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
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