def test_derivative(self):
"""Check that numerical and analytical derivatives of Q match."""
full_resolution_level = 4
neighbourhood_level = 2
full_spde = SphereMeshSPDE(level=full_resolution_level)
active_triangles = full_spde.neighbours_at_level(
neighbourhood_level, 0)
spde = SphereMeshView(full_resolution_level, active_triangles)
Q = spde.build_Q_stationary(numpy.log(1.0), numpy.log(1.0), 2)
epsilon = 0.000001
expected_dQ0 = \
((spde.build_Q_stationary(numpy.log(1.0)+epsilon, numpy.log(1.0), 2) -
spde.build_Q_stationary(numpy.log(1.0)-epsilon, numpy.log(1.0), 2)) / (2.0 * epsilon)).todense()
expected_dQ1 = \
((spde.build_Q_stationary(numpy.log(1.0), numpy.log(1.0)+epsilon, 2) -
spde.build_Q_stationary(numpy.log(1.0), numpy.log(1.0)-epsilon, 2)) / (2.0 * epsilon)).todense()
dQ0 = spde.build_dQdp_stationary(numpy.log(1.0), numpy.log(1.0), 2,
0).todense()
dQ1 = spde.build_dQdp_stationary(numpy.log(1.0), numpy.log(1.0), 2,
1).todense()
# print numpy.abs(dQ0 - expected_dQ0).ravel().max() / numpy.abs(expected_dQ0).ravel().max()
# print numpy.abs(dQ1 - expected_dQ1).ravel().max() / numpy.abs(expected_dQ1).ravel().max()
numpy.testing.assert_almost_equal(dQ0, expected_dQ0, decimal=7)
numpy.testing.assert_almost_equal(dQ1, expected_dQ1, decimal=7)
def mesh_neighbour_demo():
import advanced_standard.stats.spde.convex
import matplotlib.pyplot as plt
spde_level = 3
neighbour_level = 1
region_centre_index = 0
my_spde = SphereMeshSPDE(level=spde_level, project_onto_sphere=True)
in_indices = my_spde.neighbours_at_level(neighbour_level,
region_centre_index)
vertex_indices = np.unique(my_spde.triangulation.triangles[in_indices,
1:].ravel())
convex_mesh_triangulation = advanced_standard.stats.spde.convex.ConvexMeshSPDE(
my_spde.triangulation.vertices[vertex_indices, :])
convex_mesh_triangulation.plot_triangles(linewidths=0.5)
#my_spde.plot_triangles()
my_spde = SphereMeshSPDE(level=neighbour_level, project_onto_sphere=True)
in_indices = my_spde.neighbours_at_level(neighbour_level,
region_centre_index)
vertex_indices = np.unique(my_spde.triangulation.triangles[in_indices,
1:].ravel())
ax = plt.gca()
convex_mesh_triangulation = advanced_standard.stats.spde.convex.ConvexMeshSPDE(
my_spde.triangulation.vertices[vertex_indices, :])
convex_mesh_triangulation.plot_triangles(colors='r', ax=ax, linewidths=1.0)
centre_vertex_indices = np.unique(
my_spde.triangulation.triangles[region_centre_index, 1:].ravel())
centre_vertex_triangulation = advanced_standard.stats.spde.convex.ConvexMeshSPDE(
my_spde.triangulation.vertices[centre_vertex_indices, :])
centre_vertex_triangulation.plot_triangles(colors='b',
ax=ax,
linewidths=1.5)
plt.show()
def __init__(self,
level,
neighbourhood_level,
centre_index_at_level,
sparse_format='csr'):
full_sphere = SphereMeshSPDE(level)
active_triangle_indices = full_sphere.neighbours_at_level(
neighbourhood_level=neighbourhood_level,
centre_index_at_level=centre_index_at_level)
super(SphereMeshViewLocal, self).__init__(level,
active_triangle_indices,
sparse_format=sparse_format)