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_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]])