DLARRA(3f)

NAME
DLARRA - 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