Home > sgwt_toolbox > sgwt_ftsd.m

sgwt_ftsd

PURPOSE ^

sgwt_ftsd : Compute forward transform in spectral domain

SYNOPSIS ^

function r=sgwt_ftsd(f,g,t,L)

DESCRIPTION ^

 sgwt_ftsd : Compute forward transform in spectral domain
 
 function r=sgwt_ftsd(f,g,t,L)

 Compute forward transform by explicitly computing eigenvectors and 
 eigenvalues of graph laplacian

 Uses persistent variables to store eigenvectors, so decomposition
 will be computed only on first call

 Inputs:
 f - input data
 g - sgw kernel
 t - desired wavelet scale
 L - graph laplacian

 Outputs:
 r - output wavelet coefficients

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 % sgwt_ftsd : Compute forward transform in spectral domain
0002 %
0003 % function r=sgwt_ftsd(f,g,t,L)
0004 %
0005 % Compute forward transform by explicitly computing eigenvectors and
0006 % eigenvalues of graph laplacian
0007 %
0008 % Uses persistent variables to store eigenvectors, so decomposition
0009 % will be computed only on first call
0010 %
0011 % Inputs:
0012 % f - input data
0013 % g - sgw kernel
0014 % t - desired wavelet scale
0015 % L - graph laplacian
0016 %
0017 % Outputs:
0018 % r - output wavelet coefficients
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 r=sgwt_ftsd(f,g,t,L)
0037 persistent V D Lold
0038 if (isempty(V) || any(vec(L~=Lold)))
0039   fprintf('Diagonalizing %g x %g L (could take some time ...)\n',size(L,1),size(L,2));
0040   [V,D]=eig(full(L));
0041   Lold=L;
0042 end
0043 lambda=diag(D);
0044 fhat=V'*f;
0045 r=V*(fhat.*g(t*lambda));
0046

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