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version 1.7, 2010/12/21 13:53:43 version 1.8, 2011/11/21 20:43:08
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   *> \brief <b> ZGEEVX 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 ZGEGS + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgegs.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgegs.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgegs.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
   *                         VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
   *                         INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOBVSL, JOBVSR
   *       INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
   *      $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
   *      $                   WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> This routine is deprecated and has been replaced by routine ZGGES.
   *>
   *> ZGEGS computes the eigenvalues, Schur form, and, optionally, the
   *> left and or/right Schur vectors of a complex matrix pair (A,B).
   *> Given two square matrices A and B, the generalized Schur
   *> factorization has the form
   *> 
   *>    A = Q*S*Z**H,  B = Q*T*Z**H
   *> 
   *> where Q and Z are unitary matrices and S and T are upper triangular.
   *> The columns of Q are the left Schur vectors
   *> and the columns of Z are the right Schur vectors.
   *> 
   *> If only the eigenvalues of (A,B) are needed, the driver routine
   *> ZGEGV should be used instead.  See ZGEGV for a description of the
   *> eigenvalues of the generalized nonsymmetric eigenvalue problem
   *> (GNEP).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOBVSL
   *> \verbatim
   *>          JOBVSL is CHARACTER*1
   *>          = 'N':  do not compute the left Schur vectors;
   *>          = 'V':  compute the left Schur vectors (returned in VSL).
   *> \endverbatim
   *>
   *> \param[in] JOBVSR
   *> \verbatim
   *>          JOBVSR is CHARACTER*1
   *>          = 'N':  do not compute the right Schur vectors;
   *>          = 'V':  compute the right Schur vectors (returned in VSR).
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrices A, B, VSL, and VSR.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA, N)
   *>          On entry, the matrix A.
   *>          On exit, the upper triangular matrix S from the generalized
   *>          Schur factorization.
   *> \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.
   *>          On exit, the upper triangular matrix T from the generalized
   *>          Schur factorization.
   *> \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)
   *>          The complex scalars alpha that define the eigenvalues of
   *>          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
   *>          form of A.
   *> \endverbatim
   *>
   *> \param[out] BETA
   *> \verbatim
   *>          BETA is COMPLEX*16 array, dimension (N)
   *>          The non-negative real scalars beta that define the
   *>          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
   *>          of the triangular factor T.
   *>
   *>          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
   *>          represent the j-th eigenvalue of the matrix pair (A,B), in
   *>          one of the forms lambda = alpha/beta or mu = beta/alpha.
   *>          Since either lambda or mu may overflow, they should not,
   *>          in general, be computed.
   *> \endverbatim
   *>
   *> \param[out] VSL
   *> \verbatim
   *>          VSL is COMPLEX*16 array, dimension (LDVSL,N)
   *>          If JOBVSL = 'V', the matrix of left Schur vectors Q.
   *>          Not referenced if JOBVSL = 'N'.
   *> \endverbatim
   *>
   *> \param[in] LDVSL
   *> \verbatim
   *>          LDVSL is INTEGER
   *>          The leading dimension of the matrix VSL. LDVSL >= 1, and
   *>          if JOBVSL = 'V', LDVSL >= N.
   *> \endverbatim
   *>
   *> \param[out] VSR
   *> \verbatim
   *>          VSR is COMPLEX*16 array, dimension (LDVSR,N)
   *>          If JOBVSR = 'V', the matrix of right Schur vectors Z.
   *>          Not referenced if JOBVSR = 'N'.
   *> \endverbatim
   *>
   *> \param[in] LDVSR
   *> \verbatim
   *>          LDVSR is INTEGER
   *>          The leading dimension of the matrix VSR. LDVSR >= 1, and
   *>          if JOBVSR = 'V', LDVSR >= 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.
   *>          To compute the optimal value of LWORK, call ILAENV to get
   *>          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:
   *>          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;
   *>          the optimal LWORK is N*(NB+1).
   *>
   *>          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 (3*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.  (A,B) are not in Schur
   *>                form, but ALPHA(j) and BETA(j) should be correct for
   *>                j=INFO+1,...,N.
   *>          > N:  errors that usually indicate LAPACK problems:
   *>                =N+1: error return from ZGGBAL
   *>                =N+2: error return from ZGEQRF
   *>                =N+3: error return from ZUNMQR
   *>                =N+4: error return from ZUNGQR
   *>                =N+5: error return from ZGGHRD
   *>                =N+6: error return from ZHGEQZ (other than failed
   *>                                               iteration)
   *>                =N+7: error return from ZGGBAK (computing VSL)
   *>                =N+8: error return from ZGGBAK (computing VSR)
   *>                =N+9: error return from ZLASCL (various places)
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GEeigen
   *
   *  =====================================================================
       SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,        SUBROUTINE ZGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
      $                  VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,       $                  VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
      $                  INFO )       $                  INFO )
 *  *
 *  -- LAPACK driver routine (version 3.2) --  *  -- LAPACK driver routine (version 3.4.0) --
 *  -- 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  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR        CHARACTER          JOBVSL, JOBVSR
Line 18 Line 241
      $                   WORK( * )       $                   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  This routine is deprecated and has been replaced by routine ZGGES.  
 *  
 *  ZGEGS computes the eigenvalues, Schur form, and, optionally, the  
 *  left and or/right Schur vectors of a complex matrix pair (A,B).  
 *  Given two square matrices A and B, the generalized Schur  
 *  factorization has the form  
 *    
 *     A = Q*S*Z**H,  B = Q*T*Z**H  
 *    
 *  where Q and Z are unitary matrices and S and T are upper triangular.  
 *  The columns of Q are the left Schur vectors  
 *  and the columns of Z are the right Schur vectors.  
 *    
 *  If only the eigenvalues of (A,B) are needed, the driver routine  
 *  ZGEGV should be used instead.  See ZGEGV for a description of the  
 *  eigenvalues of the generalized nonsymmetric eigenvalue problem  
 *  (GNEP).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBVSL   (input) CHARACTER*1  
 *          = 'N':  do not compute the left Schur vectors;  
 *          = 'V':  compute the left Schur vectors (returned in VSL).  
 *  
 *  JOBVSR   (input) CHARACTER*1  
 *          = 'N':  do not compute the right Schur vectors;  
 *          = 'V':  compute the right Schur vectors (returned in VSR).  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices A, B, VSL, and VSR.  N >= 0.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)  
 *          On entry, the matrix A.  
 *          On exit, the upper triangular matrix S from the generalized  
 *          Schur factorization.  
 *  
 *  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.  
 *          On exit, the upper triangular matrix T from the generalized  
 *          Schur factorization.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of B.  LDB >= max(1,N).  
 *  
 *  ALPHA   (output) COMPLEX*16 array, dimension (N)  
 *          The complex scalars alpha that define the eigenvalues of  
 *          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur  
 *          form of A.  
 *  
 *  BETA    (output) COMPLEX*16 array, dimension (N)  
 *          The non-negative real scalars beta that define the  
 *          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element  
 *          of the triangular factor T.  
 *  
 *          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)  
 *          represent the j-th eigenvalue of the matrix pair (A,B), in  
 *          one of the forms lambda = alpha/beta or mu = beta/alpha.  
 *          Since either lambda or mu may overflow, they should not,  
 *          in general, be computed.  
 *  
 *  
 *  VSL     (output) COMPLEX*16 array, dimension (LDVSL,N)  
 *          If JOBVSL = 'V', the matrix of left Schur vectors Q.  
 *          Not referenced if JOBVSL = 'N'.  
 *  
 *  LDVSL   (input) INTEGER  
 *          The leading dimension of the matrix VSL. LDVSL >= 1, and  
 *          if JOBVSL = 'V', LDVSL >= N.  
 *  
 *  VSR     (output) COMPLEX*16 array, dimension (LDVSR,N)  
 *          If JOBVSR = 'V', the matrix of right Schur vectors Z.  
 *          Not referenced if JOBVSR = 'N'.  
 *  
 *  LDVSR   (input) INTEGER  
 *          The leading dimension of the matrix VSR. LDVSR >= 1, and  
 *          if JOBVSR = 'V', LDVSR >= 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.  
 *          To compute the optimal value of LWORK, call ILAENV to get  
 *          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:  
 *          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;  
 *          the optimal LWORK is N*(NB+1).  
 *  
 *          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) DOUBLE PRECISION array, dimension (3*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.  (A,B) are not in Schur  
 *                form, but ALPHA(j) and BETA(j) should be correct for  
 *                j=INFO+1,...,N.  
 *          > N:  errors that usually indicate LAPACK problems:  
 *                =N+1: error return from ZGGBAL  
 *                =N+2: error return from ZGEQRF  
 *                =N+3: error return from ZUNMQR  
 *                =N+4: error return from ZUNGQR  
 *                =N+5: error return from ZGGHRD  
 *                =N+6: error return from ZHGEQZ (other than failed  
 *                                               iteration)  
 *                =N+7: error return from ZGGBAK (computing VSL)  
 *                =N+8: error return from ZGGBAK (computing VSR)  
 *                =N+9: error return from ZLASCL (various places)  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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