CLAEIN - use inverse iteration to find a right or left
eigenvector corresponding to the eigenvalue W of a complex
upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B,
LDB, RWORK, EPS3, SMLNUM, INFO )
LOGICAL NOINIT, RIGHTV
INTEGER INFO, LDB, LDH, N
REAL EPS3, SMLNUM
COMPLEX W
REAL RWORK( * )
COMPLEX B( LDB, * ), H( LDH, * ), V( * )
PURPOSE
CLAEIN uses inverse iteration to find a right or left
eigenvector corresponding to the eigenvalue W of a complex
upper Hessenberg matrix H.
ARGUMENTS
RIGHTV (input) LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.
NOINIT (input) LOGICAL
= .TRUE. : no initial vector supplied in V
= .FALSE.: initial vector supplied in V.
N (input) INTEGER
The order of the matrix H. N >= 0.
H (input) COMPLEX array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH (input) INTEGER
The leading dimension of the array H. LDH >=
max(1,N).
W (input) COMPLEX
The eigenvalue of H whose corresponding right or
left eigenvector is to be computed.
V (input/output) COMPLEX array, dimension (N)
On entry, if NOINIT = .FALSE., V must contain a
starting vector for inverse iteration; otherwise V
need not be set. On exit, V contains the computed
eigenvector, normalized so that the component of
tude of a complex number (x,y) is taken to be |x|
+ |y|.
B (workspace) COMPLEX array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
RWORK (workspace) REAL array, dimension (N)
EPS3 (input) REAL
A small machine-dependent value which is used to
perturb close eigenvalues, and to replace zero
pivots.
SMLNUM (input) REAL
A machine-dependent value close to the underflow
threshold.
INFO (output) INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; V is set
to the last iterate.
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