function Vpolicy = mdp_eval_policy_matrix(P, R, discount, policy)


% mdp_eval_policy_matrix    Evaluation of the value function of 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  
%   discount = discount rate in ]0; 1[
%   policy(S) = a policy
% Evaluation -------------------------------------------------------------
%   Vpolicy(S) = value function of the 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 
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%    * Neither the name of the <ORGANIZATION> nor the names of its contributors 
%      may be used to endorse or promote products derived from this software 
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 
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% check of arguments
if iscell(P); S = size(P{1},1); else S = size(P,1); end;
if discount <= 0 || discount >= 1
    disp('--------------------------------------------------------')
    disp('MDP Toolbox ERROR: Discount rate must be in ]0; 1[')
    disp('--------------------------------------------------------')
elseif size(policy,1)~=S || any(mod(policy,1)) || any(policy<1) || any(policy>S)
    disp('--------------------------------------------------------')
    disp('MDP Toolbox ERROR: policy must be a (1xS) vector with integer from 1 to S')
    disp('--------------------------------------------------------')
else
        
    [Ppolicy, PRpolicy] = mdp_computePpolicyPRpolicy(P, R, policy);
 
    % V = PR + gPV  => (I-gP)V = PR  => V = inv(I-gP)*PR
    Vpolicy = (speye(S,S) - discount*Ppolicy) \ PRpolicy;

end
