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_pde_wrong_input():
"""test some wrong input"""
with pytest.raises(ValueError):
PDE({"t": 1})
with pytest.raises(ValueError):
PDE({"E": 1})
with pytest.raises(ValueError):
PDE({"E": 1, "t": 0})
grid = grids.UnitGrid([4])
eq = PDE({"u": 1})
assert eq.expressions == {"u": "1.0"}
with pytest.raises(ValueError):
eq.evolution_rate(FieldCollection.scalar_random_uniform(2, grid))
eq = PDE({"u": 1, "v": 2})
assert eq.expressions == {"u": "1.0", "v": "2.0"}
with pytest.raises(ValueError):
eq.evolution_rate(ScalarField.random_uniform(grid))
eq = PDE({"u": "a"})
with pytest.raises(RuntimeError):
eq.evolution_rate(ScalarField.random_uniform(grid))
eq = PDE({"x": "x"})
with pytest.raises(ValueError):
eq.evolution_rate(ScalarField(grid))
def test_pde_critical_input():
"""test some wrong input and edge cases"""
# test whether reserved symbols can be used as variables
grid = grids.UnitGrid([4])
eq = PDE({"E": 1})
res = eq.solve(ScalarField(grid), t_range=2)
np.testing.assert_allclose(res.data, 2)
with pytest.raises(ValueError):
PDE({"t": 1})
eq = PDE({"u": 1})
assert eq.expressions == {"u": "1.0"}
with pytest.raises(ValueError):
eq.evolution_rate(FieldCollection.scalar_random_uniform(2, grid))
eq = PDE({"u": 1, "v": 2})
assert eq.expressions == {"u": "1.0", "v": "2.0"}
with pytest.raises(ValueError):
eq.evolution_rate(ScalarField.random_uniform(grid))
eq = PDE({"u": "a"})
with pytest.raises(RuntimeError):
eq.evolution_rate(ScalarField.random_uniform(grid))
eq = PDE({"x": "x"})
with pytest.raises(ValueError):
eq.evolution_rate(ScalarField(grid))
def test_storage_copy(tmp_path):
""" test the copy function of StorageBase """
grid = UnitGrid([2])
field = ScalarField(grid)
storage_classes = {"None": None, "MemoryStorage": MemoryStorage}
if module_available("h5py"):
file_path = tmp_path / "test_storage_apply.hdf5"
storage_classes["FileStorage"] = functools.partial(
FileStorage, file_path)
s1 = MemoryStorage()
s1.start_writing(field, info={"b": 2})
s1.append(field.copy(data=np.array([0, 1])), 0)
s1.append(field.copy(data=np.array([1, 2])), 1)
s1.end_writing()
for name, storage_cls in storage_classes.items():
out = None if storage_cls is None else storage_cls()
s2 = s1.copy(out=out)
assert storage_cls is None or s2 is out
assert len(s2) == 2
np.testing.assert_allclose(s2.times, s1.times)
assert s2[0] == s1[0], name
assert s2[1] == s1[1], name
# test empty storage
s1 = MemoryStorage()
s2 = s1.copy()
assert len(s2) == 0
def test_kymograph_collection(tmp_path):
"""test making kymographs for field collections"""
# create some storage
field = FieldCollection([
ScalarField(UnitGrid(8), label="a"),
ScalarField(UnitGrid(8), label="b")
])
with get_memory_storage(field) as storage:
for i in range(8):
field.data = i
storage.append(field, i)
# create single kymograph
path = tmp_path / "test1.png"
plotting.plot_kymograph(storage,
field_index=1,
colorbar=True,
transpose=True,
filename=path)
assert path.stat().st_size > 0
# create multiple kymographs
path = tmp_path / "test2.png"
plotting.plot_kymographs(storage, filename=path)
assert path.stat().st_size > 0
def test_complex_operator(example_grid):
"""test using a complex operator on grid"""
r = ScalarField.random_normal(example_grid)
i = ScalarField.random_normal(example_grid)
c = r + 1j * i
assert c.is_complex
assert np.iscomplexobj(c)
c_lap = c.laplace("natural").data
np.testing.assert_allclose(c_lap.real, r.laplace("natural").data)
np.testing.assert_allclose(c_lap.imag, i.laplace("natural").data)
def test_vector_from_scalars():
"""test how to compile vector fields from scalar fields"""
g = UnitGrid([1, 2])
s1 = ScalarField(g, [[0, 1]])
s2 = ScalarField(g, [[2, 3]])
v = VectorField.from_scalars([s1, s2], label="test")
assert v.label == "test"
np.testing.assert_equal(v.data, [[[0, 1]], [[2, 3]]])
with pytest.raises(ValueError):
VectorField.from_scalars([s1, s2, s1])
def test_random_uniform_types():
"""test whether random uniform fields behave correctly for different types"""
grid = UnitGrid([8])
for dtype in [bool, int, float, complex]:
field = VectorField.random_uniform(grid, dtype=dtype)
assert field.dtype == np.dtype(dtype)
assert isinstance(field.data.flat[0].item(), dtype)
assert ScalarField.random_uniform(grid, 0, 1).dtype == np.dtype(float)
assert ScalarField.random_uniform(grid, vmin=0 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_uniform(grid, vmax=1 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_uniform(grid, 0 + 0j, 1 + 0j).dtype == np.dtype(complex)
def test_collection_plot(tmp_path):
"""test Simple simulation"""
# create some data
field = FieldCollection([
ScalarField(UnitGrid([8, 8]), label="first"),
ScalarField(UnitGrid([8, 8]))
])
with get_memory_storage(field) as storage:
storage.append(field)
path = tmp_path / "test_collection_plot.png"
plotting.plot_magnitudes(storage, filename=path)
assert path.stat().st_size > 0
def test_storage_truncation(tmp_path):
""" test whether simple trackers can be used """
file = tmp_path / "test_storage_truncation.hdf5"
for truncate in [True, False]:
storages = [MemoryStorage()]
if module_available("h5py"):
storages.append(FileStorage(file))
tracker_list = [s.tracker(interval=0.01) for s in storages]
grid = UnitGrid([8, 8])
state = ScalarField.random_uniform(grid, 0.2, 0.3)
pde = DiffusionPDE()
pde.solve(state, t_range=0.1, dt=0.001, tracker=tracker_list)
if truncate:
for storage in storages:
storage.clear()
pde.solve(state, t_range=[0.1, 0.2], dt=0.001, tracker=tracker_list)
times = np.arange(0.1, 0.201, 0.01)
if not truncate:
times = np.r_[np.arange(0, 0.101, 0.01), times]
for storage in storages:
msg = f"truncate={truncate}, storage={storage}"
np.testing.assert_allclose(storage.times, times, err_msg=msg)
assert not storage.has_collection
def test_storing_collection(tmp_path):
""" test methods specific to FieldCollections in memory storage """
grid = UnitGrid([2, 2])
f1 = ScalarField.random_uniform(grid, 0.1, 0.4, label="a")
f2 = VectorField.random_uniform(grid, 0.1, 0.4, label="b")
f3 = Tensor2Field.random_uniform(grid, 0.1, 0.4, label="c")
fc = FieldCollection([f1, f2, f3])
storage_classes = {"MemoryStorage": MemoryStorage}
if module_available("h5py"):
file_path = tmp_path / "test_storage_write.hdf5"
storage_classes["FileStorage"] = functools.partial(
FileStorage, file_path)
for storage_cls in storage_classes.values():
# store some data
storage = storage_cls()
storage.start_writing(fc)
storage.append(fc, 0)
storage.append(fc, 1)
storage.end_writing()
assert storage.has_collection
assert storage.extract_field(0)[0] == f1
assert storage.extract_field(1)[0] == f2
assert storage.extract_field(2)[0] == f3
assert storage.extract_field(0)[0].label == "a"
assert storage.extract_field(0,
label="new label")[0].label == "new label"
assert storage.extract_field(0)[0].label == "a" # do not alter label
assert storage.extract_field("a")[0] == f1
assert storage.extract_field("b")[0] == f2
assert storage.extract_field("c")[0] == f3
with pytest.raises(ValueError):
storage.extract_field("nonsense")
def get_phase_field(self,
grid: GridBase,
*,
vmin: float = 0,
vmax: float = 1,
label: str = None) -> ScalarField:
"""Creates an image of the droplet on the `grid`
Args:
grid (:class:`~pde.grids.base.GridBase`):
The grid used for discretizing the droplet phase field
vmin (float):
Minimal value the phase field will attain (far away from droplet)
vmax (float):
Maximal value the phase field will attain (inside the droplet)
label (str):
The label associated with the returned scalar field
Returns:
:class:`~pde.fields.ScalarField`: A scalar field
representing the droplet
"""
data = self._get_phase_field(grid)
data = vmin + (vmax - vmin) * data # scale data
return ScalarField(grid, data=data, label=label)
def test_scalar_arithmetics():
"""test simple arithmetics involving scalar fields"""
grid = UnitGrid([3, 4])
s = ScalarField(grid, data=2)
v = VectorField.random_uniform(grid)
for f in [v, FieldCollection([v])]:
f.data = s
assert f.data.shape == (2, 3, 4)
np.testing.assert_allclose(f.data, 2)
f += s
np.testing.assert_allclose(f.data, 4)
np.testing.assert_allclose((f + s).data, 6)
np.testing.assert_allclose((s + f).data, 6)
f -= s
np.testing.assert_allclose((f - s).data, 0)
np.testing.assert_allclose((s - f).data, 0)
f *= s
np.testing.assert_allclose(f.data, 4)
np.testing.assert_allclose((f * s).data, 8)
np.testing.assert_allclose((s * f).data, 8)
f /= s
np.testing.assert_allclose((f / s).data, 1)
with pytest.raises(TypeError):
s / f
with pytest.raises(TypeError):
s /= f
with pytest.raises(TypeError):
s *= f
def test_field_type_guessing():
""" test the ability to guess the field type """
for cls in [ScalarField, VectorField, Tensor2Field]:
grid = UnitGrid([3])
field = cls.random_normal(grid)
s = MemoryStorage()
s.start_writing(field)
s.append(field, 0)
s.append(field, 1)
# delete information
s._field = None
s.info = {}
assert not s.has_collection
assert len(s) == 2
assert s[0] == field
field = FieldCollection([ScalarField(grid), VectorField(grid)])
s = MemoryStorage()
s.start_writing(field)
s.append(field, 0)
assert s.has_collection
# delete information
s._field = None
s.info = {}
with pytest.raises(RuntimeError):
s[0]
def get_phasefield(self,
grid: GridBase = None,
label: Optional[str] = None) -> ScalarField:
"""create a phase field representing a list of droplets
Args:
grid (:class:`pde.grids.base.GridBase`):
The grid on which the phase field is created. If omitted, the
grid associated with the emulsion is used.
label (str):
Optional label for the returned scalar field
Returns:
:class:`~pde.fields.scalar.ScalarField`: the actual phase field
"""
if grid is None:
grid = self.grid
if grid is None:
raise RuntimeError("Grid needs to be specified")
if len(self) == 0:
return ScalarField(grid)
else:
result: ScalarField = self[0].get_phase_field(grid, label=label)
for d in self[1:]:
result += d.get_phase_field(grid)
np.clip(result.data, 0, 1, out=result.data)
return result
def test_pde_noise(backend):
"""test noise operator on PDE class"""
grid = grids.UnitGrid([64, 64])
state = FieldCollection([ScalarField(grid), ScalarField(grid)])
eq = PDE({"a": 0, "b": 0}, noise=0.5)
res = eq.solve(state, t_range=1, backend=backend, dt=1, tracker=None)
assert res.data.std() == pytest.approx(0.5, rel=0.1)
eq = PDE({"a": 0, "b": 0}, noise=[0.01, 2.0])
res = eq.solve(state, t_range=1, backend=backend, dt=1)
assert res.data[0].std() == pytest.approx(0.01, rel=0.1)
assert res.data[1].std() == pytest.approx(2.0, rel=0.1)
with pytest.raises(ValueError):
eq = PDE({"a": 0}, noise=[0.01, 2.0])
eq.solve(ScalarField(grid), t_range=1, backend=backend, dt=1, tracker=None)
def test_pde_bcs_error(bc):
"""test PDE with wrong boundary conditions"""
eq = PDE({"u": "laplace(u)"}, bc=bc)
grid = grids.UnitGrid([8, 8])
field = ScalarField.random_normal(grid)
for backend in ["numpy", "numba"]:
with pytest.raises(BCDataError):
eq.solve(field, t_range=1, dt=0.01, backend=backend, tracker=None)
def test_pde_time_dependent_bcs(backend):
"""test PDE with time-dependent BCs"""
field = ScalarField(grids.UnitGrid([3]))
eq = PDE({"c": "laplace(c)"}, bc={"value_expression": "Heaviside(t - 1.5)"})
storage = MemoryStorage()
eq.solve(field, t_range=10, dt=1e-2, backend=backend, tracker=storage.tracker(1))
np.testing.assert_allclose(storage[1].data, 0)
np.testing.assert_allclose(storage[-1].data, 1, rtol=1e-3)
def test_kymograph_single(tmp_path):
""" test making kymographs for single fields """
# create some storage
field = ScalarField(UnitGrid(8))
with get_memory_storage(field) as storage:
for i in range(8):
storage.append(field.copy(data=i), i)
# create single kymograph
path = tmp_path / "test1.png"
plotting.plot_kymograph(storage,
colorbar=True,
transpose=True,
filename=path)
assert path.stat().st_size > 0
# create multiple kymographs
path = tmp_path / "test2.png"
plotting.plot_kymographs(storage, filename=path)
assert path.stat().st_size > 0
def test_random_normal_types():
"""test whether random normal fields behave correctly for different types"""
grid = UnitGrid([8])
for dtype in [bool, int, float, complex]:
field = VectorField.random_normal(grid, dtype=dtype)
assert field.dtype == np.dtype(dtype)
assert isinstance(field.data.flat[0].item(), dtype)
assert ScalarField.random_normal(grid, 0, 1).dtype == np.dtype(float)
assert ScalarField.random_normal(grid, mean=0 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_normal(grid, std=1 + 0j).dtype == np.dtype(complex)
assert ScalarField.random_normal(grid, 0 + 0j, 1 + 0j).dtype == np.dtype(complex)
m = complex(np.random.random(), np.random.random())
s = complex(1 + np.random.random(), 1 + np.random.random())
grid = UnitGrid([256, 256])
field = field.random_normal(grid, m, s)
assert np.mean(field.average) == pytest.approx(m, rel=0.1, abs=0.1)
assert np.std(field.data.real) == pytest.approx(s.real, rel=0.1, abs=0.1)
assert np.std(field.data.imag) == pytest.approx(s.imag, rel=0.1, abs=0.1)
def test_storage_write(tmp_path):
"""test simple memory storage"""
dim = 5
grid = UnitGrid([dim])
field = ScalarField(grid)
storage_classes = {"MemoryStorage": MemoryStorage}
if module_available("h5py"):
file_path = tmp_path / "test_storage_write.hdf5"
storage_classes["FileStorage"] = functools.partial(
FileStorage, file_path)
for name, storage_cls in storage_classes.items():
storage = storage_cls(info={"a": 1})
storage.start_writing(field, info={"b": 2})
field.data = np.arange(dim)
storage.append(field, 0)
field.data = np.arange(dim)
storage.append(field, 1)
storage.end_writing()
assert not storage.has_collection
np.testing.assert_allclose(storage.times, np.arange(2))
for f in storage:
np.testing.assert_array_equal(f.data, np.arange(dim))
for i in range(2):
np.testing.assert_array_equal(storage[i].data, np.arange(dim))
assert {"a": 1, "b": 2}.items() <= storage.info.items()
storage = storage_cls()
storage.clear()
for i in range(3):
storage.start_writing(field)
field.data = np.arange(dim) + i
storage.append(field, i)
storage.end_writing()
np.testing.assert_allclose(storage.times,
np.arange(3),
err_msg="storage class: " + name)
def test_shapes_nfields(num, example_grid):
"""test single component field"""
fields = [ScalarField.random_uniform(example_grid) for _ in range(num)]
field = FieldCollection(fields)
data_shape = (num, ) + example_grid.shape
np.testing.assert_equal(field.data.shape, data_shape)
for pf_single in field:
np.testing.assert_equal(pf_single.data.shape, example_grid.shape)
field_c = field.copy()
np.testing.assert_allclose(field.data, field_c.data)
assert field.grid == field_c.grid
def test_pde_user_funcs():
"""test user supplied functions"""
# test a simple case
eq = PDE({"u": "get_x(gradient(u))"},
user_funcs={"get_x": lambda arr: arr[0]})
field = ScalarField.random_colored(grids.UnitGrid([32, 32]))
rhs = eq.evolution_rate(field)
np.testing.assert_allclose(rhs.data,
field.gradient("auto_periodic_neumann").data[0])
f = eq._make_pde_rhs_numba(field)
np.testing.assert_allclose(f(field.data, 0),
field.gradient("auto_periodic_neumann").data[0])
def test_memory_storage():
""" test methods specific to memory storage """
sf = ScalarField(UnitGrid([1]))
s1 = MemoryStorage()
s1.start_writing(sf)
s1.append(sf.copy(data=0), 0)
s1.append(sf.copy(data=2), 1)
s2 = MemoryStorage()
s2.start_writing(sf)
s2.append(sf.copy(data=1), 0)
s2.append(sf.copy(data=3), 1)
# test from_fields
s3 = MemoryStorage.from_fields(s1.times, [s1[0], s1[1]])
assert s3.times == s1.times
np.testing.assert_allclose(s3.data, s1.data)
# test from_collection
s3 = MemoryStorage.from_collection([s1, s2])
assert s3.times == s1.times
np.testing.assert_allclose(np.ravel(s3.data), np.arange(4))
def test_storing_extract_range(tmp_path):
"""test methods specific to FieldCollections in memory storage"""
sf = ScalarField(UnitGrid([1]))
storage_classes = {"MemoryStorage": MemoryStorage}
if module_available("h5py"):
file_path = tmp_path / "test_storage_write.hdf5"
storage_classes["FileStorage"] = functools.partial(
FileStorage, file_path)
for storage_cls in storage_classes.values():
# store some data
s1 = storage_cls()
s1.start_writing(sf)
sf.data = np.array([0])
s1.append(sf, 0)
sf.data = np.array([2])
s1.append(sf, 1)
s1.end_writing()
np.testing.assert_equal(s1[0].data, 0)
np.testing.assert_equal(s1[1].data, 2)
np.testing.assert_equal(s1[-1].data, 2)
np.testing.assert_equal(s1[-2].data, 0)
with pytest.raises(IndexError):
s1[2]
with pytest.raises(IndexError):
s1[-3]
# test extraction
s2 = s1.extract_time_range()
assert s2.times == list(s1.times)
np.testing.assert_allclose(s2.data, s1.data)
s3 = s1.extract_time_range(0.5)
assert s3.times == s1.times[:1]
np.testing.assert_allclose(s3.data, s1.data[:1])
s4 = s1.extract_time_range((0.5, 1.5))
assert s4.times == s1.times[1:]
np.testing.assert_allclose(s4.data, s1.data[1:])
def test_pde_scalar():
"""test PDE with a single scalar field"""
eq = PDE({"u": "laplace(u) + exp(-t) + sin(t)"})
assert eq.explicit_time_dependence
assert not eq.complex_valued
grid = grids.UnitGrid([8])
field = ScalarField.random_normal(grid)
res_a = eq.solve(field, t_range=1, dt=0.01, backend="numpy", tracker=None)
res_b = eq.solve(field, t_range=1, dt=0.01, backend="numba", tracker=None)
res_a.assert_field_compatible(res_b)
np.testing.assert_allclose(res_a.data, res_b.data)
def test_pde_bcs(bc):
"""test PDE with boundary conditions"""
eq = PDE({"u": "laplace(u)"}, bc=bc)
assert not eq.explicit_time_dependence
assert not eq.complex_valued
grid = grids.UnitGrid([8])
field = ScalarField.random_normal(grid)
res_a = eq.solve(field, t_range=1, dt=0.01, backend="numpy", tracker=None)
res_b = eq.solve(field, t_range=1, dt=0.01, backend="numba", tracker=None)
res_a.assert_field_compatible(res_b)
np.testing.assert_allclose(res_a.data, res_b.data)
def test_interactive_plotting():
""" test plot_interactive """
# create some data
field = ScalarField.random_uniform(UnitGrid([8]))
with get_memory_storage(field) as storage:
for i in range(8):
storage.append(field.copy(data=i), i)
plotting.plot_interactive(storage,
viewer_args={
"show": False,
"close": True
})
def test_scalar_field_plot(tmp_path):
"""test ScalarFieldPlot class"""
path = tmp_path / "test_scalar_field_plot.png"
# create some data
state = ScalarField.random_uniform(UnitGrid([16, 16]))
for scale in [(0, 1), 1, "automatic", "symmetric", "unity"]:
sfp = plotting.ScalarFieldPlot(state, scale=scale)
sfp.savefig(path)
assert path.stat().st_size > 0
sfp = plotting.ScalarFieldPlot(state, quantities={"source": None})
sfp.savefig(path)
assert path.stat().st_size > 0
def test_pde_complex():
"""test complex valued PDE"""
eq = PDE({"p": "I * laplace(p)"})
assert not eq.explicit_time_dependence
assert eq.complex_valued
field = ScalarField.random_uniform(grids.UnitGrid([4]))
assert not field.is_complex
res1 = eq.solve(field, t_range=1, dt=0.1, backend="numpy", tracker=None)
assert res1.is_complex
res2 = eq.solve(field, t_range=1, dt=0.1, backend="numpy", tracker=None)
assert res2.is_complex
np.testing.assert_allclose(res1.data, res2.data)