ztgevc(3S)

NAME
     ZTGEVC - compute some or all of the right and/or left generalized
     eigenvectors of a pair of complex upper triangular matrices (A,B)

SYNOPSIS
     SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR,
                        LDVR, MM, M, WORK, RWORK, INFO )

         CHARACTER      HOWMNY, SIDE

         INTEGER        INFO, LDA, LDB, LDVL, LDVR, M, MM, N

         LOGICAL        SELECT( * )

         DOUBLE         PRECISION RWORK( * )

         COMPLEX*16     A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, *
                        ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZTGEVC computes some or all of the right and/or left generalized
     eigenvectors of a pair of complex upper triangular matrices (A,B). The
     right generalized eigenvector x and the left generalized eigenvector y of
     (A,B) corresponding to a generalized eigenvalue w are defined by:

             (A - wB) * x = 0  and  y**H * (A - wB) = 0

     where y**H denotes the conjugate tranpose of y.

     If an eigenvalue w is determined by zero diagonal elements of both A and
     B, a unit vector is returned as the corresponding eigenvector.

     If all eigenvectors are requested, the routine may either return the
     matrices X and/or Y of right or left eigenvectors of (A,B), or the
     products Z*X and/or Q*Y, where Z and Q are input unitary matrices.  If
     (A,B) was obtained from the generalized Schur factorization of an
     original pair of matrices
        (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
     then Z*X and Q*Y are the matrices of right or left eigenvectors of A.
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, and
             backtransform them using the input matrices supplied 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.
             If HOWMNY='A' or 'B', SELECT is not referenced.  To select the
             eigenvector corresponding to the j-th eigenvalue, SELECT(j) must
             be set to .TRUE..

     N       (input) INTEGER
             The order of the matrices A and B.  N >= 0.

     A       (input) COMPLEX*16 array, dimension (LDA,N)
             The upper triangular matrix A.

     LDA     (input) INTEGER
             The leading dimension of array A.  LDA >= max(1,N).

     B       (input) COMPLEX*16 array, dimension (LDB,N)
             The upper triangular matrix B.  B must have real diagonal
             elements.

     LDB     (input) INTEGER
             The leading dimension of array B.  LDB >= 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
             (A,B); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
             eigenvectors of (A,B) specified by SELECT, stored consecutively
             in the columns of VL, in the same order as their eigenvalues.  If
             SIDE = 'R', VL is not referenced.

     LDVL    (input) INTEGER
             The leading dimension of array VL.  LDVL >= max(1,N) if SIDE =
             'L' or 'B'; LDVL >= 1 otherwise.

     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
             (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the
             right eigenvectors of (A,B) specified by SELECT, stored
             consecutively in the columns of VR, in the same order as their
             eigenvalues.  If SIDE = 'L', VR is not referenced.

     LDVR    (input) INTEGER
             The leading dimension of the array VR.  LDVR >= max(1,N) if SIDE
             = 'R' or 'B'; LDVR >= 1 otherwise.

     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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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