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RedHat 9 (Linux i386) - man page for dlaein (redhat section l)

DLAEIN(l)						  )						    DLAEIN(l)

NAME
DLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO ) LOGICAL NOINIT, RIGHTV INTEGER INFO, LDB, LDH, N DOUBLE PRECISION BIGNUM, EPS3, SMLNUM, WI, WR DOUBLE PRECISION B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )
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.
ARGUMENTS
RIGHTV (input) LOGICAL = .TRUE. : compute right eigenvector; = .FALSE.: compute left eigenvector. NOINIT (input) LOGICAL = .TRUE. : no initial vector supplied in (VR,VI). = .FALSE.: initial vector supplied in (VR,VI). N (input) INTEGER The order of the matrix H. N >= 0. H (input) DOUBLE PRECISION array, dimension (LDH,N) The upper Hessenberg matrix H. LDH (input) INTEGER The leading dimension of the array H. LDH >= max(1,N). WR (input) DOUBLE PRECISION WI (input) DOUBLE PRECISION The real and imaginary parts of the eigenvalue of H whose correspond- ing right or left eigenvector is to be computed. 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. B (workspace) DOUBLE PRECISION array, dimension (LDB,N) LDB (input) INTEGER The leading dimension of the array B. LDB >= N+1. WORK (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 piv- ots. SMLNUM (input) DOUBLE PRECISION A machine-dependent value close to the underflow threshold. BIGNUM (input) DOUBLE PRECISION A machine-dependent value close to the overflow threshold. INFO (output) INTEGER = 0: successful exit = 1: inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0. LAPACK version 3.0 15 June 2000 DLAEIN(l)


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