redhat man page for dlarre

Query: dlarre

OS: redhat

Section: l

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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 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)
Related Man Pages
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dlarre(3) - centos
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