
chsein.f(3) LAPACK chsein.f(3)
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
blocktriangular, then the jth eigenvalue can be
assumed to be an eigenvalue of the block containing
the jth 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': usersupplied 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 ith 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 ith 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 ith 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
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 chsein.f(3) 
