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shannonfanodict.m

## 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} {} 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=;
       Psum=Psum-1.00;
       else
       s=;
       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  = ;
%!  assert(shannonfanodict(1:4,P),{,,,})
%!

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