claein(3S)

NAME
     CLAEIN - 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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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