test/test_lebesgue.m

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function OK=test_lebesgue
% this is a script showing the ei_detailed construction for a function which
% empirically interpolated turns out to have the worst possible Lebesgue
% constant `\Lambda = \max_{x} \sum_{m=1}^M |\xi_m(x)| = 2^M - 1`
%

descr.maxfuncs = 10;

descr.name = 'Lebesgue-Test';
descr.verbose = 0;
descr.rb_problem_type='LebesgueTest';

[dmodel, rmodel] = gen_models(descr);

model_data = gen_model_data(dmodel);

dummy_arg_generator = SnapshotsGenerator.Random(dmodel, 'dummy', [0 1], true, false);
ei_generator = SnapshotsGenerator.SpaceOpEvals(dmodel, 'ei_bad', dummy_arg_generator, dmodel.local_op, true, false);
ei_plugin    = Greedy.Plugin.EI(ei_generator);
ei_plugin.stop_Mmax        = 3;
ei_plugin.ei_target_error  = 'interpol';
ei_plugin.compute_lebesgue = true;
ei_plugin.use_l2_error     = false;

M_train      = ParameterSampling.Uniform(dmodel.maxfuncs-1);
M_train.init_sample(dmodel);
disp(M_train.sample);
ei_algorithm = Greedy.Algorithm(ei_plugin, M_train);

detailed_data = ei_algorithm.init_basis(rmodel, model_data);
detailed_data = ei_algorithm.basis_extension(rmodel, detailed_data);

OK = (detailed_data.get_field('lebesgue') == detailed_data.get_field('max_lebesgue'));

end