NAME

       zlaein.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlaein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO)
           ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by
           inverse iteration.

Function/Subroutine Documentation

   subroutine zlaein (logical RIGHTV, logical NOINIT, integer N, complex*16, dimension( ldh, * )
       H, integer LDH, complex*16 W, complex*16, dimension( * ) V, complex*16, dimension( ldb, *
       ) B, integer LDB, double precision, dimension( * ) RWORK, double precision EPS3, double
       precision SMLNUM, integer INFO)
       ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by
       inverse iteration.

       Purpose:

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

       Parameters:
           RIGHTV

                     RIGHTV is LOGICAL
                     = .TRUE. : compute right eigenvector;
                     = .FALSE.: compute left eigenvector.

           NOINIT

                     NOINIT is LOGICAL
                     = .TRUE. : no initial vector supplied in V
                     = .FALSE.: initial vector supplied in V.

           N

                     N is INTEGER
                     The order of the matrix H.  N >= 0.

           H

                     H is COMPLEX*16 array, dimension (LDH,N)
                     The upper Hessenberg matrix H.

           LDH

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

           W

                     W is COMPLEX*16
                     The eigenvalue of H whose corresponding right or left
                     eigenvector is to be computed.

           V

                     V is 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 component of largest magnitude has magnitude 1; here
                     the magnitude of a complex number (x,y) is taken to be
                     |x| + |y|.

           B

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

           LDB

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

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N)

           EPS3

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

           SMLNUM

                     SMLNUM is DOUBLE PRECISION
                     A machine-dependent value close to the underflow threshold.

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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