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slaein

 NAME
      SLAEIN - 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 eigen-
      vector 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 ima-
              ginary parts of the computed complex eigenvector.
              The eigenvector is normalized so that the component
              of largest magnitude has magnitude 1; here the mag-
              nitude 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.