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

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