def test_tensor_divergence_cart(ndim):
"""test different tensor divergence operators"""
bcs = _get_random_grid_bcs(ndim, dx="uniform", periodic="random", rank=2)
field = Tensor2Field.random_uniform(bcs.grid)
res1 = field.divergence(bcs, backend="scipy").data
res2 = field.divergence(bcs, backend="numba").data
assert res1.shape == (ndim,) + bcs.grid.shape
np.testing.assert_allclose(res1, res2)
def test_tensors_basic():
"""test some tensor calculations"""
grid = CartesianGrid([[0.1, 0.3], [-2, 3]], [3, 4])
t1 = Tensor2Field(grid, np.full((2, 2) + grid.shape, 1))
t2 = Tensor2Field(grid, np.full((2, 2) + grid.shape, 2))
np.testing.assert_allclose(t2.average, [[2, 2], [2, 2]])
assert t1.magnitude == pytest.approx(2)
assert t1["x", "x"] == t1[0, 0]
assert t1["x", 1] == t1[0, "y"] == t1[0, 1]
t1[0, 0] = t1[0, 0]
t3 = t1 + t2
assert t3.grid == grid
np.testing.assert_allclose(t3.data, 3)
t1 += t2
np.testing.assert_allclose(t1.data, 3)
field = Tensor2Field.random_uniform(grid)
trace = field.trace()
assert isinstance(trace, ScalarField)
np.testing.assert_allclose(trace.data, field.data.trace())
t1 = Tensor2Field(grid)
t1[0, 0] = 1
t1[0, 1] = 2
t1[1, 0] = 3
t1[1, 1] = 4
for method, value in [
("min", 1),
("max", 4),
("norm", np.linalg.norm([[1, 2], [3, 4]])),
("squared_sum", 30),
("norm_squared", 30),
("trace", 5),
("invariant1", 5),
("invariant2", -1),
]:
p1 = t1.to_scalar(method)
assert p1.data.shape == grid.shape
np.testing.assert_allclose(p1.data, value)
for idx in ((1, ), (1, 2, 3), (1.5, 2), ("a", "b"), 1.0):
with pytest.raises(IndexError):
t1[idx]
t2 = FieldBase.from_state(t1.attributes, data=t1.data)
assert t1 == t2
assert t1.grid is t2.grid
attrs = Tensor2Field.unserialize_attributes(t1.attributes_serialized)
t2 = FieldBase.from_state(attrs, data=t1.data)
assert t1 == t2
assert t1.grid is not t2.grid
def test_tensor_invariants():
"""test the invariants"""
# dim == 1
f = Tensor2Field.random_uniform(UnitGrid([3]))
np.testing.assert_allclose(
f.to_scalar("invariant1").data,
f.to_scalar("invariant3").data)
np.testing.assert_allclose(f.to_scalar("invariant2").data, 0)
# dim == 2
f = Tensor2Field.random_uniform(UnitGrid([3, 3]))
invs = [f.to_scalar(f"invariant{i}").data for i in range(1, 4)]
np.testing.assert_allclose(2 * invs[1], invs[2])
a = np.random.uniform(0, 2 * np.pi) # pick random rotation angle
rot = Tensor2Field(f.grid)
rot.data[0, 0, ...] = np.cos(a)
rot.data[0, 1, ...] = np.sin(a)
rot.data[1, 0, ...] = -np.sin(a)
rot.data[1, 1, ...] = np.cos(a)
f_rot = rot @ f @ rot.transpose() # apply the transpose
for i, inv in enumerate(invs, 1):
np.testing.assert_allclose(
inv,
f_rot.to_scalar(f"invariant{i}").data,
err_msg=f"Mismatch in invariant {i}",
)
# dim == 3
from scipy.spatial.transform import Rotation
f = Tensor2Field.random_uniform(UnitGrid([1, 1, 1]))
rot = Tensor2Field(f.grid)
rot_mat = Rotation.from_rotvec(np.random.randn(3)).as_matrix()
rot.data = rot_mat.reshape(3, 3, 1, 1, 1)
f_rot = rot @ f @ rot.transpose() # apply the transpose
for i in range(1, 4):
np.testing.assert_allclose(
f.to_scalar(f"invariant{i}").data,
f_rot.to_scalar(f"invariant{i}").data,
err_msg=f"Mismatch in invariant {i}",
)
def test_collections():
"""test field collections"""
grid = UnitGrid([3, 4])
sf = ScalarField.random_uniform(grid, label="sf")
vf = VectorField.random_uniform(grid, label="vf")
tf = Tensor2Field.random_uniform(grid, label="tf")
fields = FieldCollection([sf, vf, tf])
assert fields.data.shape == (7, 3, 4)
assert isinstance(str(fields), str)
fields.data[:] = 0
np.testing.assert_allclose(sf.data, 0)
np.testing.assert_allclose(vf.data, 0)
np.testing.assert_allclose(tf.data, 0)
assert fields[0] is fields["sf"]
assert fields[1] is fields["vf"]
assert fields[2] is fields["tf"]
with pytest.raises(KeyError):
fields["42"]
sf.data = 1
vf.data = 1
tf.data = 1
np.testing.assert_allclose(fields.data, 1)
assert all(np.allclose(i, 12) for i in fields.integrals)
assert all(np.allclose(i, 1) for i in fields.averages)
assert np.allclose(fields.magnitudes, np.sqrt([1, 2, 4]))
assert sf.data.shape == (3, 4)
assert vf.data.shape == (2, 3, 4)
assert tf.data.shape == (2, 2, 3, 4)
c2 = FieldBase.from_state(fields.attributes, data=fields.data)
assert c2 == fields
assert c2.grid is grid
attrs = FieldCollection.unserialize_attributes(
fields.attributes_serialized)
c2 = FieldCollection.from_state(attrs, data=fields.data)
assert c2 == fields
assert c2.grid is not grid
fields["sf"] = 2.0
np.testing.assert_allclose(sf.data, 2)
with pytest.raises(KeyError):
fields["42"] = 0
fields.plot(subplot_args=[{}, {"scale": 1}, {"colorbar": False}])
def test_smoothing_collection():
""" test smoothing of a FieldCollection """
grid = UnitGrid([3, 4], periodic=[True, False])
sf = ScalarField.random_uniform(grid)
vf = VectorField.random_uniform(grid)
tf = Tensor2Field.random_uniform(grid)
fields = FieldCollection([sf, vf, tf])
sgm = 0.5 + np.random.random()
out = fields.smooth(sigma=sgm)
for i in range(3):
np.testing.assert_allclose(out[i].data, fields[i].smooth(sgm).data)
out.data = 0
fields.smooth(sigma=sgm, out=out)
for i in range(3):
np.testing.assert_allclose(out[i].data, fields[i].smooth(sgm).data)