dtrevc.f(3)

NAME
dtrevc.f -

SYNOPSIS

  Functions/Subroutines
subroutine dtrevc (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO)
DTREVC

Function/Subroutine Documentation

  subroutine dtrevc (characterSIDE, characterHOWMNY, logical, dimension( * )SELECT, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( ldvl, * )VL, integerLDVL, double precision, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, double precision, dimension( * )WORK, integerINFO)

DTREVC

Purpose:

     DTREVC computes some or all of the right and/or left eigenvectors of
     a real upper quasi-triangular matrix T.
     Matrices of this type are produced by the Schur factorization of
     a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR.

     The right eigenvector x and the left eigenvector y of T corresponding
     to an eigenvalue w are defined by:

        T*x = w*x,     (y**T)*T = w*(y**T)

     where y**T denotes the transpose of y.
     The eigenvalues are not input to this routine, but are read directly
     from the diagonal blocks 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 orthogonal 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.

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,
                      as indicated by the logical array SELECT.

    SELECT

              SELECT is LOGICAL array, dimension (N)
              If HOWMNY = 'S', SELECT specifies the eigenvectors to be
              computed.
              If w(j) is a real eigenvalue, the corresponding real
              eigenvector is computed if SELECT(j) is .TRUE..
              If w(j) and w(j+1) are the real and imaginary parts of a
              complex eigenvalue, the corresponding complex eigenvector is
              computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
              on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
              .FALSE..
              Not referenced if HOWMNY = 'A' or 'B'.

    N

              N is INTEGER
              The order of the matrix T. N >= 0.

    T

              T is DOUBLE PRECISION array, dimension (LDT,N)
              The upper quasi-triangular matrix T in Schur canonical form.

    LDT

              LDT is INTEGER
              The leading dimension of the array T. LDT >= max(1,N).

    VL

              VL is DOUBLE PRECISION 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 orthogonal matrix Q
              of Schur vectors returned by DHSEQR).
              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.
              A complex eigenvector corresponding to a complex eigenvalue
              is stored in two consecutive columns, the first holding the
              real part, and the second the imaginary part.
              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 DOUBLE PRECISION 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 orthogonal matrix Q
              of Schur vectors returned by DHSEQR).
              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.
              A complex eigenvector corresponding to a complex eigenvalue
              is stored in two consecutive columns, the first holding the
              real part and the second the imaginary part.
              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 real eigenvector occupies one column and each
              selected complex eigenvector occupies two columns.

    WORK

              WORK is DOUBLE PRECISION array, dimension (3*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

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 222 of file dtrevc.f.

Author

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