Fix matlab fft demo: re-add add tool scripts erroneously deleted by eee2ad44.

wrapper/matlab/tools/BitReversalPermutation.m

+function new_index = BitReversalPermutation(index)
+n=length(index);
+
+
+
+if (n == 1)
+   new_index = index; 
+else
+    index1=BitReversalPermutation(index(1:2:end));
+    index2=BitReversalPermutation(index(2:2:end));
+    new_index=[index1,index2];
+end
+
+
+    
+
+end
+

wrapper/matlab/tools/CooleyTukeyFact.m

+function [Fourier,facts] = CooleyTukeyFact(dim)
+%  Cooley-Tukey Factorization of the Fourier Matrix.
+%
+%  [Fourier,facts] = CooleyTukeyFact(dim) factorize the Fourier matrix of dimension dim
+%                    Fourier is the full-storage Fourier matrix
+%                    facts is a cell-array of sparse matrix
+%                    
+%		     Fourier = facts{1}*facts{2}*...*facts{log2(dim)+1}.
+%                    
+%                    warning : dim must be a power of 2
+%                               
+
+%
+%% source http://www.cs.cornell.edu/~bindel/class/cs5220-s10/slides/FFT.pdf
+% 
+%
+%
+% For more information on the FAuST Project, please visit the website of
+% the project :  <http://faust.gforge.inria.fr>
+%
+%% License:
+% Copyright (2016):	Nicolas Bellot,  Luc Le Magoarou, Remi Gribonval
+%			INRIA Rennes, FRANCE
+%			http://www.inria.fr/
+%
+% The FAuST Toolbox is distributed under the terms of the GNU Affero
+% General Public License.
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU Affero General Public License as published
+% by the Free Software Foundation.
+%
+% 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 Affero General Public License for more details.
+%
+% You should have received a copy of the GNU Affero General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%% Contacts:
+%   Nicolas Bellot	: nicolas.bellot@inria.fr
+%	Luc Le Magoarou	: luc.le-magoarou@inria.fr
+%	Remi Gribonval	: remi.gribonval@inria.fr
+%
+%% References:
+% [1]	Le Magoarou L. and Gribonval R., "Flexible multi-layer sparse
+%	approximations of matrices and applications", Journal of Selected
+%	Topics in Signal Processing, 2016.
+%	<https://hal.archives-ouvertes.fr/hal-01167948v1>
+
+nb_fact = log2(dim)+1;
+
+if (floor(nb_fact) ~= nb_fact)
+	error('dim must be a power of 2');
+end
+
+
+facts=cell(1,nb_fact);
+%% init permutation matrix
+index=1:dim;
+new_index = BitReversalPermutation(index);
+P=sparse(index,new_index,ones(1,dim),dim,dim);
+facts{nb_fact}=P;
+
+
+
+for q=1:nb_fact-1
+    L=2^q;
+    r=dim/L;
+    disp([ 'L*r' : num2str(L*r)]);
+    wL=exp(-2*pi*i/L);
+    index=1:L/2;
+    OmegaDiag=wL.^(index-1);
+    Omega=sparse(index,index,OmegaDiag,L/2,L/2);
+    %%Omega=diag(OmegaDiag);
+    Rhs=[speye(L/2) Omega;speye(L/2) -Omega];
+    Aq = kron(speye(r),Rhs);
+    facts{nb_fact-q}=Aq;
+end
+
+
+Fourier = dvp(facts);
+
+
+
+end
+

wrapper/matlab/tools/TransStockhamFact.m

+%% source http://www.cs.cornell.edu/~bindel/class/cs5220-s10/slides/FFT.pdf
+
+function facts = TransStockhamFact(dim)
+%  TransStockham Factorization of the Fourier Matrix.
+%
+%  facts = TransStockhamFact(dim) factorize the Fourier matrix of dimension dim
+%
+%                    facts is a cell-array of sparse matrix where the product represent the Fourier matrix
+%                    
+%
+%                    
+%                    warning : dim must be a power of 2
+%                               
+
+%
+%% source http://www.cs.cornell.edu/~bindel/class/cs5220-s10/slides/FFT.pdf
+% 
+%
+%
+% For more information on the FAuST Project, please visit the website of
+% the project :  <http://faust.gforge.inria.fr>
+%
+%% License:
+% Copyright (2016):	Nicolas Bellot,  Luc Le Magoarou, Remi Gribonval
+%			INRIA Rennes, FRANCE
+%			http://www.inria.fr/
+%
+% The FAuST Toolbox is distributed under the terms of the GNU Affero
+% General Public License.
+% This program is free software: you can redistribute it and/or modify
+% it under the terms of the GNU Affero General Public License as published
+% by the Free Software Foundation.
+%
+% 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 Affero General Public License for more details.
+%
+% You should have received a copy of the GNU Affero General Public License
+% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%
+%% Contacts:
+%   Nicolas Bellot	: nicolas.bellot@inria.fr
+%	Luc Le Magoarou	: luc.le-magoarou@inria.fr
+%	Remi Gribonval	: remi.gribonval@inria.fr
+%
+%% References:
+% [1]	Le Magoarou L. and Gribonval R., "Flexible multi-layer sparse
+%	approximations of matrices and applications", Journal of Selected
+%	Topics in Signal Processing, 2016.
+%	<https://hal.archives-ouvertes.fr/hal-01167948v1>
+nb_fact = 2*log2(dim);
+
+facts=cell(nb_fact,1);
+
+for q=1:nb_fact/2
+    L=2^q;
+    r=dim/L;
+    L_star = L/2;
+    r_star = 2 * r;
+    wL=exp(-2*i*pi/L);
+    index=1:L_star;
+    OmegaDiag=wL.^(index-1);
+    Omega=sparse(index,index,OmegaDiag,L/2,L/2);
+    BL=[speye(L_star) Omega;speye(L_star) -Omega];
+    Aq = kron(speye(r),BL);
+    
+    Id_r_star = speye(r_star);
+    Pi_r_star=Id_r_star(:,[(1:2:r_star),(2:2:r_star)]);
+    Gq = kron(Pi_r_star,speye(L_star));
+    %%nb_fact+2-2*i
+    %%nb_fact+2-2*i-1
+    facts{nb_fact+2-2*q}=Gq;
+    facts{nb_fact+2-2*q-1}=Aq;
+end
+
+
+end
+