LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sdrvsx()

subroutine sdrvsx ( integer  NSIZES,
integer, dimension( * )  NN,
integer  NTYPES,
logical, dimension( * )  DOTYPE,
integer, dimension( 4 )  ISEED,
real  THRESH,
integer  NIUNIT,
integer  NOUNIT,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( lda, * )  H,
real, dimension( lda, * )  HT,
real, dimension( * )  WR,
real, dimension( * )  WI,
real, dimension( * )  WRT,
real, dimension( * )  WIT,
real, dimension( * )  WRTMP,
real, dimension( * )  WITMP,
real, dimension( ldvs, * )  VS,
integer  LDVS,
real, dimension( ldvs, * )  VS1,
real, dimension( 17 )  RESULT,
real, dimension( * )  WORK,
integer  LWORK,
integer, dimension( * )  IWORK,
logical, dimension( * )  BWORK,
integer  INFO 
)

SDRVSX

Purpose:
    SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem
    expert driver SGEESX.

    SDRVSX uses both test matrices generated randomly depending on
    data supplied in the calling sequence, as well as on data
    read from an input file and including precomputed condition
    numbers to which it compares the ones it computes.

    When SDRVSX is called, a number of matrix "sizes" ("n's") and a
    number of matrix "types" are specified.  For each size ("n")
    and each type of matrix, one matrix will be generated and used
    to test the nonsymmetric eigenroutines.  For each matrix, 15
    tests will be performed:

    (1)     0 if T is in Schur form, 1/ulp otherwise
           (no sorting of eigenvalues)

    (2)     | A - VS T VS' | / ( n |A| ulp )

      Here VS is the matrix of Schur eigenvectors, and T is in Schur
      form  (no sorting of eigenvalues).

    (3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).

    (4)     0     if WR+sqrt(-1)*WI are eigenvalues of T
            1/ulp otherwise
            (no sorting of eigenvalues)

    (5)     0     if T(with VS) = T(without VS),
            1/ulp otherwise
            (no sorting of eigenvalues)

    (6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
            1/ulp otherwise
            (no sorting of eigenvalues)

    (7)     0 if T is in Schur form, 1/ulp otherwise
            (with sorting of eigenvalues)

    (8)     | A - VS T VS' | / ( n |A| ulp )

      Here VS is the matrix of Schur eigenvectors, and T is in Schur
      form  (with sorting of eigenvalues).

    (9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).

    (10)    0     if WR+sqrt(-1)*WI are eigenvalues of T
            1/ulp otherwise
            If workspace sufficient, also compare WR, WI with and
            without reciprocal condition numbers
            (with sorting of eigenvalues)

    (11)    0     if T(with VS) = T(without VS),
            1/ulp otherwise
            If workspace sufficient, also compare T with and without
            reciprocal condition numbers
            (with sorting of eigenvalues)

    (12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
            1/ulp otherwise
            If workspace sufficient, also compare VS with and without
            reciprocal condition numbers
            (with sorting of eigenvalues)

    (13)    if sorting worked and SDIM is the number of
            eigenvalues which were SELECTed
            If workspace sufficient, also compare SDIM with and
            without reciprocal condition numbers

    (14)    if RCONDE the same no matter if VS and/or RCONDV computed

    (15)    if RCONDV the same no matter if VS and/or RCONDE computed

    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 (transposed) Jordan block, with 1's on the diagonal.

    (4)  A diagonal matrix with evenly spaced entries
         1, ..., ULP  and random signs.
         (ULP = (first number larger than 1) - 1 )
    (5)  A diagonal matrix with geometrically spaced entries
         1, ..., ULP  and random signs.
    (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
         and random signs.

    (7)  Same as (4), but multiplied by a constant near
         the overflow threshold
    (8)  Same as (4), but multiplied by a constant near
         the underflow threshold

    (9)  A matrix of the form  U' T U, where U is orthogonal and
         T has evenly spaced entries 1, ..., ULP with random signs
         on the diagonal and random O(1) entries in the upper
         triangle.

    (10) A matrix of the form  U' T U, where U is orthogonal and
         T has geometrically spaced entries 1, ..., ULP with random
         signs on the diagonal and random O(1) entries in the upper
         triangle.

    (11) A matrix of the form  U' T U, where U is orthogonal and
         T has "clustered" entries 1, ULP,..., ULP with random
         signs on the diagonal and random O(1) entries in the upper
         triangle.

    (12) A matrix of the form  U' T U, where U is orthogonal and
         T has real or complex conjugate paired eigenvalues randomly
         chosen from ( ULP, 1 ) and random O(1) entries in the upper
         triangle.

    (13) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
         with random signs on the diagonal and random O(1) entries
         in the upper triangle.

    (14) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has geometrically spaced entries
         1, ..., ULP with random signs on the diagonal and random
         O(1) entries in the upper triangle.

    (15) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
         with random signs on the diagonal and random O(1) entries
         in the upper triangle.

    (16) A matrix of the form  X' T X, where X has condition
         SQRT( ULP ) and T has real or complex conjugate paired
         eigenvalues randomly chosen from ( ULP, 1 ) and random
         O(1) entries in the upper triangle.

    (17) Same as (16), but multiplied by a constant
         near the overflow threshold
    (18) Same as (16), but multiplied by a constant
         near the underflow threshold

    (19) Nonsymmetric matrix with random entries chosen from (-1,1).
         If N is at least 4, all entries in first two rows and last
         row, and first column and last two columns are zero.
    (20) Same as (19), but multiplied by a constant
         near the overflow threshold
    (21) Same as (19), but multiplied by a constant
         near the underflow threshold

    In addition, an input file will be read from logical unit number
    NIUNIT. The file contains matrices along with precomputed
    eigenvalues and reciprocal condition numbers for the eigenvalue
    average and right invariant subspace. For these matrices, in
    addition to tests (1) to (15) we will compute the following two
    tests:

   (16)  |RCONDE - RCDEIN| / cond(RCONDE)

      RCONDE is the reciprocal average eigenvalue condition number
      computed by SGEESX and RCDEIN (the precomputed true value)
      is supplied as input.  cond(RCONDE) is the condition number
      of RCONDE, and takes errors in computing RCONDE into account,
      so that the resulting quantity should be O(ULP). cond(RCONDE)
      is essentially given by norm(A)/RCONDV.

   (17)  |RCONDV - RCDVIN| / cond(RCONDV)

      RCONDV is the reciprocal right invariant subspace condition
      number computed by SGEESX and RCDVIN (the precomputed true
      value) is supplied as input. cond(RCONDV) is the condition
      number of RCONDV, and takes errors in computing RCONDV into
      account, so that the resulting quantity should be O(ULP).
      cond(RCONDV) is essentially given by norm(A)/RCONDE.
Parameters
[in]NSIZES
          NSIZES is INTEGER
          The number of sizes of matrices to use.  NSIZES must be at
          least zero. If it is zero, no randomly generated matrices
          are tested, but any test matrices read from NIUNIT will be
          tested.
[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]NTYPES
          NTYPES is INTEGER
          The number of elements in DOTYPE. NTYPES must be at least
          zero. If it is zero, no randomly generated test matrices
          are tested, but and test matrices read from NIUNIT will be
          tested. 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 SDRVSX 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]NIUNIT
          NIUNIT is INTEGER
          The FORTRAN unit number for reading in the data file of
          problems to solve.
[in]NOUNIT
          NOUNIT is INTEGER
          The FORTRAN unit number for printing out error messages
          (e.g., if a routine returns INFO not equal to 0.)
[out]A
          A is REAL array, dimension (LDA, max(NN))
          Used to hold the matrix whose eigenvalues are to be
          computed.  On exit, A contains the last matrix actually used.
[in]LDA
          LDA is INTEGER
          The leading dimension of A, and H. LDA must be at
          least 1 and at least max( NN ).
[out]H
          H is REAL array, dimension (LDA, max(NN))
          Another copy of the test matrix A, modified by SGEESX.
[out]HT
          HT is REAL array, dimension (LDA, max(NN))
          Yet another copy of the test matrix A, modified by SGEESX.
[out]WR
          WR is REAL array, dimension (max(NN))
[out]WI
          WI is REAL array, dimension (max(NN))

          The real and imaginary parts of the eigenvalues of A.
          On exit, WR + WI*i are the eigenvalues of the matrix in A.
[out]WRT
          WRT is REAL array, dimension (max(NN))
[out]WIT
          WIT is REAL array, dimension (max(NN))

          Like WR, WI, these arrays contain the eigenvalues of A,
          but those computed when SGEESX only computes a partial
          eigendecomposition, i.e. not Schur vectors
[out]WRTMP
          WRTMP is REAL array, dimension (max(NN))
[out]WITMP
          WITMP is REAL array, dimension (max(NN))

          More temporary storage for eigenvalues.
[out]VS
          VS is REAL array, dimension (LDVS, max(NN))
          VS holds the computed Schur vectors.
[in]LDVS
          LDVS is INTEGER
          Leading dimension of VS. Must be at least max(1,max(NN)).
[out]VS1
          VS1 is REAL array, dimension (LDVS, max(NN))
          VS1 holds another copy of the computed Schur vectors.
[out]RESULT
          RESULT is REAL array, dimension (17)
          The values computed by the 17 tests described above.
          The values are currently limited to 1/ulp, to avoid overflow.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          max(3*NN(j),2*NN(j)**2) for all j.
[out]IWORK
          IWORK is INTEGER array, dimension (max(NN)*max(NN))
[out]BWORK
          BWORK is LOGICAL array, dimension (max(NN))
[out]INFO
          INFO is INTEGER
          If 0,  successful exit.
            <0,  input parameter -INFO is incorrect
            >0,  SLATMR, SLATMS, SLATME or SGET24 returned an error
                 code and INFO is its absolute value

-----------------------------------------------------------------------

     Some Local Variables and Parameters:
     ---- ----- --------- --- ----------
     ZERO, ONE       Real 0 and 1.
     MAXTYP          The number of types defined.
     NMAX            Largest value in NN.
     NERRS           The number of tests which have exceeded THRESH
     COND, CONDS,
     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.
     RTULP, RTULPI   Square roots of the previous 4 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) )
     KCONDS(j)       Selectw whether CONDS is to be 1 or
                     1/sqrt(ulp).  (0 means irrelevant.)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 450 of file sdrvsx.f.

454 *
455 * -- LAPACK test routine --
456 * -- LAPACK is a software package provided by Univ. of Tennessee, --
457 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
458 *
459 * .. Scalar Arguments ..
460  INTEGER INFO, LDA, LDVS, LWORK, NIUNIT, NOUNIT, NSIZES,
461  $ NTYPES
462  REAL THRESH
463 * ..
464 * .. Array Arguments ..
465  LOGICAL BWORK( * ), DOTYPE( * )
466  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
467  REAL A( LDA, * ), H( LDA, * ), HT( LDA, * ),
468  $ RESULT( 17 ), VS( LDVS, * ), VS1( LDVS, * ),
469  $ WI( * ), WIT( * ), WITMP( * ), WORK( * ),
470  $ WR( * ), WRT( * ), WRTMP( * )
471 * ..
472 *
473 * =====================================================================
474 *
475 * .. Parameters ..
476  REAL ZERO, ONE
477  parameter( zero = 0.0e0, one = 1.0e0 )
478  INTEGER MAXTYP
479  parameter( maxtyp = 21 )
480 * ..
481 * .. Local Scalars ..
482  LOGICAL BADNN
483  CHARACTER*3 PATH
484  INTEGER I, IINFO, IMODE, ITYPE, IWK, J, JCOL, JSIZE,
485  $ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX,
486  $ NNWORK, NSLCT, NTEST, NTESTF, NTESTT
487  REAL ANORM, COND, CONDS, OVFL, RCDEIN, RCDVIN,
488  $ RTULP, RTULPI, ULP, ULPINV, UNFL
489 * ..
490 * .. Local Arrays ..
491  CHARACTER ADUMMA( 1 )
492  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISLCT( 20 ),
493  $ KCONDS( MAXTYP ), KMAGN( MAXTYP ),
494  $ KMODE( MAXTYP ), KTYPE( MAXTYP )
495 * ..
496 * .. Arrays in Common ..
497  LOGICAL SELVAL( 20 )
498  REAL SELWI( 20 ), SELWR( 20 )
499 * ..
500 * .. Scalars in Common ..
501  INTEGER SELDIM, SELOPT
502 * ..
503 * .. Common blocks ..
504  COMMON / sslct / selopt, seldim, selval, selwr, selwi
505 * ..
506 * .. External Functions ..
507  REAL SLAMCH
508  EXTERNAL slamch
509 * ..
510 * .. External Subroutines ..
511  EXTERNAL sget24, slabad, slasum, slatme, slatmr, slatms,
512  $ slaset, xerbla
513 * ..
514 * .. Intrinsic Functions ..
515  INTRINSIC abs, max, min, sqrt
516 * ..
517 * .. Data statements ..
518  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
519  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
520  $ 3, 1, 2, 3 /
521  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
522  $ 1, 5, 5, 5, 4, 3, 1 /
523  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
524 * ..
525 * .. Executable Statements ..
526 *
527  path( 1: 1 ) = 'Single precision'
528  path( 2: 3 ) = 'SX'
529 *
530 * Check for errors
531 *
532  ntestt = 0
533  ntestf = 0
534  info = 0
535 *
536 * Important constants
537 *
538  badnn = .false.
539 *
540 * 12 is the largest dimension in the input file of precomputed
541 * problems
542 *
543  nmax = 12
544  DO 10 j = 1, nsizes
545  nmax = max( nmax, nn( j ) )
546  IF( nn( j ).LT.0 )
547  $ badnn = .true.
548  10 CONTINUE
549 *
550 * Check for errors
551 *
552  IF( nsizes.LT.0 ) THEN
553  info = -1
554  ELSE IF( badnn ) THEN
555  info = -2
556  ELSE IF( ntypes.LT.0 ) THEN
557  info = -3
558  ELSE IF( thresh.LT.zero ) THEN
559  info = -6
560  ELSE IF( niunit.LE.0 ) THEN
561  info = -7
562  ELSE IF( nounit.LE.0 ) THEN
563  info = -8
564  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
565  info = -10
566  ELSE IF( ldvs.LT.1 .OR. ldvs.LT.nmax ) THEN
567  info = -20
568  ELSE IF( max( 3*nmax, 2*nmax**2 ).GT.lwork ) THEN
569  info = -24
570  END IF
571 *
572  IF( info.NE.0 ) THEN
573  CALL xerbla( 'SDRVSX', -info )
574  RETURN
575  END IF
576 *
577 * If nothing to do check on NIUNIT
578 *
579  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
580  $ GO TO 150
581 *
582 * More Important constants
583 *
584  unfl = slamch( 'Safe minimum' )
585  ovfl = one / unfl
586  CALL slabad( unfl, ovfl )
587  ulp = slamch( 'Precision' )
588  ulpinv = one / ulp
589  rtulp = sqrt( ulp )
590  rtulpi = one / rtulp
591 *
592 * Loop over sizes, types
593 *
594  nerrs = 0
595 *
596  DO 140 jsize = 1, nsizes
597  n = nn( jsize )
598  IF( nsizes.NE.1 ) THEN
599  mtypes = min( maxtyp, ntypes )
600  ELSE
601  mtypes = min( maxtyp+1, ntypes )
602  END IF
603 *
604  DO 130 jtype = 1, mtypes
605  IF( .NOT.dotype( jtype ) )
606  $ GO TO 130
607 *
608 * Save ISEED in case of an error.
609 *
610  DO 20 j = 1, 4
611  ioldsd( j ) = iseed( j )
612  20 CONTINUE
613 *
614 * Compute "A"
615 *
616 * Control parameters:
617 *
618 * KMAGN KCONDS KMODE KTYPE
619 * =1 O(1) 1 clustered 1 zero
620 * =2 large large clustered 2 identity
621 * =3 small exponential Jordan
622 * =4 arithmetic diagonal, (w/ eigenvalues)
623 * =5 random log symmetric, w/ eigenvalues
624 * =6 random general, w/ eigenvalues
625 * =7 random diagonal
626 * =8 random symmetric
627 * =9 random general
628 * =10 random triangular
629 *
630  IF( mtypes.GT.maxtyp )
631  $ GO TO 90
632 *
633  itype = ktype( jtype )
634  imode = kmode( jtype )
635 *
636 * Compute norm
637 *
638  GO TO ( 30, 40, 50 )kmagn( jtype )
639 *
640  30 CONTINUE
641  anorm = one
642  GO TO 60
643 *
644  40 CONTINUE
645  anorm = ovfl*ulp
646  GO TO 60
647 *
648  50 CONTINUE
649  anorm = unfl*ulpinv
650  GO TO 60
651 *
652  60 CONTINUE
653 *
654  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
655  iinfo = 0
656  cond = ulpinv
657 *
658 * Special Matrices -- Identity & Jordan block
659 *
660 * Zero
661 *
662  IF( itype.EQ.1 ) THEN
663  iinfo = 0
664 *
665  ELSE IF( itype.EQ.2 ) THEN
666 *
667 * Identity
668 *
669  DO 70 jcol = 1, n
670  a( jcol, jcol ) = anorm
671  70 CONTINUE
672 *
673  ELSE IF( itype.EQ.3 ) THEN
674 *
675 * Jordan Block
676 *
677  DO 80 jcol = 1, n
678  a( jcol, jcol ) = anorm
679  IF( jcol.GT.1 )
680  $ a( jcol, jcol-1 ) = one
681  80 CONTINUE
682 *
683  ELSE IF( itype.EQ.4 ) THEN
684 *
685 * Diagonal Matrix, [Eigen]values Specified
686 *
687  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
688  $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
689  $ iinfo )
690 *
691  ELSE IF( itype.EQ.5 ) THEN
692 *
693 * Symmetric, eigenvalues specified
694 *
695  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
696  $ anorm, n, n, 'N', a, lda, work( n+1 ),
697  $ iinfo )
698 *
699  ELSE IF( itype.EQ.6 ) THEN
700 *
701 * General, eigenvalues specified
702 *
703  IF( kconds( jtype ).EQ.1 ) THEN
704  conds = one
705  ELSE IF( kconds( jtype ).EQ.2 ) THEN
706  conds = rtulpi
707  ELSE
708  conds = zero
709  END IF
710 *
711  adumma( 1 ) = ' '
712  CALL slatme( n, 'S', iseed, work, imode, cond, one,
713  $ adumma, 'T', 'T', 'T', work( n+1 ), 4,
714  $ conds, n, n, anorm, a, lda, work( 2*n+1 ),
715  $ iinfo )
716 *
717  ELSE IF( itype.EQ.7 ) THEN
718 *
719 * Diagonal, random eigenvalues
720 *
721  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
722  $ 'T', 'N', work( n+1 ), 1, one,
723  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
724  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
725 *
726  ELSE IF( itype.EQ.8 ) THEN
727 *
728 * Symmetric, random eigenvalues
729 *
730  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
731  $ 'T', 'N', work( n+1 ), 1, one,
732  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
733  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
734 *
735  ELSE IF( itype.EQ.9 ) THEN
736 *
737 * General, random eigenvalues
738 *
739  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
740  $ 'T', 'N', work( n+1 ), 1, one,
741  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
742  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
743  IF( n.GE.4 ) THEN
744  CALL slaset( 'Full', 2, n, zero, zero, a, lda )
745  CALL slaset( 'Full', n-3, 1, zero, zero, a( 3, 1 ),
746  $ lda )
747  CALL slaset( 'Full', n-3, 2, zero, zero, a( 3, n-1 ),
748  $ lda )
749  CALL slaset( 'Full', 1, n, zero, zero, a( n, 1 ),
750  $ lda )
751  END IF
752 *
753  ELSE IF( itype.EQ.10 ) THEN
754 *
755 * Triangular, random eigenvalues
756 *
757  CALL slatmr( n, n, 'S', iseed, 'N', work, 6, one, one,
758  $ 'T', 'N', work( n+1 ), 1, one,
759  $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
760  $ zero, anorm, 'NO', a, lda, iwork, iinfo )
761 *
762  ELSE
763 *
764  iinfo = 1
765  END IF
766 *
767  IF( iinfo.NE.0 ) THEN
768  WRITE( nounit, fmt = 9991 )'Generator', iinfo, n, jtype,
769  $ ioldsd
770  info = abs( iinfo )
771  RETURN
772  END IF
773 *
774  90 CONTINUE
775 *
776 * Test for minimal and generous workspace
777 *
778  DO 120 iwk = 1, 2
779  IF( iwk.EQ.1 ) THEN
780  nnwork = 3*n
781  ELSE
782  nnwork = max( 3*n, 2*n*n )
783  END IF
784  nnwork = max( nnwork, 1 )
785 *
786  CALL sget24( .false., jtype, thresh, ioldsd, nounit, n,
787  $ a, lda, h, ht, wr, wi, wrt, wit, wrtmp,
788  $ witmp, vs, ldvs, vs1, rcdein, rcdvin, nslct,
789  $ islct, result, work, nnwork, iwork, bwork,
790  $ info )
791 *
792 * Check for RESULT(j) > THRESH
793 *
794  ntest = 0
795  nfail = 0
796  DO 100 j = 1, 15
797  IF( result( j ).GE.zero )
798  $ ntest = ntest + 1
799  IF( result( j ).GE.thresh )
800  $ nfail = nfail + 1
801  100 CONTINUE
802 *
803  IF( nfail.GT.0 )
804  $ ntestf = ntestf + 1
805  IF( ntestf.EQ.1 ) THEN
806  WRITE( nounit, fmt = 9999 )path
807  WRITE( nounit, fmt = 9998 )
808  WRITE( nounit, fmt = 9997 )
809  WRITE( nounit, fmt = 9996 )
810  WRITE( nounit, fmt = 9995 )thresh
811  WRITE( nounit, fmt = 9994 )
812  ntestf = 2
813  END IF
814 *
815  DO 110 j = 1, 15
816  IF( result( j ).GE.thresh ) THEN
817  WRITE( nounit, fmt = 9993 )n, iwk, ioldsd, jtype,
818  $ j, result( j )
819  END IF
820  110 CONTINUE
821 *
822  nerrs = nerrs + nfail
823  ntestt = ntestt + ntest
824 *
825  120 CONTINUE
826  130 CONTINUE
827  140 CONTINUE
828 *
829  150 CONTINUE
830 *
831 * Read in data from file to check accuracy of condition estimation
832 * Read input data until N=0
833 *
834  jtype = 0
835  160 CONTINUE
836  READ( niunit, fmt = *, END = 200 )N, nslct
837  IF( n.EQ.0 )
838  $ GO TO 200
839  jtype = jtype + 1
840  iseed( 1 ) = jtype
841  IF( nslct.GT.0 )
842  $ READ( niunit, fmt = * )( islct( i ), i = 1, nslct )
843  DO 170 i = 1, n
844  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
845  170 CONTINUE
846  READ( niunit, fmt = * )rcdein, rcdvin
847 *
848  CALL sget24( .true., 22, thresh, iseed, nounit, n, a, lda, h, ht,
849  $ wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1,
850  $ rcdein, rcdvin, nslct, islct, result, work, lwork,
851  $ iwork, bwork, info )
852 *
853 * Check for RESULT(j) > THRESH
854 *
855  ntest = 0
856  nfail = 0
857  DO 180 j = 1, 17
858  IF( result( j ).GE.zero )
859  $ ntest = ntest + 1
860  IF( result( j ).GE.thresh )
861  $ nfail = nfail + 1
862  180 CONTINUE
863 *
864  IF( nfail.GT.0 )
865  $ ntestf = ntestf + 1
866  IF( ntestf.EQ.1 ) THEN
867  WRITE( nounit, fmt = 9999 )path
868  WRITE( nounit, fmt = 9998 )
869  WRITE( nounit, fmt = 9997 )
870  WRITE( nounit, fmt = 9996 )
871  WRITE( nounit, fmt = 9995 )thresh
872  WRITE( nounit, fmt = 9994 )
873  ntestf = 2
874  END IF
875  DO 190 j = 1, 17
876  IF( result( j ).GE.thresh ) THEN
877  WRITE( nounit, fmt = 9992 )n, jtype, j, result( j )
878  END IF
879  190 CONTINUE
880 *
881  nerrs = nerrs + nfail
882  ntestt = ntestt + ntest
883  GO TO 160
884  200 CONTINUE
885 *
886 * Summary
887 *
888  CALL slasum( path, nounit, nerrs, ntestt )
889 *
890  9999 FORMAT( / 1x, a3, ' -- Real Schur Form Decomposition Expert ',
891  $ 'Driver', / ' Matrix types (see SDRVSX for details):' )
892 *
893  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
894  $ ' ', ' 5=Diagonal: geometr. spaced entries.',
895  $ / ' 2=Identity matrix. ', ' 6=Diagona',
896  $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
897  $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
898  $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
899  $ 'mall, evenly spaced.' )
900  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
901  $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
902  $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
903  $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
904  $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
905  $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
906  $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
907  $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
908  $ ' complx ' )
909  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
910  $ 'with small random entries.', / ' 20=Matrix with large ran',
911  $ 'dom entries. ', / )
912  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
913  $ / ' ( A denotes A on input and T denotes A on output)',
914  $ / / ' 1 = 0 if T in Schur form (no sort), ',
915  $ ' 1/ulp otherwise', /
916  $ ' 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort)',
917  $ / ' 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) ', /
918  $ ' 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort),',
919  $ ' 1/ulp otherwise', /
920  $ ' 5 = 0 if T same no matter if VS computed (no sort),',
921  $ ' 1/ulp otherwise', /
922  $ ' 6 = 0 if WR, WI same no matter if VS computed (no sort)',
923  $ ', 1/ulp otherwise' )
924  9994 FORMAT( ' 7 = 0 if T in Schur form (sort), ', ' 1/ulp otherwise',
925  $ / ' 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort)',
926  $ / ' 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) ',
927  $ / ' 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort),',
928  $ ' 1/ulp otherwise', /
929  $ ' 11 = 0 if T same no matter what else computed (sort),',
930  $ ' 1/ulp otherwise', /
931  $ ' 12 = 0 if WR, WI same no matter what else computed ',
932  $ '(sort), 1/ulp otherwise', /
933  $ ' 13 = 0 if sorting successful, 1/ulp otherwise',
934  $ / ' 14 = 0 if RCONDE same no matter what else computed,',
935  $ ' 1/ulp otherwise', /
936  $ ' 15 = 0 if RCONDv same no matter what else computed,',
937  $ ' 1/ulp otherwise', /
938  $ ' 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),',
939  $ / ' 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),' )
940  9993 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
941  $ ' type ', i2, ', test(', i2, ')=', g10.3 )
942  9992 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
943  $ g10.3 )
944  9991 FORMAT( ' SDRVSX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
945  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
946 *
947  RETURN
948 *
949 * End of SDRVSX
950 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
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 slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatme(N, DIST, ISEED, D, MODE, COND, DMAX, EI, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
SLATME
Definition: slatme.f:332
subroutine slatmr(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)
SLATMR
Definition: slatmr.f:471
subroutine sget24(COMP, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, HT, WR, WI, WRT, WIT, WRTMP, WITMP, VS, LDVS, VS1, RCDEIN, RCDVIN, NSLCT, ISLCT, RESULT, WORK, LWORK, IWORK, BWORK, INFO)
SGET24
Definition: sget24.f:343
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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