def test_design_function(self):
spde = SphereMeshSPDE(level=1, sparse_format=SPARSEFORMAT)
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
spde,
n_harmonics=3,
include_local_mean=True)
# Initialise zero state vector
state_vector = numpy.zeros((294, 1))
# Get indices of nonzero design elements
A_simulated = spde.build_A(
TestSeasonalElement.SimulatedObservationStructure(
).location_polar_coordinates())
observation_indices, vertex_indices = A_simulated.sorted_indices(
).nonzero()
# This should select observation 1
state_vector[vertex_indices[3:6], 0] = 1.0
# And this will add 0.309016994375 to it
state_vector[vertex_indices[3:6] + 84, 0] = 1.0
# Apply state vector
y = design.design_function(state_vector)
# Check observation 1 selected with appropriate sum
numpy.testing.assert_almost_equal(
y, numpy.array([[0.0], [1.309016994375]]))
def test_design_number_of_state_parameters(self):
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=1),
n_harmonics=3,
include_local_mean=True)
self.assertEqual(294, design.design_number_of_state_parameters())
def test_isnonlinear(self):
spde = SphereMeshSPDE(level=1, sparse_format=SPARSEFORMAT)
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
spde,
n_harmonics=3,
include_local_mean=True)
self.assertFalse(design.isnonlinear())
def test_design_jacobian(self):
spde = SphereMeshSPDE(level=2, sparse_format=SPARSEFORMAT)
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
spde,
n_harmonics=2,
include_local_mean=False)
A = design.design_matrix()
J = design.design_jacobian(numpy.array([]))
self.assertEqual(SPARSEFORMAT, J.getformat())
numpy.testing.assert_almost_equal(J.todense(), A.todense())
def test_design_matrix(self):
spde = SphereMeshSPDE(level=1, sparse_format=SPARSEFORMAT)
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
spde,
n_harmonics=3,
include_local_mean=True)
A = design.design_matrix()
# Check shape and sparse format
self.assertEqual((2, 294), A.shape)
self.assertEqual(SPARSEFORMAT, A.getformat())
# Check that kronecker expansion worked as expected
numpy.testing.assert_almost_equal(
A[:, 0:42].todense() * 0.951056516295, A[:, 42:84].todense())
numpy.testing.assert_almost_equal(
A[:, 0:42].todense() * -0.809016994375, A[:, 252:294].todense())
def test_build_A_time(self):
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=2),
n_harmonics=3,
include_local_mean=True)
A = design.build_A_time()
# Simulated datetime(1977, 3, 15) is precisely 0.2 through the year (which is 72 degrees of 360 degree cycle)
# Should give coefficients:
# 1.0
# sin(72 degrees)
# cos(72 degrees)
# sin(144 degrees)
# cos(144 degrees)
# sin(216 degrees)
# cos(216 degrees)
numpy.testing.assert_almost_equal(A, [[
1.0, 0.951056516295, 0.309016994375, 0.587785252292,
-0.809016994375, -0.587785252292, -0.809016994375
]])
def test_init(self):
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
SphereMeshSPDE(level=2),
n_harmonics=5,
include_local_mean=True)
self.assertTrue(
isinstance(design.observationstructure,
TestSeasonalElement.SimulatedObservationStructure))
self.assertEqual(2, design.spde.triangulation.level)
self.assertEqual(5, design.n_harmonics)
self.assertEqual(True, design.include_local_mean)
def test_build_A_space(self):
spde = SphereMeshSPDE(level=1, sparse_format=SPARSEFORMAT)
design = SeasonalElementDesign(
TestSeasonalElement.SimulatedObservationStructure(),
spde,
n_harmonics=3,
include_local_mean=True)
A = design.build_A_space()
# 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]])