slaein(l) [redhat man page]
SLAEIN(l) ) SLAEIN(l) NAME
SLAEIN - 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 SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO ) LOGICAL NOINIT, RIGHTV INTEGER INFO, LDB, LDH, N REAL BIGNUM, EPS3, SMLNUM, WI, WR REAL B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * ) PURPOSE
SLAEIN 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) REAL 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) REAL WI (input) REAL The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed. VR (input/output) REAL array, dimension (N) VI (input/output) REAL 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 imagi- nary 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) REAL array, dimension (LDB,N) LDB (input) INTEGER The leading dimension of the array B. LDB >= N+1. WORK (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. BIGNUM (input) REAL 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 SLAEIN(l)
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slaein.f(3) LAPACK slaein.f(3) NAME
slaein.f - SYNOPSIS
Functions/Subroutines subroutine slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO) SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentation subroutine slaein (logicalRIGHTV, logicalNOINIT, integerN, real, dimension( ldh, * )H, integerLDH, realWR, realWI, real, dimension( * )VR, real, dimension( * )VI, real, dimension( ldb, * )B, integerLDB, real, dimension( * )WORK, realEPS3, realSMLNUM, realBIGNUM, integerINFO) SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Purpose: SLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H. Parameters: RIGHTV RIGHTV is LOGICAL = .TRUE. : compute right eigenvector; = .FALSE.: compute left eigenvector. NOINIT NOINIT is LOGICAL = .TRUE. : no initial vector supplied in (VR,VI). = .FALSE.: initial vector supplied in (VR,VI). N N is INTEGER The order of the matrix H. N >= 0. H H is REAL array, dimension (LDH,N) The upper Hessenberg matrix H. LDH LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N). WR WR is REAL WI WI is REAL The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed. VR VR is REAL array, dimension (N) VI VI is REAL 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 B is REAL array, dimension (LDB,N) LDB LDB is INTEGER The leading dimension of the array B. LDB >= N+1. WORK WORK is REAL array, dimension (N) EPS3 EPS3 is REAL A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots. SMLNUM SMLNUM is REAL A machine-dependent value close to the underflow threshold. BIGNUM BIGNUM is REAL A machine-dependent value close to the overflow threshold. INFO INFO is 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. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Definition at line 172 of file slaein.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slaein.f(3)