ctgevc.f(3)

NAME
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 (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, complex, dimension( lds, * )S, integerLDS, complex, dimension( ldp, * )P, integerLDP, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

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 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).

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 Q (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.

Date:
    November 2011

Definition at line 219 of file ctgevc.f.

Author

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