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version 1.7, 2010/12/21 13:53:56 version 1.8, 2011/11/21 20:43:22
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   *> \brief \b ZTGEVC
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZTGEVC + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgevc.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgevc.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgevc.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
   *                          LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          HOWMNY, SIDE
   *       INTEGER            INFO, LDP, LDS, LDVL, LDVR, M, MM, N
   *       ..
   *       .. Array Arguments ..
   *       LOGICAL            SELECT( * )
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
   *      $                   VR( LDVR, * ), WORK( * )
   *       ..
   *  
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZTGEVC computes some or all of the right and/or left eigenvectors of
   *> a pair of complex matrices (S,P), where S and P are upper triangular.
   *> Matrix pairs of this type are produced by the generalized Schur
   *> factorization of a complex matrix pair (A,B):
   *> 
   *>    A = Q*S*Z**H,  B = Q*P*Z**H
   *> 
   *> as computed by ZGGHRD + ZHGEQZ.
   *> 
   *> The right eigenvector x and the left eigenvector y of (S,P)
   *> corresponding to an eigenvalue w are defined by:
   *> 
   *>    S*x = w*P*x,  (y**H)*S = w*(y**H)*P,
   *> 
   *> where y**H denotes the conjugate tranpose of y.
   *> The eigenvalues are not input to this routine, but are computed
   *> directly from the diagonal elements of S and P.
   *> 
   *> This routine returns the matrices X and/or Y of right and left
   *> eigenvectors of (S,P), or the products Z*X and/or Q*Y,
   *> where Z and Q are input matrices.
   *> If Q and Z are the unitary factors from the generalized Schur
   *> factorization of a matrix pair (A,B), then Z*X and Q*Y
   *> are the matrices of right and left eigenvectors of (A,B).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'R': compute right eigenvectors only;
   *>          = 'L': compute left eigenvectors only;
   *>          = 'B': compute both right and left eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] HOWMNY
   *> \verbatim
   *>          HOWMNY is CHARACTER*1
   *>          = 'A': compute all right and/or left eigenvectors;
   *>          = 'B': compute all right and/or left eigenvectors,
   *>                 backtransformed by the matrices in VR and/or VL;
   *>          = 'S': compute selected right and/or left eigenvectors,
   *>                 specified by the logical array SELECT.
   *> \endverbatim
   *>
   *> \param[in] SELECT
   *> \verbatim
   *>          SELECT is LOGICAL array, dimension (N)
   *>          If HOWMNY='S', SELECT specifies the eigenvectors to be
   *>          computed.  The eigenvector corresponding to the j-th
   *>          eigenvalue is computed if SELECT(j) = .TRUE..
   *>          Not referenced if HOWMNY = 'A' or 'B'.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrices S and P.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] S
   *> \verbatim
   *>          S is COMPLEX*16 array, dimension (LDS,N)
   *>          The upper triangular matrix S from a generalized Schur
   *>          factorization, as computed by ZHGEQZ.
   *> \endverbatim
   *>
   *> \param[in] LDS
   *> \verbatim
   *>          LDS is INTEGER
   *>          The leading dimension of array S.  LDS >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] P
   *> \verbatim
   *>          P is COMPLEX*16 array, dimension (LDP,N)
   *>          The upper triangular matrix P from a generalized Schur
   *>          factorization, as computed by ZHGEQZ.  P must have real
   *>          diagonal elements.
   *> \endverbatim
   *>
   *> \param[in] LDP
   *> \verbatim
   *>          LDP is INTEGER
   *>          The leading dimension of array P.  LDP >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in,out] VL
   *> \verbatim
   *>          VL is COMPLEX*16 array, dimension (LDVL,MM)
   *>          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
   *>          contain an N-by-N matrix Q (usually the unitary matrix Q
   *>          of left Schur vectors returned by ZHGEQZ).
   *>          On exit, if SIDE = 'L' or 'B', VL contains:
   *>          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
   *>          if HOWMNY = 'B', the matrix Q*Y;
   *>          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
   *>                      SELECT, stored consecutively in the columns of
   *>                      VL, in the same order as their eigenvalues.
   *>          Not referenced if SIDE = 'R'.
   *> \endverbatim
   *>
   *> \param[in] LDVL
   *> \verbatim
   *>          LDVL is INTEGER
   *>          The leading dimension of array VL.  LDVL >= 1, and if
   *>          SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.
   *> \endverbatim
   *>
   *> \param[in,out] VR
   *> \verbatim
   *>          VR is COMPLEX*16 array, dimension (LDVR,MM)
   *>          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
   *>          contain an N-by-N matrix Q (usually the unitary matrix Z
   *>          of right Schur vectors returned by ZHGEQZ).
   *>          On exit, if SIDE = 'R' or 'B', VR contains:
   *>          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
   *>          if HOWMNY = 'B', the matrix Z*X;
   *>          if HOWMNY = 'S', the right eigenvectors of (S,P) specified by
   *>                      SELECT, stored consecutively in the columns of
   *>                      VR, in the same order as their eigenvalues.
   *>          Not referenced if SIDE = 'L'.
   *> \endverbatim
   *>
   *> \param[in] LDVR
   *> \verbatim
   *>          LDVR is INTEGER
   *>          The leading dimension of the array VR.  LDVR >= 1, and if
   *>          SIDE = 'R' or 'B', LDVR >= N.
   *> \endverbatim
   *>
   *> \param[in] MM
   *> \verbatim
   *>          MM is INTEGER
   *>          The number of columns in the arrays VL and/or VR. MM >= M.
   *> \endverbatim
   *>
   *> \param[out] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of columns in the arrays VL and/or VR actually
   *>          used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M
   *>          is set to N.  Each selected eigenvector occupies one column.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (2*N)
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (2*N)
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit.
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GEcomputational
   *
   *  =====================================================================
       SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,        SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
      $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )       $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational 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          HOWMNY, SIDE        CHARACTER          HOWMNY, SIDE
Line 18 Line 236
 *     ..  *     ..
 *  *
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZTGEVC computes some or all of the right and/or left eigenvectors of  
 *  a pair of complex matrices (S,P), where S and P are upper triangular.  
 *  Matrix pairs of this type are produced by the generalized Schur  
 *  factorization of a complex matrix pair (A,B):  
 *    
 *     A = Q*S*Z**H,  B = Q*P*Z**H  
 *    
 *  as computed by ZGGHRD + ZHGEQZ.  
 *    
 *  The right eigenvector x and the left eigenvector y of (S,P)  
 *  corresponding to an eigenvalue w are defined by:  
 *    
 *     S*x = w*P*x,  (y**H)*S = w*(y**H)*P,  
 *    
 *  where y**H denotes the conjugate tranpose of y.  
 *  The eigenvalues are not input to this routine, but are computed  
 *  directly from the diagonal elements of S and P.  
 *    
 *  This routine returns the matrices X and/or Y of right and left  
 *  eigenvectors of (S,P), or the products Z*X and/or Q*Y,  
 *  where Z and Q are input matrices.  
 *  If Q and Z are the unitary factors from the generalized Schur  
 *  factorization of a matrix pair (A,B), then Z*X and Q*Y  
 *  are the matrices of right and left eigenvectors of (A,B).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'R': compute right eigenvectors only;  
 *          = 'L': compute left eigenvectors only;  
 *          = 'B': compute both right and left eigenvectors.  
 *  
 *  HOWMNY  (input) CHARACTER*1  
 *          = 'A': compute all right and/or left eigenvectors;  
 *          = 'B': compute all right and/or left eigenvectors,  
 *                 backtransformed by the matrices in VR and/or VL;  
 *          = 'S': compute selected right and/or left eigenvectors,  
 *                 specified by the logical array SELECT.  
 *  
 *  SELECT  (input) LOGICAL array, dimension (N)  
 *          If HOWMNY='S', SELECT specifies the eigenvectors to be  
 *          computed.  The eigenvector corresponding to the j-th  
 *          eigenvalue is computed if SELECT(j) = .TRUE..  
 *          Not referenced if HOWMNY = 'A' or 'B'.  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrices S and P.  N >= 0.  
 *  
 *  S       (input) COMPLEX*16 array, dimension (LDS,N)  
 *          The upper triangular matrix S from a generalized Schur  
 *          factorization, as computed by ZHGEQZ.  
 *  
 *  LDS     (input) INTEGER  
 *          The leading dimension of array S.  LDS >= max(1,N).  
 *  
 *  P       (input) COMPLEX*16 array, dimension (LDP,N)  
 *          The upper triangular matrix P from a generalized Schur  
 *          factorization, as computed by ZHGEQZ.  P must have real  
 *          diagonal elements.  
 *  
 *  LDP     (input) INTEGER  
 *          The leading dimension of array P.  LDP >= max(1,N).  
 *  
 *  VL      (input/output) COMPLEX*16 array, dimension (LDVL,MM)  
 *          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must  
 *          contain an N-by-N matrix Q (usually the unitary matrix Q  
 *          of left Schur vectors returned by ZHGEQZ).  
 *          On exit, if SIDE = 'L' or 'B', VL contains:  
 *          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);  
 *          if HOWMNY = 'B', the matrix Q*Y;  
 *          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by  
 *                      SELECT, stored consecutively in the columns of  
 *                      VL, in the same order as their eigenvalues.  
 *          Not referenced if SIDE = 'R'.  
 *  
 *  LDVL    (input) INTEGER  
 *          The leading dimension of array VL.  LDVL >= 1, and if  
 *          SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.  
 *  
 *  VR      (input/output) COMPLEX*16 array, dimension (LDVR,MM)  
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must  
 *          contain an N-by-N matrix Q (usually the unitary matrix Z  
 *          of right Schur vectors returned by ZHGEQZ).  
 *          On exit, if SIDE = 'R' or 'B', VR contains:  
 *          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);  
 *          if HOWMNY = 'B', the matrix Z*X;  
 *          if HOWMNY = 'S', the right eigenvectors of (S,P) specified by  
 *                      SELECT, stored consecutively in the columns of  
 *                      VR, in the same order as their eigenvalues.  
 *          Not referenced if SIDE = 'L'.  
 *  
 *  LDVR    (input) INTEGER  
 *          The leading dimension of the array VR.  LDVR >= 1, and if  
 *          SIDE = 'R' or 'B', LDVR >= N.  
 *  
 *  MM      (input) INTEGER  
 *          The number of columns in the arrays VL and/or VR. MM >= M.  
 *  
 *  M       (output) INTEGER  
 *          The number of columns in the arrays VL and/or VR actually  
 *          used to store the eigenvectors.  If HOWMNY = 'A' or 'B', M  
 *          is set to N.  Each selected eigenvector occupies one column.  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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