def test_global_index(self):
double_index = list(FieldSolver.double_index(np.array((9, 10, 6))))
for i in range(7):
for j in range(8):
for k in range(4):
n = i + j * 7 + k * 7 * 8
assert FieldSolver.global_index_in_matrix_to_node_ijk(
n, 9, 10, 6) == (i + 1, j + 1, k + 1)
assert FieldSolver.node_ijk_to_global_index_in_matrix(
i + 1, j + 1, k + 1, 9, 10, 6) == n
assert double_index[n] == (n, i + 1, j + 1, k + 1)
assert list(FieldSolver.double_index(np.array(
(4, 5, 3)))) == [(0, 1, 1, 1), (1, 2, 1, 1), (2, 1, 2, 1),
(3, 2, 2, 1), (4, 1, 3, 1), (5, 2, 3, 1)]
def test_eval_field_from_potential(self):
mesh = SpatialMeshConf((1.5, 2, 1),
(0.5, 1, 1)).make(BoundaryConditionsConf())
mesh.potential = np.stack([
np.array([[0., 0, 0], [1, 2, 3], [4, 3, 2], [4, 4, 4]]),
np.zeros((4, 3))
], -1)
FieldSolver.eval_fields_from_potential(mesh)
expected = np.array([[[[-2, 0, 0], [0, 0, 0]], [[-4, 0, 0], [0, 0, 0]],
[[-6, 0, 0], [0, 0, 0]]],
[[[-4, -1, 1], [0, 0, 1]], [[-3, -1, 2],
[0, 0, 2]],
[[-2, -1, 3], [0, 0, 3]]],
[[[-3, 1, 4], [0, 0, 4]], [[-2, 1, 3], [0, 0, 3]],
[[-1, 1, 2], [0, 0, 2]]],
[[[0, 0, 4], [0, 0, 4]], [[-2, 0, 4], [0, 0, 4]],
[[-4, 0, 4], [0, 0, 4]]]])
assert_array_equal(mesh.electric_field, expected)
def test_construct_equation_matrix_full_domain(self):
mesh = SpatialMeshConf((4, 6, 9),
(1, 2, 3)).make(BoundaryConditionsConf())
solver = FieldSolver(mesh, [])
solver.construct_equation_matrix_in_full_domain(5, 4, 4, 1, 2, 3)
d = -2 * (2 * 2 * 3 * 3 + 3 * 3 + 2 * 2)
x = 2 * 2 * 3 * 3
y = 3 * 3
z = 2 * 2
assert_array_equal(solver.A.toarray(),
[[d, x, 0, y, 0, 0, z, 0, 0, 0, 0, 0],
[x, d, x, 0, y, 0, 0, z, 0, 0, 0, 0],
[0, x, d, 0, 0, y, 0, 0, z, 0, 0, 0],
[y, 0, 0, d, x, 0, 0, 0, 0, z, 0, 0],
[0, y, 0, x, d, x, 0, 0, 0, 0, z, 0],
[0, 0, y, 0, x, d, 0, 0, 0, 0, 0, z],
[z, 0, 0, 0, 0, 0, d, x, 0, y, 0, 0],
[0, z, 0, 0, 0, 0, x, d, x, 0, y, 0],
[0, 0, z, 0, 0, 0, 0, x, d, 0, 0, y],
[0, 0, 0, z, 0, 0, y, 0, 0, d, x, 0],
[0, 0, 0, 0, z, 0, 0, y, 0, x, d, x],
[0, 0, 0, 0, 0, z, 0, 0, y, 0, x, d]])
def test_d2dz2(self):
a = FieldSolver.construct_d2dz2_in_3d(5, 4, 4).toarray()
assert_array_equal(a, [[-2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2]])
def test_zero_nondiag_inside_objects(self):
mesh = SpatialMeshConf((4, 6, 9),
(1, 2, 3)).make(BoundaryConditionsConf())
solver = FieldSolver(mesh, [])
region = InnerRegion('test', Box((1, 2, 3), (1, 2, 3)), 3)
solver.A = csr_matrix(np.full((12, 12), 2))
assert_array_equal(solver.A.toarray(),
[[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]])
solver.zero_nondiag_for_nodes_inside_objects(mesh, [region])
assert_array_equal(solver.A.toarray(),
[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]])
# TODO: check algorithm if on-diagonal zeros should turn into ones
solver.A = csr_matrix(
np.array([[4, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]))
solver.zero_nondiag_for_nodes_inside_objects(mesh, [region])
assert_array_equal(solver.A.toarray(),
[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
def test_init_rhs(self):
mesh = SpatialMeshConf((4, 3, 3)).make(BoundaryConditionsConf())
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(mesh)
assert_array_equal(solver.rhs, np.zeros(3 * 2 * 2))
mesh = SpatialMeshConf((4, 3, 3)).make(BoundaryConditionsConf(-2))
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(mesh)
assert_array_equal(solver.rhs,
[6, 4, 6, 6, 4, 6, 6, 4, 6, 6, 4, 6]) # what
mesh = SpatialMeshConf((4, 4, 5)).make(BoundaryConditionsConf(-2))
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(mesh)
assert_array_equal(solver.rhs, [
6, 4, 6, 4, 2, 4, 6, 4, 6, 4, 2, 4, 2, 0, 2, 4, 2, 4, 4, 2, 4, 2,
0, 2, 4, 2, 4, 6, 4, 6, 4, 2, 4, 6, 4, 6
]) # what
mesh = SpatialMeshConf((8, 12, 5),
(2, 3, 1)).make(BoundaryConditionsConf(-1))
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(mesh)
assert_array_equal(solver.rhs, [
49, 40, 49, 45, 36, 45, 49, 40, 49, 13, 4, 13, 9, 0, 9, 13, 4, 13,
13, 4, 13, 9, 0, 9, 13, 4, 13, 49, 40, 49, 45, 36, 45, 49, 40, 49
])
mesh = SpatialMeshConf((4, 6, 9),
(1, 2, 3)).make(BoundaryConditionsConf())
solver = FieldSolver(mesh, [])
mesh.charge_density = np.array([[[0, 0, 0, 0], [0, 0, 0, 0],
[0, 0, 0, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 1, 2, 0],
[0, -1, 0, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 3, 4, 0],
[0, 0, -1, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 5, 6, 0],
[0, -1, 0, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 0, 0, 0],
[0, 0, 0, 0], [0, 0, 0, 0]]])
solver.init_rhs_vector_in_full_domain(mesh)
assert_allclose(
solver.rhs, -np.array([1, 3, 5, -1, 0, -1, 2, 4, 6, 0, -1, 0]) *
np.pi * 4 * 36)
mesh = SpatialMeshConf((4, 6, 9),
(1, 2, 3)).make(BoundaryConditionsConf())
solver = FieldSolver(mesh, [])
region = InnerRegion('test', Box((1, 2, 3), (1, 2, 3)), 3)
solver.init_rhs_vector(mesh, [region])
assert_array_equal(solver.rhs, [3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0])