chsein.f (3) - Linux Manuals

NAME

chsein.f -

SYNOPSIS

Functions/Subroutines

subroutine chsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)
CHSEIN

Function/Subroutine Documentation

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

CHSEIN

Purpose:

 CHSEIN 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 CHSEQR; 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 CHSEIN 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, CHSEIN 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 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 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 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 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 array, dimension (N*N)

RWORK

          RWORK is REAL 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 chsein.f.

Author

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