Mercurial > forge
view main/comm/inst/huffmandict.m @ 2638:d2a6ba4f9e96 octave-forge
huffmandict updated to perform as wanted in the mailing list: with code-words for zero probability symbols, eventhough I wouldnt do it myself, and moreover its 'canonical huffman' which I think warrants this
author | gnumuthu |
---|---|
date | Mon, 09 Oct 2006 16:15:35 +0000 |
parents | d0c7ab30eb58 |
children | 4d910c2b101f |
line wrap: on
line source
## Copyright (C) 2006, Sep 30, 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, write to the Free Software ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA ## ## -*- texinfo -*- ## @deftypefn {Function File} {} huffmandict (@var{symb}, @var{prob}) ## @deftypefnx {Function File} {} huffmandict (@var{symb}, @var{prob}, @var{toggle}) ## @deftypefnx {Function File} {} huffmandict (@var{symb}, @var{prob}, @var{toggle}, @var{minvar}) ## ## Builds a Huffman code, given a probability list. The Huffman codes ## per symbol are output as a list of strings-per-source symbol. A zero ## probability symbol is NOT assigned any codeword as this symbol doesn't ## occur in practice anyway. ## ## @var{toggle} is an optional argument with values 1 or 0, that starts ## building a code based on 1's or 0's, defaulting to 0. Also @var{minvar} ## is a boolean value that is useful in choosing if you want to optimize ## buffer for transmission in the applications of Huffman coding, however ## it doesn't affect the type or average codeword length of the generated ## code. An example of the use of @code{huffmandict} is ## ## @example ## @group ## huffmandict(symbols, [0.5 0.25 0.15 0.1]) => CW(0,10,111,110) ## huffmandict(symbols, 0.25*ones(1,4)) => CW(11,10,01,00) ## ## prob=[0.5 0 0.25 0.15 0.1] ## dict=huffmandict(1:5,[0.5 0 0.25 0.15 0.1],1) ## entropy(prob) ## laverage(dict,prob) ## ## x = [0.20000 0.40000 0.20000 0.10000 0.10000]; ## #illustrates the minimum variance thing. ## huffmandict(1,x,0,true) #min variance tree. ## huffmandict(1,x) #normal huffman tree. ## @end group ## @end example ## ## Reference: Dr.Rao's course EE5351 Digital Video Coding, at UT-Arlington. ## @end deftypefn ## @seealso{huffmandeco, huffmanenco} ## Huffman code algorithm. ## while (uncombined_symbols_remain) ## combine least probable symbols into one with, ## their probability being the sum of the two. ## save this result as a stage at lowest order rung. ## (Moving to lowest position possible makes it non-minimum variance ## entropy coding) ## end ## ## for each (stage) ## Walk the tree we built, and assign each row either 1, ## or 0 of ## end ## ## reverse each symbol, and dump it out. ## function cw_list=huffmandict(sym,source_prob,togglecode,minvar) if nargin < 2 error("Usage: huffman_dict(source_prob,{togglecode 1-0 in code});") elseif nargin < 3 togglecode=0; minvar=0; elseif nargin < 4 minvar=0; end %need to compare to 1 if((sum(source_prob)-1.0) > 1e-7 ) error("source probabilities must add up to 1.0"); end % %need to find & eliminate the zero-probability code words. %in practice we donot need to assign anything to them. Reasoning %being that if_ it doesnt occur why bother saving its value anyway? %--(Oct 9) Actually some experts in the area dont agree to this, %and being a generic implementation we should stick to generating %CW's for_ zero symbols. Why impose a bad implementation? --Muthu % origsource_prob=source_prob; % %sort the list and know the index transpositions. kills the speed O(n^2). % L=length(source_prob); index=[1:L]; for itr1=1:L for itr2=itr1:L if(source_prob(itr1) < source_prob(itr2)) t=source_prob(itr1); source_prob(itr1)=source_prob(itr2); source_prob(itr2)=t; t=index(itr1); index(itr1)=index(itr2); index(itr2)=t; end end end stage_list={}; cw_list{1:L}=[]; stage_curr={}; stage_curr.prob_list=source_prob; stage_curr.sym_list={}; S=length(source_prob); for i=1:S; stage_curr.sym_list{i}=[i]; #cw_list{i}=""; end % % another O(n^2) part. % I=1; while (I<S) L=length(stage_curr.prob_list); nprob=stage_curr.prob_list(L-1)+stage_curr.prob_list(L); nsym=[stage_curr.sym_list{L-1}(1:end),stage_curr.sym_list{L}(1:end)]; %stage_curr; %archive old stage list. stage_list{I}=stage_curr; % %insert the new probability into the list, at the %first-position (greedy?) possible. % for i=1:(L-2) if((minvar && stage_curr.prob_list(i)<=nprob) || \ stage_curr.prob_list(i) < nprob) break; end end stage_curr.prob_list=[stage_curr.prob_list(1:i-1) nprob stage_curr.prob_list(i:L-2)]; stage_curr.sym_list={stage_curr.sym_list{1:i-1}, nsym, stage_curr.sym_list{i:L-2}}; % Loopie I=I+1; end if (togglecode==0) one_cw=1; zero_cw=0; else one_cw=0; zero_cw=1; end % % another O(n^2) part. % %printf("Exit Loop"); I=I-1; while (I>0) stage_curr=stage_list{I}; L=length(stage_curr.sym_list); clist=stage_curr.sym_list{L}; for k=1:length(clist) cw_list{1,clist(k)}=[cw_list{1,clist(k)} one_cw]; end clist=stage_curr.sym_list{L-1}; for k=1:length(clist) cw_list{1,clist(k)}=[cw_list{1,clist(k)}, zero_cw]; end % Loopie I=I-1; end % %zero all the code-words of zero-probability length, 'cos they %never occur. % S=length(source_prob); for itr=(S+1):length(origsource_prob) cw_list{1,itr}=-1; end %disp('Before resorting') %cw_list nw_list{1:L}=[]; % % Re-sort the indices according to the probability list. % L=length(source_prob); for itr=1:(L) t=cw_list{index(itr)}; nw_list{index(itr)}=cw_list{itr}; end cw_list=nw_list; %zero all the code-words of zero-probability length, 'cos they %never occur. %for itr=1:L % if(origsource_prob(itr)==0) % cw_list{itr}=""; % end %end return end %! %!assert(huffmandict(1:4,[0.5 0.25 0.15 0.1],1), {[0],[1 0],[1 1 1],[1 1 0]},0) %!assert(huffmandict(1:4,0.25*ones(1,4),1),{[1 1],[1 0],[0 1],[0 0]},0) %!assert(huffmandict(1:4,[1 0 0 0 ]),{[1],[0 1],[0 0 0],[0 0 1]},0) %!