LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cchkhb2stg()

subroutine cchkhb2stg ( 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,
real, dimension( * )  D1,
real, dimension( * )  D2,
real, dimension( * )  D3,
complex, dimension( ldu, * )  U,
integer  LDU,
complex, dimension( * )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( * )  RESULT,
integer  INFO 
)

CCHKHB2STG

Purpose:
 CCHKHB2STG 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; CCHKHB2STG checks both cases.

 CHETRD_HB2ST factors a Hermitian band matrix A as  U S U* ,
 where * means conjugate transpose, S is symmetric tridiagonal, and U is
 unitary. CHETRD_HB2ST can use either just the lower or just
 the upper triangle of A; CCHKHB2STG checks both cases.

 DSTEQR factors S as  Z D1 Z'.
 D1 is the matrix of eigenvalues computed when Z is not computed
 and from the S resulting of DSBTRD "U" (used as reference for DSYTRD_SB2ST)
 D2 is the matrix of eigenvalues computed when Z is not computed
 and from the S resulting of DSYTRD_SB2ST "U".
 D3 is the matrix of eigenvalues computed when Z is not computed
 and from the S resulting of DSYTRD_SB2ST "L".

 When CCHKHB2STG 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 )

 (5)     | D1 - D2 | / ( |D1| ulp )      where D1 is computed by
                                         DSBTRD with UPLO='U' and
                                         D2 is computed by
                                         CHETRD_HB2ST with UPLO='U'

 (6)     | D1 - D3 | / ( |D1| ulp )      where D1 is computed by
                                         DSBTRD with UPLO='U' and
                                         D3 is computed by
                                         CHETRD_HB2ST with UPLO='L'

 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,
          CCHKHB2STG 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,
          CCHKHB2STG 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, CCHKHB2STG
          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 CCHKHB2STG 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]D1
          D1 is REAL array, dimension (max(NN))
          Used store eigenvalues resulting from the tridiagonal
          form using the DSBTRD.
[out]D2
          D2 is REAL array, dimension (max(NN))
[out]D3
          D3 is REAL array, dimension (max(NN))
[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 337 of file cchkhb2stg.f.

341 *
342 * -- LAPACK test routine --
343 * -- LAPACK is a software package provided by Univ. of Tennessee, --
344 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
345 *
346 * .. Scalar Arguments ..
347  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES,
348  $ NWDTHS
349  REAL THRESH
350 * ..
351 * .. Array Arguments ..
352  LOGICAL DOTYPE( * )
353  INTEGER ISEED( 4 ), KK( * ), NN( * )
354  REAL RESULT( * ), RWORK( * ), SD( * ), SE( * ),
355  $ D1( * ), D2( * ), D3( * )
356  COMPLEX A( LDA, * ), U( LDU, * ), WORK( * )
357 * ..
358 *
359 * =====================================================================
360 *
361 * .. Parameters ..
362  COMPLEX CZERO, CONE
363  parameter( czero = ( 0.0e+0, 0.0e+0 ),
364  $ cone = ( 1.0e+0, 0.0e+0 ) )
365  REAL ZERO, ONE, TWO, TEN
366  parameter( zero = 0.0e+0, one = 1.0e+0, two = 2.0e+0,
367  $ ten = 10.0e+0 )
368  REAL HALF
369  parameter( half = one / two )
370  INTEGER MAXTYP
371  parameter( maxtyp = 15 )
372 * ..
373 * .. Local Scalars ..
374  LOGICAL BADNN, BADNNB
375  INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE,
376  $ JTYPE, JWIDTH, K, KMAX, LH, LW, MTYPES, N,
377  $ NERRS, NMATS, NMAX, NTEST, NTESTT
378  REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
379  $ TEMP1, TEMP2, TEMP3, TEMP4, ULP, ULPINV, UNFL
380 * ..
381 * .. Local Arrays ..
382  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
383  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
384 * ..
385 * .. External Functions ..
386  REAL SLAMCH
387  EXTERNAL slamch
388 * ..
389 * .. External Subroutines ..
390  EXTERNAL slasum, xerbla, chbt21, chbtrd, clacpy, claset,
392 * ..
393 * .. Intrinsic Functions ..
394  INTRINSIC abs, real, conjg, max, min, sqrt
395 * ..
396 * .. Data statements ..
397  DATA ktype / 1, 2, 5*4, 5*5, 3*8 /
398  DATA kmagn / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
399  $ 2, 3 /
400  DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
401  $ 0, 0 /
402 * ..
403 * .. Executable Statements ..
404 *
405 * Check for errors
406 *
407  ntestt = 0
408  info = 0
409 *
410 * Important constants
411 *
412  badnn = .false.
413  nmax = 1
414  DO 10 j = 1, nsizes
415  nmax = max( nmax, nn( j ) )
416  IF( nn( j ).LT.0 )
417  $ badnn = .true.
418  10 CONTINUE
419 *
420  badnnb = .false.
421  kmax = 0
422  DO 20 j = 1, nsizes
423  kmax = max( kmax, kk( j ) )
424  IF( kk( j ).LT.0 )
425  $ badnnb = .true.
426  20 CONTINUE
427  kmax = min( nmax-1, kmax )
428 *
429 * Check for errors
430 *
431  IF( nsizes.LT.0 ) THEN
432  info = -1
433  ELSE IF( badnn ) THEN
434  info = -2
435  ELSE IF( nwdths.LT.0 ) THEN
436  info = -3
437  ELSE IF( badnnb ) THEN
438  info = -4
439  ELSE IF( ntypes.LT.0 ) THEN
440  info = -5
441  ELSE IF( lda.LT.kmax+1 ) THEN
442  info = -11
443  ELSE IF( ldu.LT.nmax ) THEN
444  info = -15
445  ELSE IF( ( max( lda, nmax )+1 )*nmax.GT.lwork ) THEN
446  info = -17
447  END IF
448 *
449  IF( info.NE.0 ) THEN
450  CALL xerbla( 'CCHKHB2STG', -info )
451  RETURN
452  END IF
453 *
454 * Quick return if possible
455 *
456  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 .OR. nwdths.EQ.0 )
457  $ RETURN
458 *
459 * More Important constants
460 *
461  unfl = slamch( 'Safe minimum' )
462  ovfl = one / unfl
463  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
464  ulpinv = one / ulp
465  rtunfl = sqrt( unfl )
466  rtovfl = sqrt( ovfl )
467 *
468 * Loop over sizes, types
469 *
470  nerrs = 0
471  nmats = 0
472 *
473  DO 190 jsize = 1, nsizes
474  n = nn( jsize )
475  aninv = one / real( max( 1, n ) )
476 *
477  DO 180 jwidth = 1, nwdths
478  k = kk( jwidth )
479  IF( k.GT.n )
480  $ GO TO 180
481  k = max( 0, min( n-1, k ) )
482 *
483  IF( nsizes.NE.1 ) THEN
484  mtypes = min( maxtyp, ntypes )
485  ELSE
486  mtypes = min( maxtyp+1, ntypes )
487  END IF
488 *
489  DO 170 jtype = 1, mtypes
490  IF( .NOT.dotype( jtype ) )
491  $ GO TO 170
492  nmats = nmats + 1
493  ntest = 0
494 *
495  DO 30 j = 1, 4
496  ioldsd( j ) = iseed( j )
497  30 CONTINUE
498 *
499 * Compute "A".
500 * Store as "Upper"; later, we will copy to other format.
501 *
502 * Control parameters:
503 *
504 * KMAGN KMODE KTYPE
505 * =1 O(1) clustered 1 zero
506 * =2 large clustered 2 identity
507 * =3 small exponential (none)
508 * =4 arithmetic diagonal, (w/ eigenvalues)
509 * =5 random log hermitian, w/ eigenvalues
510 * =6 random (none)
511 * =7 random diagonal
512 * =8 random hermitian
513 * =9 positive definite
514 * =10 diagonally dominant tridiagonal
515 *
516  IF( mtypes.GT.maxtyp )
517  $ GO TO 100
518 *
519  itype = ktype( jtype )
520  imode = kmode( jtype )
521 *
522 * Compute norm
523 *
524  GO TO ( 40, 50, 60 )kmagn( jtype )
525 *
526  40 CONTINUE
527  anorm = one
528  GO TO 70
529 *
530  50 CONTINUE
531  anorm = ( rtovfl*ulp )*aninv
532  GO TO 70
533 *
534  60 CONTINUE
535  anorm = rtunfl*n*ulpinv
536  GO TO 70
537 *
538  70 CONTINUE
539 *
540  CALL claset( 'Full', lda, n, czero, czero, a, lda )
541  iinfo = 0
542  IF( jtype.LE.15 ) THEN
543  cond = ulpinv
544  ELSE
545  cond = ulpinv*aninv / ten
546  END IF
547 *
548 * Special Matrices -- Identity & Jordan block
549 *
550 * Zero
551 *
552  IF( itype.EQ.1 ) THEN
553  iinfo = 0
554 *
555  ELSE IF( itype.EQ.2 ) THEN
556 *
557 * Identity
558 *
559  DO 80 jcol = 1, n
560  a( k+1, jcol ) = anorm
561  80 CONTINUE
562 *
563  ELSE IF( itype.EQ.4 ) THEN
564 *
565 * Diagonal Matrix, [Eigen]values Specified
566 *
567  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode,
568  $ cond, anorm, 0, 0, 'Q', a( k+1, 1 ), lda,
569  $ work, iinfo )
570 *
571  ELSE IF( itype.EQ.5 ) THEN
572 *
573 * Hermitian, eigenvalues specified
574 *
575  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode,
576  $ cond, anorm, k, k, 'Q', a, lda, work,
577  $ iinfo )
578 *
579  ELSE IF( itype.EQ.7 ) THEN
580 *
581 * Diagonal, random eigenvalues
582 *
583  CALL clatmr( n, n, 'S', iseed, 'H', work, 6, one,
584  $ cone, 'T', 'N', work( n+1 ), 1, one,
585  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
586  $ zero, anorm, 'Q', a( k+1, 1 ), lda,
587  $ idumma, iinfo )
588 *
589  ELSE IF( itype.EQ.8 ) THEN
590 *
591 * Hermitian, random eigenvalues
592 *
593  CALL clatmr( n, n, 'S', iseed, 'H', work, 6, one,
594  $ cone, 'T', 'N', work( n+1 ), 1, one,
595  $ work( 2*n+1 ), 1, one, 'N', idumma, k, k,
596  $ zero, anorm, 'Q', a, lda, idumma, iinfo )
597 *
598  ELSE IF( itype.EQ.9 ) THEN
599 *
600 * Positive definite, eigenvalues specified.
601 *
602  CALL clatms( n, n, 'S', iseed, 'P', rwork, imode,
603  $ cond, anorm, k, k, 'Q', a, lda,
604  $ work( n+1 ), iinfo )
605 *
606  ELSE IF( itype.EQ.10 ) THEN
607 *
608 * Positive definite tridiagonal, eigenvalues specified.
609 *
610  IF( n.GT.1 )
611  $ k = max( 1, k )
612  CALL clatms( n, n, 'S', iseed, 'P', rwork, imode,
613  $ cond, anorm, 1, 1, 'Q', a( k, 1 ), lda,
614  $ work, iinfo )
615  DO 90 i = 2, n
616  temp1 = abs( a( k, i ) ) /
617  $ sqrt( abs( a( k+1, i-1 )*a( k+1, i ) ) )
618  IF( temp1.GT.half ) THEN
619  a( k, i ) = half*sqrt( abs( a( k+1,
620  $ i-1 )*a( k+1, i ) ) )
621  END IF
622  90 CONTINUE
623 *
624  ELSE
625 *
626  iinfo = 1
627  END IF
628 *
629  IF( iinfo.NE.0 ) THEN
630  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n,
631  $ jtype, ioldsd
632  info = abs( iinfo )
633  RETURN
634  END IF
635 *
636  100 CONTINUE
637 *
638 * Call CHBTRD to compute S and U from upper triangle.
639 *
640  CALL clacpy( ' ', k+1, n, a, lda, work, lda )
641 *
642  ntest = 1
643  CALL chbtrd( 'V', 'U', n, k, work, lda, sd, se, u, ldu,
644  $ work( lda*n+1 ), iinfo )
645 *
646  IF( iinfo.NE.0 ) THEN
647  WRITE( nounit, fmt = 9999 )'CHBTRD(U)', iinfo, n,
648  $ jtype, ioldsd
649  info = abs( iinfo )
650  IF( iinfo.LT.0 ) THEN
651  RETURN
652  ELSE
653  result( 1 ) = ulpinv
654  GO TO 150
655  END IF
656  END IF
657 *
658 * Do tests 1 and 2
659 *
660  CALL chbt21( 'Upper', n, k, 1, a, lda, sd, se, u, ldu,
661  $ work, rwork, result( 1 ) )
662 *
663 * Before converting A into lower for DSBTRD, run DSYTRD_SB2ST
664 * otherwise matrix A will be converted to lower and then need
665 * to be converted back to upper in order to run the upper case
666 * ofDSYTRD_SB2ST
667 *
668 * Compute D1 the eigenvalues resulting from the tridiagonal
669 * form using the DSBTRD and used as reference to compare
670 * with the DSYTRD_SB2ST routine
671 *
672 * Compute D1 from the DSBTRD and used as reference for the
673 * DSYTRD_SB2ST
674 *
675  CALL scopy( n, sd, 1, d1, 1 )
676  IF( n.GT.0 )
677  $ CALL scopy( n-1, se, 1, rwork, 1 )
678 *
679  CALL csteqr( 'N', n, d1, rwork, work, ldu,
680  $ rwork( n+1 ), iinfo )
681  IF( iinfo.NE.0 ) THEN
682  WRITE( nounit, fmt = 9999 )'CSTEQR(N)', iinfo, n,
683  $ jtype, ioldsd
684  info = abs( iinfo )
685  IF( iinfo.LT.0 ) THEN
686  RETURN
687  ELSE
688  result( 5 ) = ulpinv
689  GO TO 150
690  END IF
691  END IF
692 *
693 * DSYTRD_SB2ST Upper case is used to compute D2.
694 * Note to set SD and SE to zero to be sure not reusing
695 * the one from above. Compare it with D1 computed
696 * using the DSBTRD.
697 *
698  CALL slaset( 'Full', n, 1, zero, zero, sd, n )
699  CALL slaset( 'Full', n, 1, zero, zero, se, n )
700  CALL clacpy( ' ', k+1, n, a, lda, u, ldu )
701  lh = max(1, 4*n)
702  lw = lwork - lh
703  CALL chetrd_hb2st( 'N', 'N', "U", n, k, u, ldu, sd, se,
704  $ work, lh, work( lh+1 ), lw, iinfo )
705 *
706 * Compute D2 from the DSYTRD_SB2ST Upper case
707 *
708  CALL scopy( n, sd, 1, d2, 1 )
709  IF( n.GT.0 )
710  $ CALL scopy( n-1, se, 1, rwork, 1 )
711 *
712  CALL csteqr( 'N', n, d2, rwork, work, ldu,
713  $ rwork( n+1 ), iinfo )
714  IF( iinfo.NE.0 ) THEN
715  WRITE( nounit, fmt = 9999 )'CSTEQR(N)', iinfo, n,
716  $ jtype, ioldsd
717  info = abs( iinfo )
718  IF( iinfo.LT.0 ) THEN
719  RETURN
720  ELSE
721  result( 5 ) = ulpinv
722  GO TO 150
723  END IF
724  END IF
725 *
726 * Convert A from Upper-Triangle-Only storage to
727 * Lower-Triangle-Only storage.
728 *
729  DO 120 jc = 1, n
730  DO 110 jr = 0, min( k, n-jc )
731  a( jr+1, jc ) = conjg( a( k+1-jr, jc+jr ) )
732  110 CONTINUE
733  120 CONTINUE
734  DO 140 jc = n + 1 - k, n
735  DO 130 jr = min( k, n-jc ) + 1, k
736  a( jr+1, jc ) = zero
737  130 CONTINUE
738  140 CONTINUE
739 *
740 * Call CHBTRD to compute S and U from lower triangle
741 *
742  CALL clacpy( ' ', k+1, n, a, lda, work, lda )
743 *
744  ntest = 3
745  CALL chbtrd( 'V', 'L', n, k, work, lda, sd, se, u, ldu,
746  $ work( lda*n+1 ), iinfo )
747 *
748  IF( iinfo.NE.0 ) THEN
749  WRITE( nounit, fmt = 9999 )'CHBTRD(L)', iinfo, n,
750  $ jtype, ioldsd
751  info = abs( iinfo )
752  IF( iinfo.LT.0 ) THEN
753  RETURN
754  ELSE
755  result( 3 ) = ulpinv
756  GO TO 150
757  END IF
758  END IF
759  ntest = 4
760 *
761 * Do tests 3 and 4
762 *
763  CALL chbt21( 'Lower', n, k, 1, a, lda, sd, se, u, ldu,
764  $ work, rwork, result( 3 ) )
765 *
766 * DSYTRD_SB2ST Lower case is used to compute D3.
767 * Note to set SD and SE to zero to be sure not reusing
768 * the one from above. Compare it with D1 computed
769 * using the DSBTRD.
770 *
771  CALL slaset( 'Full', n, 1, zero, zero, sd, n )
772  CALL slaset( 'Full', n, 1, zero, zero, se, n )
773  CALL clacpy( ' ', k+1, n, a, lda, u, ldu )
774  lh = max(1, 4*n)
775  lw = lwork - lh
776  CALL chetrd_hb2st( 'N', 'N', "L", n, k, u, ldu, sd, se,
777  $ work, lh, work( lh+1 ), lw, iinfo )
778 *
779 * Compute D3 from the 2-stage Upper case
780 *
781  CALL scopy( n, sd, 1, d3, 1 )
782  IF( n.GT.0 )
783  $ CALL scopy( n-1, se, 1, rwork, 1 )
784 *
785  CALL csteqr( 'N', n, d3, rwork, work, ldu,
786  $ rwork( n+1 ), iinfo )
787  IF( iinfo.NE.0 ) THEN
788  WRITE( nounit, fmt = 9999 )'CSTEQR(N)', iinfo, n,
789  $ jtype, ioldsd
790  info = abs( iinfo )
791  IF( iinfo.LT.0 ) THEN
792  RETURN
793  ELSE
794  result( 6 ) = ulpinv
795  GO TO 150
796  END IF
797  END IF
798 *
799 *
800 * Do Tests 3 and 4 which are similar to 11 and 12 but with the
801 * D1 computed using the standard 1-stage reduction as reference
802 *
803  ntest = 6
804  temp1 = zero
805  temp2 = zero
806  temp3 = zero
807  temp4 = zero
808 *
809  DO 151 j = 1, n
810  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
811  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
812  temp3 = max( temp3, abs( d1( j ) ), abs( d3( j ) ) )
813  temp4 = max( temp4, abs( d1( j )-d3( j ) ) )
814  151 CONTINUE
815 *
816  result(5) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
817  result(6) = temp4 / max( unfl, ulp*max( temp3, temp4 ) )
818 *
819 * End of Loop -- Check for RESULT(j) > THRESH
820 *
821  150 CONTINUE
822  ntestt = ntestt + ntest
823 *
824 * Print out tests which fail.
825 *
826  DO 160 jr = 1, ntest
827  IF( result( jr ).GE.thresh ) THEN
828 *
829 * If this is the first test to fail,
830 * print a header to the data file.
831 *
832  IF( nerrs.EQ.0 ) THEN
833  WRITE( nounit, fmt = 9998 )'CHB'
834  WRITE( nounit, fmt = 9997 )
835  WRITE( nounit, fmt = 9996 )
836  WRITE( nounit, fmt = 9995 )'Hermitian'
837  WRITE( nounit, fmt = 9994 )'unitary', '*',
838  $ 'conjugate transpose', ( '*', j = 1, 6 )
839  END IF
840  nerrs = nerrs + 1
841  WRITE( nounit, fmt = 9993 )n, k, ioldsd, jtype,
842  $ jr, result( jr )
843  END IF
844  160 CONTINUE
845 *
846  170 CONTINUE
847  180 CONTINUE
848  190 CONTINUE
849 *
850 * Summary
851 *
852  CALL slasum( 'CHB', nounit, nerrs, ntestt )
853  RETURN
854 *
855  9999 FORMAT( ' CCHKHB2STG: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
856  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
857  9998 FORMAT( / 1x, a3,
858  $ ' -- Complex Hermitian Banded Tridiagonal Reduction Routines'
859  $ )
860  9997 FORMAT( ' Matrix types (see SCHK23 for details): ' )
861 *
862  9996 FORMAT( / ' Special Matrices:',
863  $ / ' 1=Zero matrix. ',
864  $ ' 5=Diagonal: clustered entries.',
865  $ / ' 2=Identity matrix. ',
866  $ ' 6=Diagonal: large, evenly spaced.',
867  $ / ' 3=Diagonal: evenly spaced entries. ',
868  $ ' 7=Diagonal: small, evenly spaced.',
869  $ / ' 4=Diagonal: geometr. spaced entries.' )
870  9995 FORMAT( ' Dense ', a, ' Banded Matrices:',
871  $ / ' 8=Evenly spaced eigenvals. ',
872  $ ' 12=Small, evenly spaced eigenvals.',
873  $ / ' 9=Geometrically spaced eigenvals. ',
874  $ ' 13=Matrix with random O(1) entries.',
875  $ / ' 10=Clustered eigenvalues. ',
876  $ ' 14=Matrix with large random entries.',
877  $ / ' 11=Large, evenly spaced eigenvals. ',
878  $ ' 15=Matrix with small random entries.' )
879 *
880  9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', a, ',',
881  $ / 20x, a, ' means ', a, '.', / ' UPLO=''U'':',
882  $ / ' 1= | A - U S U', a1, ' | / ( |A| n ulp ) ',
883  $ ' 2= | I - U U', a1, ' | / ( n ulp )', / ' UPLO=''L'':',
884  $ / ' 3= | A - U S U', a1, ' | / ( |A| n ulp ) ',
885  $ ' 4= | I - U U', a1, ' | / ( n ulp )' / ' Eig check:',
886  $ /' 5= | D1 - D2', '', ' | / ( |D1| ulp ) ',
887  $ ' 6= | D1 - D3', '', ' | / ( |D1| ulp ) ' )
888  9993 FORMAT( ' N=', i5, ', K=', i4, ', seed=', 4( i4, ',' ), ' type ',
889  $ i2, ', test(', i2, ')=', g10.3 )
890 *
891 * End of CCHKHB2STG
892 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
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 chetrd_hb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T
Definition: chetrd_hb2st.F:230
subroutine chbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD
Definition: chbtrd.f:163
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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