LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sget23()

subroutine sget23 ( logical  COMP,
character  BALANC,
integer  JTYPE,
real  THRESH,
integer, dimension( 4 )  ISEED,
integer  NOUNIT,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( lda, * )  H,
real, dimension( * )  WR,
real, dimension( * )  WI,
real, dimension( * )  WR1,
real, dimension( * )  WI1,
real, dimension( ldvl, * )  VL,
integer  LDVL,
real, dimension( ldvr, * )  VR,
integer  LDVR,
real, 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,
real, dimension( * )  WORK,
integer  LWORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SGET23

Purpose:
    SGET23  checks the nonsymmetric eigenvalue problem driver SGEEVX.
    If COMP = .FALSE., the first 8 of the following tests will be
    performed on the input matrix A, and also test 9 if LWORK is
    sufficiently large.
    if COMP is .TRUE. all 11 tests will be performed.

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

      Here VR is the matrix of unit right eigenvectors.
      W is a block diagonal matrix, with a 1x1 block for each
      real eigenvalue and a 2x2 block for each complex conjugate
      pair.  If eigenvalues j and j+1 are a complex conjugate pair,
      so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the
      2 x 2 block corresponding to the pair will be:

              (  wr  wi  )
              ( -wi  wr  )

      Such a block multiplying an n x 2 matrix  ( ur ui ) on the
      right will be the same as multiplying  ur + i*ui  by  wr + i*wi.

    (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)     0 if W(full) = W(partial), 1/ulp otherwise

      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)     0 if VR(full) = VR(partial), 1/ulp otherwise

      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)     0 if VL(full) = VL(partial), 1/ulp otherwise

      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)     0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise

      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.

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

      RCONDV is the reciprocal right eigenvector condition number
      computed by SGEEVX 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 SGEEVX 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]COMP
          COMP is LOGICAL
          COMP describes which input tests to perform:
            = .FALSE. if the computed condition numbers are not to
                      be tested against RCDVIN and RCDEIN
            = .TRUE.  if they are to be compared
[in]BALANC
          BALANC is CHARACTER
          Describes the balancing option to be tested.
            = 'N' for no permuting or diagonal scaling
            = 'P' for permuting but no diagonal scaling
            = 'S' for no permuting but diagonal scaling
            = 'B' for permuting and diagonal scaling
[in]JTYPE
          JTYPE is INTEGER
          Type of input matrix. Used to label output if error occurs.
[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]ISEED
          ISEED is INTEGER array, dimension (4)
          If COMP = .FALSE., the random number generator seed
          used to produce matrix.
          If COMP = .TRUE., ISEED(1) = the number of the example.
          Used to label output if error occurs.
[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.)
[in]N
          N is INTEGER
          The dimension of A. N must be at least 0.
[in,out]A
          A is REAL array, dimension (LDA,N)
          Used to hold the matrix whose eigenvalues are to be
          computed.
[in]LDA
          LDA is INTEGER
          The leading dimension of A, and H. LDA must be at
          least 1 and at least N.
[out]H
          H is REAL array, dimension (LDA,N)
          Another copy of the test matrix A, modified by SGEEVX.
[out]WR
          WR is REAL array, dimension (N)
[out]WI
          WI is REAL array, dimension (N)

          The real and imaginary parts of the eigenvalues of A.
          On exit, WR + WI*i are the eigenvalues of the matrix in A.
[out]WR1
          WR1 is REAL array, dimension (N)
[out]WI1
          WI1 is REAL array, dimension (N)

          Like WR, WI, these arrays contain the eigenvalues of A,
          but those computed when SGEEVX only computes a partial
          eigendecomposition, i.e. not the eigenvalues and left
          and right eigenvectors.
[out]VL
          VL is REAL array, dimension (LDVL,N)
          VL holds the computed left eigenvectors.
[in]LDVL
          LDVL is INTEGER
          Leading dimension of VL. Must be at least max(1,N).
[out]VR
          VR is REAL array, dimension (LDVR,N)
          VR holds the computed right eigenvectors.
[in]LDVR
          LDVR is INTEGER
          Leading dimension of VR. Must be at least max(1,N).
[out]LRE
          LRE is REAL array, dimension (LDLRE,N)
          LRE holds the computed right or left eigenvectors.
[in]LDLRE
          LDLRE is INTEGER
          Leading dimension of LRE. Must be at least max(1,N).
[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 11 tests described above.
          The values are currently limited to 1/ulp, to avoid
          overflow.
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed.
[out]IWORK
          IWORK is INTEGER array, dimension (2*N)
[out]INFO
          INFO is INTEGER
          If 0,  successful exit.
          If <0, input parameter -INFO had an incorrect value.
          If >0, SGEEVX returned an error code, the absolute
                 value of which is returned.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 380 of file sget23.f.

380 *
381 * -- LAPACK test routine (version 3.7.0) --
382 * -- LAPACK is a software package provided by Univ. of Tennessee, --
383 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
384 * December 2016
385 *
386 * .. Scalar Arguments ..
387  LOGICAL comp
388  CHARACTER balanc
389  INTEGER info, jtype, lda, ldlre, ldvl, ldvr, lwork, n,
390  $ nounit
391  REAL thresh
392 * ..
393 * .. Array Arguments ..
394  INTEGER iseed( 4 ), iwork( * )
395  REAL a( lda, * ), h( lda, * ), lre( ldlre, * ),
396  $ rcdein( * ), rcdvin( * ), rcnde1( * ),
397  $ rcndv1( * ), rconde( * ), rcondv( * ),
398  $ result( 11 ), scale( * ), scale1( * ),
399  $ vl( ldvl, * ), vr( ldvr, * ), wi( * ),
400  $ wi1( * ), work( * ), wr( * ), wr1( * )
401 * ..
402 *
403 * =====================================================================
404 *
405 *
406 * .. Parameters ..
407  REAL zero, one, two
408  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0 )
409  REAL epsin
410  parameter( epsin = 5.9605e-8 )
411 * ..
412 * .. Local Scalars ..
413  LOGICAL balok, nobal
414  CHARACTER sense
415  INTEGER i, ihi, ihi1, iinfo, ilo, ilo1, isens, isensm,
416  $ j, jj, kmin
417  REAL abnrm, abnrm1, eps, smlnum, tnrm, tol, tolin,
418  $ ulp, ulpinv, v, vimin, vmax, vmx, vrmin, vrmx,
419  $ vtst
420 * ..
421 * .. Local Arrays ..
422  CHARACTER sens( 2 )
423  REAL dum( 1 ), res( 2 )
424 * ..
425 * .. External Functions ..
426  LOGICAL lsame
427  REAL slamch, slapy2, snrm2
428  EXTERNAL lsame, slamch, slapy2, snrm2
429 * ..
430 * .. External Subroutines ..
431  EXTERNAL sgeevx, sget22, slacpy, xerbla
432 * ..
433 * .. Intrinsic Functions ..
434  INTRINSIC abs, max, min, real
435 * ..
436 * .. Data statements ..
437  DATA sens / 'N', 'V' /
438 * ..
439 * .. Executable Statements ..
440 *
441 * Check for errors
442 *
443  nobal = lsame( balanc, 'N' )
444  balok = nobal .OR. lsame( balanc, 'P' ) .OR.
445  $ lsame( balanc, 'S' ) .OR. lsame( balanc, 'B' )
446  info = 0
447  IF( .NOT.balok ) THEN
448  info = -2
449  ELSE IF( thresh.LT.zero ) THEN
450  info = -4
451  ELSE IF( nounit.LE.0 ) THEN
452  info = -6
453  ELSE IF( n.LT.0 ) THEN
454  info = -7
455  ELSE IF( lda.LT.1 .OR. lda.LT.n ) THEN
456  info = -9
457  ELSE IF( ldvl.LT.1 .OR. ldvl.LT.n ) THEN
458  info = -16
459  ELSE IF( ldvr.LT.1 .OR. ldvr.LT.n ) THEN
460  info = -18
461  ELSE IF( ldlre.LT.1 .OR. ldlre.LT.n ) THEN
462  info = -20
463  ELSE IF( lwork.LT.3*n .OR. ( comp .AND. lwork.LT.6*n+n*n ) ) THEN
464  info = -31
465  END IF
466 *
467  IF( info.NE.0 ) THEN
468  CALL xerbla( 'SGET23', -info )
469  RETURN
470  END IF
471 *
472 * Quick return if nothing to do
473 *
474  DO 10 i = 1, 11
475  result( i ) = -one
476  10 CONTINUE
477 *
478  IF( n.EQ.0 )
479  $ RETURN
480 *
481 * More Important constants
482 *
483  ulp = slamch( 'Precision' )
484  smlnum = slamch( 'S' )
485  ulpinv = one / ulp
486 *
487 * Compute eigenvalues and eigenvectors, and test them
488 *
489  IF( lwork.GE.6*n+n*n ) THEN
490  sense = 'B'
491  isensm = 2
492  ELSE
493  sense = 'E'
494  isensm = 1
495  END IF
496  CALL slacpy( 'F', n, n, a, lda, h, lda )
497  CALL sgeevx( balanc, 'V', 'V', sense, n, h, lda, wr, wi, vl, ldvl,
498  $ vr, ldvr, ilo, ihi, scale, abnrm, rconde, rcondv,
499  $ work, lwork, iwork, iinfo )
500  IF( iinfo.NE.0 ) THEN
501  result( 1 ) = ulpinv
502  IF( jtype.NE.22 ) THEN
503  WRITE( nounit, fmt = 9998 )'SGEEVX1', iinfo, n, jtype,
504  $ balanc, iseed
505  ELSE
506  WRITE( nounit, fmt = 9999 )'SGEEVX1', iinfo, n, iseed( 1 )
507  END IF
508  info = abs( iinfo )
509  RETURN
510  END IF
511 *
512 * Do Test (1)
513 *
514  CALL sget22( 'N', 'N', 'N', n, a, lda, vr, ldvr, wr, wi, work,
515  $ res )
516  result( 1 ) = res( 1 )
517 *
518 * Do Test (2)
519 *
520  CALL sget22( 'T', 'N', 'T', n, a, lda, vl, ldvl, wr, wi, work,
521  $ res )
522  result( 2 ) = res( 1 )
523 *
524 * Do Test (3)
525 *
526  DO 30 j = 1, n
527  tnrm = one
528  IF( wi( j ).EQ.zero ) THEN
529  tnrm = snrm2( n, vr( 1, j ), 1 )
530  ELSE IF( wi( j ).GT.zero ) THEN
531  tnrm = slapy2( snrm2( n, vr( 1, j ), 1 ),
532  $ snrm2( n, vr( 1, j+1 ), 1 ) )
533  END IF
534  result( 3 ) = max( result( 3 ),
535  $ min( ulpinv, abs( tnrm-one ) / ulp ) )
536  IF( wi( j ).GT.zero ) THEN
537  vmx = zero
538  vrmx = zero
539  DO 20 jj = 1, n
540  vtst = slapy2( vr( jj, j ), vr( jj, j+1 ) )
541  IF( vtst.GT.vmx )
542  $ vmx = vtst
543  IF( vr( jj, j+1 ).EQ.zero .AND. abs( vr( jj, j ) ).GT.
544  $ vrmx )vrmx = abs( vr( jj, j ) )
545  20 CONTINUE
546  IF( vrmx / vmx.LT.one-two*ulp )
547  $ result( 3 ) = ulpinv
548  END IF
549  30 CONTINUE
550 *
551 * Do Test (4)
552 *
553  DO 50 j = 1, n
554  tnrm = one
555  IF( wi( j ).EQ.zero ) THEN
556  tnrm = snrm2( n, vl( 1, j ), 1 )
557  ELSE IF( wi( j ).GT.zero ) THEN
558  tnrm = slapy2( snrm2( n, vl( 1, j ), 1 ),
559  $ snrm2( n, vl( 1, j+1 ), 1 ) )
560  END IF
561  result( 4 ) = max( result( 4 ),
562  $ min( ulpinv, abs( tnrm-one ) / ulp ) )
563  IF( wi( j ).GT.zero ) THEN
564  vmx = zero
565  vrmx = zero
566  DO 40 jj = 1, n
567  vtst = slapy2( vl( jj, j ), vl( jj, j+1 ) )
568  IF( vtst.GT.vmx )
569  $ vmx = vtst
570  IF( vl( jj, j+1 ).EQ.zero .AND. abs( vl( jj, j ) ).GT.
571  $ vrmx )vrmx = abs( vl( jj, j ) )
572  40 CONTINUE
573  IF( vrmx / vmx.LT.one-two*ulp )
574  $ result( 4 ) = ulpinv
575  END IF
576  50 CONTINUE
577 *
578 * Test for all options of computing condition numbers
579 *
580  DO 200 isens = 1, isensm
581 *
582  sense = sens( isens )
583 *
584 * Compute eigenvalues only, and test them
585 *
586  CALL slacpy( 'F', n, n, a, lda, h, lda )
587  CALL sgeevx( balanc, 'N', 'N', sense, n, h, lda, wr1, wi1, dum,
588  $ 1, dum, 1, ilo1, ihi1, scale1, abnrm1, rcnde1,
589  $ rcndv1, work, lwork, iwork, iinfo )
590  IF( iinfo.NE.0 ) THEN
591  result( 1 ) = ulpinv
592  IF( jtype.NE.22 ) THEN
593  WRITE( nounit, fmt = 9998 )'SGEEVX2', iinfo, n, jtype,
594  $ balanc, iseed
595  ELSE
596  WRITE( nounit, fmt = 9999 )'SGEEVX2', iinfo, n,
597  $ iseed( 1 )
598  END IF
599  info = abs( iinfo )
600  GO TO 190
601  END IF
602 *
603 * Do Test (5)
604 *
605  DO 60 j = 1, n
606  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
607  $ result( 5 ) = ulpinv
608  60 CONTINUE
609 *
610 * Do Test (8)
611 *
612  IF( .NOT.nobal ) THEN
613  DO 70 j = 1, n
614  IF( scale( j ).NE.scale1( j ) )
615  $ result( 8 ) = ulpinv
616  70 CONTINUE
617  IF( ilo.NE.ilo1 )
618  $ result( 8 ) = ulpinv
619  IF( ihi.NE.ihi1 )
620  $ result( 8 ) = ulpinv
621  IF( abnrm.NE.abnrm1 )
622  $ result( 8 ) = ulpinv
623  END IF
624 *
625 * Do Test (9)
626 *
627  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
628  DO 80 j = 1, n
629  IF( rcondv( j ).NE.rcndv1( j ) )
630  $ result( 9 ) = ulpinv
631  80 CONTINUE
632  END IF
633 *
634 * Compute eigenvalues and right eigenvectors, and test them
635 *
636  CALL slacpy( 'F', n, n, a, lda, h, lda )
637  CALL sgeevx( balanc, 'N', 'V', sense, n, h, lda, wr1, wi1, dum,
638  $ 1, lre, ldlre, ilo1, ihi1, scale1, abnrm1, rcnde1,
639  $ rcndv1, work, lwork, iwork, iinfo )
640  IF( iinfo.NE.0 ) THEN
641  result( 1 ) = ulpinv
642  IF( jtype.NE.22 ) THEN
643  WRITE( nounit, fmt = 9998 )'SGEEVX3', iinfo, n, jtype,
644  $ balanc, iseed
645  ELSE
646  WRITE( nounit, fmt = 9999 )'SGEEVX3', iinfo, n,
647  $ iseed( 1 )
648  END IF
649  info = abs( iinfo )
650  GO TO 190
651  END IF
652 *
653 * Do Test (5) again
654 *
655  DO 90 j = 1, n
656  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
657  $ result( 5 ) = ulpinv
658  90 CONTINUE
659 *
660 * Do Test (6)
661 *
662  DO 110 j = 1, n
663  DO 100 jj = 1, n
664  IF( vr( j, jj ).NE.lre( j, jj ) )
665  $ result( 6 ) = ulpinv
666  100 CONTINUE
667  110 CONTINUE
668 *
669 * Do Test (8) again
670 *
671  IF( .NOT.nobal ) THEN
672  DO 120 j = 1, n
673  IF( scale( j ).NE.scale1( j ) )
674  $ result( 8 ) = ulpinv
675  120 CONTINUE
676  IF( ilo.NE.ilo1 )
677  $ result( 8 ) = ulpinv
678  IF( ihi.NE.ihi1 )
679  $ result( 8 ) = ulpinv
680  IF( abnrm.NE.abnrm1 )
681  $ result( 8 ) = ulpinv
682  END IF
683 *
684 * Do Test (9) again
685 *
686  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
687  DO 130 j = 1, n
688  IF( rcondv( j ).NE.rcndv1( j ) )
689  $ result( 9 ) = ulpinv
690  130 CONTINUE
691  END IF
692 *
693 * Compute eigenvalues and left eigenvectors, and test them
694 *
695  CALL slacpy( 'F', n, n, a, lda, h, lda )
696  CALL sgeevx( balanc, 'V', 'N', sense, n, h, lda, wr1, wi1, lre,
697  $ ldlre, dum, 1, ilo1, ihi1, scale1, abnrm1, rcnde1,
698  $ rcndv1, work, lwork, iwork, iinfo )
699  IF( iinfo.NE.0 ) THEN
700  result( 1 ) = ulpinv
701  IF( jtype.NE.22 ) THEN
702  WRITE( nounit, fmt = 9998 )'SGEEVX4', iinfo, n, jtype,
703  $ balanc, iseed
704  ELSE
705  WRITE( nounit, fmt = 9999 )'SGEEVX4', iinfo, n,
706  $ iseed( 1 )
707  END IF
708  info = abs( iinfo )
709  GO TO 190
710  END IF
711 *
712 * Do Test (5) again
713 *
714  DO 140 j = 1, n
715  IF( wr( j ).NE.wr1( j ) .OR. wi( j ).NE.wi1( j ) )
716  $ result( 5 ) = ulpinv
717  140 CONTINUE
718 *
719 * Do Test (7)
720 *
721  DO 160 j = 1, n
722  DO 150 jj = 1, n
723  IF( vl( j, jj ).NE.lre( j, jj ) )
724  $ result( 7 ) = ulpinv
725  150 CONTINUE
726  160 CONTINUE
727 *
728 * Do Test (8) again
729 *
730  IF( .NOT.nobal ) THEN
731  DO 170 j = 1, n
732  IF( scale( j ).NE.scale1( j ) )
733  $ result( 8 ) = ulpinv
734  170 CONTINUE
735  IF( ilo.NE.ilo1 )
736  $ result( 8 ) = ulpinv
737  IF( ihi.NE.ihi1 )
738  $ result( 8 ) = ulpinv
739  IF( abnrm.NE.abnrm1 )
740  $ result( 8 ) = ulpinv
741  END IF
742 *
743 * Do Test (9) again
744 *
745  IF( isens.EQ.2 .AND. n.GT.1 ) THEN
746  DO 180 j = 1, n
747  IF( rcondv( j ).NE.rcndv1( j ) )
748  $ result( 9 ) = ulpinv
749  180 CONTINUE
750  END IF
751 *
752  190 CONTINUE
753 *
754  200 CONTINUE
755 *
756 * If COMP, compare condition numbers to precomputed ones
757 *
758  IF( comp ) THEN
759  CALL slacpy( 'F', n, n, a, lda, h, lda )
760  CALL sgeevx( 'N', 'V', 'V', 'B', n, h, lda, wr, wi, vl, ldvl,
761  $ vr, ldvr, ilo, ihi, scale, abnrm, rconde, rcondv,
762  $ work, lwork, iwork, iinfo )
763  IF( iinfo.NE.0 ) THEN
764  result( 1 ) = ulpinv
765  WRITE( nounit, fmt = 9999 )'SGEEVX5', iinfo, n, iseed( 1 )
766  info = abs( iinfo )
767  GO TO 250
768  END IF
769 *
770 * Sort eigenvalues and condition numbers lexicographically
771 * to compare with inputs
772 *
773  DO 220 i = 1, n - 1
774  kmin = i
775  vrmin = wr( i )
776  vimin = wi( i )
777  DO 210 j = i + 1, n
778  IF( wr( j ).LT.vrmin ) THEN
779  kmin = j
780  vrmin = wr( j )
781  vimin = wi( j )
782  END IF
783  210 CONTINUE
784  wr( kmin ) = wr( i )
785  wi( kmin ) = wi( i )
786  wr( i ) = vrmin
787  wi( i ) = vimin
788  vrmin = rconde( kmin )
789  rconde( kmin ) = rconde( i )
790  rconde( i ) = vrmin
791  vrmin = rcondv( kmin )
792  rcondv( kmin ) = rcondv( i )
793  rcondv( i ) = vrmin
794  220 CONTINUE
795 *
796 * Compare condition numbers for eigenvectors
797 * taking their condition numbers into account
798 *
799  result( 10 ) = zero
800  eps = max( epsin, ulp )
801  v = max( REAL( n )*eps*abnrm, smlnum )
802  IF( abnrm.EQ.zero )
803  $ v = one
804  DO 230 i = 1, n
805  IF( v.GT.rcondv( i )*rconde( i ) ) THEN
806  tol = rcondv( i )
807  ELSE
808  tol = v / rconde( i )
809  END IF
810  IF( v.GT.rcdvin( i )*rcdein( i ) ) THEN
811  tolin = rcdvin( i )
812  ELSE
813  tolin = v / rcdein( i )
814  END IF
815  tol = max( tol, smlnum / eps )
816  tolin = max( tolin, smlnum / eps )
817  IF( eps*( rcdvin( i )-tolin ).GT.rcondv( i )+tol ) THEN
818  vmax = one / eps
819  ELSE IF( rcdvin( i )-tolin.GT.rcondv( i )+tol ) THEN
820  vmax = ( rcdvin( i )-tolin ) / ( rcondv( i )+tol )
821  ELSE IF( rcdvin( i )+tolin.LT.eps*( rcondv( i )-tol ) ) THEN
822  vmax = one / eps
823  ELSE IF( rcdvin( i )+tolin.LT.rcondv( i )-tol ) THEN
824  vmax = ( rcondv( i )-tol ) / ( rcdvin( i )+tolin )
825  ELSE
826  vmax = one
827  END IF
828  result( 10 ) = max( result( 10 ), vmax )
829  230 CONTINUE
830 *
831 * Compare condition numbers for eigenvalues
832 * taking their condition numbers into account
833 *
834  result( 11 ) = zero
835  DO 240 i = 1, n
836  IF( v.GT.rcondv( i ) ) THEN
837  tol = one
838  ELSE
839  tol = v / rcondv( i )
840  END IF
841  IF( v.GT.rcdvin( i ) ) THEN
842  tolin = one
843  ELSE
844  tolin = v / rcdvin( i )
845  END IF
846  tol = max( tol, smlnum / eps )
847  tolin = max( tolin, smlnum / eps )
848  IF( eps*( rcdein( i )-tolin ).GT.rconde( i )+tol ) THEN
849  vmax = one / eps
850  ELSE IF( rcdein( i )-tolin.GT.rconde( i )+tol ) THEN
851  vmax = ( rcdein( i )-tolin ) / ( rconde( i )+tol )
852  ELSE IF( rcdein( i )+tolin.LT.eps*( rconde( i )-tol ) ) THEN
853  vmax = one / eps
854  ELSE IF( rcdein( i )+tolin.LT.rconde( i )-tol ) THEN
855  vmax = ( rconde( i )-tol ) / ( rcdein( i )+tolin )
856  ELSE
857  vmax = one
858  END IF
859  result( 11 ) = max( result( 11 ), vmax )
860  240 CONTINUE
861  250 CONTINUE
862 *
863  END IF
864 *
865  9999 FORMAT( ' SGET23: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
866  $ i6, ', INPUT EXAMPLE NUMBER = ', i4 )
867  9998 FORMAT( ' SGET23: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
868  $ i6, ', JTYPE=', i6, ', BALANC = ', a, ', ISEED=(',
869  $ 3( i5, ',' ), i5, ')' )
870 *
871  RETURN
872 *
873 * End of SGET23
874 *
real function snrm2(N, X, INCX)
SNRM2
Definition: snrm2.f:76
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine sget22(TRANSA, TRANSE, TRANSW, N, A, LDA, E, LDE, WR, WI, WORK, RESULT)
SGET22
Definition: sget22.f:169
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine sgeevx(BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE, RCONDV, WORK, LWORK, IWORK, INFO)
SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices ...
Definition: sgeevx.f:307
real function slapy2(X, Y)
SLAPY2 returns sqrt(x2+y2).
Definition: slapy2.f:65
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
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