.TH DLARRA 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
DLARRA - splitting points with threshold SPLTOL
.SH SYNOPSIS
.TP 19
SUBROUTINE DLARRA(
N, D, E, E2, SPLTOL, TNRM,
NSPLIT, ISPLIT, INFO )
.TP 19
.ti +4
IMPLICIT
NONE
.TP 19
.ti +4
INTEGER
INFO, N, NSPLIT
.TP 19
.ti +4
DOUBLE
PRECISION SPLTOL, TNRM
.TP 19
.ti +4
INTEGER
ISPLIT( * )
.TP 19
.ti +4
DOUBLE
PRECISION D( * ), E( * ), E2( * )
.SH PURPOSE
Compute the splitting points with threshold SPLTOL.
DLARRA sets any "small" off-diagonal elements to zero.
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The order of the matrix. N > 0.
.TP 8
D (input) DOUBLE PRECISION array, dimension (N)
On entry, the N diagonal elements of the tridiagonal
matrix T.
.TP 8
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal
elements of the tridiagonal matrix T; E(N) need not be set.
On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
are set to zero, the other entries of E are untouched.
.TP 8
E2 (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the first (N-1) entries contain the SQUARES of the
subdiagonal elements of the tridiagonal matrix T;
E2(N) need not be set.
On exit, the entries E2( ISPLIT( I ) ),
1 <= I <= NSPLIT, have been set to zero
SPLTOL (input) DOUBLE PRECISION
The threshold for splitting. Two criteria can be used:
.br
SPLTOL<0 : criterion based on absolute off-diagonal value
.br
SPLTOL>0 : criterion that preserves relative accuracy
TNRM (input) DOUBLE PRECISION
The norm of the matrix.
.TP 8
NSPLIT (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
.TP 8
ISPLIT (output) INTEGER array, dimension (N)
The splitting points, at which T breaks up into blocks.
The first block consists of rows/columns 1 to ISPLIT(1),
the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
etc., and the NSPLIT-th consists of rows/columns
ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
.TP 8
INFO (output) INTEGER
= 0: successful exit
.SH FURTHER DETAILS
Based on contributions by
.br
Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
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Inderjit Dhillon, University of Texas, Austin, USA
.br
Osni Marques, LBNL/NERSC, USA
.br
Christof Voemel, University of California, Berkeley, USA