LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.)```

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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