CLAEIN(3)      LAPACK routine of NEC Numeric Library Collection      CLAEIN(3)



NAME
       CLAEIN

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



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

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

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

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

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

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

           V         (input/output)
                     V is 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         (output)
                     B is COMPLEX array, dimension (LDB,N)

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

           RWORK     (output)
                     RWORK is REAL array, dimension (N)

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

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

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



LAPACK routine                  31 October 2017                      CLAEIN(3)