DLARRB(3S)DLARRB(3S)NAMEDLARRB - 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).
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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 ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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