% Example demonstrates how to optimize Relative Entropy with linear
% constraints using Riskprog subroutine.
% Discrete distribution with 100,000 atoms (variables) is estimated.

clear;
% load data 
load 'Data_CS_Entropyr';

% set number of variables for result verification
I = 100000;

% set solver parameters in internal structure "stroptions".
stroptions.Linearization = 'On';
stroptions.Precision = 9;
stroptions.Solver = 'BULDOZER';

% optimize problem
[p_res, fval, status, output] = riskprog ('entropyr', [], p', [],[],[],[],[], Aeq , beq, lb,[], '', stroptions);

% timing
fprintf('Data loading time = %f sec.\n', output.data_loading_time);
fprintf('Preprocessing time = %f sec.\n', output.preprocessing_time);
fprintf('Solving time = %f sec.\n', output.solving_time);

% display optimization result
fprintf('Objective value from Riskprog = %.10f\n', fval);

% verify result
val_optimal = 0.0;
for i=1:I
    val_optimal = val_optimal + p_res(i)*log(p_res(i)/p(i));
end

% display verification result 
fprintf('Objective calculated for verification = %.10f\n', val_optimal);


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