LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cggevx()

subroutine cggevx ( character  BALANC,
character  JOBVL,
character  JOBVR,
character  SENSE,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( * )  ALPHA,
complex, dimension( * )  BETA,
complex, dimension( ldvl, * )  VL,
integer  LDVL,
complex, dimension( ldvr, * )  VR,
integer  LDVR,
integer  ILO,
integer  IHI,
real, dimension( * )  LSCALE,
real, dimension( * )  RSCALE,
real  ABNRM,
real  BBNRM,
real, dimension( * )  RCONDE,
real, dimension( * )  RCONDV,
complex, dimension( * )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
logical, dimension( * )  BWORK,
integer  INFO 
)

CGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Download CGGEVX + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
 (A,B) the generalized eigenvalues, and optionally, the left and/or
 right generalized eigenvectors.

 Optionally, it also computes a balancing transformation to improve
 the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
 LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
 the eigenvalues (RCONDE), and reciprocal condition numbers for the
 right eigenvectors (RCONDV).

 A generalized eigenvalue for a pair of matrices (A,B) is a scalar
 lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
 singular. It is usually represented as the pair (alpha,beta), as
 there is a reasonable interpretation for beta=0, and even for both
 being zero.

 The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
 of (A,B) satisfies
                  A * v(j) = lambda(j) * B * v(j) .
 The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
 of (A,B) satisfies
                  u(j)**H * A  = lambda(j) * u(j)**H * B.
 where u(j)**H is the conjugate-transpose of u(j).
Parameters
[in]BALANC
          BALANC is CHARACTER*1
          Specifies the balance option to be performed:
          = 'N':  do not diagonally scale or permute;
          = 'P':  permute only;
          = 'S':  scale only;
          = 'B':  both permute and scale.
          Computed reciprocal condition numbers will be for the
          matrices after permuting and/or balancing. Permuting does
          not change condition numbers (in exact arithmetic), but
          balancing does.
[in]JOBVL
          JOBVL is CHARACTER*1
          = 'N':  do not compute the left generalized eigenvectors;
          = 'V':  compute the left generalized eigenvectors.
[in]JOBVR
          JOBVR is CHARACTER*1
          = 'N':  do not compute the right generalized eigenvectors;
          = 'V':  compute the right generalized eigenvectors.
[in]SENSE
          SENSE is CHARACTER*1
          Determines which reciprocal condition numbers are computed.
          = 'N': none are computed;
          = 'E': computed for eigenvalues only;
          = 'V': computed for eigenvectors only;
          = 'B': computed for eigenvalues and eigenvectors.
[in]N
          N is INTEGER
          The order of the matrices A, B, VL, and VR.  N >= 0.
[in,out]A
          A is COMPLEX array, dimension (LDA, N)
          On entry, the matrix A in the pair (A,B).
          On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'
          or both, then A contains the first part of the complex Schur
          form of the "balanced" versions of the input A and B.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  LDA >= max(1,N).
[in,out]B
          B is COMPLEX array, dimension (LDB, N)
          On entry, the matrix B in the pair (A,B).
          On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'
          or both, then B contains the second part of the complex
          Schur form of the "balanced" versions of the input A and B.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  LDB >= max(1,N).
[out]ALPHA
          ALPHA is COMPLEX array, dimension (N)
[out]BETA
          BETA is COMPLEX array, dimension (N)
          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized
          eigenvalues.

          Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or
          underflow, and BETA(j) may even be zero.  Thus, the user
          should avoid naively computing the ratio ALPHA/BETA.
          However, ALPHA will be always less than and usually
          comparable with norm(A) in magnitude, and BETA always less
          than and usually comparable with norm(B).
[out]VL
          VL is COMPLEX array, dimension (LDVL,N)
          If JOBVL = 'V', the left generalized eigenvectors u(j) are
          stored one after another in the columns of VL, in the same
          order as their eigenvalues.
          Each eigenvector will be scaled so the largest component
          will have abs(real part) + abs(imag. part) = 1.
          Not referenced if JOBVL = 'N'.
[in]LDVL
          LDVL is INTEGER
          The leading dimension of the matrix VL. LDVL >= 1, and
          if JOBVL = 'V', LDVL >= N.
[out]VR
          VR is COMPLEX array, dimension (LDVR,N)
          If JOBVR = 'V', the right generalized eigenvectors v(j) are
          stored one after another in the columns of VR, in the same
          order as their eigenvalues.
          Each eigenvector will be scaled so the largest component
          will have abs(real part) + abs(imag. part) = 1.
          Not referenced if JOBVR = 'N'.
[in]LDVR
          LDVR is INTEGER
          The leading dimension of the matrix VR. LDVR >= 1, and
          if JOBVR = 'V', LDVR >= N.
[out]ILO
          ILO is INTEGER
[out]IHI
          IHI is INTEGER
          ILO and IHI are integer values such that on exit
          A(i,j) = 0 and B(i,j) = 0 if i > j and
          j = 1,...,ILO-1 or i = IHI+1,...,N.
          If BALANC = 'N' or 'S', ILO = 1 and IHI = N.
[out]LSCALE
          LSCALE is REAL array, dimension (N)
          Details of the permutations and scaling factors applied
          to the left side of A and B.  If PL(j) is the index of the
          row interchanged with row j, and DL(j) is the scaling
          factor applied to row j, then
            LSCALE(j) = PL(j)  for j = 1,...,ILO-1
                      = DL(j)  for j = ILO,...,IHI
                      = PL(j)  for j = IHI+1,...,N.
          The order in which the interchanges are made is N to IHI+1,
          then 1 to ILO-1.
[out]RSCALE
          RSCALE is REAL array, dimension (N)
          Details of the permutations and scaling factors applied
          to the right side of A and B.  If PR(j) is the index of the
          column interchanged with column j, and DR(j) is the scaling
          factor applied to column j, then
            RSCALE(j) = PR(j)  for j = 1,...,ILO-1
                      = DR(j)  for j = ILO,...,IHI
                      = PR(j)  for j = IHI+1,...,N
          The order in which the interchanges are made is N to IHI+1,
          then 1 to ILO-1.
[out]ABNRM
          ABNRM is REAL
          The one-norm of the balanced matrix A.
[out]BBNRM
          BBNRM is REAL
          The one-norm of the balanced matrix B.
[out]RCONDE
          RCONDE is REAL array, dimension (N)
          If SENSE = 'E' or 'B', the reciprocal condition numbers of
          the eigenvalues, stored in consecutive elements of the array.
          If SENSE = 'N' or 'V', RCONDE is not referenced.
[out]RCONDV
          RCONDV is REAL array, dimension (N)
          If SENSE = 'V' or 'B', the estimated reciprocal condition
          numbers of the eigenvectors, stored in consecutive elements
          of the array. If the eigenvalues cannot be reordered to
          compute RCONDV(j), RCONDV(j) is set to 0; this can only occur
          when the true value would be very small anyway.
          If SENSE = 'N' or 'E', RCONDV is not referenced.
[out]WORK
          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= max(1,2*N).
          If SENSE = 'E', LWORK >= max(1,4*N).
          If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N).

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]RWORK
          RWORK is REAL array, dimension (lrwork)
          lrwork must be at least max(1,6*N) if BALANC = 'S' or 'B',
          and at least max(1,2*N) otherwise.
          Real workspace.
[out]IWORK
          IWORK is INTEGER array, dimension (N+2)
          If SENSE = 'E', IWORK is not referenced.
[out]BWORK
          BWORK is LOGICAL array, dimension (N)
          If SENSE = 'N', BWORK is not referenced.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          = 1,...,N:
                The QZ iteration failed.  No eigenvectors have been
                calculated, but ALPHA(j) and BETA(j) should be correct
                for j=INFO+1,...,N.
          > N:  =N+1: other than QZ iteration failed in CHGEQZ.
                =N+2: error return from CTGEVC.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  Balancing a matrix pair (A,B) includes, first, permuting rows and
  columns to isolate eigenvalues, second, applying diagonal similarity
  transformation to the rows and columns to make the rows and columns
  as close in norm as possible. The computed reciprocal condition
  numbers correspond to the balanced matrix. Permuting rows and columns
  will not change the condition numbers (in exact arithmetic) but
  diagonal scaling will.  For further explanation of balancing, see
  section 4.11.1.2 of LAPACK Users' Guide.

  An approximate error bound on the chordal distance between the i-th
  computed generalized eigenvalue w and the corresponding exact
  eigenvalue lambda is

       chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)

  An approximate error bound for the angle between the i-th computed
  eigenvector VL(i) or VR(i) is given by

       EPS * norm(ABNRM, BBNRM) / DIF(i).

  For further explanation of the reciprocal condition numbers RCONDE
  and RCONDV, see section 4.11 of LAPACK User's Guide.

Definition at line 370 of file cggevx.f.

374*
375* -- LAPACK driver routine --
376* -- LAPACK is a software package provided by Univ. of Tennessee, --
377* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
378*
379* .. Scalar Arguments ..
380 CHARACTER BALANC, JOBVL, JOBVR, SENSE
381 INTEGER IHI, ILO, INFO, LDA, LDB, LDVL, LDVR, LWORK, N
382 REAL ABNRM, BBNRM
383* ..
384* .. Array Arguments ..
385 LOGICAL BWORK( * )
386 INTEGER IWORK( * )
387 REAL LSCALE( * ), RCONDE( * ), RCONDV( * ),
388 $ RSCALE( * ), RWORK( * )
389 COMPLEX A( LDA, * ), ALPHA( * ), B( LDB, * ),
390 $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
391 $ WORK( * )
392* ..
393*
394* =====================================================================
395*
396* .. Parameters ..
397 REAL ZERO, ONE
398 parameter( zero = 0.0e+0, one = 1.0e+0 )
399 COMPLEX CZERO, CONE
400 parameter( czero = ( 0.0e+0, 0.0e+0 ),
401 $ cone = ( 1.0e+0, 0.0e+0 ) )
402* ..
403* .. Local Scalars ..
404 LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, NOSCL,
405 $ WANTSB, WANTSE, WANTSN, WANTSV
406 CHARACTER CHTEMP
407 INTEGER I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
408 $ ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK, MINWRK
409 REAL ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
410 $ SMLNUM, TEMP
411 COMPLEX X
412* ..
413* .. Local Arrays ..
414 LOGICAL LDUMMA( 1 )
415* ..
416* .. External Subroutines ..
417 EXTERNAL cgeqrf, cggbak, cggbal, cgghrd, chgeqz, clacpy,
420* ..
421* .. External Functions ..
422 LOGICAL LSAME
423 INTEGER ILAENV
424 REAL CLANGE, SLAMCH
425 EXTERNAL lsame, ilaenv, clange, slamch
426* ..
427* .. Intrinsic Functions ..
428 INTRINSIC abs, aimag, max, real, sqrt
429* ..
430* .. Statement Functions ..
431 REAL ABS1
432* ..
433* .. Statement Function definitions ..
434 abs1( x ) = abs( real( x ) ) + abs( aimag( x ) )
435* ..
436* .. Executable Statements ..
437*
438* Decode the input arguments
439*
440 IF( lsame( jobvl, 'N' ) ) THEN
441 ijobvl = 1
442 ilvl = .false.
443 ELSE IF( lsame( jobvl, 'V' ) ) THEN
444 ijobvl = 2
445 ilvl = .true.
446 ELSE
447 ijobvl = -1
448 ilvl = .false.
449 END IF
450*
451 IF( lsame( jobvr, 'N' ) ) THEN
452 ijobvr = 1
453 ilvr = .false.
454 ELSE IF( lsame( jobvr, 'V' ) ) THEN
455 ijobvr = 2
456 ilvr = .true.
457 ELSE
458 ijobvr = -1
459 ilvr = .false.
460 END IF
461 ilv = ilvl .OR. ilvr
462*
463 noscl = lsame( balanc, 'N' ) .OR. lsame( balanc, 'P' )
464 wantsn = lsame( sense, 'N' )
465 wantse = lsame( sense, 'E' )
466 wantsv = lsame( sense, 'V' )
467 wantsb = lsame( sense, 'B' )
468*
469* Test the input arguments
470*
471 info = 0
472 lquery = ( lwork.EQ.-1 )
473 IF( .NOT.( noscl .OR. lsame( balanc,'S' ) .OR.
474 $ lsame( balanc, 'B' ) ) ) THEN
475 info = -1
476 ELSE IF( ijobvl.LE.0 ) THEN
477 info = -2
478 ELSE IF( ijobvr.LE.0 ) THEN
479 info = -3
480 ELSE IF( .NOT.( wantsn .OR. wantse .OR. wantsb .OR. wantsv ) )
481 $ THEN
482 info = -4
483 ELSE IF( n.LT.0 ) THEN
484 info = -5
485 ELSE IF( lda.LT.max( 1, n ) ) THEN
486 info = -7
487 ELSE IF( ldb.LT.max( 1, n ) ) THEN
488 info = -9
489 ELSE IF( ldvl.LT.1 .OR. ( ilvl .AND. ldvl.LT.n ) ) THEN
490 info = -13
491 ELSE IF( ldvr.LT.1 .OR. ( ilvr .AND. ldvr.LT.n ) ) THEN
492 info = -15
493 END IF
494*
495* Compute workspace
496* (Note: Comments in the code beginning "Workspace:" describe the
497* minimal amount of workspace needed at that point in the code,
498* as well as the preferred amount for good performance.
499* NB refers to the optimal block size for the immediately
500* following subroutine, as returned by ILAENV. The workspace is
501* computed assuming ILO = 1 and IHI = N, the worst case.)
502*
503 IF( info.EQ.0 ) THEN
504 IF( n.EQ.0 ) THEN
505 minwrk = 1
506 maxwrk = 1
507 ELSE
508 minwrk = 2*n
509 IF( wantse ) THEN
510 minwrk = 4*n
511 ELSE IF( wantsv .OR. wantsb ) THEN
512 minwrk = 2*n*( n + 1)
513 END IF
514 maxwrk = minwrk
515 maxwrk = max( maxwrk,
516 $ n + n*ilaenv( 1, 'CGEQRF', ' ', n, 1, n, 0 ) )
517 maxwrk = max( maxwrk,
518 $ n + n*ilaenv( 1, 'CUNMQR', ' ', n, 1, n, 0 ) )
519 IF( ilvl ) THEN
520 maxwrk = max( maxwrk, n +
521 $ n*ilaenv( 1, 'CUNGQR', ' ', n, 1, n, 0 ) )
522 END IF
523 END IF
524 work( 1 ) = maxwrk
525*
526 IF( lwork.LT.minwrk .AND. .NOT.lquery ) THEN
527 info = -25
528 END IF
529 END IF
530*
531 IF( info.NE.0 ) THEN
532 CALL xerbla( 'CGGEVX', -info )
533 RETURN
534 ELSE IF( lquery ) THEN
535 RETURN
536 END IF
537*
538* Quick return if possible
539*
540 IF( n.EQ.0 )
541 $ RETURN
542*
543* Get machine constants
544*
545 eps = slamch( 'P' )
546 smlnum = slamch( 'S' )
547 bignum = one / smlnum
548 CALL slabad( smlnum, bignum )
549 smlnum = sqrt( smlnum ) / eps
550 bignum = one / smlnum
551*
552* Scale A if max element outside range [SMLNUM,BIGNUM]
553*
554 anrm = clange( 'M', n, n, a, lda, rwork )
555 ilascl = .false.
556 IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
557 anrmto = smlnum
558 ilascl = .true.
559 ELSE IF( anrm.GT.bignum ) THEN
560 anrmto = bignum
561 ilascl = .true.
562 END IF
563 IF( ilascl )
564 $ CALL clascl( 'G', 0, 0, anrm, anrmto, n, n, a, lda, ierr )
565*
566* Scale B if max element outside range [SMLNUM,BIGNUM]
567*
568 bnrm = clange( 'M', n, n, b, ldb, rwork )
569 ilbscl = .false.
570 IF( bnrm.GT.zero .AND. bnrm.LT.smlnum ) THEN
571 bnrmto = smlnum
572 ilbscl = .true.
573 ELSE IF( bnrm.GT.bignum ) THEN
574 bnrmto = bignum
575 ilbscl = .true.
576 END IF
577 IF( ilbscl )
578 $ CALL clascl( 'G', 0, 0, bnrm, bnrmto, n, n, b, ldb, ierr )
579*
580* Permute and/or balance the matrix pair (A,B)
581* (Real Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise)
582*
583 CALL cggbal( balanc, n, a, lda, b, ldb, ilo, ihi, lscale, rscale,
584 $ rwork, ierr )
585*
586* Compute ABNRM and BBNRM
587*
588 abnrm = clange( '1', n, n, a, lda, rwork( 1 ) )
589 IF( ilascl ) THEN
590 rwork( 1 ) = abnrm
591 CALL slascl( 'G', 0, 0, anrmto, anrm, 1, 1, rwork( 1 ), 1,
592 $ ierr )
593 abnrm = rwork( 1 )
594 END IF
595*
596 bbnrm = clange( '1', n, n, b, ldb, rwork( 1 ) )
597 IF( ilbscl ) THEN
598 rwork( 1 ) = bbnrm
599 CALL slascl( 'G', 0, 0, bnrmto, bnrm, 1, 1, rwork( 1 ), 1,
600 $ ierr )
601 bbnrm = rwork( 1 )
602 END IF
603*
604* Reduce B to triangular form (QR decomposition of B)
605* (Complex Workspace: need N, prefer N*NB )
606*
607 irows = ihi + 1 - ilo
608 IF( ilv .OR. .NOT.wantsn ) THEN
609 icols = n + 1 - ilo
610 ELSE
611 icols = irows
612 END IF
613 itau = 1
614 iwrk = itau + irows
615 CALL cgeqrf( irows, icols, b( ilo, ilo ), ldb, work( itau ),
616 $ work( iwrk ), lwork+1-iwrk, ierr )
617*
618* Apply the unitary transformation to A
619* (Complex Workspace: need N, prefer N*NB)
620*
621 CALL cunmqr( 'L', 'C', irows, icols, irows, b( ilo, ilo ), ldb,
622 $ work( itau ), a( ilo, ilo ), lda, work( iwrk ),
623 $ lwork+1-iwrk, ierr )
624*
625* Initialize VL and/or VR
626* (Workspace: need N, prefer N*NB)
627*
628 IF( ilvl ) THEN
629 CALL claset( 'Full', n, n, czero, cone, vl, ldvl )
630 IF( irows.GT.1 ) THEN
631 CALL clacpy( 'L', irows-1, irows-1, b( ilo+1, ilo ), ldb,
632 $ vl( ilo+1, ilo ), ldvl )
633 END IF
634 CALL cungqr( irows, irows, irows, vl( ilo, ilo ), ldvl,
635 $ work( itau ), work( iwrk ), lwork+1-iwrk, ierr )
636 END IF
637*
638 IF( ilvr )
639 $ CALL claset( 'Full', n, n, czero, cone, vr, ldvr )
640*
641* Reduce to generalized Hessenberg form
642* (Workspace: none needed)
643*
644 IF( ilv .OR. .NOT.wantsn ) THEN
645*
646* Eigenvectors requested -- work on whole matrix.
647*
648 CALL cgghrd( jobvl, jobvr, n, ilo, ihi, a, lda, b, ldb, vl,
649 $ ldvl, vr, ldvr, ierr )
650 ELSE
651 CALL cgghrd( 'N', 'N', irows, 1, irows, a( ilo, ilo ), lda,
652 $ b( ilo, ilo ), ldb, vl, ldvl, vr, ldvr, ierr )
653 END IF
654*
655* Perform QZ algorithm (Compute eigenvalues, and optionally, the
656* Schur forms and Schur vectors)
657* (Complex Workspace: need N)
658* (Real Workspace: need N)
659*
660 iwrk = itau
661 IF( ilv .OR. .NOT.wantsn ) THEN
662 chtemp = 'S'
663 ELSE
664 chtemp = 'E'
665 END IF
666*
667 CALL chgeqz( chtemp, jobvl, jobvr, n, ilo, ihi, a, lda, b, ldb,
668 $ alpha, beta, vl, ldvl, vr, ldvr, work( iwrk ),
669 $ lwork+1-iwrk, rwork, ierr )
670 IF( ierr.NE.0 ) THEN
671 IF( ierr.GT.0 .AND. ierr.LE.n ) THEN
672 info = ierr
673 ELSE IF( ierr.GT.n .AND. ierr.LE.2*n ) THEN
674 info = ierr - n
675 ELSE
676 info = n + 1
677 END IF
678 GO TO 90
679 END IF
680*
681* Compute Eigenvectors and estimate condition numbers if desired
682* CTGEVC: (Complex Workspace: need 2*N )
683* (Real Workspace: need 2*N )
684* CTGSNA: (Complex Workspace: need 2*N*N if SENSE='V' or 'B')
685* (Integer Workspace: need N+2 )
686*
687 IF( ilv .OR. .NOT.wantsn ) THEN
688 IF( ilv ) THEN
689 IF( ilvl ) THEN
690 IF( ilvr ) THEN
691 chtemp = 'B'
692 ELSE
693 chtemp = 'L'
694 END IF
695 ELSE
696 chtemp = 'R'
697 END IF
698*
699 CALL ctgevc( chtemp, 'B', ldumma, n, a, lda, b, ldb, vl,
700 $ ldvl, vr, ldvr, n, in, work( iwrk ), rwork,
701 $ ierr )
702 IF( ierr.NE.0 ) THEN
703 info = n + 2
704 GO TO 90
705 END IF
706 END IF
707*
708 IF( .NOT.wantsn ) THEN
709*
710* compute eigenvectors (CTGEVC) and estimate condition
711* numbers (CTGSNA). Note that the definition of the condition
712* number is not invariant under transformation (u,v) to
713* (Q*u, Z*v), where (u,v) are eigenvectors of the generalized
714* Schur form (S,T), Q and Z are orthogonal matrices. In order
715* to avoid using extra 2*N*N workspace, we have to
716* re-calculate eigenvectors and estimate the condition numbers
717* one at a time.
718*
719 DO 20 i = 1, n
720*
721 DO 10 j = 1, n
722 bwork( j ) = .false.
723 10 CONTINUE
724 bwork( i ) = .true.
725*
726 iwrk = n + 1
727 iwrk1 = iwrk + n
728*
729 IF( wantse .OR. wantsb ) THEN
730 CALL ctgevc( 'B', 'S', bwork, n, a, lda, b, ldb,
731 $ work( 1 ), n, work( iwrk ), n, 1, m,
732 $ work( iwrk1 ), rwork, ierr )
733 IF( ierr.NE.0 ) THEN
734 info = n + 2
735 GO TO 90
736 END IF
737 END IF
738*
739 CALL ctgsna( sense, 'S', bwork, n, a, lda, b, ldb,
740 $ work( 1 ), n, work( iwrk ), n, rconde( i ),
741 $ rcondv( i ), 1, m, work( iwrk1 ),
742 $ lwork-iwrk1+1, iwork, ierr )
743*
744 20 CONTINUE
745 END IF
746 END IF
747*
748* Undo balancing on VL and VR and normalization
749* (Workspace: none needed)
750*
751 IF( ilvl ) THEN
752 CALL cggbak( balanc, 'L', n, ilo, ihi, lscale, rscale, n, vl,
753 $ ldvl, ierr )
754*
755 DO 50 jc = 1, n
756 temp = zero
757 DO 30 jr = 1, n
758 temp = max( temp, abs1( vl( jr, jc ) ) )
759 30 CONTINUE
760 IF( temp.LT.smlnum )
761 $ GO TO 50
762 temp = one / temp
763 DO 40 jr = 1, n
764 vl( jr, jc ) = vl( jr, jc )*temp
765 40 CONTINUE
766 50 CONTINUE
767 END IF
768*
769 IF( ilvr ) THEN
770 CALL cggbak( balanc, 'R', n, ilo, ihi, lscale, rscale, n, vr,
771 $ ldvr, ierr )
772 DO 80 jc = 1, n
773 temp = zero
774 DO 60 jr = 1, n
775 temp = max( temp, abs1( vr( jr, jc ) ) )
776 60 CONTINUE
777 IF( temp.LT.smlnum )
778 $ GO TO 80
779 temp = one / temp
780 DO 70 jr = 1, n
781 vr( jr, jc ) = vr( jr, jc )*temp
782 70 CONTINUE
783 80 CONTINUE
784 END IF
785*
786* Undo scaling if necessary
787*
788 90 CONTINUE
789*
790 IF( ilascl )
791 $ CALL clascl( 'G', 0, 0, anrmto, anrm, n, 1, alpha, n, ierr )
792*
793 IF( ilbscl )
794 $ CALL clascl( 'G', 0, 0, bnrmto, bnrm, n, 1, beta, n, ierr )
795*
796 work( 1 ) = maxwrk
797 RETURN
798*
799* End of CGGEVX
800*
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine slascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: slascl.f:143
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cggbal(JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, WORK, INFO)
CGGBAL
Definition: cggbal.f:177
subroutine cggbak(JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, LDV, INFO)
CGGBAK
Definition: cggbak.f:148
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:115
subroutine chgeqz(JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO)
CHGEQZ
Definition: chgeqz.f:284
subroutine cgeqrf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRF
Definition: cgeqrf.f:146
subroutine ctgevc(SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTGEVC
Definition: ctgevc.f:219
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 clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:143
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
subroutine ctgsna(JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, IWORK, INFO)
CTGSNA
Definition: ctgsna.f:311
subroutine cunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMQR
Definition: cunmqr.f:168
subroutine cgghrd(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
CGGHRD
Definition: cgghrd.f:204
subroutine cungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CUNGQR
Definition: cungqr.f:128
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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