shsein.f man page

shsein.f —

Synopsis

Functions/Subroutines

subroutine shsein (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
SHSEIN

Function/Subroutine Documentation

subroutine shsein (character SIDE, character EIGSRC, character INITV, logical, dimension( * ) SELECT, integer N, real, dimension( ldh, * ) H, integer LDH, real, dimension( * ) WR, real, dimension( * ) WI, real, dimension( ldvl, * ) VL, integer LDVL, real, dimension( ldvr, * ) VR, integer LDVR, integer MM, integer M, real, dimension( * ) WORK, integer, dimension( * ) IFAILL, integer, dimension( * ) IFAILR, integer INFO)

SHSEIN  

Purpose:

 SHSEIN uses inverse iteration to find specified right and/or left
 eigenvectors of a real 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 (WR,WI):
          = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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
          real eigenvector corresponding to a real eigenvalue WR(j),
          SELECT(j) must be set to .TRUE.. To select the complex
          eigenvector corresponding to a complex eigenvalue
          (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)),
          either SELECT(j) or SELECT(j+1) or both must be set to
          .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is
          .FALSE..

N

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

H

          H is REAL array, dimension (LDH,N)
          The upper Hessenberg matrix H.
          If a NaN is detected in H, the routine will return with INFO=-6.

LDH

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

WR

          WR is REAL array, dimension (N)

WI

          WI is REAL array, dimension (N)

          On entry, the real and imaginary parts of the eigenvalues of
          H; a complex conjugate pair of eigenvalues must be stored in
          consecutive elements of WR and WI.
          On exit, WR may have been altered since close eigenvalues
          are perturbed slightly in searching for independent
          eigenvectors.

VL

          VL is REAL 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(s) 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. 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.
          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 REAL 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(s) 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. 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.
          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; each selected real eigenvector
          occupies one column and each selected complex eigenvector
          occupies two columns.

WORK

          WORK is REAL array, dimension ((N+2)*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 the i-th and (i+1)th
          columns of VL hold a complex eigenvector, then IFAILL(i) and
          IFAILL(i+1) are set to the same value.
          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 the i-th and (i+1)th
          columns of VR hold a complex eigenvector, then IFAILR(i) and
          IFAILR(i+1) are set to the same value.
          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:

December 2016

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 265 of file shsein.f.

Author

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Referenced By

The man page shsein(3) is an alias of shsein.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK