.TH CLAEIN 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLAEIN - inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H .SH SYNOPSIS .TP 19 SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO ) .TP 19 .ti +4 LOGICAL NOINIT, RIGHTV .TP 19 .ti +4 INTEGER INFO, LDB, LDH, N .TP 19 .ti +4 REAL EPS3, SMLNUM .TP 19 .ti +4 COMPLEX W .TP 19 .ti +4 REAL RWORK( * ) .TP 19 .ti +4 COMPLEX B( LDB, * ), H( LDH, * ), V( * ) .SH PURPOSE CLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H. .SH ARGUMENTS .TP 9 RIGHTV (input) LOGICAL = .TRUE. : compute right eigenvector; .br = .FALSE.: compute left eigenvector. .TP 9 NOINIT (input) LOGICAL .br = .TRUE. : no initial vector supplied in V .br = .FALSE.: initial vector supplied in V. .TP 8 N (input) INTEGER The order of the matrix H. N >= 0. .TP 8 H (input) COMPLEX array, dimension (LDH,N) The upper Hessenberg matrix H. .TP 8 LDH (input) INTEGER The leading dimension of the array H. LDH >= max(1,N). .TP 8 W (input) COMPLEX The eigenvalue of H whose corresponding right or left eigenvector is to be computed. .TP 8 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|. .TP 8 B (workspace) COMPLEX array, dimension (LDB,N) .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 RWORK (workspace) REAL array, dimension (N) .TP 8 EPS3 (input) REAL A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots. .TP 8 SMLNUM (input) REAL A machine-dependent value close to the underflow threshold. .TP 8 INFO (output) INTEGER = 0: successful exit .br = 1: inverse iteration did not converge; V is set to the last iterate.