DLARRB man page on IRIX

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DLARRB(3S)							    DLARRB(3S)

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( * )

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
     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).

									Page 1

DLARRB(3S)							    DLARRB(3S)

     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

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

     This man page is available only online.

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