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iCAPs/packages/gspbox/operators/gsp_ngwft_frame_matrix.m
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gsp_ngwft_frame_matrix.m
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function [ F ] = gsp_ngwft_frame_matrix(G, g, param)
%GSP_NGWFT_FRAME_MATRIX Create the matrix of the GWFT frame
% Usage: F = gsp_ngwft_frame_matrix(G, g, param);
% F = gsp_ngwft_frame_matrix(G, g);
%
% Input parameters:
% G : Graph
% g : window
% param : Structure of optional parameter
% Output parameters:
% F : Frame
%
% This function compute the graph windowed Fourier transform frame. In
% might require a lot of memory. we create a matrix of size N^2*N.
%
% param a Matlab structure containing the following fields:
%
% param.verbose : 0 no log, 1 print main steps, 2 print all steps.
% By default, it is 1.
%
% Url: http://lts2research.epfl.ch/gsp/doc/operators/gsp_ngwft_frame_matrix.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% AUTHOR : Nathanael Perraudin
% TESTING: test_fast_gwft
% Optional input arguments
if nargin<4, param=struct; end
if ~isfield(param, 'verbose'), param.verbose=1 ; end
if param.verbose && G.N>256
warning('Create a big matrix, you can use other methods.');
end
% Compute the translate of g
ghat=G.U'*g;
Ftrans=sqrt(G.N)*G.U*(repmat(ghat,1,G.N).*G.U');
F = gsp_repmatline(Ftrans,1,G.N) .* ...
repmat(repmat(1./G.U(:,1),1,G.N).*G.U,1,G.N);
% Normalization
F = F./repmat(sqrt(sum(abs(F).^2,1)),G.N,1);
end
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