dpfast.m

function [p,q,D,sc] = dpfast(M,C,T,G)
% [p,q,D,sc] = dpfast(M,C,T,G) 
%    Use dynamic programming to find a min-cost path through matrix M.
%    Return state sequence in p,q; full min cost matrix as D and 
%    local costs along best path in sc.
%    This version gives the same results as dp.m, but uses dpcore.mex
%    to run ~200x faster.
%    C is a step matrix, with rows (i step, j step, cost factor)
%    Default is [1 1 1.0;0 1 1.0;1 0 1.0];
%    Another good one is [1 1 1;1 0 1;0 1 1;1 2 2;2 1 2]
%    T selects traceback origin: 0 is to any edge; 1 is top right (default);
%    T > 1 finds path to min of anti-diagonal T points away from top-right.
%    Optional G defines length of 'gulleys' for T=0 mode; default 0.5
%    (i.e. accept path to only 50% of edge nearest top-right)
% 2003-04-04,2005-04-04 dpwe@ee.columbia.edu $Header: /Users/dpwe/projects/dtw/RCS/dpfast.m,v 1.6 2008/03/14 14:40:50 dpwe Exp dpwe $

% Copyright (c) 2003 Dan Ellis <dpwe@ee.columbia.edu>
% released under GPL - see file COPYRIGHT

if nargin < 2
  % Default step / cost matrix
  C = [1 1 1.0;0 1 1.0;1 0 1.0];
end

if nargin < 3
  % Default: path to top-right
  T = 1;
end

if nargin < 4
  % how big are gulleys?
  G = 0.5;  % half the extent
end

if sum(isnan(M(:)))>0
  error('dpwe:dpfast:NAN','Error: Cost matrix includes NaNs');
end

if min(M(:)) < 0
  disp('Warning: cost matrix includes negative values; results may not be what you expect');
end

[r,c] = size(M);

% Core cumulative cost calculation coded as mex
[D,phi] = dpcore(M,C);

p = [];
q = [];

%% Traceback from top left?
%i = r; 
%j = c;

if T == 0
  % Traceback from lowest cost "to edge" (gulleys)
  TE = D(r,:);
  RE = D(:,c);
  % eliminate points not in gulleys
  TE(1:round((1-G)*c)) = max(max(D));
  RE(1:round((1-G)*r)) = max(max(D));
  if (min(TE) < min(RE))
    i = r;
    j = max(find(TE==min(TE)));
  else
    i = max(find(RE==min(RE)));
    j = c;
  end
else
  if min(size(D)) == 1
    % degenerate D has only one row or one column - messes up diag
    i = r;
    j = c;
  else
    % Traceback from min of antidiagonal
    %stepback = floor(0.1*c);
    stepback = T;
    slice = diag(fliplr(D),-(r-stepback));
    [mm,ii] = min(slice);
    i = r - stepback + ii;
    j = c + 1 - ii;
  end
end

p=i;
q=j;

sc = M(p,q);

while i > 1 || j > 1

  %disp(['i=',num2str(i),' j=',num2str(j)]);
  tb = phi(i,j);
  i = i - C(tb,1);
  j = j - C(tb,2);
  
  p = [i,p];
  q = [j,q];
  sc = [M(i,j),sc];
end