DLARRE(l)								 )								 DLARRE(l)

NAME

       DLARRE  -  the  tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the
       numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T

SYNOPSIS

       SUBROUTINE DLARRE( N, D, E, TOL, NSPLIT, ISPLIT, M, W, WOFF, GERSCH, WORK, INFO )

	   INTEGER	  INFO, M, N, NSPLIT

	   DOUBLE	  PRECISION TOL

	   INTEGER	  ISPLIT( * )

	   DOUBLE	  PRECISION D( * ), E( * ), GERSCH( * ), W( * ), WOFF( * ), WORK( * )

PURPOSE

       Given the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the  num-
       bers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T. The representations
       and eigenvalues found are then used by DSTEGR to compute the eigenvectors of a symmetric tridiagonal matrix. Currently, the base  represen-
       tations	are  limited  to being positive or negative definite, and the eigenvalues of the definite matrices are found by the dqds algorithm
       (subroutine DLASQ2). As an added benefit, DLARRE also outputs the n Gerschgorin
       intervals for each L_i D_i L_i^T.

ARGUMENTS

       N       (input) INTEGER
	       The order of the matrix.

       D       (input/output) DOUBLE PRECISION array, dimension (N)
	       On entry, the n diagonal elements of the tridiagonal matrix T.  On exit, the n diagonal elements of the diagonal matrices D_i.

       E       (input/output) DOUBLE PRECISION array, dimension (N)
	       On entry, the (n-1) subdiagonal elements of the tridiagonal matrix T; E(N) need not be set.  On exit, the subdiagonal  elements	of
	       the unit bidiagonal matrices L_i.

       TOL     (input) DOUBLE PRECISION
	       The threshold for splitting. If on input |E(i)| < TOL, then the matrix T is split into smaller blocks.

       NSPLIT  (input) INTEGER
	       The number of blocks T splits into. 1 <= NSPLIT <= N.

       ISPLIT  (output) INTEGER array, dimension (2*N)
	       The splitting points, at which T breaks up into submatrices.  The first submatrix consists of rows/columns 1 to ISPLIT(1), the sec-
	       ond 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.

       M       (output) INTEGER
	       The total number of eigenvalues (of all the L_i D_i L_i^T) found.

       W       (output) DOUBLE PRECISION array, dimension (N)
	       The first M elements contain the eigenvalues. The eigenvalues of each of the blocks, L_i D_i L_i^T, are sorted in ascending order.

       WOFF    (output) DOUBLE PRECISION array, dimension (N)
	       The NSPLIT base points sigma_i.

       GERSCH  (output) DOUBLE PRECISION array, dimension (2*N)
	       The n Gerschgorin intervals.

       WORK    (input) DOUBLE PRECISION array, dimension (4*N???)
	       Workspace.

       INFO    (output) INTEGER
	       Output error code from DLASQ2

FURTHER DETAILS

       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA

LAPACK version 3.0						   15 June 2000 							 DLARRE(l)