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RedHat 9 (Linux i386) - man page for slarrf (redhat section l)

SLARRF(l)					)					SLARRF(l)

NAME
       SLARRF  -  the  initial	representation L D L^T and its cluster of close eigenvalues (in a
       relative measure), W( IFIRST ), W( IFIRST+1 ), ..

SYNOPSIS
       SUBROUTINE SLARRF( N, D, L, LD, LLD, IFIRST, ILAST, W, DPLUS, LPLUS, WORK, IWORK, INFO )

	   INTEGER	  IFIRST, ILAST, INFO, N

	   INTEGER	  IWORK( * )

	   REAL 	  D( * ), DPLUS( * ), L( * ), LD( * ), LLD( * ), LPLUS(  *  ),	W(  *  ),
			  WORK( * )

PURPOSE
       Given  the initial representation L D L^T and its cluster of close eigenvalues (in a rela-
       tive measure), W( IFIRST ), W( IFIRST+1 ), ... W( ILAST ), SLARRF finds a  new  relatively
       robust  representation  L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
       eigenvalues of L(+) D(+) L(+)^T is relatively isolated.

ARGUMENTS
       N       (input) INTEGER
	       The order of the matrix.

       D       (input) REAL array, dimension (N)
	       The n diagonal elements of the diagonal matrix D.

       L       (input) REAL array, dimension (N-1)
	       The (n-1) subdiagonal elements of the unit bidiagonal matrix L.

       LD      (input) REAL array, dimension (N-1)
	       The n-1 elements L(i)*D(i).

       LLD     (input) REAL array, dimension (N-1)
	       The n-1 elements L(i)*L(i)*D(i).

       IFIRST  (input) INTEGER
	       The index of the first eigenvalue in the cluster.

       ILAST   (input) INTEGER
	       The index of the last eigenvalue in the cluster.

       W       (input/output) REAL array, dimension (N)
	       On input, the eigenvalues of L D L^T in ascending order.  W( IFIRST )  through  W(
	       ILAST  )  form the cluster of relatively close eigenalues.  On output, W( IFIRST )
	       thru' W( ILAST ) are estimates of  the  corresponding  eigenvalues  of  L(+)  D(+)
	       L(+)^T.

       SIGMA   (input) REAL
	       The shift used to form L(+) D(+) L(+)^T.

       DPLUS   (output) REAL array, dimension (N)
	       The n diagonal elements of the diagonal matrix D(+).

       LPLUS   (output) REAL array, dimension (N)
	       The  first  (n-1)  elements  of LPLUS contain the subdiagonal elements of the unit
	       bidiagonal matrix L(+). LPLUS( N ) is set to SIGMA.

       WORK    (input) REAL array, dimension (???)
	       Workspace.

FURTHER DETAILS
       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0			   15 June 2000 				SLARRF(l)


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