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## Copyright (C) 2006 Muthiah Annamalai <muthiah.annamalai@uta.edu>
##
## 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 2 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/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} narysource (@var{probability_dist},@var{n_order})
##
## This function creates a N-ary order source using the given
## @var{probability_dist} (as a column vector) of a 1-order source
## building a probability distribution of size
## len(@var{probability_dist})^@var{order}. Basically
## if you have X-symbol distribution with a N-ary source then we have,
## in the resultant N-ary source with a X^N symbols. The function is equivalent
## to the definitions of a q-ary order source.
##
## @example
## @group
## pdist=[1 2 3 4]./10;
## ndist = narysource(pdist,2)
## @result{} [ 0.010000 0.020000 0.030000 0.040000 0.020000 0.040000 0.060000 0.080000 0.030000 0.060000 0.090000 0.120000 0.040000 0.080000 0.120000 0.160000]
## @end group
## @end example
## @end deftypefn
## @seealso{entropy}
function opdist=narysource(pdist,order)
if(nargin < 2)
error('usage: ndist=narysource(pdist,order_n);')
end
## #Method 1
## opdist=pdist;
## for idx=1:(order-1)
## L=length(opdist);
## ndist=[];
## for idy=1:L
## ndist=[ndist opdist(idy)*[pdist]];
## end
## opdist=ndist;
## end
##
## tic; narysource([1:4]./10,4); toc
## tic; narysource([1:4]./10,10);toc
## #Method 2
L=length(pdist);
opdist=pdist;## 1XN
pdist=pdist';## Nx1
for idx=2:order
opdist=pdist*opdist;## Nx1 * 1XN^k
opdist=reshape(opdist,1,L^idx);## 1xN^(k+1)
end
return
end
%!
%!assert(narysource([1:4]./10,2),[ 0.010000 0.020000 0.030000 0.040000 0.020000 0.040000 0.060000 0.080000 0.030000 0.060000 0.090000 0.120000 0.040000 0.080000 0.120000 0.160000],1e-5);
%!