.TH SLARRA 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME SLARRA - splitting points with threshold SPLTOL .SH SYNOPSIS .TP 19 SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO ) .TP 19 .ti +4 IMPLICIT NONE .TP 19 .ti +4 INTEGER INFO, N, NSPLIT .TP 19 .ti +4 REAL SPLTOL, TNRM .TP 19 .ti +4 INTEGER ISPLIT( * ) .TP 19 .ti +4 REAL D( * ), E( * ), E2( * ) .SH PURPOSE Compute the splitting points with threshold SPLTOL. SLARRA sets any "small" off-diagonal elements to zero. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix. N > 0. .TP 8 D (input) REAL array, dimension (N) On entry, the N diagonal elements of the tridiagonal matrix T. .TP 8 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. .TP 8 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: .br SPLTOL<0 : criterion based on absolute off-diagonal value .br SPLTOL>0 : criterion that preserves relative accuracy TNRM (input) REAL The norm of the matrix. .TP 8 NSPLIT (output) INTEGER The number of blocks T splits into. 1 <= NSPLIT <= N. .TP 8 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. .TP 8 INFO (output) INTEGER = 0: successful exit .SH FURTHER DETAILS Based on contributions by .br Beresford Parlett, University of California, Berkeley, USA Jim Demmel, University of California, Berkeley, USA .br Inderjit Dhillon, University of Texas, Austin, USA .br Osni Marques, LBNL/NERSC, USA .br Christof Voemel, University of California, Berkeley, USA