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iCAPs/packages/gspbox/utils/gsp_norm_tig.m
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gsp_norm_tig.m
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function [ ntig ] = gsp_norm_tig( G,g, exact,M,param )
%GSP_NORM_TIG Compute the norm of the tig of a frame
% Usage: gsp_norm_tig( G,g );
% gsp_norm_tig( G,g, exact );
%
% Input parameters:
% G : Graph
% g : filterbank
% exact : Exact method (default 1)
% M : Order for the approximation (default 50)
% Output parameters:
% ntig : norm of tig
%
% This function compute the norm of all atoms of the filterbank g.
%
% If exact is set to one, you can compute the norm chunk by chunk by
% setting M to the size of the desired chunk. If M is -1, then
% parpool is used.
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/utils/gsp_norm_tig.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
% Date : 22 December 2014
% Tesing: gsp_test_tig
if nargin<3
exact = 1;
end
if nargin<4
if exact
M = G.N;
else
M = 50;
end
end
if nargin<5
param = struct;
end
if iscell(G)
NG = length(G);
ntig = cell(NG,1);
for ii =1:NG
ntig{ii} = gsp_norm_tig( G{ii},g{ii}, exact,M ,param);
end
return
end
Nf = length(g);
N = G.N;
if exact
if M == -1
if isempty(gcp('nocreate'))
parpool
end
% parfor n = 1:N;
% xin = zeros(N,1);
% xin(n)= 1;
% tig = gsp_vec2mat(gsp_filter_analysis(G,g,xin,param),Nf);
% ntigt = sum(abs(tig).^2);
% ntig(:,n) = reshape(ntigt,Nf,1);
% end
M = abs(M);
N = ceil(G.N / M); % Chunks of M to save runtime memory.
ntig = zeros(Nf,G.N);
ntig2 = zeros(Nf*M,(N-1));
parfor n = 1:(N-1);
xin = zeros(G.N,M);
for ii = 1:M
xin(ii+(n-1)*M,ii)= 1;
end
tig = gsp_vec2mat(gsp_filter_analysis(G,g,xin),Nf);
ntigt = sum(abs(tig).^2);
ntig2(:,n) = reshape(ntigt,Nf*M,1);
end
for n = 1:(N-1)
ntig(:,(1:M)+(n-1)*M) = reshape(ntig2(:,n),Nf,M);
end
M = G.N - M * (N-1);
xin = zeros(G.N,M);
for ii = 1:M
xin(ii+G.N-M,ii) = 1;
end
tig = gsp_vec2mat(gsp_filter_analysis(G,g,xin),Nf);
ntigt = sum(abs(tig).^2);
ntig(:,(end-M+1) : end) = reshape(ntigt,Nf,M);
else
N = ceil(G.N / M); % Chunks of 1000 to save runtime memory.
ntig = zeros(Nf,G.N);
for n = 1:(N-1);
xin = zeros(G.N,M);
for ii = 1:M
xin(ii+(n-1)*M,ii)= 1;
end
tig = gsp_vec2mat(gsp_filter_analysis(G,g,xin,param),Nf);
ntigt = sum(abs(tig).^2);
ntig(:,(1:M)+(n-1)*M) = reshape(ntigt,Nf,M);
end
M = G.N - M * (N-1);
xin = zeros(G.N,M);
for ii = 1:M
xin(ii+G.N-M,ii) = 1;
end
tig = gsp_vec2mat(gsp_filter_analysis(G,g,xin,param),Nf);
ntigt = sum(abs(tig).^2);
ntig(:,(end-M+1) : end) = reshape(ntigt,Nf,M);
end
ntig = ntig';
else
WN = randn(N,M);
filter_WN = gsp_vec2mat(gsp_filter_analysis(G,g,WN,param),Nf);
ntig = sum(abs(filter_WN).^2,3)/M;
end
ntig = sqrt(ntig);
end
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