CTGEVC (3lapack)

compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)

SYNOPSIS

  SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR,
                     LDVR, MM, M, WORK, RWORK, INFO )

      CHARACTER      HOWMNY, SIDE

      INTEGER        INFO, LDA, LDB, LDVL, LDVR, M, MM, N

      LOGICAL        SELECT( * )

      REAL           RWORK( * )

      COMPLEX        A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, * ),
                     WORK( * )

PURPOSE

  CTGEVC computes some or all of the right and/or left generalized
  eigenvectors of a pair of complex upper triangular matrices (A,B).

  The right generalized eigenvector x and the left generalized eigenvector y
  of (A,B) corresponding to a generalized eigenvalue w are defined by:

          (A - wB) * x = 0  and  y**H * (A - wB) = 0

  where y**H denotes the conjugate tranpose of y.

  If an eigenvalue w is determined by zero diagonal elements of both A and B,
  a unit vector is returned as the corresponding eigenvector.

  If all eigenvectors are requested, the routine may either return the
  matrices X and/or Y of right or left eigenvectors of (A,B), or the products
  Z*X and/or Q*Y, where Z and Q are input unitary matrices.  If (A,B) was
  obtained from the generalized Schur factorization of an original pair of
  matrices
     (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
  then Z*X and Q*Y are the matrices of right or left eigenvectors of A.

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, and
          backtransform them using the input matrices supplied 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.
          If HOWMNY='A' or 'B', SELECT is not referenced.  To select the
          eigenvector corresponding to the j-th eigenvalue, SELECT(j) must be
          set to .TRUE..

  N       (input) INTEGER
          The order of the matrices A and B.  N >= 0.

  A       (input) COMPLEX array, dimension (LDA,N)
          The upper triangular matrix A.

  LDA     (input) INTEGER
          The leading dimension of array A.  LDA >= max(1,N).

  B       (input) COMPLEX array, dimension (LDB,N)
          The upper triangular matrix B.  B must have real diagonal elements.

  LDB     (input) INTEGER
          The leading dimension of array B.  LDB >= max(1,N).

  VL      (input/output) 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 (A,B); if
          HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left
          eigenvectors of (A,B) specified by SELECT, stored consecutively in
          the columns of VL, in the same order as their eigenvalues.  If SIDE
          = 'R', VL is not referenced.

  LDVL    (input) INTEGER
          The leading dimension of array VL.  LDVL >= max(1,N) if SIDE = 'L'
          or 'B'; LDVL >= 1 otherwise.

  VR      (input/output) 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
          (A,B); if HOWMNY = 'B', the matrix Z*X; if HOWMNY = 'S', the right
          eigenvectors of (A,B) specified by SELECT, stored consecutively in
          the columns of VR, in the same order as their eigenvalues.  If SIDE
          = 'L', VR is not referenced.

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

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

  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 array, dimension (2*N)

  RWORK   (workspace) REAL array, dimension (2*N)

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