SRC/ctgevc.f(3)

NAME
SRC/ctgevc.f

SYNOPSIS

  Functions/Subroutines
subroutine ctgevc (side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
CTGEVC

Function/Subroutine Documentation

  subroutine ctgevc (character side, character howmny, logical, dimension( * ) select, integer n, complex, dimension( lds, * ) s, integer lds, complex, dimension( ldp, * ) p, integer ldp, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CTGEVC

Purpose:

    !>
    !> CTGEVC 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 CGGHRD + CHGEQZ.
    !>
    !> 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 transpose 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).
    !>

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 by the matrices in VR and/or VL;
    !>          = 'S': compute selected right and/or left eigenvectors,
    !>                 specified 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 matrices S and P.  N >= 0.
    !>

    S

    !>          S is COMPLEX array, dimension (LDS,N)
    !>          The upper triangular matrix S from a generalized Schur
    !>          factorization, as computed by CHGEQZ.
    !>

    LDS

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

    P

    !>          P is COMPLEX array, dimension (LDP,N)
    !>          The upper triangular matrix P from a generalized Schur
    !>          factorization, as computed by CHGEQZ.  P must have real
    !>          diagonal elements.
    !>

    LDP

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

    VL

    !>          VL is COMPLEX 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 CHGEQZ).
    !>          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

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

    VR

    !>          VR is COMPLEX array, dimension (LDVR,MM)
    !>          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
    !>          contain an N-by-N matrix Z (usually the unitary matrix Z
    !>          of right Schur vectors returned by CHGEQZ).
    !>          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

    !>          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 array, dimension (2*N)
    !>

    RWORK

    !>          RWORK is REAL array, dimension (2*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.

Definition at line 217 of file ctgevc.f.

Author

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