NAME

       slaein.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM,
           BIGNUM, INFO)
           SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by
           inverse iteration.

Function/Subroutine Documentation

   subroutine slaein (logical RIGHTV, logical NOINIT, integer N, real, dimension( ldh, * ) H,
       integer LDH, real WR, real WI, real, dimension( * ) VR, real, dimension( * ) VI, real,
       dimension( ldb, * ) B, integer LDB, real, dimension( * ) WORK, real EPS3, real SMLNUM,
       real BIGNUM, integer INFO)
       SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by
       inverse iteration.

       Purpose:

            SLAEIN uses inverse iteration to find a right or left eigenvector
            corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI).
                     = .FALSE.: initial vector supplied in (VR,VI).

           N

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

           H

                     H is REAL array, dimension (LDH,N)
                     The upper Hessenberg matrix H.

           LDH

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

           WR

                     WR is REAL

           WI

                     WI is REAL
                     The real and imaginary parts of the eigenvalue of H whose
                     corresponding right or left eigenvector is to be computed.

           VR

                     VR is REAL array, dimension (N)

           VI

                     VI is 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 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

                     B is REAL array, dimension (LDB,N)

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= N+1.

           WORK

                     WORK is REAL array, dimension (N)

           EPS3

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

           SMLNUM

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

           BIGNUM

                     BIGNUM is REAL
                     A machine-dependent value close to the overflow threshold.

           INFO

                     INFO is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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