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version 1.7, 2010/12/21 13:53:45 version 1.16, 2017/06/17 11:06:45
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   *> \brief <b> ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZGGEV + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggev.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggev.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggev.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
   *                         VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBVL, JOBVR
   *       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
   *      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ),
   *      $                   WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGGEV 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.
   *>
   *> 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 generalized eigenvector v(j) corresponding to the
   *> generalized eigenvalue lambda(j) of (A,B) satisfies
   *>
   *>              A * v(j) = lambda(j) * B * v(j).
   *>
   *> The left generalized eigenvector u(j) corresponding to the
   *> generalized eigenvalues 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).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBVL
   *> \verbatim
   *>          JOBVL is CHARACTER*1
   *>          = 'N':  do not compute the left generalized eigenvectors;
   *>          = 'V':  compute the left generalized eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] JOBVR
   *> \verbatim
   *>          JOBVR is CHARACTER*1
   *>          = 'N':  do not compute the right generalized eigenvectors;
   *>          = 'V':  compute the right generalized eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrices A, B, VL, and VR.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the matrix A in the pair (A,B).
   *>          On exit, A has been overwritten.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is COMPLEX*16 array, dimension (LDB, N)
   *>          On entry, the matrix B in the pair (A,B).
   *>          On exit, B has been overwritten.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of B.  LDB >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] ALPHA
   *> \verbatim
   *>          ALPHA is COMPLEX*16 array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] BETA
   *> \verbatim
   *>          BETA is COMPLEX*16 array, dimension (N)
   *>          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
   *>          generalized eigenvalues.
   *>
   *>          Note: the quotients 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).
   *> \endverbatim
   *>
   *> \param[out] VL
   *> \verbatim
   *>          VL is COMPLEX*16 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 is scaled so the largest component has
   *>          abs(real part) + abs(imag. part) = 1.
   *>          Not referenced if JOBVL = 'N'.
   *> \endverbatim
   *>
   *> \param[in] LDVL
   *> \verbatim
   *>          LDVL is INTEGER
   *>          The leading dimension of the matrix VL. LDVL >= 1, and
   *>          if JOBVL = 'V', LDVL >= N.
   *> \endverbatim
   *>
   *> \param[out] VR
   *> \verbatim
   *>          VR is COMPLEX*16 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 is scaled so the largest component has
   *>          abs(real part) + abs(imag. part) = 1.
   *>          Not referenced if JOBVR = 'N'.
   *> \endverbatim
   *>
   *> \param[in] LDVR
   *> \verbatim
   *>          LDVR is INTEGER
   *>          The leading dimension of the matrix VR. LDVR >= 1, and
   *>          if JOBVR = 'V', LDVR >= N.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
   *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is INTEGER
   *>          The dimension of the array WORK.  LWORK >= max(1,2*N).
   *>          For good performance, LWORK must generally be larger.
   *>
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (8*N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          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 then QZ iteration failed in DHGEQZ,
   *>                =N+2: error return from DTGEVC.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \date April 2012
   *
   *> \ingroup complex16GEeigen
   *
   *  =====================================================================
       SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,        SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
      $                  VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )       $                  VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver routine (version 3.7.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     April 2012
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR        CHARACTER          JOBVL, JOBVR
Line 17 Line 233
      $                   WORK( * )       $                   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGGEV 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.  
 *  
 *  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 generalized eigenvector v(j) corresponding to the  
 *  generalized eigenvalue lambda(j) of (A,B) satisfies  
 *  
 *               A * v(j) = lambda(j) * B * v(j).  
 *  
 *  The left generalized eigenvector u(j) corresponding to the  
 *  generalized eigenvalues 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).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBVL   (input) CHARACTER*1  
 *          = 'N':  do not compute the left generalized eigenvectors;  
 *          = 'V':  compute the left generalized eigenvectors.  
 *  
 *  JOBVR   (input) CHARACTER*1  
 *          = 'N':  do not compute the right generalized eigenvectors;  
 *          = 'V':  compute the right generalized eigenvectors.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A, B, VL, and VR.  N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the matrix A in the pair (A,B).  
 *          On exit, A has been overwritten.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of A.  LDA >= max(1,N).  
 *  
 *  B       (input/output) COMPLEX*16 array, dimension (LDB, N)  
 *          On entry, the matrix B in the pair (A,B).  
 *          On exit, B has been overwritten.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of B.  LDB >= max(1,N).  
 *  
 *  ALPHA   (output) COMPLEX*16 array, dimension (N)  
 *  BETA    (output) COMPLEX*16 array, dimension (N)  
 *          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the  
 *          generalized eigenvalues.  
 *  
 *          Note: the quotients 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).  
 *  
 *  VL      (output) COMPLEX*16 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 is scaled so the largest component has  
 *          abs(real part) + abs(imag. part) = 1.  
 *          Not referenced if JOBVL = 'N'.  
 *  
 *  LDVL    (input) INTEGER  
 *          The leading dimension of the matrix VL. LDVL >= 1, and  
 *          if JOBVL = 'V', LDVL >= N.  
 *  
 *  VR      (output) COMPLEX*16 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 is scaled so the largest component has  
 *          abs(real part) + abs(imag. part) = 1.  
 *          Not referenced if JOBVR = 'N'.  
 *  
 *  LDVR    (input) INTEGER  
 *          The leading dimension of the matrix VR. LDVR >= 1, and  
 *          if JOBVR = 'V', LDVR >= N.  
 *  
 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  LWORK >= max(1,2*N).  
 *          For good performance, LWORK must generally be larger.  
 *  
 *          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.  
 *  
 *  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (8*N)  
 *  
 *  INFO    (output) 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 then QZ iteration failed in DHGEQZ,  
 *                =N+2: error return from DTGEVC.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 439 Line 542
 *  *
 *     Undo scaling if necessary  *     Undo scaling if necessary
 *  *
      70 CONTINUE
   *
       IF( ILASCL )        IF( ILASCL )
      $   CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )       $   CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR )
 *  *
       IF( ILBSCL )        IF( ILBSCL )
      $   CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )       $   CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
 *  *
    70 CONTINUE  
       WORK( 1 ) = LWKOPT        WORK( 1 ) = LWKOPT
 *  
       RETURN        RETURN
 *  *
 *     End of ZGGEV  *     End of ZGGEV
Removed from v.1.7  
changed lines
  Added in v.1.16

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