.TH DLAEIN 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLAEIN - inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H .SH SYNOPSIS .TP 19 SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO ) .TP 19 .ti +4 LOGICAL NOINIT, RIGHTV .TP 19 .ti +4 INTEGER INFO, LDB, LDH, N .TP 19 .ti +4 DOUBLE PRECISION BIGNUM, EPS3, SMLNUM, WI, WR .TP 19 .ti +4 DOUBLE PRECISION B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * ) .SH PURPOSE DLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI). .br = .FALSE.: initial vector supplied in (VR,VI). .TP 8 N (input) INTEGER The order of the matrix H. N >= 0. .TP 8 H (input) DOUBLE PRECISION 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 WR (input) DOUBLE PRECISION WI (input) DOUBLE PRECISION The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed. .TP 8 VR (input/output) DOUBLE PRECISION array, dimension (N) VI (input/output) DOUBLE PRECISION array, dimension (N) On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real starting vector for inverse iteration using the real eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real and imaginary parts of a complex starting vector for inverse iteration using the complex eigenvalue (WR,WI); otherwise VR and VI need not be set. On exit, if WI = 0.0 (real eigenvalue), VR contains the computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), VR and VI contain the real and imaginary parts of the computed complex eigenvector. The eigenvector is 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|. VI is not referenced if WI = 0.0. .TP 8 B (workspace) DOUBLE PRECISION array, dimension (LDB,N) .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= N+1. .TP 7 WORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 EPS3 (input) DOUBLE PRECISION A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots. .TP 8 SMLNUM (input) DOUBLE PRECISION A machine-dependent value close to the underflow threshold. .TP 8 BIGNUM (input) DOUBLE PRECISION A machine-dependent value close to the overflow threshold. .TP 8 INFO (output) INTEGER = 0: successful exit .br = 1: inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0.