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%    Copyright (c) 2004.  Takayuki Osogami.  All Rights Reserved.   %
%                                                                   %
% Permission to use, copy, modify, and distribute this source code  %
% and its documentation for any purpose, without fee, and without   %
% a written agreement, is hereby granted, provided that the above   %
% copyright notice, this paragraph and the following two paragraphs %
% appear in all copies, modifications, and distributions.           %
% Created by Takayuki Osogami, Department of Computer Science,      %
% Carnegie Mellon University.                                       %
%                                                                   %
% IN NO EVENT SHALL THE AUTHOR BE LIABLE TO ANY PARTY FOR ANY       %
% DAMAGES, INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS   %
% SOURCE CODE AND ITS DOCUMENTATION, EVEN IF THE AUTHOR HAS BEEN    %
% ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.                        %
%                                                                   %
% THE AUTHOR SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,      %
% BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY     %
% AND FITNESS FOR A PARTICULAR PURPOSE.  THE SOURCE CODE AND        %
% ACCOMPANYING DOCUMENTATION, IF ANY, PROVIDED HEREUNDER IS         %
% PROVIDED "AS IS."  THE AUTHOR HAS NO OBLIGATION TO PROVIDE        %
% MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.    %
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%
% Usage: [tau,T] = convolutionofPH(tau1,T1,tau2,T2)
% 
% Given two PH distributions, (tau1,T1) and (tau2,T2),
% the function returns the convolution of the two,
% which is also a PH distribution (tau,T).
%
% author: Takayuki Osogami
%         Department of Computer Science
%         Carnegie Mellon University
%         osogami@cs.cmu.edu
% date: June 6, 2004

function [tau,T] = convolutionofPH(tau1,T1,tau2,T2)

tau0 = 1 - sum(tau1);
if( tau0 == 0 )
  tau = [tau1,zeros(size(tau2))];
else
  tau = [tau1,tau0*tau2];
end

dim1 = size(T1);
e = ones(dim1(1),1);
t = - T1 * e;
dim2 = size(T2);
T = [T1                     t*tau2;
     zeros(dim2(1),dim1(2)) T2     ];