slaein.f - Man Page

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.

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.

Definition at line 170 of file slaein.f.