ZLAEIN(3F)ZLAEIN(3F)NAMEZLAEIN - use inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3,
SMLNUM, INFO )
LOGICAL NOINIT, RIGHTV
INTEGER INFO, LDB, LDH, N
DOUBLE PRECISION EPS3, SMLNUM
COMPLEX*16 W
DOUBLE PRECISION RWORK( * )
COMPLEX*16 B( LDB, * ), H( LDH, * ), V( * )
PURPOSEZLAEIN 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*16 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*16
The eigenvalue of H whose corresponding right or left eigenvector
is to be computed.
V (input/output) COMPLEX*16 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 largest magnitude has magnitude 1; here the
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ZLAEIN(3F)ZLAEIN(3F)
magnitude of a complex number (x,y) is taken to be |x| + |y|.
B (workspace) COMPLEX*16 array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
EPS3 (input) DOUBLE PRECISION
A small machine-dependent value which is used to perturb close
eigenvalues, and to replace zero pivots.
SMLNUM (input) DOUBLE PRECISION
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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