def run_prior_solve():
componentstorage = TestComponentDefinition()
solutionstorage = SpaceTimeComponentSolutionStorage_InMemory()
printstats=True
compute_uncertainties = False
method='EXACT'
compute_sample=False
sample_size=1
compute_prior_sample=True
component = SpaceTimeComponent(componentstorage, solutionstorage, printstats, compute_uncertainties, method, compute_sample, sample_size, compute_prior_sample)
component_solution = component.component_solution()
component_solution.update()
def test_process_observations_compute_sample(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
number_of_samples = 200
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_sample=True,
sample_size=number_of_samples)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertTrue(s.compute_sample)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
numpy.random.seed(0)
s.update()
# In this case we are considering the last iteration of model solving, hence sample should have been stored
computed_sample = s.solutionstorage.state_sample
self.assertEqual((2, number_of_samples), computed_sample.shape)
numpy.random.seed(0)
variate = scipy.random.normal(0.0, 1.0, (2, number_of_samples))
expected_posterior_precision = numpy.array([[13.25, -16.5],
[-16.5, 80.65]])
# check result
numpy.testing.assert_almost_equal(
numpy.dot(variate.T, variate),
numpy.dot(computed_sample.T,
numpy.dot(expected_posterior_precision,
computed_sample)))
def test_process_observations_no_uncertainties(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
sample_size=666)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertFalse(s.compute_uncertainties)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
s.update()
numpy.testing.assert_almost_equal(
s.solutionstorage.state, numpy.array([-0.60697861, 1.78530506]))
# No marginal variances should have been computed at all, same for the sample
self.assertEqual(None, s.solutionstorage.state_marginal_std)
self.assertEqual(None, s.solutionstorage.state_sample)
for time, expected_array in zip([21, 532], [
numpy.array([-1.5 * -0.60697861 + 2.2 * 1.78530506]),
numpy.array([3.3 * 1.78530506])
]):
# Observation at time t=t* should be design matrix for that time multiplied by expected state
numpy.testing.assert_almost_equal(
s.solution_observation_expected_value(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
expected_array)
# In this case we are considering a generical model solving iteration for the model, no marginal variances stored, hence we expect 0. as observation uncertainties
numpy.testing.assert_array_equal(
s.solution_observation_expected_uncertainties(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
0.)
# check samples are zero
numpy.testing.assert_array_equal(
0.,
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(t=time)))
# check default number of samples
self.assertEqual(
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(
t=time)).shape[1], 666)
def test_process_observations_compute_uncertainties(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertTrue(s.compute_uncertainties)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
s.update()
# No sample should have been computed at all
self.assertEqual(None, s.solutionstorage.state_sample)
# In this case we are considering the last iteration of model solving, hence marginal variances should have been stored
expected_marginal_std = numpy.sqrt(
numpy.diag(
numpy.linalg.inv(numpy.array([[13.25, -16.5], [-16.5,
80.65]]))))
numpy.testing.assert_array_almost_equal(
s.solutionstorage.state_marginal_std, expected_marginal_std)
# Now we compute the projection of marginal variances onto the given observations
for time in [532]:
# Observation at time t=t* should be design matrix for that time multiplied by expected state
expected_projection = TestSpaceTimeComponentSolution.TestDesign(
t=time).design_function(expected_marginal_std)
numpy.testing.assert_almost_equal(
s.solution_observation_expected_uncertainties(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
expected_projection)
# check samples are zero
numpy.testing.assert_array_equal(
0.,
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(t=time)))
# check default number of samples
self.assertEqual(
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(
t=time)).shape[1], 1)
