NAME
CLAEIN - uses 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 largest magnitude has magnitude 1; here the magnitude 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.