SLAEIN (3) Linux Manual Page

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

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