/usr/share/octave/packages/communications-1.2.1/shannonfanodict.m is in octave-communications-common 1.2.1-2.
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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 Shannon-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
## @seealso{shannonfanoenc, shannonfanodec}
## @end deftypefn
function cw_list = shannonfanodict (symbol, P)
if (nargin != 2)
print_usage ();
endif
DMAX = length (P);
S = 1:DMAX;
if (sum (P) - 1.000 > 1e-7)
error ("shannonfanodict: the elements of P must add up to 1");
endif
##
## 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;
endif
endfor
endfor
## 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.
endif
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];
endif
endfor
cw_list{itr} = s;
endfor
## re-arrange the list accroding to input prob list.
cw_list2 = {};
for i = 1:length (cw_list)
cw_list2{i} = cw_list{S(i)};
endfor
cw_list = cw_list2;
endfunction
%!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]})
%% Test input validation
%!error shannonfanodict ()
%!error shannonfanodict (1)
%!error shannonfanodict (1, 2, 3)
%!error shannonfanodict (1, [0.5 0.5 0.5])
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