def test_design_jacobian(self):
design = LocalDesign(TestLocalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=1))
numpy.testing.assert_equal(
design.design_matrix().todense(),
design.design_jacobian(currentstate=None).todense())
def test_init(self):
obs = TestCombinationElement.SimulatedObservationStructure()
spde = SphereMeshSPDE(0)
design = CombinationDesign(
[GrandMeanDesign(2), LocalDesign(obs, spde)])
self.assertEqual(2, len(design.designlist))
self.assertTrue(isinstance(design.designlist[0], GrandMeanDesign))
self.assertTrue(isinstance(design.designlist[1], LocalDesign))
def test_design_function(self):
# Build design
design = LocalDesign(TestLocalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=1))
# Indices from design matrix indicate vertex weights that produce observation locations
observation_indices, vertex_indices = design.design_matrix(
).sorted_indices().nonzero()
# A vector that is 176.0
# except in location 0 where it is 82.0
# and in location 1 where it is -8.888
statevector = numpy.tile(176.0, (42, 1))
statevector[vertex_indices[0:3]] = 272.0
statevector[vertex_indices[3:6]] = -8.888
# Evaluate this - should get the two numbers back
numpy.testing.assert_almost_equal(design.design_function(statevector),
[[272.0], [-8.888]])
def test_design_matrix(self):
spde = SphereMeshSPDE(level=1)
design = LocalDesign(TestLocalElement.SimulatedObservationStructure(),
spde)
A = design.design_matrix()
# Check sparse format
self.assertEqual(SPARSEFORMAT, A.getformat())
# Shape should be number of obs x number of vertices (basis functions)
self.assertEqual((2, 42), A.shape)
# Two triangles means 6 points are non-zero
self.assertEqual(6, len(A.nonzero()[0]))
# Get and check indices of nonzero design elements
observation_indices, vertex_indices = A.sorted_indices().nonzero()
numpy.testing.assert_equal(observation_indices, [0, 0, 0, 1, 1, 1])
self.assertEqual((6, ), vertex_indices.shape)
# Vertices of observations 0 and 1
# (one row per vertex, one column per coordinate)
vertices0 = spde.triangulation.points[vertex_indices[0:3], :]
vertices1 = spde.triangulation.points[vertex_indices[3:6], :]
# Multiply vertices by the weights from A and sum to get cartesian locations
testpoint0 = A[0, vertex_indices[0:3]] * vertices0
testpoint1 = A[1, vertex_indices[3:6]] * vertices1
# Check results correspond to original polar coordinates
numpy.testing.assert_almost_equal(cartesian_to_polar2d(testpoint0),
[[15.0, -7.0]])
numpy.testing.assert_almost_equal(cartesian_to_polar2d(testpoint1),
[[5.0, 100.0]])
def test_element_states(self):
obs = TestCombinationElement.SimulatedObservationStructure()
spde = SphereMeshSPDE(0)
design = CombinationDesign(
[GrandMeanDesign(obs),
LocalDesign(obs, spde)])
states = design.element_states(
numpy.array([
270.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0,
12.0
]))
self.assertTrue(isinstance(states, list))
self.assertEqual(2, len(states))
numpy.testing.assert_equal(states[0], [270.0])
numpy.testing.assert_equal(
states[1],
[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0])
def test_design_jacobian(self):
obs = TestCombinationElement.SimulatedObservationStructure()
spde = SphereMeshSPDE(1)
design = CombinationDesign(
[GrandMeanDesign(2), LocalDesign(obs, spde)])
# Make a state vector full of a test value 561 which should never actually get accessed
state_vector = numpy.tile(561.0, (47, 1))
J = design.design_jacobian(state_vector)
# A-matrix for comparison
A = spde.build_A(obs.location_polar_coordinates())
# Should have ones at start for global mean
J_expected = numpy.hstack([numpy.array([[1.0], [1.0]]), A.todense()])
# Check as exepcted
self.assertEqual(SPARSEFORMAT, J.getformat())
numpy.testing.assert_equal(J_expected, J.todense())
def test_design_function(self):
obs = TestCombinationElement.SimulatedObservationStructure()
spde = SphereMeshSPDE(1)
design = CombinationDesign(
[GrandMeanDesign(2), LocalDesign(obs, spde)])
A = spde.build_A(obs.location_polar_coordinates())
observation_indices, vertex_indices = A.sorted_indices().nonzero()
# Make a state vector full of a test value 561 which should never actually get accessed
state_vector = numpy.tile(561.0, (47, 1))
# Set the grand mean to 20.0
state_vector[0, 0] = 20.0
# Choose some numbers for observations of interest
state_vector[(vertex_indices[0:3] + 1), 0] = 43.5
state_vector[(vertex_indices[3:6] + 1), 0] = -27.0
# Should end up with (20.0 + 43.5) and (20.0 - 27.0)
y = design.design_function(state_vector)
numpy.testing.assert_almost_equal(y, [[63.5], [-7.0]])
def test_design_number_of_state_parameters(self):
spde = SphereMeshSPDE(level=1)
design = LocalDesign(TestLocalElement.SimulatedObservationStructure(),
spde)
self.assertEqual(42, design.design_number_of_state_parameters())
def test_isnonlinear(self):
design = LocalDesign(TestLocalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=1))
self.assertFalse(design.isnonlinear())