 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cdrvev()

 subroutine cdrvev ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, 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( 7 ) RESULT, complex, dimension( * ) WORK, integer NWORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer INFO )

CDRVEV

Purpose:
```    CDRVEV  checks the nonsymmetric eigenvalue problem driver CGEEV.

When CDRVEV 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, 7
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 whether largest component real

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

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

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

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

W(full) denotes the eigenvalues computed when both VR and VL
are also computed, and W(partial) denotes the eigenvalues
computed when only W, only W and VR, or only W and VL are
computed.

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

VR(full) denotes the right eigenvectors computed when both VR
and VL are computed, and VR(partial) denotes the result
when only VR is computed.

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

VL(full) denotes the left eigenvectors computed when both VR
and VL are also computed, and VL(partial) denotes the result
when only VL is 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```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, CDRVEV does nothing. It must be at least zero.``` [in] NN ``` NN is INTEGER array, dimension (NSIZES) An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, CDRVEV does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .``` [in] DOTYPE ``` DOTYPE is LOGICAL array, dimension (NTYPES) If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored.``` [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to CDRVEV to continue the same random number sequence.``` [in] THRESH ``` THRESH is REAL A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.``` [in] NOUNIT ``` NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)``` [out] A ``` A is COMPLEX 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 COMPLEX array, dimension (LDA, max(NN)) Another copy of the test matrix A, modified by CGEEV.``` [out] W ``` W is COMPLEX array, dimension (max(NN)) The eigenvalues of A. On exit, W are the eigenvalues of the matrix in A.``` [out] W1 ``` W1 is COMPLEX array, dimension (max(NN)) Like W, this array contains the eigenvalues of A, but those computed when CGEEV 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)) VL holds the computed left eigenvectors.``` [in] LDVL ``` LDVL is INTEGER Leading dimension of VL. Must be at least max(1,max(NN)).``` [out] VR ``` VR is COMPLEX array, dimension (LDVR, max(NN)) VR holds the computed right eigenvectors.``` [in] LDVR ``` LDVR is INTEGER Leading dimension of VR. Must be at least max(1,max(NN)).``` [out] LRE ``` LRE is COMPLEX array, dimension (LDLRE, max(NN)) 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)).``` [out] RESULT ``` RESULT is REAL array, dimension (7) 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 5*NN(j)+2*NN(j)**2 for all j.``` [out] RWORK ` RWORK is REAL array, dimension (2*max(NN))` [out] IWORK ` IWORK is INTEGER array, dimension (max(NN))` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some NN(j) < 0 -3: NTYPES < 0 -6: THRESH < 0 -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). -14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). -16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). -18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). -21: NWORK too small. If CLATMR, CLATMS, CLATME or CGEEV returns an error code, the absolute value of it is returned. ----------------------------------------------------------------------- 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.)```

Definition at line 387 of file cdrvev.f.

391 *
392 * -- LAPACK test routine --
393 * -- LAPACK is a software package provided by Univ. of Tennessee, --
394 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
395 *
396 * .. Scalar Arguments ..
397  INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES,
398  \$ NTYPES, NWORK
399  REAL THRESH
400 * ..
401 * .. Array Arguments ..
402  LOGICAL DOTYPE( * )
403  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
404  REAL RESULT( 7 ), RWORK( * )
405  COMPLEX A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ),
406  \$ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ),
407  \$ WORK( * )
408 * ..
409 *
410 * =====================================================================
411 *
412 * .. Parameters ..
413  COMPLEX CZERO
414  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
415  COMPLEX CONE
416  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
417  REAL ZERO, ONE
418  parameter( zero = 0.0e+0, one = 1.0e+0 )
419  REAL TWO
420  parameter( two = 2.0e+0 )
421  INTEGER MAXTYP
422  parameter( maxtyp = 21 )
423 * ..
424 * .. Local Scalars ..
426  CHARACTER*3 PATH
427  INTEGER IINFO, IMODE, ITYPE, IWK, J, JCOL, JJ, JSIZE,
428  \$ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX,
429  \$ NNWORK, NTEST, NTESTF, NTESTT
430  REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM,
431  \$ ULP, ULPINV, UNFL, VMX, VRMX, VTST
432 * ..
433 * .. Local Arrays ..
434  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ),
435  \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
436  \$ KTYPE( MAXTYP )
437  REAL RES( 2 )
438  COMPLEX DUM( 1 )
439 * ..
440 * .. External Functions ..
441  REAL SCNRM2, SLAMCH
442  EXTERNAL scnrm2, slamch
443 * ..
444 * .. External Subroutines ..
445  EXTERNAL cgeev, cget22, clacpy, clatme, clatmr, clatms,
447 * ..
448 * .. Intrinsic Functions ..
449  INTRINSIC abs, aimag, cmplx, max, min, real, sqrt
450 * ..
451 * .. Data statements ..
452  DATA ktype / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 /
453  DATA kmagn / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2,
454  \$ 3, 1, 2, 3 /
455  DATA kmode / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3,
456  \$ 1, 5, 5, 5, 4, 3, 1 /
457  DATA kconds / 3*0, 5*0, 4*1, 6*2, 3*0 /
458 * ..
459 * .. Executable Statements ..
460 *
461  path( 1: 1 ) = 'Complex precision'
462  path( 2: 3 ) = 'EV'
463 *
464 * Check for errors
465 *
466  ntestt = 0
467  ntestf = 0
468  info = 0
469 *
470 * Important constants
471 *
473  nmax = 0
474  DO 10 j = 1, nsizes
475  nmax = max( nmax, nn( j ) )
476  IF( nn( j ).LT.0 )
478  10 CONTINUE
479 *
480 * Check for errors
481 *
482  IF( nsizes.LT.0 ) THEN
483  info = -1
484  ELSE IF( badnn ) THEN
485  info = -2
486  ELSE IF( ntypes.LT.0 ) THEN
487  info = -3
488  ELSE IF( thresh.LT.zero ) THEN
489  info = -6
490  ELSE IF( nounit.LE.0 ) THEN
491  info = -7
492  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
493  info = -9
494  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.nmax ) THEN
495  info = -14
496  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.nmax ) THEN
497  info = -16
498  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.nmax ) THEN
499  info = -28
500  ELSE IF( 5*nmax+2*nmax**2.GT.nwork ) THEN
501  info = -21
502  END IF
503 *
504  IF( info.NE.0 ) THEN
505  CALL xerbla( 'CDRVEV', -info )
506  RETURN
507  END IF
508 *
509 * Quick return if nothing to do
510 *
511  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
512  \$ RETURN
513 *
514 * More Important constants
515 *
516  unfl = slamch( 'Safe minimum' )
517  ovfl = one / unfl
518  CALL slabad( unfl, ovfl )
519  ulp = slamch( 'Precision' )
520  ulpinv = one / ulp
521  rtulp = sqrt( ulp )
522  rtulpi = one / rtulp
523 *
524 * Loop over sizes, types
525 *
526  nerrs = 0
527 *
528  DO 270 jsize = 1, nsizes
529  n = nn( jsize )
530  IF( nsizes.NE.1 ) THEN
531  mtypes = min( maxtyp, ntypes )
532  ELSE
533  mtypes = min( maxtyp+1, ntypes )
534  END IF
535 *
536  DO 260 jtype = 1, mtypes
537  IF( .NOT.dotype( jtype ) )
538  \$ GO TO 260
539 *
540 * Save ISEED in case of an error.
541 *
542  DO 20 j = 1, 4
543  ioldsd( j ) = iseed( j )
544  20 CONTINUE
545 *
546 * Compute "A"
547 *
548 * Control parameters:
549 *
550 * KMAGN KCONDS KMODE KTYPE
551 * =1 O(1) 1 clustered 1 zero
552 * =2 large large clustered 2 identity
553 * =3 small exponential Jordan
554 * =4 arithmetic diagonal, (w/ eigenvalues)
555 * =5 random log symmetric, w/ eigenvalues
556 * =6 random general, w/ eigenvalues
557 * =7 random diagonal
558 * =8 random symmetric
559 * =9 random general
560 * =10 random triangular
561 *
562  IF( mtypes.GT.maxtyp )
563  \$ GO TO 90
564 *
565  itype = ktype( jtype )
566  imode = kmode( jtype )
567 *
568 * Compute norm
569 *
570  GO TO ( 30, 40, 50 )kmagn( jtype )
571 *
572  30 CONTINUE
573  anorm = one
574  GO TO 60
575 *
576  40 CONTINUE
577  anorm = ovfl*ulp
578  GO TO 60
579 *
580  50 CONTINUE
581  anorm = unfl*ulpinv
582  GO TO 60
583 *
584  60 CONTINUE
585 *
586  CALL claset( 'Full', lda, n, czero, czero, a, lda )
587  iinfo = 0
588  cond = ulpinv
589 *
590 * Special Matrices -- Identity & Jordan block
591 *
592 * Zero
593 *
594  IF( itype.EQ.1 ) THEN
595  iinfo = 0
596 *
597  ELSE IF( itype.EQ.2 ) THEN
598 *
599 * Identity
600 *
601  DO 70 jcol = 1, n
602  a( jcol, jcol ) = cmplx( anorm )
603  70 CONTINUE
604 *
605  ELSE IF( itype.EQ.3 ) THEN
606 *
607 * Jordan Block
608 *
609  DO 80 jcol = 1, n
610  a( jcol, jcol ) = cmplx( anorm )
611  IF( jcol.GT.1 )
612  \$ a( jcol, jcol-1 ) = cone
613  80 CONTINUE
614 *
615  ELSE IF( itype.EQ.4 ) THEN
616 *
617 * Diagonal Matrix, [Eigen]values Specified
618 *
619  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
620  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
621  \$ iinfo )
622 *
623  ELSE IF( itype.EQ.5 ) THEN
624 *
625 * Hermitian, eigenvalues specified
626 *
627  CALL clatms( n, n, 'S', iseed, 'H', rwork, imode, cond,
628  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
629  \$ iinfo )
630 *
631  ELSE IF( itype.EQ.6 ) THEN
632 *
633 * General, eigenvalues specified
634 *
635  IF( kconds( jtype ).EQ.1 ) THEN
636  conds = one
637  ELSE IF( kconds( jtype ).EQ.2 ) THEN
638  conds = rtulpi
639  ELSE
640  conds = zero
641  END IF
642 *
643  CALL clatme( n, 'D', iseed, work, imode, cond, cone,
644  \$ 'T', 'T', 'T', rwork, 4, conds, n, n,
645  \$ anorm, a, lda, work( 2*n+1 ), iinfo )
646 *
647  ELSE IF( itype.EQ.7 ) THEN
648 *
649 * Diagonal, random eigenvalues
650 *
651  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
652  \$ 'T', 'N', work( n+1 ), 1, one,
653  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
654  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
655 *
656  ELSE IF( itype.EQ.8 ) THEN
657 *
658 * Symmetric, random eigenvalues
659 *
660  CALL clatmr( n, n, 'D', iseed, 'H', work, 6, one, cone,
661  \$ 'T', 'N', work( n+1 ), 1, one,
662  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
663  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
664 *
665  ELSE IF( itype.EQ.9 ) THEN
666 *
667 * General, random eigenvalues
668 *
669  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
670  \$ 'T', 'N', work( n+1 ), 1, one,
671  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
672  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
673  IF( n.GE.4 ) THEN
674  CALL claset( 'Full', 2, n, czero, czero, a, lda )
675  CALL claset( 'Full', n-3, 1, czero, czero, a( 3, 1 ),
676  \$ lda )
677  CALL claset( 'Full', n-3, 2, czero, czero,
678  \$ a( 3, n-1 ), lda )
679  CALL claset( 'Full', 1, n, czero, czero, a( n, 1 ),
680  \$ lda )
681  END IF
682 *
683  ELSE IF( itype.EQ.10 ) THEN
684 *
685 * Triangular, random eigenvalues
686 *
687  CALL clatmr( n, n, 'D', iseed, 'N', work, 6, one, cone,
688  \$ 'T', 'N', work( n+1 ), 1, one,
689  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, 0,
690  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
691 *
692  ELSE
693 *
694  iinfo = 1
695  END IF
696 *
697  IF( iinfo.NE.0 ) THEN
698  WRITE( nounit, fmt = 9993 )'Generator', iinfo, n, jtype,
699  \$ ioldsd
700  info = abs( iinfo )
701  RETURN
702  END IF
703 *
704  90 CONTINUE
705 *
706 * Test for minimal and generous workspace
707 *
708  DO 250 iwk = 1, 2
709  IF( iwk.EQ.1 ) THEN
710  nnwork = 2*n
711  ELSE
712  nnwork = 5*n + 2*n**2
713  END IF
714  nnwork = max( nnwork, 1 )
715 *
716 * Initialize RESULT
717 *
718  DO 100 j = 1, 7
719  result( j ) = -one
720  100 CONTINUE
721 *
722 * Compute eigenvalues and eigenvectors, and test them
723 *
724  CALL clacpy( 'F', n, n, a, lda, h, lda )
725  CALL cgeev( 'V', 'V', n, h, lda, w, vl, ldvl, vr, ldvr,
726  \$ work, nnwork, rwork, iinfo )
727  IF( iinfo.NE.0 ) THEN
728  result( 1 ) = ulpinv
729  WRITE( nounit, fmt = 9993 )'CGEEV1', iinfo, n, jtype,
730  \$ ioldsd
731  info = abs( iinfo )
732  GO TO 220
733  END IF
734 *
735 * Do Test (1)
736 *
737  CALL cget22( 'N', 'N', 'N', n, a, lda, vr, ldvr, w, work,
738  \$ rwork, res )
739  result( 1 ) = res( 1 )
740 *
741 * Do Test (2)
742 *
743  CALL cget22( 'C', 'N', 'C', n, a, lda, vl, ldvl, w, work,
744  \$ rwork, res )
745  result( 2 ) = res( 1 )
746 *
747 * Do Test (3)
748 *
749  DO 120 j = 1, n
750  tnrm = scnrm2( n, vr( 1, j ), 1 )
751  result( 3 ) = max( result( 3 ),
752  \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
753  vmx = zero
754  vrmx = zero
755  DO 110 jj = 1, n
756  vtst = abs( vr( jj, j ) )
757  IF( vtst.GT.vmx )
758  \$ vmx = vtst
759  IF( aimag( vr( jj, j ) ).EQ.zero .AND.
760  \$ abs( real( vr( jj, j ) ) ).GT.vrmx )
761  \$ vrmx = abs( real( vr( jj, j ) ) )
762  110 CONTINUE
763  IF( vrmx / vmx.LT.one-two*ulp )
764  \$ result( 3 ) = ulpinv
765  120 CONTINUE
766 *
767 * Do Test (4)
768 *
769  DO 140 j = 1, n
770  tnrm = scnrm2( n, vl( 1, j ), 1 )
771  result( 4 ) = max( result( 4 ),
772  \$ min( ulpinv, abs( tnrm-one ) / ulp ) )
773  vmx = zero
774  vrmx = zero
775  DO 130 jj = 1, n
776  vtst = abs( vl( jj, j ) )
777  IF( vtst.GT.vmx )
778  \$ vmx = vtst
779  IF( aimag( vl( jj, j ) ).EQ.zero .AND.
780  \$ abs( real( vl( jj, j ) ) ).GT.vrmx )
781  \$ vrmx = abs( real( vl( jj, j ) ) )
782  130 CONTINUE
783  IF( vrmx / vmx.LT.one-two*ulp )
784  \$ result( 4 ) = ulpinv
785  140 CONTINUE
786 *
787 * Compute eigenvalues only, and test them
788 *
789  CALL clacpy( 'F', n, n, a, lda, h, lda )
790  CALL cgeev( 'N', 'N', n, h, lda, w1, dum, 1, dum, 1,
791  \$ work, nnwork, rwork, iinfo )
792  IF( iinfo.NE.0 ) THEN
793  result( 1 ) = ulpinv
794  WRITE( nounit, fmt = 9993 )'CGEEV2', iinfo, n, jtype,
795  \$ ioldsd
796  info = abs( iinfo )
797  GO TO 220
798  END IF
799 *
800 * Do Test (5)
801 *
802  DO 150 j = 1, n
803  IF( w( j ).NE.w1( j ) )
804  \$ result( 5 ) = ulpinv
805  150 CONTINUE
806 *
807 * Compute eigenvalues and right eigenvectors, and test them
808 *
809  CALL clacpy( 'F', n, n, a, lda, h, lda )
810  CALL cgeev( 'N', 'V', n, h, lda, w1, dum, 1, lre, ldlre,
811  \$ work, nnwork, rwork, iinfo )
812  IF( iinfo.NE.0 ) THEN
813  result( 1 ) = ulpinv
814  WRITE( nounit, fmt = 9993 )'CGEEV3', iinfo, n, jtype,
815  \$ ioldsd
816  info = abs( iinfo )
817  GO TO 220
818  END IF
819 *
820 * Do Test (5) again
821 *
822  DO 160 j = 1, n
823  IF( w( j ).NE.w1( j ) )
824  \$ result( 5 ) = ulpinv
825  160 CONTINUE
826 *
827 * Do Test (6)
828 *
829  DO 180 j = 1, n
830  DO 170 jj = 1, n
831  IF( vr( j, jj ).NE.lre( j, jj ) )
832  \$ result( 6 ) = ulpinv
833  170 CONTINUE
834  180 CONTINUE
835 *
836 * Compute eigenvalues and left eigenvectors, and test them
837 *
838  CALL clacpy( 'F', n, n, a, lda, h, lda )
839  CALL cgeev( 'V', 'N', n, h, lda, w1, lre, ldlre, dum, 1,
840  \$ work, nnwork, rwork, iinfo )
841  IF( iinfo.NE.0 ) THEN
842  result( 1 ) = ulpinv
843  WRITE( nounit, fmt = 9993 )'CGEEV4', iinfo, n, jtype,
844  \$ ioldsd
845  info = abs( iinfo )
846  GO TO 220
847  END IF
848 *
849 * Do Test (5) again
850 *
851  DO 190 j = 1, n
852  IF( w( j ).NE.w1( j ) )
853  \$ result( 5 ) = ulpinv
854  190 CONTINUE
855 *
856 * Do Test (7)
857 *
858  DO 210 j = 1, n
859  DO 200 jj = 1, n
860  IF( vl( j, jj ).NE.lre( j, jj ) )
861  \$ result( 7 ) = ulpinv
862  200 CONTINUE
863  210 CONTINUE
864 *
865 * End of Loop -- Check for RESULT(j) > THRESH
866 *
867  220 CONTINUE
868 *
869  ntest = 0
870  nfail = 0
871  DO 230 j = 1, 7
872  IF( result( j ).GE.zero )
873  \$ ntest = ntest + 1
874  IF( result( j ).GE.thresh )
875  \$ nfail = nfail + 1
876  230 CONTINUE
877 *
878  IF( nfail.GT.0 )
879  \$ ntestf = ntestf + 1
880  IF( ntestf.EQ.1 ) THEN
881  WRITE( nounit, fmt = 9999 )path
882  WRITE( nounit, fmt = 9998 )
883  WRITE( nounit, fmt = 9997 )
884  WRITE( nounit, fmt = 9996 )
885  WRITE( nounit, fmt = 9995 )thresh
886  ntestf = 2
887  END IF
888 *
889  DO 240 j = 1, 7
890  IF( result( j ).GE.thresh ) THEN
891  WRITE( nounit, fmt = 9994 )n, iwk, ioldsd, jtype,
892  \$ j, result( j )
893  END IF
894  240 CONTINUE
895 *
896  nerrs = nerrs + nfail
897  ntestt = ntestt + ntest
898 *
899  250 CONTINUE
900  260 CONTINUE
901  270 CONTINUE
902 *
903 * Summary
904 *
905  CALL slasum( path, nounit, nerrs, ntestt )
906 *
907  9999 FORMAT( / 1x, a3, ' -- Complex Eigenvalue-Eigenvector ',
908  \$ 'Decomposition Driver', /
909  \$ ' Matrix types (see CDRVEV for details): ' )
910 *
911  9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ',
912  \$ ' ', ' 5=Diagonal: geometr. spaced entries.',
913  \$ / ' 2=Identity matrix. ', ' 6=Diagona',
914  \$ 'l: clustered entries.', / ' 3=Transposed Jordan block. ',
915  \$ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ',
916  \$ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s',
917  \$ 'mall, evenly spaced.' )
918  9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev',
919  \$ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e',
920  \$ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ',
921  \$ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond',
922  \$ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp',
923  \$ 'lex ', a6, / ' 12=Well-cond., random complex ', a6, ' ',
924  \$ ' 17=Ill-cond., large rand. complx ', a4, / ' 13=Ill-condi',
925  \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.',
926  \$ ' complx ', a4 )
927  9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ',
928  \$ 'with small random entries.', / ' 20=Matrix with large ran',
929  \$ 'dom entries. ', / )
930  9995 FORMAT( ' Tests performed with test threshold =', f8.2,
931  \$ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ',
932  \$ / ' 2 = | conj-trans(A) VL - VL conj-trans(W) | /',
933  \$ ' ( n |A| ulp ) ', / ' 3 = | |VR(i)| - 1 | / ulp ',
934  \$ / ' 4 = | |VL(i)| - 1 | / ulp ',
935  \$ / ' 5 = 0 if W same no matter if VR or VL computed,',
936  \$ ' 1/ulp otherwise', /
937  \$ ' 6 = 0 if VR same no matter if VL computed,',
938  \$ ' 1/ulp otherwise', /
939  \$ ' 7 = 0 if VL same no matter if VR computed,',
940  \$ ' 1/ulp otherwise', / )
941  9994 FORMAT( ' N=', i5, ', IWK=', i2, ', seed=', 4( i4, ',' ),
942  \$ ' type ', i2, ', test(', i2, ')=', g10.3 )
943  9993 FORMAT( ' CDRVEV: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
944  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
945 *
946  RETURN
947 *
948 * End of CDRVEV
949 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cget22(TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, W, WORK, RWORK, RESULT)
CGET22
Definition: cget22.f:144
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 cgeev(JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Definition: cgeev.f:180
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
real(wp) function scnrm2(n, x, incx)
SCNRM2
Definition: scnrm2.f90:90
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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