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dlarrb(l) [redhat man page]

DLARRB(l)								 )								 DLARRB(l)

NAME

       DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,

SYNOPSIS

       SUBROUTINE DLARRB( N, D, L, LD, LLD, IFIRST, ILAST, SIGMA, RELTOL, W, WGAP, WERR, WORK, IWORK, INFO )

	   INTEGER	  IFIRST, ILAST, INFO, N

	   DOUBLE	  PRECISION RELTOL, SIGMA

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION D( * ), L( * ), LD( * ), LLD( * ), W( * ), WERR( * ), WGAP( * ), WORK( * )

PURPOSE

       Given  the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T, W( IFIRST
       ) thru' W( ILAST ), to more accuracy. Intervals [left, right] are maintained by storing their mid-points and semi-widths in  the  arrays  W
       and WERR respectively.

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.

       SIGMA   (input) DOUBLE PRECISION
	       The shift used to form L D L^T (see DLARRF).

       RELTOL  (input) DOUBLE PRECISION
	       The relative tolerance.

       W       (input/output) DOUBLE PRECISION array, dimension (N)
	       On  input,  W( IFIRST ) thru' W( ILAST ) are estimates of the corresponding eigenvalues of L D L^T.  On output, these estimates are
	       ``refined''.

       WGAP    (input/output) DOUBLE PRECISION array, dimension (N)
	       The gaps between the eigenvalues of L D L^T. Very small gaps are changed on output.

       WERR    (input/output) DOUBLE PRECISION array, dimension (N)
	       On input, WERR( IFIRST ) thru' WERR( ILAST ) are the errors in the estimates W( IFIRST ) thru' W( ILAST ).  On  output,	these  are
	       the ``refined'' errors.

       WORK    (input) DOUBLE PRECISION array, dimension (???)
	       Workspace.

       IWORK   (input) INTEGER array, dimension (2*N)
	       Workspace.

       INFO    (output) INTEGER
	       Error flag.

FURTHER DETAILS

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

LAPACK version 3.0						   15 June 2000 							 DLARRB(l)

Check Out this Related 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)
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