/usr/share/octave/packages/communications-1.1.1/shannonfanodict.m is in octave-communications-common 1.1.1-1.
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##
## 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/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} shannonfanodict (@var{symbols},@var{symbol_probabilites})
##
## Returns the code dictionary for source using shanno fano algorithm.
## Dictionary is built from @var{symbol_probabilities} using the shannon
## fano scheme. Output is a dictionary cell-array, which
## are codewords, and correspond to the order of input probability.
##
## @example
## @group
## CW=shannonfanodict(1:4,[0.5 0.25 0.15 0.1]);
## assert(redundancy(CW,[0.5 0.25 0.15 0.1]),0.25841,0.001)
## shannonfanodict(1:5,[0.35 0.17 0.17 0.16 0.15])
## shannonfanodict(1:8,[8 7 6 5 5 4 3 2]./40)
## @end group
## @end example
## @end deftypefn
## @seealso{shannonfanoenc, shannonfanodec}
##
function cw_list=shannonfanodict(symbol,P)
if nargin < 2
error('Usage: shannonfanodict(symbol,P); see help');
end
DMAX=length(P);
S=1:DMAX;
if(sum(P)-1.000 > 1e-7)
error('Sum of probabilities must be 1.000');
end
#
#FIXME: Is there any other way of doing the
#topological sort? Insertion sort is bad.
#
#Sort the probability list in
#descending/non-increasing order.
#Using plain vanilla insertion sort.
#
for i=1:DMAX
for j=i:DMAX
if(P(i) < P(j))
#Swap prob
t=P(i);
P(i)=P(j);
P(j)=t;
#Swap symb
t=S(i);
S(i)=S(j);
S(j)=t;
end
end
end
#Now for each symbol you need to
#create code as first [-log p(i)] bits of
#cumulative function sum(p(1:i))
#
#printf("Shannon Codes\n");
#data_table=zeros(1,DMAX);
cw_list={};
for itr=1:DMAX
if(P(itr)~=0)
digits=ceil(-log2(P(itr))); #somany digits needed.
else
digits=0; #dont assign digits for zero probability symbols.
end
Psum = sum([0 P](1:itr)); #Cumulative probability
s=[];
for i=1:digits;
Psum=2*Psum;
if(Psum >= 1.00)
s=[s 1];
Psum=Psum-1.00;
else
s=[s 0];
end
end
cw_list{itr}=s;
end
#re-arrange the list accroding to input prob list.
cw_list2={};
for i=1:length(cw_list)
cw_list2{i}=cw_list{S(i)};
end
cw_list=cw_list2;
return;
end
%!shared CW,P
%!test
%! P = [0.5 0.25 0.15 0.1];
%! assert(shannonfanodict(1:4,P),{[0],[1 0],[1 1 0],[1 1 1 0]})
%!
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