Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3 - 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
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.

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

FURTHERDETAILS

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 (version 3.2.2)   April 2011                            DLARRA(3lapack)