dlaein-f(3)

dlaein.f –

Synopsis

Functions/Subroutines

subroutine dlaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Function/Subroutine Documentation

subroutine dlaein (logicalRIGHTV, logicalNOINIT, integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionWR, double precisionWI, double precision, dimension( * )VR, double precision, dimension( * )VI, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )WORK, double precisionEPS3, double precisionSMLNUM, double precisionBIGNUM, integerINFO)

DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

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.

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 is INTEGER
 The order of the matrix H. N >= 0.

 H is DOUBLE PRECISION 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 is DOUBLE PRECISION

 WI is DOUBLE PRECISION
 The real and imaginary parts of the eigenvalue of H whose
 corresponding right or left eigenvector is to be computed.

 VR is DOUBLE PRECISION array, dimension (N)

 VI is 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 is DOUBLE PRECISION array, dimension (LDB,N)

LDB

 LDB is INTEGER
 The leading dimension of the array B. LDB >= N+1.

WORK

 WORK is DOUBLE PRECISION array, dimension (N)

EPS3

 EPS3 is DOUBLE PRECISION
 A small machine-dependent value which is used to perturb
 close eigenvalues, and to replace zero pivots.

SMLNUM

 SMLNUM is DOUBLE PRECISION
 A machine-dependent value close to the underflow threshold.

BIGNUM

 BIGNUM is DOUBLE PRECISION
 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 dlaein.f.

Author

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