slarrb(3S)

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

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

         INTEGER        IFIRST, ILAST, INFO, N

         REAL           RELTOL, SIGMA

         INTEGER        IWORK( * )

         REAL           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, SLARRB 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) 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.

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

     RELTOL  (input) REAL
             The relative tolerance.

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

     WERR    (input/output) REAL 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) REAL 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)

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