detailed_simulation.m

function sim_data = detailed_simulation(model, model_data)
% DETAILED_SIMULATION
% Perform a detailed simulation, i.e. a high-dimensional solve of the DARE.
%

sim_data = DARE.SimData;

[E,A,B,C,Q,R] = model.assemble(model_data);

t = tic;
if exist('LowRankDARE.m', 'file') && model.n > 30
    sim_data.Z = LowRankDARE(E,A, B, C, Q, R);
else
    if model.n > 100
        warning('Using MATLAB solver dare. This can be slow for large dimensions.')
    end
    
    [P,~,~] = dare(full(A), full(B), full(C'*Q*C), full(R), [], full(E));
    sim_data.P = P;

    [V,D] = svd(sim_data.P, 'econ');
    D = sqrt(diag(D));
    s = sum(D);

    for k = 1:length(D)
        if sum(D(1:k))/s>1-1e-7, break; end
    end

    sim_data.Z = real(V*diag(D));
    sim_data.Z = sim_data.Z(:, 1:k);
end
sim_data.time = toc(t);
sim_data.K = (R + B'*sim_data.Z*sim_data.Z'*B)\B'*sim_data.Z*sim_data.Z'*A;