
686  170 CONTINUE
687  180 CONTINUE
688  190 CONTINUE
689 *
690 * Summary
691 *
692  CALL slasum( 'CHB', nounit, nerrs, ntestt )
693  RETURN
694 *
695  9999 FORMAT( ' CCHKHB: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
696  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
697  9998 FORMAT( / 1x, a3,
698  $ ' -- Complex Hermitian Banded Tridiagonal Reduction Routines'
699  $ )
700  9997 FORMAT( ' Matrix types (see SCHK23 for details): ' )
701 *
702  9996 FORMAT( / ' Special Matrices:',
703  $ / ' 1=Zero matrix. ',
704  $ ' 5=Diagonal: clustered entries.',
705  $ / ' 2=Identity matrix. ',
706  $ ' 6=Diagonal: large, evenly spaced.',
707  $ / ' 3=Diagonal: evenly spaced entries. ',
708  $ ' 7=Diagonal: small, evenly spaced.',
709  $ / ' 4=Diagonal: geometr. spaced entries.' )
710  9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
711  $ / ' 8=Evenly spaced eigenvals. ',
712  $ ' 12=Small, evenly spaced eigenvals.',
713  $ / ' 9=Geometrically spaced eigenvals. ',
714  $ ' 13=Matrix with random O(1) entries.',
715  $ / ' 10=Clustered eigenvalues. ',
716  $ ' 14=Matrix with large random entries.',
717  $ / ' 11=Large, evenly spaced eigenvals. ',
718  $ ' 15=Matrix with small random entries.' )
719 *
720  9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
721  $ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
722  $ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
723  $ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
724  $ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
725  $ ' 4= | I - U U', a1, ' | / ( n ulp )' )
726  9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
727  $ i2, ', test(', i2, ')=', g10.3 )
728 *
729 * End of CCHKHB
730 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine chbt21(UPLO, N, KA, KS, A, LDA, D, E, U, LDU, WORK, RWORK, RESULT)
CHBT21
Definition: chbt21.f:152
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 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 chbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD
Definition: chbtrd.f:163
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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