test_compare_real_error_estimated_error.m

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%% model initialisation

params = [];
params.coarse_factor =  16;
model = advection_fv_output_opt_model(params);

model.rb_init_data_basis = @RB_init_data_basis_lin_evol_opt;









%%compare estimated to real error


%model = advection_fv_output_opt_model([]);


model.RB_stop_Nmax = 15;

model_data = gen_model_data(model);

detailed_data = gen_detailed_data(model, model_data);

save('TestBasis_coarse16.mat','model','detailed_data');

%% Load
load('TestBasis_coarse16.mat');

reduced_data = gen_reduced_data(model, detailed_data);

model = set_mu(model, [0.25,0.25,0.25]);

sim_data_rb = rb_simulation(model, reduced_data);

sim_data_rb = rb_reconstruction(model, detailed_data, sim_data_rb);

sim_data_det = detailed_simulation(model, model_data);


%-----------------
A = model_data.W;

difference = sim_data_rb.U - sim_data_det.U;

sim_data = sim_data_det;
sim_data.U = difference;
plot_sim_data(model, model_data, sim_data, []);

%plot_sim_data(model, model_data, sim_data_det, []);
%plot_sim_data(model, model_data, sim_data_rb, []);

nt = size(sim_data_rb.U,2);
real_error = zeros(1,nt);
for n=1:nt
    real_error(n) = sqrt(difference(:,n)'*A*difference(:,n));
end

t=1:nt;

plot(t, real_error);
hold on;
plot(t,sim_data_rb.Delta);


keyboard;

%% Fehlertest durch hinzufügen von trajektorie

params = [];
params.coarse_factor =  16;
model = advection_fv_output_opt_model(params);

model.rb_init_data_basis = @RB_init_data_basis_lin_evol_opt;


model.RB_stop_Nmax = 15;

model_data = gen_model_data(model);

detailed_data = gen_detailed_data(model, model_data);

model = set_mu(model, [0,1,1]);

reduced_data = gen_reduced_data (model, detailed_data);
sim_data_red = rb_simulation(model, reduced_data);
Delta = sim_data_red.Delta(end);



sim_data = detailed_simulation(model, model_data);
U = sim_data.U;
[phi,S,V] = svds(U,50);

detailed_data.RB = [detailed_data.RB,phi];

reduced_data = gen_reduced_data(model, detailed_data);

sim_data_new = rb_simulation(model, reduced_data);

Delta_new = sim_data_new.Delta(end);

Delta
Delta_new


%% Mit PCA basis generieren


params = [];
params.coarse_factor =  16;
model = advection_fv_output_opt_model(params);

model.RB_generation_mode=  'PCA_trajectories';
M=[0,0,0;0,0,1;0,1,0;1,0,0;0,1,1;1,0,1;1,1,1;1,1,0];

for i = 1:size(M,1)
model.RB_mu_list{i} = M(i,:);
end

model_data = gen_model_data(model);
detailed_data = gen_detailed_data(model, model_data);
save('PCA_basis_coarse16.mat', 'model', 'detailed_data', 'model_data');