dlaein(3)

NAME

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