mdp_computePpolicyPRpolicy(P, R, policy)

function [Ppolicy, PRpolicy] = mdp_computePpolicyPRpolicy(P, R, policy)


% mdp_computePpolicyPRpolicy  Computes the transition matrix and the reward matrix for a policy
% Arguments --------------------------------------------------------------
% Let S = number of states, A = number of actions
%   P(SxSxA)  = transition matrix 
%              P could be an array with 3 dimensions or 
%              a cell array (1xA), each cell containing a matrix (SxS) possibly sparse
%   R(SxSxA) or (SxA) = reward matrix
%              R could be an array with 3 dimensions (SxSxA) or 
%              a cell array (1xA), each cell containing a sparse matrix (SxS) or
%              a 2D array(SxA) possibly sparse  
%   policy(S) = a policy
% Evaluation -------------------------------------------------------------
%   Ppolicy(SxS)  = transition matrix for policy
%   PRpolicy(S)   = reward matrix for policy

% MDPtoolbox: Markov Decision Processes Toolbox
% Copyright (C) 2009  INRA
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%      this list of conditions and the following disclaimer in the documentation 
%      and/or other materials provided with the distribution.
%    * Neither the name of the <ORGANIZATION> nor the names of its contributors 
%      may be used to endorse or promote products derived from this software 
%      without specific prior written permission.
% 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 HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
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if iscell(P)
    A = length(P);
else
    A = size(P,3);
end

for a=1:A % avoid looping over S
    
    ind = find(policy == a); % the rows that use action a
    if ~isempty(ind)
        if iscell(P)
            Ppolicy(ind,:) = P{a}(ind,:);
        else
            Ppolicy(ind,:) = P(ind,:,a);
        end
        PR = mdp_computePR(P,R);
        PRpolicy(ind,1) = PR(ind,a);
    end
end

if issparse(PR)
    PRpolicy = sparse(PRpolicy);
end