slaein(3S)

NAME
     SLAEIN - use inverse iteration to find a right or left eigenvector
     corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix
     H

SYNOPSIS
     SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB,
                        WORK, EPS3, SMLNUM, BIGNUM, INFO )

         LOGICAL        NOINIT, RIGHTV

         INTEGER        INFO, LDB, LDH, N

         REAL           BIGNUM, EPS3, SMLNUM, WI, WR

         REAL           B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )

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

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

     H       (input) REAL array, dimension (LDH,N)
             The upper Hessenberg matrix H.
     LDH     (input) INTEGER
             The leading dimension of the array H.  LDH >= max(1,N).

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

     VR      (input/output) REAL array, dimension (N)
             VI      (input/output) 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       (workspace) REAL array, dimension (LDB,N)

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

     WORK   (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.

     BIGNUM  (input) REAL
             A machine-dependent value close to the overflow threshold.

     INFO    (output) 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.

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

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