Home > sgwt_toolbox > sgwt_rough_lmax.m

sgwt_rough_lmax

PURPOSE ^

sgwt_rough_lmax : Rough upper bound on maximum eigenvalue of L

SYNOPSIS ^

function lmax=sgwt_rough_lmax(L)

DESCRIPTION ^

 sgwt_rough_lmax : Rough upper bound on maximum eigenvalue of L
 
 function lmax=sgwt_rough_lmax(L)
 
 Runs Arnoldi algorithm with a large tolerance, then increases
 calculated maximum eigenvalue by 1 percent. For much of the SGWT
 machinery, we need to approximate the wavelet kernels on an
 interval that contains the spectrum of L. The only cost of using
 a larger interval is that the polynomial approximation over the
 larger interval may be a slightly worse approxmation on the
 actual spectrum. As this is a very mild effect, it is not likely
 necessary to obtain very tight bonds on the spectrum of L

 Inputs : 
 L - input graph Laplacian

 Outputs :
 lmax - estimated upper bound on maximum eigenvalue of L

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % sgwt_rough_lmax : Rough upper bound on maximum eigenvalue of L
0002 %
0003 % function lmax=sgwt_rough_lmax(L)
0004 %
0005 % Runs Arnoldi algorithm with a large tolerance, then increases
0006 % calculated maximum eigenvalue by 1 percent. For much of the SGWT
0007 % machinery, we need to approximate the wavelet kernels on an
0008 % interval that contains the spectrum of L. The only cost of using
0009 % a larger interval is that the polynomial approximation over the
0010 % larger interval may be a slightly worse approxmation on the
0011 % actual spectrum. As this is a very mild effect, it is not likely
0012 % necessary to obtain very tight bonds on the spectrum of L
0013 %
0014 % Inputs :
0015 % L - input graph Laplacian
0016 %
0017 % Outputs :
0018 % lmax - estimated upper bound on maximum eigenvalue of L
0019 
0020 % This file is part of the SGWT toolbox (Spectral Graph Wavelet Transform toolbox)
0021 % Copyright (C) 2010, David K. Hammond.
0022 %
0023 % The SGWT toolbox is free software: you can redistribute it and/or modify
0024 % it under the terms of the GNU General Public License as published by
0025 % the Free Software Foundation, either version 3 of the License, or
0026 % (at your option) any later version.
0027 %
0028 % The SGWT toolbox is distributed in the hope that it will be useful,
0029 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0030 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0031 % GNU General Public License for more details.
0032 %
0033 % You should have received a copy of the GNU General Public License
0034 % along with the SGWT toolbox.  If not, see <http://www.gnu.org/licenses/>.
0035 
0036 function lmax=sgwt_rough_lmax(L)
0037 opts=struct('tol',5e-3,'p',10,'disp',0);
0038 lmax=eigs(L,1,'lm',opts);
0039 lmax=lmax*1.01; % just increase by 1 percent to be robust to error

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