SRC/ctrevc3.f(3)

NAME
SRC/ctrevc3.f

SYNOPSIS

  Functions/Subroutines
subroutine ctrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info)
CTREVC3

Function/Subroutine Documentation

  subroutine ctrevc3 (character side, character howmny, logical, dimension( * ) select, integer n, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer info)

CTREVC3

Purpose:

     CTREVC3 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 CHSEQR.
     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.
     This uses a Level 3 BLAS version of the back transformation.

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 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 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 CHSEQR).
              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 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 CHSEQR).
              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 array, dimension (MAX(1,LWORK))

    LWORK

              LWORK is INTEGER
              The dimension of array WORK. LWORK >= max(1,2*N).
              For optimum performance, LWORK >= N + 2*N*NB, where NB is
              the optimal blocksize.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    RWORK

              RWORK is REAL array, dimension (LRWORK)

    LRWORK

              LRWORK is INTEGER
              The dimension of array RWORK. LRWORK >= max(1,N).
              If LRWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the RWORK array, returns
              this value as the first entry of the RWORK array, and no error
              message related to LRWORK is issued by XERBLA.

    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.

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|.

Definition at line 242 of file ctrevc3.f.

Author

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