LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cdrgvx()

subroutine cdrgvx ( integer  NSIZE,
real  THRESH,
integer  NIN,
integer  NOUT,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( lda, * )  B,
complex, dimension( lda, * )  AI,
complex, dimension( lda, * )  BI,
complex, dimension( * )  ALPHA,
complex, dimension( * )  BETA,
complex, dimension( lda, * )  VL,
complex, dimension( lda, * )  VR,
integer  ILO,
integer  IHI,
real, dimension( * )  LSCALE,
real, dimension( * )  RSCALE,
real, dimension( * )  S,
real, dimension( * )  STRU,
real, dimension( * )  DIF,
real, dimension( * )  DIFTRU,
complex, dimension( * )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer  LIWORK,
real, dimension( 4 )  RESULT,
logical, dimension( * )  BWORK,
integer  INFO 
)

CDRGVX

Purpose:
 CDRGVX checks the nonsymmetric generalized eigenvalue problem
 expert driver CGGEVX.

 CGGEVX computes the generalized eigenvalues, (optionally) the left
 and/or right eigenvectors, (optionally) computes a balancing
 transformation to improve the conditioning, and (optionally)
 reciprocal condition numbers for the eigenvalues and eigenvectors.

 When CDRGVX is called with NSIZE > 0, two types of test matrix pairs
 are generated by the subroutine SLATM6 and test the driver CGGEVX.
 The test matrices have the known exact condition numbers for
 eigenvalues. For the condition numbers of the eigenvectors
 corresponding the first and last eigenvalues are also know
 ``exactly'' (see CLATM6).
 For each matrix pair, the following tests will be performed and
 compared with the threshold THRESH.

 (1) max over all left eigenvalue/-vector pairs (beta/alpha,l) of

    | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )

     where l**H is the conjugate tranpose of l.

 (2) max over all right eigenvalue/-vector pairs (beta/alpha,r) of

       | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )

 (3) The condition number S(i) of eigenvalues computed by CGGEVX
     differs less than a factor THRESH from the exact S(i) (see
     CLATM6).

 (4) DIF(i) computed by CTGSNA differs less than a factor 10*THRESH
     from the exact value (for the 1st and 5th vectors only).

 Test Matrices
 =============

 Two kinds of test matrix pairs
          (A, B) = inverse(YH) * (Da, Db) * inverse(X)
 are used in the tests:

 1: Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
          0   2+a   0    0    0         0   1   0   0   0
          0    0   3+a   0    0         0   0   1   0   0
          0    0    0   4+a   0         0   0   0   1   0
          0    0    0    0   5+a ,      0   0   0   0   1 , and

 2: Da =  1   -1    0    0    0    Db = 1   0   0   0   0
          1    1    0    0    0         0   1   0   0   0
          0    0    1    0    0         0   0   1   0   0
          0    0    0   1+a  1+b        0   0   0   1   0
          0    0    0  -1-b  1+a ,      0   0   0   0   1 .

 In both cases the same inverse(YH) and inverse(X) are used to compute
 (A, B), giving the exact eigenvectors to (A,B) as (YH, X):

 YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
         0    1   -y    y   -y         0   1   x  -x  -x
         0    0    1    0    0         0   0   1   0   0
         0    0    0    1    0         0   0   0   1   0
         0    0    0    0    1,        0   0   0   0   1 , where

 a, b, x and y will have all values independently of each other from
 { sqrt(sqrt(ULP)),  0.1,  1,  10,  1/sqrt(sqrt(ULP)) }.
Parameters
[in]NSIZE
          NSIZE is INTEGER
          The number of sizes of matrices to use.  NSIZE must be at
          least zero. If it is zero, no randomly generated matrices
          are tested, but any test matrices read from NIN will be
          tested.  If it is not zero, then N = 5.
[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]NIN
          NIN is INTEGER
          The FORTRAN unit number for reading in the data file of
          problems to solve.
[in]NOUT
          NOUT is INTEGER
          The FORTRAN unit number for printing out error messages
          (e.g., if a routine returns IINFO not equal to 0.)
[out]A
          A is COMPLEX array, dimension (LDA, NSIZE)
          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, B, AI, BI, Ao, and Bo.
          It must be at least 1 and at least NSIZE.
[out]B
          B is COMPLEX array, dimension (LDA, NSIZE)
          Used to hold the matrix whose eigenvalues are to be
          computed.  On exit, B contains the last matrix actually used.
[out]AI
          AI is COMPLEX array, dimension (LDA, NSIZE)
          Copy of A, modified by CGGEVX.
[out]BI
          BI is COMPLEX array, dimension (LDA, NSIZE)
          Copy of B, modified by CGGEVX.
[out]ALPHA
          ALPHA is COMPLEX array, dimension (NSIZE)
[out]BETA
          BETA is COMPLEX array, dimension (NSIZE)

          On exit, ALPHA/BETA are the eigenvalues.
[out]VL
          VL is COMPLEX array, dimension (LDA, NSIZE)
          VL holds the left eigenvectors computed by CGGEVX.
[out]VR
          VR is COMPLEX array, dimension (LDA, NSIZE)
          VR holds the right eigenvectors computed by CGGEVX.
[out]ILO
                ILO is INTEGER
[out]IHI
                IHI is INTEGER
[out]LSCALE
                LSCALE is REAL array, dimension (N)
[out]RSCALE
                RSCALE is REAL array, dimension (N)
[out]S
                S is REAL array, dimension (N)
[out]STRU
                STRU is REAL array, dimension (N)
[out]DIF
                DIF is REAL array, dimension (N)
[out]DIFTRU
                DIFTRU is REAL array, dimension (N)
[out]WORK
          WORK is COMPLEX array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          Leading dimension of WORK.  LWORK >= 2*N*N + 2*N
[out]RWORK
          RWORK is REAL array, dimension (6*N)
[out]IWORK
          IWORK is INTEGER array, dimension (LIWORK)
[in]LIWORK
          LIWORK is INTEGER
          Leading dimension of IWORK.  LIWORK >= N+2.
[out]RESULT
                RESULT is REAL array, dimension (4)
[out]BWORK
          BWORK is LOGICAL array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  A routine returned an error code.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2016

Definition at line 300 of file cdrgvx.f.

300 *
301 * -- LAPACK test routine (version 3.7.0) --
302 * -- LAPACK is a software package provided by Univ. of Tennessee, --
303 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
304 * June 2016
305 *
306 * .. Scalar Arguments ..
307  INTEGER ihi, ilo, info, lda, liwork, lwork, nin, nout,
308  $ nsize
309  REAL thresh
310 * ..
311 * .. Array Arguments ..
312  LOGICAL bwork( * )
313  INTEGER iwork( * )
314  REAL dif( * ), diftru( * ), lscale( * ),
315  $ result( 4 ), rscale( * ), rwork( * ), s( * ),
316  $ stru( * )
317  COMPLEX a( lda, * ), ai( lda, * ), alpha( * ),
318  $ b( lda, * ), beta( * ), bi( lda, * ),
319  $ vl( lda, * ), vr( lda, * ), work( * )
320 * ..
321 *
322 * =====================================================================
323 *
324 * .. Parameters ..
325  REAL zero, one, ten, tnth, half
326  parameter( zero = 0.0e+0, one = 1.0e+0, ten = 1.0e+1,
327  $ tnth = 1.0e-1, half = 0.5e+0 )
328 * ..
329 * .. Local Scalars ..
330  INTEGER i, iptype, iwa, iwb, iwx, iwy, j, linfo,
331  $ maxwrk, minwrk, n, nerrs, nmax, nptknt, ntestt
332  REAL abnorm, anorm, bnorm, ratio1, ratio2, thrsh2,
333  $ ulp, ulpinv
334 * ..
335 * .. Local Arrays ..
336  COMPLEX weight( 5 )
337 * ..
338 * .. External Functions ..
339  INTEGER ilaenv
340  REAL clange, slamch
341  EXTERNAL ilaenv, clange, slamch
342 * ..
343 * .. External Subroutines ..
344  EXTERNAL alasvm, cget52, cggevx, clacpy, clatm6, xerbla
345 * ..
346 * .. Intrinsic Functions ..
347  INTRINSIC abs, cmplx, max, sqrt
348 * ..
349 * .. Executable Statements ..
350 *
351 * Check for errors
352 *
353  info = 0
354 *
355  nmax = 5
356 *
357  IF( nsize.LT.0 ) THEN
358  info = -1
359  ELSE IF( thresh.LT.zero ) THEN
360  info = -2
361  ELSE IF( nin.LE.0 ) THEN
362  info = -3
363  ELSE IF( nout.LE.0 ) THEN
364  info = -4
365  ELSE IF( lda.LT.1 .OR. lda.LT.nmax ) THEN
366  info = -6
367  ELSE IF( liwork.LT.nmax+2 ) THEN
368  info = -26
369  END IF
370 *
371 * Compute workspace
372 * (Note: Comments in the code beginning "Workspace:" describe the
373 * minimal amount of workspace needed at that point in the code,
374 * as well as the preferred amount for good performance.
375 * NB refers to the optimal block size for the immediately
376 * following subroutine, as returned by ILAENV.)
377 *
378  minwrk = 1
379  IF( info.EQ.0 .AND. lwork.GE.1 ) THEN
380  minwrk = 2*nmax*( nmax+1 )
381  maxwrk = nmax*( 1+ilaenv( 1, 'CGEQRF', ' ', nmax, 1, nmax,
382  $ 0 ) )
383  maxwrk = max( maxwrk, 2*nmax*( nmax+1 ) )
384  work( 1 ) = maxwrk
385  END IF
386 *
387  IF( lwork.LT.minwrk )
388  $ info = -23
389 *
390  IF( info.NE.0 ) THEN
391  CALL xerbla( 'CDRGVX', -info )
392  RETURN
393  END IF
394 *
395  n = 5
396  ulp = slamch( 'P' )
397  ulpinv = one / ulp
398  thrsh2 = ten*thresh
399  nerrs = 0
400  nptknt = 0
401  ntestt = 0
402 *
403  IF( nsize.EQ.0 )
404  $ GO TO 90
405 *
406 * Parameters used for generating test matrices.
407 *
408  weight( 1 ) = cmplx( tnth, zero )
409  weight( 2 ) = cmplx( half, zero )
410  weight( 3 ) = one
411  weight( 4 ) = one / weight( 2 )
412  weight( 5 ) = one / weight( 1 )
413 *
414  DO 80 iptype = 1, 2
415  DO 70 iwa = 1, 5
416  DO 60 iwb = 1, 5
417  DO 50 iwx = 1, 5
418  DO 40 iwy = 1, 5
419 *
420 * generated a pair of test matrix
421 *
422  CALL clatm6( iptype, 5, a, lda, b, vr, lda, vl,
423  $ lda, weight( iwa ), weight( iwb ),
424  $ weight( iwx ), weight( iwy ), stru,
425  $ diftru )
426 *
427 * Compute eigenvalues/eigenvectors of (A, B).
428 * Compute eigenvalue/eigenvector condition numbers
429 * using computed eigenvectors.
430 *
431  CALL clacpy( 'F', n, n, a, lda, ai, lda )
432  CALL clacpy( 'F', n, n, b, lda, bi, lda )
433 *
434  CALL cggevx( 'N', 'V', 'V', 'B', n, ai, lda, bi,
435  $ lda, alpha, beta, vl, lda, vr, lda,
436  $ ilo, ihi, lscale, rscale, anorm,
437  $ bnorm, s, dif, work, lwork, rwork,
438  $ iwork, bwork, linfo )
439  IF( linfo.NE.0 ) THEN
440  WRITE( nout, fmt = 9999 )'CGGEVX', linfo, n,
441  $ iptype, iwa, iwb, iwx, iwy
442  GO TO 30
443  END IF
444 *
445 * Compute the norm(A, B)
446 *
447  CALL clacpy( 'Full', n, n, ai, lda, work, n )
448  CALL clacpy( 'Full', n, n, bi, lda, work( n*n+1 ),
449  $ n )
450  abnorm = clange( 'Fro', n, 2*n, work, n, rwork )
451 *
452 * Tests (1) and (2)
453 *
454  result( 1 ) = zero
455  CALL cget52( .true., n, a, lda, b, lda, vl, lda,
456  $ alpha, beta, work, rwork,
457  $ result( 1 ) )
458  IF( result( 2 ).GT.thresh ) THEN
459  WRITE( nout, fmt = 9998 )'Left', 'CGGEVX',
460  $ result( 2 ), n, iptype, iwa, iwb, iwx, iwy
461  END IF
462 *
463  result( 2 ) = zero
464  CALL cget52( .false., n, a, lda, b, lda, vr, lda,
465  $ alpha, beta, work, rwork,
466  $ result( 2 ) )
467  IF( result( 3 ).GT.thresh ) THEN
468  WRITE( nout, fmt = 9998 )'Right', 'CGGEVX',
469  $ result( 3 ), n, iptype, iwa, iwb, iwx, iwy
470  END IF
471 *
472 * Test (3)
473 *
474  result( 3 ) = zero
475  DO 10 i = 1, n
476  IF( s( i ).EQ.zero ) THEN
477  IF( stru( i ).GT.abnorm*ulp )
478  $ result( 3 ) = ulpinv
479  ELSE IF( stru( i ).EQ.zero ) THEN
480  IF( s( i ).GT.abnorm*ulp )
481  $ result( 3 ) = ulpinv
482  ELSE
483  rwork( i ) = max( abs( stru( i ) / s( i ) ),
484  $ abs( s( i ) / stru( i ) ) )
485  result( 3 ) = max( result( 3 ), rwork( i ) )
486  END IF
487  10 CONTINUE
488 *
489 * Test (4)
490 *
491  result( 4 ) = zero
492  IF( dif( 1 ).EQ.zero ) THEN
493  IF( diftru( 1 ).GT.abnorm*ulp )
494  $ result( 4 ) = ulpinv
495  ELSE IF( diftru( 1 ).EQ.zero ) THEN
496  IF( dif( 1 ).GT.abnorm*ulp )
497  $ result( 4 ) = ulpinv
498  ELSE IF( dif( 5 ).EQ.zero ) THEN
499  IF( diftru( 5 ).GT.abnorm*ulp )
500  $ result( 4 ) = ulpinv
501  ELSE IF( diftru( 5 ).EQ.zero ) THEN
502  IF( dif( 5 ).GT.abnorm*ulp )
503  $ result( 4 ) = ulpinv
504  ELSE
505  ratio1 = max( abs( diftru( 1 ) / dif( 1 ) ),
506  $ abs( dif( 1 ) / diftru( 1 ) ) )
507  ratio2 = max( abs( diftru( 5 ) / dif( 5 ) ),
508  $ abs( dif( 5 ) / diftru( 5 ) ) )
509  result( 4 ) = max( ratio1, ratio2 )
510  END IF
511 *
512  ntestt = ntestt + 4
513 *
514 * Print out tests which fail.
515 *
516  DO 20 j = 1, 4
517  IF( ( result( j ).GE.thrsh2 .AND. j.GE.4 ) .OR.
518  $ ( result( j ).GE.thresh .AND. j.LE.3 ) )
519  $ THEN
520 *
521 * If this is the first test to fail,
522 * print a header to the data file.
523 *
524  IF( nerrs.EQ.0 ) THEN
525  WRITE( nout, fmt = 9997 )'CXV'
526 *
527 * Print out messages for built-in examples
528 *
529 * Matrix types
530 *
531  WRITE( nout, fmt = 9995 )
532  WRITE( nout, fmt = 9994 )
533  WRITE( nout, fmt = 9993 )
534 *
535 * Tests performed
536 *
537  WRITE( nout, fmt = 9992 )'''',
538  $ 'transpose', ''''
539 *
540  END IF
541  nerrs = nerrs + 1
542  IF( result( j ).LT.10000.0 ) THEN
543  WRITE( nout, fmt = 9991 )iptype, iwa,
544  $ iwb, iwx, iwy, j, result( j )
545  ELSE
546  WRITE( nout, fmt = 9990 )iptype, iwa,
547  $ iwb, iwx, iwy, j, result( j )
548  END IF
549  END IF
550  20 CONTINUE
551 *
552  30 CONTINUE
553 *
554  40 CONTINUE
555  50 CONTINUE
556  60 CONTINUE
557  70 CONTINUE
558  80 CONTINUE
559 *
560  GO TO 150
561 *
562  90 CONTINUE
563 *
564 * Read in data from file to check accuracy of condition estimation
565 * Read input data until N=0
566 *
567  READ( nin, fmt = *, end = 150 )n
568  IF( n.EQ.0 )
569  $ GO TO 150
570  DO 100 i = 1, n
571  READ( nin, fmt = * )( a( i, j ), j = 1, n )
572  100 CONTINUE
573  DO 110 i = 1, n
574  READ( nin, fmt = * )( b( i, j ), j = 1, n )
575  110 CONTINUE
576  READ( nin, fmt = * )( stru( i ), i = 1, n )
577  READ( nin, fmt = * )( diftru( i ), i = 1, n )
578 *
579  nptknt = nptknt + 1
580 *
581 * Compute eigenvalues/eigenvectors of (A, B).
582 * Compute eigenvalue/eigenvector condition numbers
583 * using computed eigenvectors.
584 *
585  CALL clacpy( 'F', n, n, a, lda, ai, lda )
586  CALL clacpy( 'F', n, n, b, lda, bi, lda )
587 *
588  CALL cggevx( 'N', 'V', 'V', 'B', n, ai, lda, bi, lda, alpha, beta,
589  $ vl, lda, vr, lda, ilo, ihi, lscale, rscale, anorm,
590  $ bnorm, s, dif, work, lwork, rwork, iwork, bwork,
591  $ linfo )
592 *
593  IF( linfo.NE.0 ) THEN
594  WRITE( nout, fmt = 9987 )'CGGEVX', linfo, n, nptknt
595  GO TO 140
596  END IF
597 *
598 * Compute the norm(A, B)
599 *
600  CALL clacpy( 'Full', n, n, ai, lda, work, n )
601  CALL clacpy( 'Full', n, n, bi, lda, work( n*n+1 ), n )
602  abnorm = clange( 'Fro', n, 2*n, work, n, rwork )
603 *
604 * Tests (1) and (2)
605 *
606  result( 1 ) = zero
607  CALL cget52( .true., n, a, lda, b, lda, vl, lda, alpha, beta,
608  $ work, rwork, result( 1 ) )
609  IF( result( 2 ).GT.thresh ) THEN
610  WRITE( nout, fmt = 9986 )'Left', 'CGGEVX', result( 2 ), n,
611  $ nptknt
612  END IF
613 *
614  result( 2 ) = zero
615  CALL cget52( .false., n, a, lda, b, lda, vr, lda, alpha, beta,
616  $ work, rwork, result( 2 ) )
617  IF( result( 3 ).GT.thresh ) THEN
618  WRITE( nout, fmt = 9986 )'Right', 'CGGEVX', result( 3 ), n,
619  $ nptknt
620  END IF
621 *
622 * Test (3)
623 *
624  result( 3 ) = zero
625  DO 120 i = 1, n
626  IF( s( i ).EQ.zero ) THEN
627  IF( stru( i ).GT.abnorm*ulp )
628  $ result( 3 ) = ulpinv
629  ELSE IF( stru( i ).EQ.zero ) THEN
630  IF( s( i ).GT.abnorm*ulp )
631  $ result( 3 ) = ulpinv
632  ELSE
633  rwork( i ) = max( abs( stru( i ) / s( i ) ),
634  $ abs( s( i ) / stru( i ) ) )
635  result( 3 ) = max( result( 3 ), rwork( i ) )
636  END IF
637  120 CONTINUE
638 *
639 * Test (4)
640 *
641  result( 4 ) = zero
642  IF( dif( 1 ).EQ.zero ) THEN
643  IF( diftru( 1 ).GT.abnorm*ulp )
644  $ result( 4 ) = ulpinv
645  ELSE IF( diftru( 1 ).EQ.zero ) THEN
646  IF( dif( 1 ).GT.abnorm*ulp )
647  $ result( 4 ) = ulpinv
648  ELSE IF( dif( 5 ).EQ.zero ) THEN
649  IF( diftru( 5 ).GT.abnorm*ulp )
650  $ result( 4 ) = ulpinv
651  ELSE IF( diftru( 5 ).EQ.zero ) THEN
652  IF( dif( 5 ).GT.abnorm*ulp )
653  $ result( 4 ) = ulpinv
654  ELSE
655  ratio1 = max( abs( diftru( 1 ) / dif( 1 ) ),
656  $ abs( dif( 1 ) / diftru( 1 ) ) )
657  ratio2 = max( abs( diftru( 5 ) / dif( 5 ) ),
658  $ abs( dif( 5 ) / diftru( 5 ) ) )
659  result( 4 ) = max( ratio1, ratio2 )
660  END IF
661 *
662  ntestt = ntestt + 4
663 *
664 * Print out tests which fail.
665 *
666  DO 130 j = 1, 4
667  IF( result( j ).GE.thrsh2 ) THEN
668 *
669 * If this is the first test to fail,
670 * print a header to the data file.
671 *
672  IF( nerrs.EQ.0 ) THEN
673  WRITE( nout, fmt = 9997 )'CXV'
674 *
675 * Print out messages for built-in examples
676 *
677 * Matrix types
678 *
679  WRITE( nout, fmt = 9996 )
680 *
681 * Tests performed
682 *
683  WRITE( nout, fmt = 9992 )'''', 'transpose', ''''
684 *
685  END IF
686  nerrs = nerrs + 1
687  IF( result( j ).LT.10000.0 ) THEN
688  WRITE( nout, fmt = 9989 )nptknt, n, j, result( j )
689  ELSE
690  WRITE( nout, fmt = 9988 )nptknt, n, j, result( j )
691  END IF
692  END IF
693  130 CONTINUE
694 *
695  140 CONTINUE
696 *
697  GO TO 90
698  150 CONTINUE
699 *
700 * Summary
701 *
702  CALL alasvm( 'CXV', nout, nerrs, ntestt, 0 )
703 *
704  work( 1 ) = maxwrk
705 *
706  RETURN
707 *
708  9999 FORMAT( ' CDRGVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
709  $ i6, ', JTYPE=', i6, ')' )
710 *
711  9998 FORMAT( ' CDRGVX: ', a, ' Eigenvectors from ', a, ' incorrectly ',
712  $ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 9x,
713  $ 'N=', i6, ', JTYPE=', i6, ', IWA=', i5, ', IWB=', i5,
714  $ ', IWX=', i5, ', IWY=', i5 )
715 *
716  9997 FORMAT( / 1x, a3, ' -- Complex Expert Eigenvalue/vector',
717  $ ' problem driver' )
718 *
719  9996 FORMAT( 'Input Example' )
720 *
721  9995 FORMAT( ' Matrix types: ', / )
722 *
723  9994 FORMAT( ' TYPE 1: Da is diagonal, Db is identity, ',
724  $ / ' A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) ',
725  $ / ' YH and X are left and right eigenvectors. ', / )
726 *
727  9993 FORMAT( ' TYPE 2: Da is quasi-diagonal, Db is identity, ',
728  $ / ' A = Y^(-H) Da X^(-1), B = Y^(-H) Db X^(-1) ',
729  $ / ' YH and X are left and right eigenvectors. ', / )
730 *
731  9992 FORMAT( / ' Tests performed: ', / 4x,
732  $ ' a is alpha, b is beta, l is a left eigenvector, ', / 4x,
733  $ ' r is a right eigenvector and ', a, ' means ', a, '.',
734  $ / ' 1 = max | ( b A - a B )', a, ' l | / const.',
735  $ / ' 2 = max | ( b A - a B ) r | / const.',
736  $ / ' 3 = max ( Sest/Stru, Stru/Sest ) ',
737  $ ' over all eigenvalues', /
738  $ ' 4 = max( DIFest/DIFtru, DIFtru/DIFest ) ',
739  $ ' over the 1st and 5th eigenvectors', / )
740 *
741  9991 FORMAT( ' Type=', i2, ',', ' IWA=', i2, ', IWB=', i2, ', IWX=',
742  $ i2, ', IWY=', i2, ', result ', i2, ' is', 0p, f8.2 )
743 *
744  9990 FORMAT( ' Type=', i2, ',', ' IWA=', i2, ', IWB=', i2, ', IWX=',
745  $ i2, ', IWY=', i2, ', result ', i2, ' is', 1p, e10.3 )
746 *
747  9989 FORMAT( ' Input example #', i2, ', matrix order=', i4, ',',
748  $ ' result ', i2, ' is', 0p, f8.2 )
749 *
750  9988 FORMAT( ' Input example #', i2, ', matrix order=', i4, ',',
751  $ ' result ', i2, ' is', 1p, e10.3 )
752 *
753  9987 FORMAT( ' CDRGVX: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
754  $ i6, ', Input example #', i2, ')' )
755 *
756  9986 FORMAT( ' CDRGVX: ', a, ' Eigenvectors from ', a, ' incorrectly ',
757  $ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 9x,
758  $ 'N=', i6, ', Input Example #', i2, ')' )
759 *
760 * End of CDRGVX
761 *
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cggevx(BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, ILO, IHI, LSCALE, RSCALE, ABNRM, BBNRM, RCONDE, RCONDV, WORK, LWORK, RWORK, IWORK, BWORK, INFO)
CGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices ...
Definition: cggevx.f:376
subroutine cget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHA, BETA, WORK, RWORK, RESULT)
CGET52
Definition: cget52.f:163
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
subroutine clatm6(TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, BETA, WX, WY, S, DIF)
CLATM6
Definition: clatm6.f:176
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