NAME

       ztrevc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ztrevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK,
           RWORK, INFO)
           ZTREVC

Function/Subroutine Documentation

   subroutine ztrevc (character SIDE, character HOWMNY, logical, dimension( * ) SELECT, integer
       N, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( ldvl, * ) VL,
       integer LDVL, complex*16, dimension( ldvr, * ) VR, integer LDVR, integer MM, integer M,
       complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)
       ZTREVC

       Purpose:

            ZTREVC computes some or all of the right and/or left eigenvectors of
            a complex upper triangular matrix T.
            Matrices of this type are produced by the Schur factorization of
            a complex general matrix:  A = Q*T*Q**H, as computed by ZHSEQR.

            The right eigenvector x and the left eigenvector y of T corresponding
            to an eigenvalue w are defined by:

                         T*x = w*x,     (y**H)*T = w*(y**H)

            where y**H denotes the conjugate transpose of the vector y.
            The eigenvalues are not input to this routine, but are read directly
            from the diagonal of T.

            This routine returns the matrices X and/or Y of right and left
            eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
            input matrix.  If Q is the unitary factor that reduces a matrix A to
            Schur form T, then Q*X and Q*Y are the matrices of right and left
            eigenvectors of A.

       Parameters:
           SIDE

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

           HOWMNY

                     HOWMNY is CHARACTER*1
                     = 'A':  compute all right and/or left eigenvectors;
                     = 'B':  compute all right and/or left eigenvectors,
                             backtransformed using the matrices supplied in
                             VR and/or VL;
                     = 'S':  compute selected right and/or left eigenvectors,
                             as indicated by the logical array SELECT.

           SELECT

                     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

                     N is INTEGER
                     The order of the matrix T. N >= 0.

           T

                     T is COMPLEX*16 array, dimension (LDT,N)
                     The upper triangular matrix T.  T is modified, but restored
                     on exit.

           LDT

                     LDT is INTEGER
                     The leading dimension of the array T. LDT >= max(1,N).

           VL

                     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
                     Schur vectors returned by ZHSEQR).
                     On exit, if SIDE = 'L' or 'B', VL contains:
                     if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
                     if HOWMNY = 'B', the matrix Q*Y;
                     if HOWMNY = 'S', the left eigenvectors of T specified by
                                      SELECT, stored consecutively in the columns
                                      of VL, in the same order as their
                                      eigenvalues.
                     Not referenced if SIDE = 'R'.

           LDVL

                     LDVL is INTEGER
                     The leading dimension of the array VL.  LDVL >= 1, and if
                     SIDE = 'L' or 'B', LDVL >= N.

           VR

                     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 Q of
                     Schur vectors returned by ZHSEQR).
                     On exit, if SIDE = 'R' or 'B', VR contains:
                     if HOWMNY = 'A', the matrix X of right eigenvectors of T;
                     if HOWMNY = 'B', the matrix Q*X;
                     if HOWMNY = 'S', the right eigenvectors of T specified by
                                      SELECT, stored consecutively in the columns
                                      of VR, in the same order as their
                                      eigenvalues.
                     Not referenced if SIDE = 'L'.

           LDVR

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

           MM

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

           M

                     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

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

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N)

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Further Details:

             The algorithm used in this program is basically backward (forward)
             substitution, with scaling to make the the code robust against
             possible overflow.

             Each eigenvector is normalized so that the element of largest
             magnitude has magnitude 1; here the magnitude of a complex number
             (x,y) is taken to be |x| + |y|.

Author

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