LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cdrvvx()

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.

Definition at line 491 of file cdrvvx.f.

496*
497* -- LAPACK test routine --
498* -- LAPACK is a software package provided by Univ. of Tennessee, --
499* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
500*
501* .. Scalar Arguments ..
502 INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT,
503 $ NSIZES, NTYPES, NWORK
504 REAL THRESH
505* ..
506* .. Array Arguments ..
507 LOGICAL DOTYPE( * )
508 INTEGER ISEED( 4 ), NN( * )
509 REAL RCDEIN( * ), RCDVIN( * ), RCNDE1( * ),
510 $ RCNDV1( * ), RCONDE( * ), RCONDV( * ),
511 $ RESULT( 11 ), RWORK( * ), SCALE( * ),
512 $ SCALE1( * )
513 COMPLEX A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
514 $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
515 $ WORK( * )
516* ..
517*
518* =====================================================================
519*
520* .. Parameters ..
521 COMPLEX CZERO
522 parameter( czero = ( 0.0e+0, 0.0e+0 ) )
523 COMPLEX CONE
524 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
525 REAL ZERO, ONE
526 parameter( zero = 0.0e+0, one = 1.0e+0 )
527 INTEGER MAXTYP
528 parameter( maxtyp = 21 )
529* ..
530* .. Local Scalars ..
531 LOGICAL BADNN
532 CHARACTER BALANC
533 CHARACTER*3 PATH
534 INTEGER I, IBAL, IINFO, IMODE, ISRT, ITYPE, IWK, J,
535 $ JCOL, JSIZE, JTYPE, MTYPES, N, NERRS,
536 $ NFAIL, NMAX, NNWORK, NTEST, NTESTF, NTESTT
537 REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, ULP,
538 $ ULPINV, UNFL, WI, WR
539* ..
540* .. Local Arrays ..
541 CHARACTER BAL( 4 )
542 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
543 $ KMAGN( MAXTYP ), KMODE( MAXTYP ),
544 $ KTYPE( MAXTYP )
545* ..
546* .. External Functions ..
547 REAL SLAMCH
548 EXTERNAL slamch
549* ..
550* .. External Subroutines ..
551 EXTERNAL cget23, clatme, clatmr, clatms, claset, slabad,
552 $ slasum, xerbla
553* ..
554* .. Intrinsic Functions ..
555 INTRINSIC abs, cmplx, max, min, sqrt
556* ..
557* .. Data statements ..
558 DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
559 DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
560 $ 3, 1, 2, 3 /
561 DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
562 $ 1, 5, 5, 5, 4, 3, 1 /
563 DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
564 DATA bal / 'N', 'P', 'S', 'B' /
565* ..
566* .. Executable Statements ..
567*
568 path( 1: 1 ) = 'Complex precision'
569 path( 2: 3 ) = 'VX'
570*
571* Check for errors
572*
573 ntestt = 0
574 ntestf = 0
575 info = 0
576*
577* Important constants
578*
579 badnn = .false.
580*
581* 7 is the largest dimension in the input file of precomputed
582* problems
583*
584 nmax = 7
585 DO 10 j = 1, nsizes
586 nmax = max( nmax, nn( j ) )
587 IF( nn( j ).LT.0 )
588 $ badnn = .true.
589 10 CONTINUE
590*
591* Check for errors
592*
593 IF( nsizes.LT.0 ) THEN
594 info = -1
595 ELSE IF( badnn ) THEN
596 info = -2
597 ELSE IF( ntypes.LT.0 ) THEN
598 info = -3
599 ELSE IF( thresh.LT.zero ) THEN
600 info = -6
601 ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
602 info = -10
603 ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
604 info = -15
605 ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
606 info = -17
607 ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
608 info = -19
609 ELSE IF( 6*nmax+2*nmax**2.GT.nwork ) THEN
610 info = -30
611 END IF
612*
613 IF( info.NE.0 ) THEN
614 CALL xerbla( 'CDRVVX', -info )
615 RETURN
616 END IF
617*
618* If nothing to do check on NIUNIT
619*
620 IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
621 $ GO TO 160
622*
623* More Important constants
624*
625 unfl = slamch( 'Safe minimum' )
626 ovfl = one / unfl
627 CALL slabad( unfl, ovfl )
628 ulp = slamch( 'Precision' )
629 ulpinv = one / ulp
630 rtulp = sqrt( ulp )
631 rtulpi = one / rtulp
632*
633* Loop over sizes, types
634*
635 nerrs = 0
636*
637 DO 150 jsize = 1, nsizes
638 n = nn( jsize )
639 IF( nsizes.NE.1 ) THEN
640 mtypes = min( maxtyp, ntypes )
641 ELSE
642 mtypes = min( maxtyp+1, ntypes )
643 END IF
644*
645 DO 140 jtype = 1, mtypes
646 IF( .NOT.dotype( jtype ) )
647 $ GO TO 140
648*
649* Save ISEED in case of an error.
650*
651 DO 20 j = 1, 4
652 ioldsd( j ) = iseed( j )
653 20 CONTINUE
654*
655* Compute "A"
656*
657* Control parameters:
658*
659* KMAGN KCONDS KMODE KTYPE
660* =1 O(1) 1 clustered 1 zero
661* =2 large large clustered 2 identity
662* =3 small exponential Jordan
663* =4 arithmetic diagonal, (w/ eigenvalues)
664* =5 random log symmetric, w/ eigenvalues
665* =6 random general, w/ eigenvalues
666* =7 random diagonal
667* =8 random symmetric
668* =9 random general
669* =10 random triangular
670*
671 IF( mtypes.GT.maxtyp )
672 $ GO TO 90
673*
674 itype = ktype( jtype )
675 imode = kmode( jtype )
676*
677* Compute norm
678*
679 GO TO ( 30, 40, 50 )kmagn( jtype )
680*
681 30 CONTINUE
682 anorm = one
683 GO TO 60
684*
685 40 CONTINUE
686 anorm = ovfl*ulp
687 GO TO 60
688*
689 50 CONTINUE
690 anorm = unfl*ulpinv
691 GO TO 60
692*
693 60 CONTINUE
694*
695 CALL claset( 'Full', lda, n, czero, czero, a, lda )
696 iinfo = 0
697 cond = ulpinv
698*
699* Special Matrices -- Identity & Jordan block
700*
701* Zero
702*
703 IF( itype.EQ.1 ) THEN
704 iinfo = 0
705*
706 ELSE IF( itype.EQ.2 ) THEN
707*
708* Identity
709*
710 DO 70 jcol = 1, n
711 a( jcol, jcol ) = anorm
712 70 CONTINUE
713*
714 ELSE IF( itype.EQ.3 ) THEN
715*
716* Jordan Block
717*
718 DO 80 jcol = 1, n
719 a( jcol, jcol ) = anorm
720 IF( jcol.GT.1 )
721 $ a( jcol, jcol-1 ) = one
722 80 CONTINUE
723*
724 ELSE IF( itype.EQ.4 ) THEN
725*
726* Diagonal Matrix, [Eigen]values Specified
727*
728 CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
729 $ anorm, 0, 0, 'N', a, lda, work( n+1 ),
730 $ iinfo )
731*
732 ELSE IF( itype.EQ.5 ) THEN
733*
734* Symmetric, eigenvalues specified
735*
736 CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
737 $ anorm, n, n, 'N', a, lda, work( n+1 ),
738 $ iinfo )
739*
740 ELSE IF( itype.EQ.6 ) THEN
741*
742* General, eigenvalues specified
743*
744 IF( kconds( jtype ).EQ.1 ) THEN
745 conds = one
746 ELSE IF( kconds( jtype ).EQ.2 ) THEN
747 conds = rtulpi
748 ELSE
749 conds = zero
750 END IF
751*
752 CALL clatme( n, 'D', iseed, work, imode, cond, cone,
753 $ 'T', 'T', 'T', rwork, 4, conds, n, n, anorm,
754 $ a, lda, work( 2*n+1 ), iinfo )
755*
756 ELSE IF( itype.EQ.7 ) THEN
757*
758* Diagonal, random eigenvalues
759*
760 CALL clatmr( n, n, 'D', iseed, 'S', work, 6, one, cone,
761 $ 'T', 'N', work( n+1 ), 1, one,
762 $ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
763 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
764*
765 ELSE IF( itype.EQ.8 ) THEN
766*
767* Symmetric, random eigenvalues
768*
769 CALL clatmr( n, n, 'D', iseed, 'H', work, 6, one, cone,
770 $ 'T', 'N', work( n+1 ), 1, one,
771 $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
772 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
773*
774 ELSE IF( itype.EQ.9 ) THEN
775*
776* General, random eigenvalues
777*
778 CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
779 $ 'T', 'N', work( n+1 ), 1, one,
780 $ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
781 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
782 IF( n.GE.4 ) THEN
783 CALL claset( 'Full', 2, n, czero, czero, a, lda )
784 CALL claset( 'Full', n-3, 1, czero, czero, a( 3, 1 ),
785 $ lda )
786 CALL claset( 'Full', n-3, 2, czero, czero,
787 $ a( 3, n-1 ), lda )
788 CALL claset( 'Full', 1, n, czero, czero, a( n, 1 ),
789 $ lda )
790 END IF
791*
792 ELSE IF( itype.EQ.10 ) THEN
793*
794* Triangular, random eigenvalues
795*
796 CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
797 $ 'T', 'N', work( n+1 ), 1, one,
798 $ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
799 $ zero, anorm, 'NO', a, lda, idumma, iinfo )
800*
801 ELSE
802*
803 iinfo = 1
804 END IF
805*
806 IF( iinfo.NE.0 ) THEN
807 WRITE( nounit, fmt = 9992 )'Generator', iinfo, n, jtype,
808 $ ioldsd
809 info = abs( iinfo )
810 RETURN
811 END IF
812*
813 90 CONTINUE
814*
815* Test for minimal and generous workspace
816*
817 DO 130 iwk = 1, 3
818 IF( iwk.EQ.1 ) THEN
819 nnwork = 2*n
820 ELSE IF( iwk.EQ.2 ) THEN
821 nnwork = 2*n + n**2
822 ELSE
823 nnwork = 6*n + 2*n**2
824 END IF
825 nnwork = max( nnwork, 1 )
826*
827* Test for all balancing options
828*
829 DO 120 ibal = 1, 4
830 balanc = bal( ibal )
831*
832* Perform tests
833*
834 CALL cget23( .false., 0, balanc, jtype, thresh,
835 $ ioldsd, nounit, n, a, lda, h, w, w1, vl,
836 $ ldvl, vr, ldvr, lre, ldlre, rcondv,
837 $ rcndv1, rcdvin, rconde, rcnde1, rcdein,
838 $ scale, scale1, result, work, nnwork,
839 $ rwork, info )
840*
841* Check for RESULT(j) > THRESH
842*
843 ntest = 0
844 nfail = 0
845 DO 100 j = 1, 9
846 IF( result( j ).GE.zero )
847 $ ntest = ntest + 1
848 IF( result( j ).GE.thresh )
849 $ nfail = nfail + 1
850 100 CONTINUE
851*
852 IF( nfail.GT.0 )
853 $ ntestf = ntestf + 1
854 IF( ntestf.EQ.1 ) THEN
855 WRITE( nounit, fmt = 9999 )path
856 WRITE( nounit, fmt = 9998 )
857 WRITE( nounit, fmt = 9997 )
858 WRITE( nounit, fmt = 9996 )
859 WRITE( nounit, fmt = 9995 )thresh
860 ntestf = 2
861 END IF
862*
863 DO 110 j = 1, 9
864 IF( result( j ).GE.thresh ) THEN
865 WRITE( nounit, fmt = 9994 )balanc, n, iwk,
866 $ ioldsd, jtype, j, result( j )
867 END IF
868 110 CONTINUE
869*
870 nerrs = nerrs + nfail
871 ntestt = ntestt + ntest
872*
873 120 CONTINUE
874 130 CONTINUE
875 140 CONTINUE
876 150 CONTINUE
877*
878 160 CONTINUE
879*
880* Read in data from file to check accuracy of condition estimation.
881* Assume input eigenvalues are sorted lexicographically (increasing
882* by real part, then decreasing by imaginary part)
883*
884 jtype = 0
885 170 CONTINUE
886 READ( niunit, fmt = *, END = 220 )N, isrt
887*
888* Read input data until N=0
889*
890 IF( n.EQ.0 )
891 $ GO TO 220
892 jtype = jtype + 1
893 iseed( 1 ) = jtype
894 DO 180 i = 1, n
895 READ( niunit, fmt = * )( a( i, j ), j = 1, n )
896 180 CONTINUE
897 DO 190 i = 1, n
898 READ( niunit, fmt = * )wr, wi, rcdein( i ), rcdvin( i )
899 w1( i ) = cmplx( wr, wi )
900 190 CONTINUE
901 CALL cget23( .true., isrt, 'N', 22, thresh, iseed, nounit, n, a,
902 $ lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre,
903 $ rcondv, rcndv1, rcdvin, rconde, rcnde1, rcdein,
904 $ scale, scale1, result, work, 6*n+2*n**2, rwork,
905 $ info )
906*
907* Check for RESULT(j) > THRESH
908*
909 ntest = 0
910 nfail = 0
911 DO 200 j = 1, 11
912 IF( result( j ).GE.zero )
913 $ ntest = ntest + 1
914 IF( result( j ).GE.thresh )
915 $ nfail = nfail + 1
916 200 CONTINUE
917*
918 IF( nfail.GT.0 )
919 $ ntestf = ntestf + 1
920 IF( ntestf.EQ.1 ) THEN
921 WRITE( nounit, fmt = 9999 )path
922 WRITE( nounit, fmt = 9998 )
923 WRITE( nounit, fmt = 9997 )
924 WRITE( nounit, fmt = 9996 )
925 WRITE( nounit, fmt = 9995 )thresh
926 ntestf = 2
927 END IF
928*
929 DO 210 j = 1, 11
930 IF( result( j ).GE.thresh ) THEN
931 WRITE( nounit, fmt = 9993 )n, jtype, j, result( j )
932 END IF
933 210 CONTINUE
934*
935 nerrs = nerrs + nfail
936 ntestt = ntestt + ntest
937 GO TO 170
938 220 CONTINUE
939*
940* Summary
941*
942 CALL slasum( path, nounit, nerrs, ntestt )
943*
944 9999 FORMAT( / 1x, a3, ' -- Complex Eigenvalue-Eigenvector ',
945 $ 'Decomposition Expert Driver',
946 $ / ' Matrix types (see CDRVVX for details): ' )
947*
948 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
949 $ ' ', ' 5=Diagonal: geometr. spaced entries.',
950 $ / ' 2=Identity matrix. ', ' 6=Diagona',
951 $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
952 $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
953 $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
954 $ 'mall, evenly spaced.' )
955 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
956 $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
957 $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
958 $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
959 $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
960 $ 'lex ', / ' 12=Well-cond., random complex ', ' ',
961 $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi',
962 $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
963 $ ' complx ' )
964 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
965 $ 'with small random entries.', / ' 20=Matrix with large ran',
966 $ 'dom entries. ', ' 22=Matrix read from input file', / )
967 9995 FORMAT( ' Tests performed with test threshold =', f8.2,
968 $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
969 $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ',
970 $ / ' 3 = | |VR(i)| - 1 | / ulp ',
971 $ / ' 4 = | |VL(i)| - 1 | / ulp ',
972 $ / ' 5 = 0 if W same no matter if VR or VL computed,',
973 $ ' 1/ulp otherwise', /
974 $ ' 6 = 0 if VR same no matter what else computed,',
975 $ ' 1/ulp otherwise', /
976 $ ' 7 = 0 if VL same no matter what else computed,',
977 $ ' 1/ulp otherwise', /
978 $ ' 8 = 0 if RCONDV same no matter what else computed,',
979 $ ' 1/ulp otherwise', /
980 $ ' 9 = 0 if SCALE, ILO, IHI, ABNRM same no matter what else',
981 $ ' computed, 1/ulp otherwise',
982 $ / ' 10 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV),',
983 $ / ' 11 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE),' )
984 9994 FORMAT( ' BALANC=''', a1, ''',N=', i4, ',IWK=', i1, ', seed=',
985 $ 4( i4, ',' ), ' type ', i2, ', test(', i2, ')=', g10.3 )
986 9993 FORMAT( ' N=', i5, ', input example =', i3, ', test(', i2, ')=',
987 $ g10.3 )
988 9992 FORMAT( ' CDRVVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
989 $ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
990*
991 RETURN
992*
993* End of CDRVVX
994*
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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:368
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:332
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:301
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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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