logsumexp.m

function s = logsumexp(x, dim)
% Returns log(sum(exp(x),dim)) while avoiding numerical underflow.
% Default is dim = 1 (columns).
% Written by Mo Chen (mochen@ie.cuhk.edu.hk). March 2009.

% Downloaded from:
% http://www.mathworks.com/matlabcentral/fileexchange/28899-logsumexp/content/logsumexp.m
% 
% Copyright (c) 2010, Michael Chen
% All rights reserved.

% Redistribution and use in source and binary forms, with or without 
% modification, are permitted provided that the following conditions are 
% met:

%     * Redistributions of source code must retain the above copyright 
%       notice, this list of conditions and the following disclaimer.
%     * Redistributions in binary form must reproduce the above copyright 
%       notice, this list of conditions and the following disclaimer in 
%       the documentation and/or other materials provided with the distribution
      
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
% POSSIBILITY OF SUCH DAMAGE.

if nargin == 1, 
    % Determine which dimension sum will use
    dim = find(size(x)~=1,1);
    if isempty(dim), dim = 1; end
end

% subtract the largest in each column
y = max(x,[],dim);
x = bsxfun(@minus,x,y);
s = y + log(sum(exp(x),dim));
i = find(~isfinite(y));
if ~isempty(i)
    s(i) = y(i);
end