DLARRF(3S)DLARRF(3S)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( * )
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 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).
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DLARRF(3S)DLARRF(3S)
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
eigenalues. 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.
IWORK (input) INTEGER array, dimension (???)
Workspace.
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = 1, IFIRST and ILAST had illegal values
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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