def test_boundary_interpolation_2d():
"""test boundary interpolation for 2d fields"""
grid = CartesianGrid([[0.1, 0.3], [-2, 3]], [3, 3])
field = ScalarField.random_normal(grid)
# test boundary interpolation
bndry_val = np.random.randn(3)
for bndry in grid._iter_boundaries():
val = field.get_boundary_values(*bndry, bc={"value": bndry_val})
np.testing.assert_allclose(val, bndry_val)
def test_interpolation_to_grid_fields():
""" test whether data is interpolated correctly for different fields """
grid = CartesianGrid([[0, 2 * np.pi]] * 2, 6)
grid2 = CartesianGrid([[0, 2 * np.pi]] * 2, 8)
vf = VectorField.from_expression(grid, ["sin(y)", "cos(x)"])
sf = vf[0] # test extraction of fields
fc = FieldCollection([sf, vf])
for f in [sf, vf, fc]:
f2 = f.interpolate_to_grid(grid2, method="numba")
f3 = f2.interpolate_to_grid(grid, method="numba")
np.testing.assert_allclose(f.data, f3.data, atol=0.2, rtol=0.2)
def test_smoothing():
"""test smoothing on different grids"""
for grid in [
CartesianGrid([[-2, 3]], 4),
UnitGrid(7, periodic=False),
UnitGrid(7, periodic=True),
]:
f1 = ScalarField.random_uniform(grid)
sigma = 0.5 + np.random.random()
# this assumes that the grid periodicity is the same for all axes
mode = "wrap" if grid.periodic[0] else "reflect"
s = sigma / grid.typical_discretization
expected = ndimage.gaussian_filter(f1.data, sigma=s, mode=mode)
out = f1.smooth(sigma)
np.testing.assert_allclose(out.data, expected)
out.data = 0 # reset data
f1.smooth(sigma, out=out).data
np.testing.assert_allclose(out.data, expected)
# test one simple higher order smoothing
tf = Tensor2Field.random_uniform(grid)
assert tf.data.shape == tf.smooth(1).data.shape
# test in-place smoothing
g = UnitGrid([8, 8])
f1 = ScalarField.random_normal(g)
f2 = f1.smooth(3)
f1.smooth(3, out=f1)
np.testing.assert_allclose(f1.data, f2.data)
def test_scalars():
"""test some scalar fields"""
grid = CartesianGrid([[0.1, 0.3], [-2, 3]], [3, 4])
s1 = ScalarField(grid, np.full(grid.shape, 1))
s2 = ScalarField(grid, np.full(grid.shape, 2))
assert s1.average == pytest.approx(1)
assert s1.magnitude == pytest.approx(1)
s3 = s1 + s2
assert s3.grid == grid
np.testing.assert_allclose(s3.data, 3)
s1 += s2
np.testing.assert_allclose(s1.data, 3)
s2 = FieldBase.from_state(s1.attributes, data=s1.data)
assert s1 == s2
assert s1.grid is s2.grid
attrs = ScalarField.unserialize_attributes(s1.attributes_serialized)
s2 = FieldBase.from_state(attrs, data=s1.data)
assert s1 == s2
assert s1.grid is not s2.grid
# test options for plotting images
if module_available("matplotlib"):
s1.plot(transpose=True, colorbar=True)
s3 = ScalarField(grid, s1)
assert s1 is not s3
assert s1 == s3
assert s1.grid is s3.grid
# multiplication with numpy arrays
arr = np.random.randn(*grid.shape)
np.testing.assert_allclose((arr * s1).data, (s1 * arr).data)
def test_get_length_scale():
"""test determining the length scale"""
grid = CartesianGrid([[0, 8 * np.pi]], 64, periodic=True)
c = ScalarField(grid, np.sin(grid.axes_coords[0]))
for method in ["structure_factor_mean", "structure_factor_maximum"]:
s = image_analysis.get_length_scale(c, method=method)
assert s == pytest.approx(2 * np.pi, rel=0.1)
def test_localization_perturbed_3d(periodic):
"""tests localization of perturbed 3d droplets"""
size = 8
pos = np.random.uniform(-2, 2, size=3)
radius = np.random.uniform(2, 3)
width = np.random.uniform(0.5, 1.5)
ampls = np.random.uniform(-0.01, 0.01, size=3)
d1 = PerturbedDroplet3D(pos, radius, interface_width=width, amplitudes=ampls)
a = np.random.random(3) - size / 2
b = np.random.random(3) + size / 2
grid = CartesianGrid(np.c_[a, b], 2 * size, periodic=periodic)
assert grid.dim == 3
field = d1.get_phase_field(grid)
emulsion = image_analysis.locate_droplets(field, refine=True, modes=d1.modes)
assert len(emulsion) == 1
d2 = emulsion[0]
msg = "size=%d, periodic=%s, %s != %s" % (size, periodic, d1, d2)
np.testing.assert_almost_equal(d1.position, d2.position, decimal=1, err_msg=msg)
assert d1.radius == pytest.approx(d2.radius, rel=1e-4)
assert d1.interface_width == pytest.approx(d2.interface_width, rel=1e-3)
np.testing.assert_allclose(
d1.amplitudes[3:], d2.amplitudes[3:], rtol=0.5, err_msg=msg
)
def test_poisson_solver_1d():
""" test the poisson solver on 1d grids """
# solve Laplace's equation
grid = UnitGrid([4])
field = ScalarField(grid)
res = field.solve_poisson([{"value": -1}, {"value": 3}])
np.testing.assert_allclose(res.data, grid.axes_coords[0] - 1)
res = field.solve_poisson([{"value": -1}, {"derivative": 1}])
np.testing.assert_allclose(res.data, grid.axes_coords[0] - 1)
# test Poisson equation with 2nd Order BC
res = field.solve_poisson([{"value": -1}, "extrapolate"])
# solve Poisson's equation
grid = CartesianGrid([[0, 1]], 4)
field = ScalarField(grid, data=1)
res = field.copy()
field.solve_poisson([{"value": 1}, {"derivative": 1}], out=res)
xs = grid.axes_coords[0]
np.testing.assert_allclose(res.data, 1 + 0.5 * xs**2, rtol=1e-2)
# test inconsistent problem
field.data = 1
with pytest.raises(RuntimeError, match="Neumann"):
field.solve_poisson({"derivative": 0})
def test_boundary_interpolation_2d():
"""test boundary interpolation for 2d fields"""
grid = CartesianGrid([[0.1, 0.3], [-2, 3]], [3, 3])
field = ScalarField.random_normal(grid)
# test boundary interpolation
bndry_val = np.random.randn(3)
for bndry in grid._iter_boundaries():
val = field.get_boundary_values(*bndry, bc={"value": bndry_val})
np.testing.assert_allclose(val, bndry_val)
# boundary conditions have already been enforced
ev = field.make_get_boundary_values(*bndry)
out = ev()
np.testing.assert_allclose(out, bndry_val)
ev(data_full=field._data_full, out=out)
np.testing.assert_allclose(out, bndry_val)
def test_piecewise_expressions():
"""test special expressions for creating fields"""
grid = CartesianGrid([[0, 4]], 32)
field = ScalarField.from_expression(grid,
"Piecewise((x**2, x>2), (1+x, x<=2))")
x = grid.axes_coords[0]
field_data = np.piecewise(x, [x > 2, x <= 2],
[lambda x: x**2, lambda x: 1 + x])
np.testing.assert_allclose(field.data, field_data)
def test_interpolation_to_grid_fields(ndim):
"""test whether data is interpolated correctly for different fields"""
grid = CartesianGrid([[0, 2 * np.pi]] * ndim, 6)
grid2 = CartesianGrid([[0, 2 * np.pi]] * ndim, 8)
if ndim == 1:
vf = VectorField.from_expression(grid, ["cos(x)"])
elif ndim == 2:
vf = VectorField.from_expression(grid, ["sin(y)", "cos(x)"])
sf = vf[0] # test extraction of fields
fc = FieldCollection([sf, vf])
for f in [sf, vf, fc]:
# test self-interpolation
f0 = f.interpolate_to_grid(grid, backend="numba")
np.testing.assert_allclose(f.data, f0.data, atol=1e-15)
# test interpolation to finer grid and back
f2 = f.interpolate_to_grid(grid2, backend="numba")
f3 = f2.interpolate_to_grid(grid, backend="numba")
np.testing.assert_allclose(f.data, f3.data, atol=0.2, rtol=0.2)
def test_laplacian():
"""test the gradient operator"""
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16], periodic=True)
s = ScalarField.random_harmonic(grid, axis_combination=np.add, modes=1)
s_lap = s.laplace("natural")
assert s_lap.data.shape == (16, 16)
np.testing.assert_allclose(s_lap.data, -s.data, rtol=0.1, atol=0.1)
s.laplace("natural", out=s_lap)
assert s_lap.data.shape == (16, 16)
np.testing.assert_allclose(s_lap.data, -s.data, rtol=0.1, atol=0.1)
def test_structure_factor_random():
"""test the structure factor function for random input"""
g1 = CartesianGrid([[0, 10]] * 2, 64, periodic=True)
f1 = ScalarField.random_colored(g1, -2)
# test invariance with re-meshing
g2 = CartesianGrid([[0, 10]] * 2, [128, 64], periodic=True)
f2 = f1.interpolate_to_grid(g2)
ks = np.linspace(0.2, 3)
k1, s1 = image_analysis.get_structure_factor(f1, wave_numbers=ks)
k2, s2 = image_analysis.get_structure_factor(f2, wave_numbers=ks)
np.testing.assert_equal(ks, k1)
np.testing.assert_equal(ks, k2)
np.testing.assert_allclose(s1, s2, atol=0.05)
# test invariance with respect to scaling
k2, s2 = image_analysis.get_structure_factor(100 * f1, wave_numbers=ks)
np.testing.assert_equal(ks, k2)
np.testing.assert_allclose(s1, s2, atol=0.05)
def test_fluctuations():
"""test the scaling of fluctuations"""
for dim in [1, 2]:
for size in [256, 512]:
if dim == 1:
size **= 2
grid = CartesianGrid([[0, 1]] * dim, [size] * dim)
std = 1 + np.random.random()
for field_cls in [ScalarField, VectorField, Tensor2Field]:
s = field_cls.random_normal(
grid, mean=np.random.random(), std=std, scaling="physical"
)
expect = np.full([dim] * field_cls.rank, std)
np.testing.assert_allclose(s.fluctuations, expect, rtol=0.1)
def test_gradient():
"""test the gradient operator"""
grid = CartesianGrid([[0, 2 * np.pi], [0, 2 * np.pi]], [16, 16], periodic=True)
x, y = grid.cell_coords[..., 0], grid.cell_coords[..., 1]
data = np.cos(x) + np.sin(y)
s = ScalarField(grid, data)
v = s.gradient("natural")
assert v.data.shape == (2, 16, 16)
np.testing.assert_allclose(v.data[0], -np.sin(x), rtol=0.1, atol=0.1)
np.testing.assert_allclose(v.data[1], np.cos(y), rtol=0.1, atol=0.1)
s.gradient("natural", out=v)
assert v.data.shape == (2, 16, 16)
np.testing.assert_allclose(v.data[0], -np.sin(x), rtol=0.1, atol=0.1)
np.testing.assert_allclose(v.data[1], np.cos(y), rtol=0.1, atol=0.1)
def test_poisson_solver_2d():
""" test the poisson solver on 2d grids """
grid = CartesianGrid([[0, 2 * np.pi]] * 2, 16)
bcs = [{"value": "sin(y)"}, {"value": "sin(x)"}]
# solve Laplace's equation
field = ScalarField(grid)
res = field.solve_poisson(bcs)
xs = grid.cell_coords[..., 0]
ys = grid.cell_coords[..., 1]
# analytical solution was obtained with Mathematica
expect = (np.cosh(np.pi - ys) * np.sin(xs) +
np.cosh(np.pi - xs) * np.sin(ys)) / np.cosh(np.pi)
np.testing.assert_allclose(res.data, expect, atol=1e-2, rtol=1e-2)
# test more complex case for exceptions
res = field.solve_poisson([{"value": "sin(y)"}, {"curvature": "sin(x)"}])
def test_localization_sym_rect(periodic):
"""tests simple droplets localization in 2d with a rectangular grid"""
size = 16
pos = np.random.uniform(-4, 4, size=2)
radius = np.random.uniform(2, 5)
width = np.random.uniform(0.5, 1.5)
d1 = DiffuseDroplet(pos, radius, interface_width=width)
a = np.random.random(2) - size / 2
b = np.random.random(2) + size / 2
grid = CartesianGrid(np.c_[a, b], 3 * size, periodic=periodic)
field = d1.get_phase_field(grid)
emulsion = image_analysis.locate_droplets(field, refine=True)
assert len(emulsion) == 1
d2 = emulsion[0]
np.testing.assert_almost_equal(d1.position, d2.position)
assert d1.radius == pytest.approx(d2.radius, rel=1e-5)
assert d1.interface_width == pytest.approx(d2.interface_width)
emulsion = image_analysis.locate_droplets(ScalarField(grid))
assert len(emulsion) == 0