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## ctgevc()

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

Download CTGEVC + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  SIDE

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

  [in]

  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.
      !>

  [in]

  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'.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrices S and P.  N >= 0.
      !>

  [in]

  S

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

  [in]

  LDS

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

  [in]

  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.
      !>

  [in]

  LDP

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

  [in,out]

  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'.
      !>

  [in]

  LDVL

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

  [in,out]

  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'.
      !>

  [in]

  LDVR

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

  [in]

  MM

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

  [out]

  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.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (2*N)
      !>

  [out]

  RWORK

      !>          RWORK is REAL array, dimension (2*N)
      !>

  [out]

  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.