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