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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 represen‐
       tations 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  ele‐
       ments  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  representa‐
       tions  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  eigenvec‐
       tors of a symmetric tridiagonal matrix. Currently, the base representa‐
       tions are limited to being positive or negative definite, and  the  ei‐
       genvalues  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 ele‐
	       ments 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 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.

       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)
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