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

      LOGICAL        NOINIT, RIGHTV

      INTEGER        INFO, LDB, LDH, N

      DOUBLE         PRECISION BIGNUM, EPS3, SMLNUM, WI, WR

      DOUBLE         PRECISION B( LDB, * ), H( LDH, * ), VI( * ), VR( * ),
                     WORK( * )

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.

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

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

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

  WORK   (workspace) DOUBLE PRECISION array, dimension (N)

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

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

  BIGNUM  (input) DOUBLE PRECISION
          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.