Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - 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

SYNOPSIS

       SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL,  VR,  LDVR,  MM,  M,
                          WORK, RWORK, INFO )

           CHARACTER      HOWMNY, SIDE

           INTEGER        INFO, LDP, LDS, LDVL, LDVR, M, MM, N

           LOGICAL        SELECT( * )

           DOUBLE         PRECISION RWORK( * )

           COMPLEX*16     P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )

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.

 LAPACK routine (version 3.2)               April 2011                            ZTGEVC(3lapack)