slarra(3) [centos man page]
slarra.f(3) LAPACK slarra.f(3) NAME
slarra.f - SYNOPSIS
Functions/Subroutines subroutine slarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) SLARRA computes the splitting points with the specified threshold. Function/Subroutine Documentation subroutine slarra (integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( * )E2, realSPLTOL, realTNRM, integerNSPLIT, integer, dimension( * )ISPLIT, integerINFO) SLARRA computes the splitting points with the specified threshold. Purpose: Compute the splitting points with threshold SPLTOL. SLARRA sets any "small" off-diagonal elements to zero. Parameters: N N is INTEGER The order of the matrix. N > 0. D D is REAL array, dimension (N) On entry, the N diagonal elements of the tridiagonal matrix T. E E is REAL array, dimension (N) On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched. E2 E2 is REAL array, dimension (N) On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero SPLTOL SPLTOL is REAL The threshold for splitting. Two criteria can be used: SPLTOL<0 : criterion based on absolute off-diagonal value SPLTOL>0 : criterion that preserves relative accuracy TNRM TNRM is REAL The norm of the matrix. NSPLIT NSPLIT is INTEGER The number of blocks T splits into. 1 <= NSPLIT <= N. ISPLIT ISPLIT is INTEGER array, dimension (N) The splitting points, at which T breaks up into blocks. The first block 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. INFO INFO is INTEGER = 0: successful exit Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Contributors: Beresford Parlett, University of California, Berkeley, USA Jim Demmel, University of California, Berkeley, USA Inderjit Dhillon, University of Texas, Austin, USA Osni Marques, LBNL/NERSC, USA Christof Voemel, University of California, Berkeley, USA Definition at line 136 of file slarra.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slarra.f(3)
Check Out this Related Man Page
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)