


ZLAEIN(3f)    LAPACK auxiliary routine (version 3.1)   ZLAEIN(3f)


NAME
       ZLAEIN  -  inverse iteration to find a right or left eigenvector corre-
       sponding to the eigenvalue W of a complex upper Hessenberg matrix H

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

           LOGICAL        NOINIT, RIGHTV

           INTEGER        INFO, LDB, LDH, N

           DOUBLE         PRECISION EPS3, SMLNUM

           COMPLEX*16     W

           DOUBLE         PRECISION RWORK( * )

           COMPLEX*16     B( LDB, * ), H( LDH, * ), V( * )

PURPOSE
       ZLAEIN  uses inverse iteration to find a right or left eigenvector cor-
       responding 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*16 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*16
               The eigenvalue of H whose corresponding right or left eigenvec-
               tor is to be computed.

       V       (input/output) COMPLEX*16 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  com-
               ponent of largest magnitude has magnitude 1; here the magnitude
               of a complex number (x,y) is taken to be |x| + |y|.




 LAPACK auxiliary routine November 2006                         1





ZLAEIN(3f)    LAPACK auxiliary routine (version 3.1)   ZLAEIN(3f)


       B       (workspace) COMPLEX*16 array, dimension (LDB,N)

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

       RWORK   (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.

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







































 LAPACK auxiliary routine November 2006                         2


