ZTGEVC(3)      LAPACK routine of NEC Numeric Library Collection      ZTGEVC(3)



NAME
       ZTGEVC

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



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)
                     SIDE is CHARACTER*1
                     = 'R': compute right eigenvectors only;
                     = 'L': compute left eigenvectors only;
                     = 'B': compute both right and left eigenvectors.

           HOWMNY    (input)
                     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.

           SELECT    (input)
                     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'.

           N         (input)
                     N is INTEGER
                     The order of the matrices S and P.  N >= 0.

           S         (input)
                     S is COMPLEX*16 array, dimension (LDS,N)
                     The upper triangular matrix S from a generalized Schur
                     factorization, as computed by ZHGEQZ.

           LDS       (input)
                     LDS is INTEGER
                     The leading dimension of array S.  LDS >= max(1,N).

           P         (input)
                     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.

           LDP       (input)
                     LDP is INTEGER
                     The leading dimension of array P.  LDP >= max(1,N).

           VL        (input/output)
                     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'.

           LDVL      (input)
                     LDVL is INTEGER
                     The leading dimension of array VL.  LDVL >= 1, and if
                     SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.

           VR        (input/output)
                     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'.

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

           MM        (input)
                     MM is INTEGER
                     The number of columns in the arrays VL and/or VR. MM >= M.

           M         (output)
                     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.

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (2*N)

           RWORK     (output)
                     RWORK is DOUBLE PRECISION array, dimension (2*N)

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.



LAPACK routine                  31 October 2017                      ZTGEVC(3)