Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - the splitting points with threshold SPLTOL

**SYNOPSIS**

SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO ) IMPLICIT NONE INTEGER INFO, N, NSPLIT REAL SPLTOL, TNRM INTEGER ISPLIT( * ) REAL D( * ), E( * ), E2( * )

**PURPOSE**

Compute the splitting points with threshold SPLTOL. SLARRA sets any "small" off-diagonal elements to zero.

**ARGUMENTS**

N (input) INTEGER The order of the matrix. N > 0. D (input) REAL array, dimension (N) On entry, the N diagonal elements of the tridiagonal matrix T. E (input/output) REAL 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) REAL 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) REAL 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) REAL 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 (version 3.2) April 2011 SLARRA(3lapack)