redhat man page for slarre

SLARRE(l)								 )								 SLARRE(l)

NAME
       SLARRE  -  the  tridiagonal matrix T, SLARRE 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 SLARRE( N, D, E, TOL, NSPLIT, ISPLIT, M, W, WOFF, GERSCH, WORK, INFO )

	   INTEGER	  INFO, M, N, NSPLIT

	   REAL 	  TOL

	   INTEGER	  ISPLIT( * )

	   REAL 	  D( * ), E( * ), GERSCH( * ), W( * ), WOFF( * ), WORK( * )

PURPOSE
       Given the tridiagonal matrix T, SLARRE 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 SSTEGR 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 SLASQ2). As an added benefit, SLARRE 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) REAL 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) REAL 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) REAL
	       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) REAL 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) REAL array, dimension (N)
	       The NSPLIT base points sigma_i.

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

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

       INFO    (output) INTEGER
	       Output error code from SLASQ2

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

LAPACK version 3.0						   15 June 2000 							 SLARRE(l)