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 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

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