SLAEIN (3lapack)

use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H

SYNOPSIS

  SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK,
                     EPS3, SMLNUM, BIGNUM, INFO )

      LOGICAL        NOINIT, RIGHTV

      INTEGER        INFO, LDB, LDH, N

      REAL           BIGNUM, EPS3, SMLNUM, WI, WR

      REAL           B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )

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.

ARGUMENTS

  RIGHTV   (input) LOGICAL
           = .TRUE. : compute right eigenvector;
           = .FALSE.: compute left eigenvector.

  NOINIT   (input) LOGICAL
           = .TRUE. : no initial vector supplied in (VR,VI).
           = .FALSE.: initial vector supplied in (VR,VI).

  N       (input) INTEGER
          The order of the matrix H.  N >= 0.

  H       (input) REAL array, dimension (LDH,N)
          The upper Hessenberg matrix H.

  LDH     (input) INTEGER
          The leading dimension of the array H.  LDH >= max(1,N).

  WR      (input) REAL
          WI      (input) REAL The real and imaginary parts of the eigenvalue
          of H whose corresponding right or left eigenvector is to be
          computed.

  VR      (input/output) REAL array, dimension (N)
          VI      (input/output) 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       (workspace) REAL array, dimension (LDB,N)

  LDB     (input) INTEGER
          The leading dimension of the array B.  LDB >= N+1.

  WORK   (workspace) REAL array, dimension (N)

  EPS3    (input) REAL
          A small machine-dependent value which is used to perturb close
          eigenvalues, and to replace zero pivots.

  SMLNUM  (input) REAL
          A machine-dependent value close to the underflow threshold.

  BIGNUM  (input) REAL
          A machine-dependent value close to the overflow threshold.

  INFO    (output) 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.