def test_nonuniform_all_with_pickle(self):
for i in range(100):
extents1D = [random.choice(self.extents) for _ in range(1)]
extents2D = [random.choice(self.extents) for _ in range(2)]
extents3D = [random.choice(self.extents) for _ in range(3)]
bases1D = [random.choice(self.bases) for _ in range(1)]
bases2D = [random.choice(self.bases) for _ in range(2)]
bases3D = [random.choice(self.bases) for _ in range(3)]
quadratures1D = [random.choice(self.quadratures) for _ in range(1)]
quadratures2D = [random.choice(self.quadratures) for _ in range(2)]
quadratures3D = [random.choice(self.quadratures) for _ in range(3)]
m1 = Mesh1D(extents1D, bases1D, quadratures1D)
m2 = Mesh2D(extents2D, bases2D, quadratures2D)
m3 = Mesh3D(extents3D, bases3D, quadratures3D)
# Use pickle protocol 2 for Py2 compatibility
m1 = pickle.loads(pickle.dumps(m1, protocol=2))
m2 = pickle.loads(pickle.dumps(m2, protocol=2))
m3 = pickle.loads(pickle.dumps(m3, protocol=2))
self.check_extents(m1, extents1D)
self.check_extents(m2, extents2D)
self.check_extents(m3, extents3D)
self.check_basis(m1, bases1D)
self.check_basis(m2, bases2D)
self.check_basis(m3, bases3D)
self.check_quadrature(m1, quadratures1D)
self.check_quadrature(m2, quadratures2D)
self.check_quadrature(m3, quadratures3D)
def test_collocation_points_chebyshev_gauss(self):
for num_coll_points in range(2, 13):
coefs = np.zeros(num_coll_points + 1)
coefs[-1] = 1.
coll_points_numpy = chebyshev.chebroots(coefs)
mesh = Mesh1D(num_coll_points, Basis.Chebyshev, Quadrature.Gauss)
coll_points_spectre = collocation_points(mesh)
np.testing.assert_allclose(coll_points_numpy, coll_points_spectre,
1e-12, 1e-12)
def test_collocation_points_chebyshev_gauss_lobatto(self):
for num_coll_points in range(2, 13):
coefs = np.zeros(num_coll_points)
coefs[-1] = 1.
coll_points_numpy = np.concatenate(
([-1.], chebyshev.Chebyshev(coefs).deriv().roots(), [1.]))
mesh = Mesh1D(num_coll_points, Basis.Chebyshev,
Quadrature.GaussLobatto)
coll_points_spectre = collocation_points(mesh)
np.testing.assert_allclose(coll_points_numpy, coll_points_spectre,
1e-12, 1e-12)
def test_slices(self):
for dim in range(3):
for basis in self.bases:
for quadrature in self.quadratures:
# the mesh constructor of dimension dim + 1
Mesh = self.Mesh[dim]
extents = [
random.choice(self.extents) for _ in range(dim + 1)
]
mesh = Mesh(extents, basis, quadrature)
self.assertEqual(mesh.slices(), [
Mesh1D(extent, basis, quadrature) for extent in extents
])
def test_modal_to_nodal_matrix_chebyshev(self):
for quadrature in [Quadrature.Gauss, Quadrature.GaussLobatto]:
for num_coll_points in range(2, 13):
mesh = Mesh1D(num_coll_points, Basis.Chebyshev, quadrature)
coll_points = collocation_points(mesh)
mtn_numpy = chebyshev.chebvander(coll_points,
num_coll_points - 1)
mtn_spectre = modal_to_nodal_matrix(mesh)
np.testing.assert_allclose(mtn_spectre, mtn_numpy, 1e-12,
1e-12)
ntm_spectre = nodal_to_modal_matrix(mesh)
np.testing.assert_allclose(np.matmul(mtn_spectre, ntm_spectre),
np.identity(num_coll_points), 1e-12,
1e-12)
def test_nonuniform_extents(self):
for basis in self.bases:
for quadrature in self.quadratures:
for i in range(100):
extents1D = [random.choice(self.extents) for _ in range(1)]
extents2D = [random.choice(self.extents) for _ in range(2)]
extents3D = [random.choice(self.extents) for _ in range(3)]
m1 = Mesh1D(extents1D, basis, quadrature)
m2 = Mesh2D(extents2D, basis, quadrature)
m3 = Mesh3D(extents3D, basis, quadrature)
self.check_extents(m1, extents1D)
self.check_extents(m2, extents2D)
self.check_extents(m3, extents3D)
def test_uniform(self):
for extent in range(12):
for basis in self.bases:
for quadrature in self.quadratures:
m1 = Mesh1D(extent, basis, quadrature)
m2 = Mesh2D(extent, basis, quadrature)
m3 = Mesh3D(extent, basis, quadrature)
self.assertEqual(m1.dim, 1)
self.assertEqual(m2.dim, 2)
self.assertEqual(m3.dim, 3)
self.check_extents(m1, [extent])
self.check_extents(m2, [extent, extent])
self.check_extents(m3, [extent, extent, extent])
self.check_basis(m1, [basis])
self.check_basis(m2, [basis, basis])
self.check_basis(m3, [basis, basis, basis])
self.check_quadrature(m1, [quadrature])
self.check_quadrature(m2, [quadrature, quadrature])
self.check_quadrature(m3,
[quadrature, quadrature, quadrature])