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dlarrf(l) [redhat man page]

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 eigenvalues (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 eige-
	       nalues.	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 elements 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)

Check Out this Related Man Page

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 relative 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 eige-
	       nalues.	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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