CLAEIN (3lapack)

use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

SYNOPSIS

  SUBROUTINE CLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3,
                     SMLNUM, INFO )

      LOGICAL        NOINIT, RIGHTV

      INTEGER        INFO, LDB, LDH, N

      REAL           EPS3, SMLNUM

      COMPLEX        W

      REAL           RWORK( * )

      COMPLEX        B( LDB, * ), H( LDH, * ), V( * )

PURPOSE

  CLAEIN uses inverse iteration to find a right or left eigenvector
  corresponding to the eigenvalue W of a complex 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 V
           = .FALSE.: initial vector supplied in V.

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

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

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

  W       (input) COMPLEX
          The eigenvalue of H whose corresponding right or left eigenvector
          is to be computed.

  V       (input/output) COMPLEX array, dimension (N)
          On entry, if NOINIT = .FALSE., V must contain a starting vector for
          inverse iteration; otherwise V need not be set.  On exit, V
          contains the computed eigenvector, 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|.

  B       (workspace) COMPLEX array, dimension (LDB,N)

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

  RWORK   (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.

  INFO    (output) INTEGER
          = 0:  successful exit
          = 1:  inverse iteration did not converge; V is set to the last
          iterate.