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  4. dlarra(l)

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DLARRA(1) LAPACK auxiliary routine (version 3.2) DLARRA(1)

NAME

DLARRA - the splitting points with threshold SPLTOL

SYNOPSIS

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

The order of the matrix. N > 0.
On entry, the N diagonal elements of the tridiagonal matrix T.
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.
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.
The number of blocks T splits into. 1 <= NSPLIT <= 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.
= 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

November 2008 LAPACK auxiliary routine (version 3.2)