def test_init_rhs(self, backend):
mesh = MeshGrid.from_step((4, 3, 3), 1)
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(ArrayOnGrid(mesh),
ArrayOnGrid(mesh))
assert_array_equal(solver.rhs, np.zeros(3 * 2 * 2))
pot = ArrayOnGrid(mesh)
pot.apply_boundary_values(BoundaryConditionsConf(-2))
solver.init_rhs_vector_in_full_domain(ArrayOnGrid(mesh), pot)
assert_array_equal(solver.rhs,
[6, 4, 6, 6, 4, 6, 6, 4, 6, 6, 4, 6]) # what
del solver
mesh = MeshGrid.from_step((4, 4, 5), 1)
pot = ArrayOnGrid(mesh)
pot.apply_boundary_values(BoundaryConditionsConf(-2))
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(ArrayOnGrid(mesh), pot)
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
del solver
mesh = MeshGrid.from_step((8, 12, 5), (2, 3, 1))
pot = ArrayOnGrid(mesh)
pot.apply_boundary_values(BoundaryConditionsConf(-1))
solver = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(ArrayOnGrid(mesh), pot)
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
])
del solver
mesh = MeshGrid.from_step((4, 6, 9), (1, 2, 3))
charge = ArrayOnGrid(mesh)
charge._data = 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 = FieldSolver(mesh, [])
solver.init_rhs_vector_in_full_domain(charge, ArrayOnGrid(mesh))
assert_allclose(
solver.rhs, -np.array([1, 3, 5, -1, 0, -1, 2, 4, 6, 0, -1, 0]) *
np.pi * 4 * 36)
solver = FieldSolver(mesh, [])
nodep = solver.generate_nodes_in_regions(
[InnerRegion('test', Box((1, 2, 3), (1, 2, 3)), 3)])
solver.nodes_in_regions, solver.potential_in_regions = nodep
solver.init_rhs_vector(ArrayOnGrid(mesh), ArrayOnGrid(mesh))
assert_array_equal(solver.rhs, [3, 3, 0, 3, 3, 0, 3, 3, 0, 3, 3, 0])
def test_zero_nondiag_inside_objects(self, backend):
mesh = MeshGrid.from_step((4, 6, 9), (1, 2, 3))
solver = FieldSolver(
mesh, [InnerRegion('test', Box((1, 2, 3), (1, 2, 3)), 3)])
a = scipy.sparse.coo_matrix(np.full((12, 12), 2))
assert_array_equal(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]])
result = solver.zero_nondiag_for_nodes_inside_objects(a)
assert_array_equal(result.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]])
a = scipy.sparse.coo_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]]))
result = solver.zero_nondiag_for_nodes_inside_objects(a)
assert_array_equal(result.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_generate_nodes_in_regions(self, backend):
mesh = MeshGrid.from_step((4, 6, 9), (1, 2, 3))
solver = FieldSolver(mesh, [])
inner_regions = [InnerRegion('test', Box((1, 2, 3), (1, 2, 3)), 3)]
nodes, potential = solver.generate_nodes_in_regions(inner_regions)
assert_array_equal(nodes, [0, 1, 3, 4, 6, 7, 9, 10])
assert_array_equal(potential, [3, 3, 3, 3, 3, 3, 3, 3])
def test_do_init_warnings(self, capsys, caplog):
MeshGrid.from_step((12, 12, 12), (5, 5, 7))
out, err = capsys.readouterr()
assert out == ""
assert err == ""
assert caplog.record_tuples == [
('root', logging.WARNING,
"X step on spatial grid was reduced to 4.000 from 5.000 to fit in a round number of cells."
),
('root', logging.WARNING,
"Y step on spatial grid was reduced to 4.000 from 5.000 to fit in a round number of cells."
),
('root', logging.WARNING,
"Z step on spatial grid was reduced to 6.000 from 7.000 to fit in a round number of cells."
),
]
def __init__(self,
name,
electric_or_magnetic,
field_filename,
xp=numpy,
array_class=ArrayOnGrid):
if not os.path.exists(field_filename):
raise FileNotFoundError("Field file not found")
raw = numpy.loadtxt(field_filename, skiprows=1)
# assume X Y Z Fx Fy Fz columns
# sort by column 0, then 1, then 2
# https://stackoverflow.com/a/38194077
ind = raw[:, 2].argsort() # First sort doesn't need to be stable.
raw = raw[ind]
ind = raw[:, 1].argsort(kind='mergesort')
raw = raw[ind]
ind = raw[:, 0].argsort(kind='mergesort')
raw = raw[ind]
size = (raw[-1, :3] - raw[0, :3])
origin = raw[0, :3]
dist = raw[:, :3] - raw[0, :3]
step = dist.min(axis=0, where=dist > 0, initial=dist.max())
grid = MeshGrid.from_step(size, step, origin)
field = xp.asarray(raw[:, 3:].reshape((*grid.n_nodes, 3)))
super().__init__(name, electric_or_magnetic,
array_class(grid, 3, field))
self.field_filename = field_filename
def test_node_coordinates(self):
coords = np.array([[[[0., 0., 0.], [0., 0., 3.]],
[[0., 1., 0.], [0., 1., 3.]],
[[0., 2., 0.], [0., 2., 3.]]],
[[[2., 0., 0.], [2., 0., 3.]],
[[2., 1., 0.], [2., 1., 3.]],
[[2., 2., 0.], [2., 2., 3.]]],
[[[4., 0., 0.], [4., 0., 3.]],
[[4., 1., 0.], [4., 1., 3.]],
[[4., 2., 0.], [4., 2., 3.]]]])
assert_array_equal(
MeshGrid.from_step((4, 2, 3), (2, 1, 3)).node_coordinates, coords)
assert_array_equal(
MeshGrid.from_step((4, 2, 3), (2, 1, 3),
(1, 2, 3.14)).node_coordinates,
coords + [1, 2, 3.14])
def test_do_init(self):
a = ArrayOnGrid(MeshGrid.from_step((12, 12, 12), (4, 4, 6)))
a.apply_boundary_values(BoundaryConditionsConf(1, 2, 3, 4, 5, 6))
expected = np.array([[[5., 1., 6.], [5., 1., 6.], [5., 1., 6.],
[5., 1., 6.]],
[[5., 3., 6.], [5., 0., 6.], [5., 0., 6.],
[5., 4., 6.]],
[[5., 3., 6.], [5., 0., 6.], [5., 0., 6.],
[5., 4., 6.]],
[[5., 2., 6.], [5., 2., 6.], [5., 2., 6.],
[5., 2., 6.]]])
assert_array_equal(a.data, expected)
def test_transfer_solution_to_spat_mesh(self):
mesh = MeshGrid.from_step((4, 6, 9), (1, 2, 3))
solver = FieldSolver(mesh, [])
solver.phi_vec = np.array(range(1, 3 * 2 * 2 + 1))
potential = ArrayOnGrid(mesh)
solver.transfer_solution_to_spat_mesh(potential)
assert_array_equal(
potential.data[1:-1, 1:-1, 1:-1],
[[[1, 7], [4, 10]], [[2, 8], [5, 11]], [[3, 9], [6, 12]]])
assert_array_equal(
potential.data,
[[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 1, 7, 0], [0, 4, 10, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 2, 8, 0], [0, 5, 11, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 3, 9, 0], [0, 6, 12, 0], [0, 0, 0, 0]],
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]])
def test_construct_equation_matrix(self):
mesh = MeshGrid.from_step((4, 6, 9), (1, 2, 3))
solver = FieldSolver(mesh, [])
solver.construct_equation_matrix()
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_do_init_ranges(self):
with raises(ValueError):
MeshGrid.from_step((10, 20), (2, 1, 3))
with raises(ValueError):
MeshGrid.from_step(((1, 2), 3), (1, 1, 1))
with raises(ValueError):
MeshGrid.from_step((10, 10, 10), [[2, 1, 3], [4, 5, 6], [7, 8, 9]],
BoundaryConditionsConf(3.14))
with raises(ValueError):
MeshGrid.from_step((10, 10, -30), (2, 1, 3))
with raises(ValueError):
MeshGrid.from_step((10, 10, 10), (2, -2, 3))
mesh = MeshGrid.from_step((10, 10, 10), (17, 2, 3))
assert tuple(mesh.cell) == (10, 2, 2.5)
def test_cell(self):
assert_array_equal(MeshGrid(10, 11, 7).cell, (1, 1, 1))
assert_array_equal(
MeshGrid.from_step(10, [1, 2, 4]).cell, [1, 2, 10 / 3])
def test_from_step(self):
assert_dataclass_eq(MeshGrid.from_step(10, 1, 7), MeshGrid(10, 11, 7))
assert_dataclass_eq(MeshGrid.from_step([10, 20, 5], [1, 4, 1]),
MeshGrid([10, 20, 5], [11, 6, 6]))
assert_dataclass_eq(MeshGrid.from_step(10, [1, 2, 4]),
MeshGrid(10, [11, 6, 4]))