eop_theta_functional.m

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function y = eop_theta_functional(U, v)
% sim_data.y = eop_theta_functional(sim_data.U, v)
%
% this function realises the evaluation of the functional
% l(P^M;\mu) = -1/|\Omega_0|*int_{\Omega_0}\frac{\partial P^M}{\partial t}(x) dx
% with \Omega_0 being a subset of \Omega.
%
% sim_data being the result of a lin_evol_detailed_simulation and v being
% the riest-representant of the theta-functional aquired via
% [v, ~] = model.operators_output(model, model_data);
% with model.name_output_functional = 'theta'

% Dominik Garmatter 26.03 2012

dP_dt = zeros(size(U,1),size(U,2)-1);
% it is \frac{\partial P}{\partial t}\approx\frac{P^k-P^(k-1)}{\delta t},
% so the following matrix is formed
for i = 1 : size(dP_dt,2)
    dP_dt(:,i) = U(:,i+1) - U(:,i);
end

y = (v(:)') * dP_dt; % evaluates the functional

end