LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
subroutine cdrvvx ( integer  NSIZES,
integer, dimension( * )  NN,
integer  NTYPES,
logical, dimension( * )  DOTYPE,
integer, dimension( 4 )  ISEED,
real  THRESH,
integer  NIUNIT,
integer  NOUNIT,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( lda, * )  H,
complex, dimension( * )  W,
complex, dimension( * )  W1,
complex, dimension( ldvl, * )  VL,
integer  LDVL,
complex, dimension( ldvr, * )  VR,
integer  LDVR,
complex, dimension( ldlre, * )  LRE,
integer  LDLRE,
real, dimension( * )  RCONDV,
real, dimension( * )  RCNDV1,
real, dimension( * )  RCDVIN,
real, dimension( * )  RCONDE,
real, dimension( * )  RCNDE1,
real, dimension( * )  RCDEIN,
real, dimension( * )  SCALE,
real, dimension( * )  SCALE1,
real, dimension( 11 )  RESULT,
complex, dimension( * )  WORK,
integer  NWORK,
real, dimension( * )  RWORK,
integer  INFO 
)

CDRVVX

Purpose:
    CDRVVX  checks the nonsymmetric eigenvalue problem expert driver
    CGEEVX.

    CDRVVX 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 CDRVVX is called, a number of matrix "sizes" ("n's") and a
    number of matrix "types" are specified in the calling sequence.
    For each size ("n") and each type of matrix, one matrix will be
    generated and used to test the nonsymmetric eigenroutines.  For
    each matrix, 9 tests will be performed:

    (1)     | A * VR - VR * W | / ( n |A| ulp )

      Here VR is the matrix of unit right eigenvectors.
      W is a diagonal matrix with diagonal entries W(j).

    (2)     | A**H  * VL - VL * W**H | / ( n |A| ulp )

      Here VL is the matrix of unit left eigenvectors, A**H is the
      conjugate transpose of A, and W is as above.

    (3)     | |VR(i)| - 1 | / ulp and largest component real

      VR(i) denotes the i-th column of VR.

    (4)     | |VL(i)| - 1 | / ulp and largest component real

      VL(i) denotes the i-th column of VL.

    (5)     W(full) = W(partial)

      W(full) denotes the eigenvalues computed when VR, VL, RCONDV
      and RCONDE are also computed, and W(partial) denotes the
      eigenvalues computed when only some of VR, VL, RCONDV, and
      RCONDE are computed.

    (6)     VR(full) = VR(partial)

      VR(full) denotes the right eigenvectors computed when VL, RCONDV
      and RCONDE are computed, and VR(partial) denotes the result
      when only some of VL and RCONDV are computed.

    (7)     VL(full) = VL(partial)

      VL(full) denotes the left eigenvectors computed when VR, RCONDV
      and RCONDE are computed, and VL(partial) denotes the result
      when only some of VR and RCONDV are computed.

    (8)     0 if SCALE, ILO, IHI, ABNRM (full) =
                 SCALE, ILO, IHI, ABNRM (partial)
            1/ulp otherwise

      SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
      (full) is when VR, VL, RCONDE and RCONDV are also computed, and
      (partial) is when some are not computed.

    (9)     RCONDV(full) = RCONDV(partial)

      RCONDV(full) denotes the reciprocal condition numbers of the
      right eigenvectors computed when VR, VL and RCONDE are also
      computed. RCONDV(partial) denotes the reciprocal condition
      numbers when only some of VR, VL and RCONDE are 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 complex angles.
         (ULP = (first number larger than 1) - 1 )
    (5)  A diagonal matrix with geometrically spaced entries
         1, ..., ULP  and random complex angles.
    (6)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
         and random complex angles.

    (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 unitary and
         T has evenly spaced entries 1, ..., ULP with random complex
         angles on the diagonal and random O(1) entries in the upper
         triangle.

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

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

    (12) A matrix of the form  U' T U, where U is unitary and
         T has complex eigenvalues randomly chosen from
         ULP < |z| < 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 complex angles 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 complex angles 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 complex angles 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 complex eigenvalues randomly chosen
         from ULP < |z| < 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 |z| < 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 eigenvalues
    and right eigenvectors. For these matrices, in addition to tests
    (1) to (9) we will compute the following two tests:

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

      RCONDV is the reciprocal right eigenvector condition number
      computed by CGEEVX 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.

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

      RCONDE is the reciprocal eigenvalue condition number
      computed by CGEEVX 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.
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 CDRVVX 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 COMPLEX array, dimension (LDA, max(NN,12))
          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, 12 ). (12 is the
          dimension of the largest matrix on the precomputed
          input file.)
[out]H
          H is COMPLEX array, dimension (LDA, max(NN,12))
          Another copy of the test matrix A, modified by CGEEVX.
[out]W
          W is COMPLEX array, dimension (max(NN,12))
          Contains the eigenvalues of A.
[out]W1
          W1 is COMPLEX array, dimension (max(NN,12))
          Like W, this array contains the eigenvalues of A,
          but those computed when CGEEVX only computes a partial
          eigendecomposition, i.e. not the eigenvalues and left
          and right eigenvectors.
[out]VL
          VL is COMPLEX array, dimension (LDVL, max(NN,12))
          VL holds the computed left eigenvectors.
[in]LDVL
          LDVL is INTEGER
          Leading dimension of VL. Must be at least max(1,max(NN,12)).
[out]VR
          VR is COMPLEX array, dimension (LDVR, max(NN,12))
          VR holds the computed right eigenvectors.
[in]LDVR
          LDVR is INTEGER
          Leading dimension of VR. Must be at least max(1,max(NN,12)).
[out]LRE
          LRE is COMPLEX array, dimension (LDLRE, max(NN,12))
          LRE holds the computed right or left eigenvectors.
[in]LDLRE
          LDLRE is INTEGER
          Leading dimension of LRE. Must be at least max(1,max(NN,12))
[out]RCONDV
          RCONDV is REAL array, dimension (N)
          RCONDV holds the computed reciprocal condition numbers
          for eigenvectors.
[out]RCNDV1
          RCNDV1 is REAL array, dimension (N)
          RCNDV1 holds more computed reciprocal condition numbers
          for eigenvectors.
[in]RCDVIN
          RCDVIN is REAL array, dimension (N)
          When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
          condition numbers for eigenvectors to be compared with
          RCONDV.
[out]RCONDE
          RCONDE is REAL array, dimension (N)
          RCONDE holds the computed reciprocal condition numbers
          for eigenvalues.
[out]RCNDE1
          RCNDE1 is REAL array, dimension (N)
          RCNDE1 holds more computed reciprocal condition numbers
          for eigenvalues.
[in]RCDEIN
          RCDEIN is REAL array, dimension (N)
          When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
          condition numbers for eigenvalues to be compared with
          RCONDE.
[out]SCALE
          SCALE is REAL array, dimension (N)
          Holds information describing balancing of matrix.
[out]SCALE1
          SCALE1 is REAL array, dimension (N)
          Holds information describing balancing of matrix.
[out]RESULT
          RESULT is REAL array, dimension (11)
          The values computed by the seven tests described above.
          The values are currently limited to 1/ulp, to avoid
          overflow.
[out]WORK
          WORK is COMPLEX array, dimension (NWORK)
[in]NWORK
          NWORK is INTEGER
          The number of entries in WORK.  This must be at least
          max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) =
          max(    360     ,6*NN(j)+2*NN(j)**2)    for all j.
[out]RWORK
          RWORK is REAL array, dimension (2*max(NN,12))
[out]INFO
          INFO is INTEGER
          If 0,  then successful exit.
          If <0, then input parameter -INFO is incorrect.
          If >0, CLATMR, CLATMS, CLATME or CGET23 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 or 12.
     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.
Date
June 2016

Definition at line 498 of file cdrvvx.f.

498 *
499 * -- LAPACK test routine (version 3.6.1) --
500 * -- LAPACK is a software package provided by Univ. of Tennessee, --
501 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
502 * June 2016
503 *
504 * .. Scalar Arguments ..
505  INTEGER info, lda, ldlre, ldvl, ldvr, niunit, nounit,
506  $ nsizes, ntypes, nwork
507  REAL thresh
508 * ..
509 * .. Array Arguments ..
510  LOGICAL dotype( * )
511  INTEGER iseed( 4 ), nn( * )
512  REAL rcdein( * ), rcdvin( * ), rcnde1( * ),
513  $ rcndv1( * ), rconde( * ), rcondv( * ),
514  $ result( 11 ), rwork( * ), scale( * ),
515  $ scale1( * )
516  COMPLEX a( lda, * ), h( lda, * ), lre( ldlre, * ),
517  $ vl( ldvl, * ), vr( ldvr, * ), w( * ), w1( * ),
518  $ work( * )
519 * ..
520 *
521 * =====================================================================
522 *
523 * .. Parameters ..
524  COMPLEX czero
525  parameter ( czero = ( 0.0e+0, 0.0e+0 ) )
526  COMPLEX cone
527  parameter ( cone = ( 1.0e+0, 0.0e+0 ) )
528  REAL zero, one
529  parameter ( zero = 0.0e+0, one = 1.0e+0 )
530  INTEGER maxtyp
531  parameter ( maxtyp = 21 )
532 * ..
533 * .. Local Scalars ..
534  LOGICAL badnn
535  CHARACTER balanc
536  CHARACTER*3 path
537  INTEGER i, ibal, iinfo, imode, isrt, itype, iwk, j,
538  $ jcol, jsize, jtype, mtypes, n, nerrs,
539  $ nfail, nmax, nnwork, ntest, ntestf, ntestt
540  REAL anorm, cond, conds, ovfl, rtulp, rtulpi, ulp,
541  $ ulpinv, unfl, wi, wr
542 * ..
543 * .. Local Arrays ..
544  CHARACTER bal( 4 )
545  INTEGER idumma( 1 ), ioldsd( 4 ), kconds( maxtyp ),
546  $ kmagn( maxtyp ), kmode( maxtyp ),
547  $ ktype( maxtyp )
548 * ..
549 * .. External Functions ..
550  REAL slamch
551  EXTERNAL slamch
552 * ..
553 * .. External Subroutines ..
554  EXTERNAL cget23, clatme, clatmr, clatms, claset, slabad,
555  $ slasum, xerbla
556 * ..
557 * .. Intrinsic Functions ..
558  INTRINSIC abs, cmplx, max, min, sqrt
559 * ..
560 * .. Data statements ..
561  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
562  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
563  $ 3, 1, 2, 3 /
564  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
565  $ 1, 5, 5, 5, 4, 3, 1 /
566  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
567  DATA bal / 'N', 'P', 'S', 'B' /
568 * ..
569 * .. Executable Statements ..
570 *
571  path( 1: 1 ) = 'Complex precision'
572  path( 2: 3 ) = 'VX'
573 *
574 * Check for errors
575 *
576  ntestt = 0
577  ntestf = 0
578  info = 0
579 *
580 * Important constants
581 *
582  badnn = .false.
583 *
584 * 7 is the largest dimension in the input file of precomputed
585 * problems
586 *
587  nmax = 7
588  DO 10 j = 1, nsizes
589  nmax = max( nmax, nn( j ) )
590  IF( nn( j ).LT.0 )
591  $ badnn = .true.
592  10 CONTINUE
593 *
594 * Check for errors
595 *
596  IF( nsizes.LT.0 ) THEN
597  info = -1
598  ELSE IF( badnn ) THEN
599  info = -2
600  ELSE IF( ntypes.LT.0 ) THEN
601  info = -3
602  ELSE IF( thresh.LT.zero ) THEN
603  info = -6
604  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
605  info = -10
606  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
607  info = -15
608  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
609  info = -17
610  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
611  info = -19
612  ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
613  info = -30
614  END IF
615 *
616  IF( info.NE.0 ) THEN
617  CALL xerbla( 'CDRVVX', -info )
618  RETURN
619  END IF
620 *
621 * If nothing to do check on NIUNIT
622 *
623  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
624  $ GO TO 160
625 *
626 * More Important constants
627 *
628  unfl = slamch( 'Safe minimum' )
629  ovfl = one / unfl
630  CALL slabad( unfl, ovfl )
631  ulp = slamch( 'Precision' )
632  ulpinv = one / ulp
633  rtulp = sqrt( ulp )
634  rtulpi = one / rtulp
635 *
636 * Loop over sizes, types
637 *
638  nerrs = 0
639 *
640  DO 150 jsize = 1, nsizes
641  n = nn( jsize )
642  IF( nsizes.NE.1 ) THEN
643  mtypes = min( maxtyp, ntypes )
644  ELSE
645  mtypes = min( maxtyp+1, ntypes )
646  END IF
647 *
648  DO 140 jtype = 1, mtypes
649  IF( .NOT.dotype( jtype ) )
650  $ GO TO 140
651 *
652 * Save ISEED in case of an error.
653 *
654  DO 20 j = 1, 4
655  ioldsd( j ) = iseed( j )
656  20 CONTINUE
657 *
658 * Compute "A"
659 *
660 * Control parameters:
661 *
662 * KMAGN KCONDS KMODE KTYPE
663 * =1 O(1) 1 clustered 1 zero
664 * =2 large large clustered 2 identity
665 * =3 small exponential Jordan
666 * =4 arithmetic diagonal, (w/ eigenvalues)
667 * =5 random log symmetric, w/ eigenvalues
668 * =6 random general, w/ eigenvalues
669 * =7 random diagonal
670 * =8 random symmetric
671 * =9 random general
672 * =10 random triangular
673 *
674  IF( mtypes.GT.maxtyp )
675  $ GO TO 90
676 *
677  itype = ktype( jtype )
678  imode = kmode( jtype )
679 *
680 * Compute norm
681 *
682  GO TO ( 30, 40, 50 )kmagn( jtype )
683 *
684  30 CONTINUE
685  anorm = one
686  GO TO 60
687 *
688  40 CONTINUE
689  anorm = ovfl*ulp
690  GO TO 60
691 *
692  50 CONTINUE
693  anorm = unfl*ulpinv
694  GO TO 60
695 *
696  60 CONTINUE
697 *
698  CALL claset( 'Full', lda, n, czero, czero, a, lda )
699  iinfo = 0
700  cond = ulpinv
701 *
702 * Special Matrices -- Identity & Jordan block
703 *
704 * Zero
705 *
706  IF( itype.EQ.1 ) THEN
707  iinfo = 0
708 *
709  ELSE IF( itype.EQ.2 ) THEN
710 *
711 * Identity
712 *
713  DO 70 jcol = 1, n
714  a( jcol, jcol ) = anorm
715  70 CONTINUE
716 *
717  ELSE IF( itype.EQ.3 ) THEN
718 *
719 * Jordan Block
720 *
721  DO 80 jcol = 1, n
722  a( jcol, jcol ) = anorm
723  IF( jcol.GT.1 )
724  $ a( jcol, jcol-1 ) = one
725  80 CONTINUE
726 *
727  ELSE IF( itype.EQ.4 ) THEN
728 *
729 * Diagonal Matrix, [Eigen]values Specified
730 *
731  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
732  $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
733  $ iinfo )
734 *
735  ELSE IF( itype.EQ.5 ) THEN
736 *
737 * Symmetric, eigenvalues specified
738 *
739  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
740  $ anorm, n, n, 'N', a, lda, work( n+1 ),
741  $ iinfo )
742 *
743  ELSE IF( itype.EQ.6 ) THEN
744 *
745 * General, eigenvalues specified
746 *
747  IF( kconds( jtype ).EQ.1 ) THEN
748  conds = one
749  ELSE IF( kconds( jtype ).EQ.2 ) THEN
750  conds = rtulpi
751  ELSE
752  conds = zero
753  END IF
754 *
755  CALL clatme( n, 'D', iseed, work, imode, cond, cone,
756  $ 'T', 'T', 'T', rwork, 4, conds, n, n, anorm,
757  $ a, lda, work( 2*n+1 ), iinfo )
758 *
759  ELSE IF( itype.EQ.7 ) THEN
760 *
761 * Diagonal, random eigenvalues
762 *
763  CALL clatmr( n, n, 'D', iseed, 'S', work, 6, one, cone,
764  $ 'T', 'N', work( n+1 ), 1, one,
765  $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
766  $ zero, anorm, 'NO', a, lda, idumma, iinfo )
767 *
768  ELSE IF( itype.EQ.8 ) THEN
769 *
770 * Symmetric, random eigenvalues
771 *
772  CALL clatmr( n, n, 'D', iseed, 'H', work, 6, one, cone,
773  $ 'T', 'N', work( n+1 ), 1, one,
774  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
775  $ zero, anorm, 'NO', a, lda, idumma, iinfo )
776 *
777  ELSE IF( itype.EQ.9 ) THEN
778 *
779 * General, random eigenvalues
780 *
781  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
782  $ 'T', 'N', work( n+1 ), 1, one,
783  $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
784  $ zero, anorm, 'NO', a, lda, idumma, iinfo )
785  IF( n.GE.4 ) THEN
786  CALL claset( 'Full', 2, n, czero, czero, a, lda )
787  CALL claset( 'Full', n-3, 1, czero, czero, a( 3, 1 ),
788  $ lda )
789  CALL claset( 'Full', n-3, 2, czero, czero,
790  $ a( 3, n-1 ), lda )
791  CALL claset( 'Full', 1, n, czero, czero, a( n, 1 ),
792  $ lda )
793  END IF
794 *
795  ELSE IF( itype.EQ.10 ) THEN
796 *
797 * Triangular, random eigenvalues
798 *
799  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
800  $ 'T', 'N', work( n+1 ), 1, one,
801  $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
802  $ zero, anorm, 'NO', a, lda, idumma, iinfo )
803 *
804  ELSE
805 *
806  iinfo = 1
807  END IF
808 *
809  IF( iinfo.NE.0 ) THEN
810  WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
811  $ ioldsd
812  info = abs( iinfo )
813  RETURN
814  END IF
815 *
816  90 CONTINUE
817 *
818 * Test for minimal and generous workspace
819 *
820  DO 130 iwk = 1, 3
821  IF( iwk.EQ.1 ) THEN
822  nnwork = 2*n
823  ELSE IF( iwk.EQ.2 ) THEN
824  nnwork = 2*n + n**2
825  ELSE
826  nnwork = 6*n + 2*n**2
827  END IF
828  nnwork = max( nnwork, 1 )
829 *
830 * Test for all balancing options
831 *
832  DO 120 ibal = 1, 4
833  balanc = bal( ibal )
834 *
835 * Perform tests
836 *
837  CALL cget23( .false., 0, balanc, jtype, thresh,
838  $ ioldsd, nounit, n, a, lda, h, w, w1, vl,
839  $ ldvl, vr, ldvr, lre, ldlre, rcondv,
840  $ rcndv1, rcdvin, rconde, rcnde1, rcdein,
841  $ scale, scale1, result, work, nnwork,
842  $ rwork, info )
843 *
844 * Check for RESULT(j) > THRESH
845 *
846  ntest = 0
847  nfail = 0
848  DO 100 j = 1, 9
849  IF( result( j ).GE.zero )
850  $ ntest = ntest + 1
851  IF( result( j ).GE.thresh )
852  $ nfail = nfail + 1
853  100 CONTINUE
854 *
855  IF( nfail.GT.0 )
856  $ ntestf = ntestf + 1
857  IF( ntestf.EQ.1 ) THEN
858  WRITE( nounit, fmt = 9999 )path
859  WRITE( nounit, fmt = 9998 )
860  WRITE( nounit, fmt = 9997 )
861  WRITE( nounit, fmt = 9996 )
862  WRITE( nounit, fmt = 9995 )thresh
863  ntestf = 2
864  END IF
865 *
866  DO 110 j = 1, 9
867  IF( result( j ).GE.thresh ) THEN
868  WRITE( nounit, fmt = 9994 )balanc, n, iwk,
869  $ ioldsd, jtype, j, result( j )
870  END IF
871  110 CONTINUE
872 *
873  nerrs = nerrs + nfail
874  ntestt = ntestt + ntest
875 *
876  120 CONTINUE
877  130 CONTINUE
878  140 CONTINUE
879  150 CONTINUE
880 *
881  160 CONTINUE
882 *
883 * Read in data from file to check accuracy of condition estimation.
884 * Assume input eigenvalues are sorted lexicographically (increasing
885 * by real part, then decreasing by imaginary part)
886 *
887  jtype = 0
888  170 CONTINUE
889  READ( niunit, fmt = *, end = 220 )n, isrt
890 *
891 * Read input data until N=0
892 *
893  IF( n.EQ.0 )
894  $ GO TO 220
895  jtype = jtype + 1
896  iseed( 1 ) = jtype
897  DO 180 i = 1, n
898  READ( niunit, fmt = * )( a( i, j ), j = 1, n )
899  180 CONTINUE
900  DO 190 i = 1, n
901  READ( niunit, fmt = * )wr, wi, rcdein( i ), rcdvin( i )
902  w1( i ) = cmplx( wr, wi )
903  190 CONTINUE
904  CALL cget23( .true., isrt, 'N', 22, thresh, iseed, nounit, n, a,
905  $ lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre,
906  $ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
907  $ scale, scale1, result, work, 6*n+2*n**2, rwork,
908  $ info )
909 *
910 * Check for RESULT(j) > THRESH
911 *
912  ntest = 0
913  nfail = 0
914  DO 200 j = 1, 11
915  IF( result( j ).GE.zero )
916  $ ntest = ntest + 1
917  IF( result( j ).GE.thresh )
918  $ nfail = nfail + 1
919  200 CONTINUE
920 *
921  IF( nfail.GT.0 )
922  $ ntestf = ntestf + 1
923  IF( ntestf.EQ.1 ) THEN
924  WRITE( nounit, fmt = 9999 )path
925  WRITE( nounit, fmt = 9998 )
926  WRITE( nounit, fmt = 9997 )
927  WRITE( nounit, fmt = 9996 )
928  WRITE( nounit, fmt = 9995 )thresh
929  ntestf = 2
930  END IF
931 *
932  DO 210 j = 1, 11
933  IF( result( j ).GE.thresh ) THEN
934  WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
935  END IF
936  210 CONTINUE
937 *
938  nerrs = nerrs + nfail
939  ntestt = ntestt + ntest
940  GO TO 170
941  220 CONTINUE
942 *
943 * Summary
944 *
945  CALL slasum( path, nounit, nerrs, ntestt )
946 *
947  9999 FORMAT( / 1x, a3, ' -- Complex Eigenvalue-Eigenvector ',
948  $ 'Decomposition Expert Driver',
949  $ / ' Matrix types (see CDRVVX for details): ' )
950 *
951  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
952  $ ' ', ' 5=Diagonal: geometr. spaced entries.',
953  $ / ' 2=Identity matrix. ', ' 6=Diagona',
954  $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
955  $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
956  $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
957  $ 'mall, evenly spaced.' )
958  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
959  $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
960  $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
961  $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
962  $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
963  $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
964  $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
965  $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
966  $ ' complx ' )
967  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
968  $ 'with small random entries.', / ' 20=Matrix with large ran',
969  $ 'dom entries. ', ' 22=Matrix read from input file', / )
970  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
971  $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
972  $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
973  $ / ' 3 = | |VR(i)| - 1 | / ulp ',
974  $ / ' 4 = | |VL(i)| - 1 | / ulp ',
975  $ / ' 5 = 0 if W same no matter if VR or VL computed,',
976  $ ' 1/ulp otherwise', /
977  $ ' 6 = 0 if VR same no matter what else computed,',
978  $ ' 1/ulp otherwise', /
979  $ ' 7 = 0 if VL same no matter what else computed,',
980  $ ' 1/ulp otherwise', /
981  $ ' 8 = 0 if RCONDV same no matter what else computed,',
982  $ ' 1/ulp otherwise', /
983  $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
984  $ ' computed, 1/ulp otherwise',
985  $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
986  $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
987  9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
988  $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
989  9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
990  $ g10.3 )
991  9992 FORMAT( ' CDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
992  $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
993 *
994  RETURN
995 *
996 * End of CDRVVX
997 *
subroutine cget23(COMP, ISRT, BALANC, JTYPE, THRESH, ISEED, NOUNIT, N, A, LDA, H, W, W1, VL, LDVL, VR, LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, WORK, LWORK, RWORK, INFO)
CGET23
Definition: cget23.f:370
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:492
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:76
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:108
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:334
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:42
subroutine clatme(N, DIST, ISEED, D, MODE, COND, DMAX, RSIGN, UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, A, LDA, WORK, INFO)
CLATME
Definition: clatme.f:303

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