zhsein.f man page

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.
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).

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 2013

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 244 of file zhsein.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zhsein(3) is an alias of zhsein.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK