zhsein.f(3)

NAME
zhsein.f -

SYNOPSIS

  Functions/Subroutines
subroutine zhsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
ZHSEIN

Function/Subroutine Documentation

  subroutine zhsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( * )SELECT, integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16, dimension( * )W, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)

ZHSEIN

Purpose:

     ZHSEIN uses inverse iteration to find specified right and/or left
     eigenvectors of a complex upper Hessenberg matrix H.
     The right eigenvector x and the left eigenvector y of the matrix H
     corresponding to an eigenvalue w are defined by:
                  H * x = w * x,     y**h * H = w * y**h
     where y**h denotes the conjugate transpose of the vector y.

Parameters:
    SIDE

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

    EIGSRC

              EIGSRC is CHARACTER*1
              Specifies the source of eigenvalues supplied in W:
              = 'Q': the eigenvalues were found using ZHSEQR; thus, if
                     H has zero subdiagonal elements, and so is
                     block-triangular, then the j-th eigenvalue can be
                     assumed to be an eigenvalue of the block containing
                     the j-th row/column.  This property allows ZHSEIN to
                     perform inverse iteration on just one diagonal block.
              = 'N': no assumptions are made on the correspondence
                     between eigenvalues and diagonal blocks.  In this
                     case, ZHSEIN must always perform inverse iteration
                     using the whole matrix H.

    INITV

              INITV is CHARACTER*1
              = 'N': no initial vectors are supplied;
              = 'U': user-supplied initial vectors are stored in the arrays
                     VL and/or VR.

    SELECT

              SELECT is LOGICAL array, dimension (N)
              Specifies the eigenvectors to be computed. To select the
              eigenvector corresponding to the eigenvalue W(j),
              SELECT(j) must be set to .TRUE..

    N

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

    H

              H is COMPLEX*16 array, dimension (LDH,N)
              The upper Hessenberg matrix H.

    LDH

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

    W

              W is COMPLEX*16 array, dimension (N)
              On entry, the eigenvalues of H.
              On exit, the real parts of W may have been altered since
              close eigenvalues are perturbed slightly in searching for
              independent eigenvectors.

    VL

              VL is COMPLEX*16 array, dimension (LDVL,MM)
              On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
              contain starting vectors for the inverse iteration for the
              left eigenvectors; the starting vector for each eigenvector
              must be in the same column in which the eigenvector will be
              stored.
              On exit, if SIDE = 'L' or 'B', the left eigenvectors
              specified by SELECT will be stored consecutively in the
              columns of VL, in the same order as their eigenvalues.
              If SIDE = 'R', VL is not referenced.

    LDVL

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

    VR

              VR is COMPLEX*16 array, dimension (LDVR,MM)
              On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
              contain starting vectors for the inverse iteration for the
              right eigenvectors; the starting vector for each eigenvector
              must be in the same column in which the eigenvector will be
              stored.
              On exit, if SIDE = 'R' or 'B', the right eigenvectors
              specified by SELECT will be stored consecutively in the
              columns of VR, in the same order as their eigenvalues.
              If SIDE = 'L', VR is not referenced.

    LDVR

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

    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 required to
              store the eigenvectors (= the number of .TRUE. elements in
              SELECT).

    WORK

              WORK is COMPLEX*16 array, dimension (N*N)

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (N)

    IFAILL

              IFAILL is INTEGER array, dimension (MM)
              If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
              eigenvector in the i-th column of VL (corresponding to the
              eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
              eigenvector converged satisfactorily.
              If SIDE = 'R', IFAILL is not referenced.

    IFAILR

              IFAILR is INTEGER array, dimension (MM)
              If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
              eigenvector in the i-th column of VR (corresponding to the
              eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
              eigenvector converged satisfactorily.
              If SIDE = 'L', IFAILR is not referenced.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, i is the number of eigenvectors which
                    failed to converge; see IFAILL and IFAILR for further
                    details.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Further Details:

      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 243 of file zhsein.f.

Author

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