dlarrf man page on YellowDog

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DLARRF(l)			       )			     DLARRF(l)

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

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

	   INTEGER	  IFIRST, ILAST, INFO, N

	   INTEGER	  IWORK( * )

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

PURPOSE
       Given the initial representation L D L^T and its cluster of  close  ei‐
       genvalues  (in  a relative measure), W( IFIRST ), W( IFIRST+1 ), ... W(
       ILAST ), DLARRF 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) DOUBLE PRECISION array, dimension (N)
	       The n diagonal elements of the diagonal matrix D.

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

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

       LLD     (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
	       The shift used to form L(+) D(+) L(+)^T.

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

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

       WORK    (input) DOUBLE PRECISION 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			     DLARRF(l)
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