DLARRA(1) LAPACK auxiliary routine (version 3.2) DLARRA(1)NAME
DLARRA - the splitting points with threshold SPLTOL
SYNOPSIS
SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )
IMPLICIT NONE
INTEGER INFO, N, NSPLIT
DOUBLE PRECISION SPLTOL, TNRM
INTEGER ISPLIT( * )
DOUBLE PRECISION D( * ), E( * ), E2( * )
PURPOSE
Compute the splitting points with threshold SPLTOL. DLARRA sets any
"small" off-diagonal elements to zero.
ARGUMENTS
N (input) INTEGER
The order of the matrix. N > 0.
D (input) DOUBLE PRECISION array, dimension (N)
On entry, the N diagonal elements of the tridiagonal matrix T.
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal ele‐
ments 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.
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:
SPLTOL<0 : criterion based on absolute off-diagonal value
SPLTOL>0 : criterion that preserves relative accuracy TNRM
(input) DOUBLE PRECISION The norm of the matrix.
NSPLIT (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
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.
INFO (output) INTEGER
= 0: successful exit
FURTHER DETAILS
Based on contributions by
Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA
Inderjit Dhillon, University of Texas, Austin, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
LAPACK auxiliary routine (versioNovember 2008 DLARRA(1)
