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RedHat 9 (Linux i386) - man page for slarre (redhat section l)

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 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. The representa-
       tions and eigenvalues found are then used by SSTEGR to compute the eigenvectors of a  sym-
       metric  tridiagonal matrix. Currently, the base representations are limited to being posi-
       tive 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 Ger-
       schgorin
       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 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) 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)


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