def test_nontrivial_orientations(self):
"""Ensure that orientations are applied to the right particles."""
box = self.get_cubic_box(6)
points = np.array([[-1.0, 0.0, 0.0]], dtype=np.float32)
query_points = np.array([[0.9, 0.1, 0.0]], dtype=np.float32)
for angles in ([0], [np.pi / 4]):
for query_angles in ([0.01], [np.pi / 4 + 0.01]):
max_width = 2
nbins = 4
self.limits = (max_width, ) * 2
self.bins = (nbins, nbins, nbins)
pmft = freud.pmft.PMFTXYT(max_width, max_width, nbins)
pmft.compute((box, points), angles, query_points, query_angles)
query_orientation = rowan.from_axis_angle([0, 0, 1],
query_angles[0])
orientation = rowan.from_axis_angle([0, 0, 1], angles[0])
assert tuple(np.asarray(np.where(
pmft.bin_counts)).flatten()) == self.get_bin(
query_points[0], points[0], query_orientation,
orientation)
assert np.sum(pmft.bin_counts) == 1
def test_disordered(self):
# do not need positions, just orientations
N = 1000
axes = np.zeros(shape=(N, 3), dtype=np.float32)
angles = np.zeros(shape=N, dtype=np.float32)
# pick axis at random
ax_list = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0],
[1, 0, 1], [0, 1, 1], [1, 1, 1]],
dtype=np.float32)
ax_list /= np.linalg.norm(ax_list, axis=-1)[:, np.newaxis]
for i in range(N):
axes[i] = ax_list[i % ax_list.shape[0]]
# generate disordered orientations
np.random.seed(0)
angles = np.random.uniform(low=np.pi / 4.0, high=np.pi / 2.0, size=N)
orientations = rowan.from_axis_angle(axes, angles)
# create cubatic object
cubatic = freud.order.Cubatic(5.0, 0.001, 0.95, 10)
cubatic.compute(orientations)
# get the op
op = cubatic.order
pop = cubatic.particle_order
op_max = np.nanmax(pop)
npt.assert_array_less(op, 0.3, err_msg="Cubatic Order is > 0.3")
npt.assert_array_less(
op_max,
0.2,
err_msg="per particle order parameter value is too high")
def test_convex_polygon_distance_to_surface_unit_area_ngon_rotated(shape, ):
"""Check shape distance consistency with the final edge wraparound."""
theta = np.linspace(0, 2 * np.pi, 1000000)
# Try a positive rotation.
verts = rowan.rotate(rowan.from_axis_angle([0, 0, 1], 0.1), shape.vertices)
shape = ConvexPolygon(verts)
distance = shape.distance_to_surface(theta)
assert_distance_to_surface_2d(shape, theta, distance)
# Now try a negative rotation.
verts = rowan.rotate(rowan.from_axis_angle([0, 0, 1], -0.2),
shape.vertices)
shape = ConvexPolygon(verts)
distance = shape.distance_to_surface(theta)
assert_distance_to_surface_2d(shape, theta, distance)
def test_equivalent(self):
"""Perform a rotation and ensure that we can recover it"""
# Test on an octahedron
points = [[1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0], [0, 0, 1],
[0, 0, -1]]
# This is just a selected subset
eq = [
from_axis_angle([0, 0, 1], a)
for a in [0, np.pi / 2, np.pi, 3 * np.pi / 2]
]
np.random.seed(0)
rotation = random.rand(1)
translation = np.random.rand(1, 3)
transformed_points = rotate(rotation, points) + translation
q, t = mapping.procrustes(points,
transformed_points,
equivalent_quaternions=eq)
# Sort the points in a deterministic manner for comparison
recovered_points = rotate(q, points) + t
ordered_recovered_points = recovered_points[np.argsort(
recovered_points[:, 0])]
ordered_transformed_points = transformed_points[np.argsort(
transformed_points[:, 0])]
self.assertTrue(
np.allclose(ordered_recovered_points, ordered_transformed_points))
def test_icp_exact(self):
"""Ensure that ICP is exact for corresponding inputs"""
# Note that we do not bother to test the non-unique matching since we
# know it provides very poor results.
np.random.seed(0)
# First test using unique matching, which should work
for i in range(2, 6):
num_points = 2**i
points = np.random.rand(num_points, 3)
rotation = from_axis_angle([0.3, 0.3, 0.3], 0.3)
translation = np.random.rand(1, 3)
transformed_points = rotate(rotation, points) + translation
q, t, indices = mapping.icp(points,
transformed_points,
return_indices=True)
q = from_matrix(q)
# In the case of just two points, the mapping is not unique,
# so we don't check the mapping itself, just the result.
if i > 1:
self.assertTrue(
np.logical_or(
np.allclose(rotation, q),
np.allclose(rotation, -q),
))
self.assertTrue(np.allclose(translation, t))
self.assertTrue(
np.allclose(transformed_points,
rotate(q, points[indices]) + t))
def test_icp_mismatched(self):
"""See how ICP works for non-corresponding inputs. Have set some
reasonable threshold for testing purposes."""
np.random.seed(0)
# First test using unique matching, which should work
for i in range(2, 6):
num_points = 2**i
points = np.random.rand(num_points, 3)
rotation = from_axis_angle([0.3, 0.3, 0.3], 0.3)
translation = np.random.rand(1, 3)
permutation = np.random.permutation(num_points)
transformed_points = rotate(rotation,
points[permutation]) + translation
q, t, indices = mapping.icp(points,
transformed_points,
return_indices=True)
q = from_matrix(q)
deltas = transformed_points - (rotate(q, points[indices]) + t)
norms = np.linalg.norm(deltas, axis=-1)
# This is purely a heuristic, since we can't guarantee exact matches
self.assertTrue(np.mean(norms) < 0.5)
def s3_unitcell(f):
"""Open solid unit cell
Args
----
f : float
The patch offset statepoint parameter
Assumes f = ±1 corresponds to the patch on the vertex
"""
import hoomd
N = 2
a1 = np.array([1, 0, 0])
theta = np.deg2rad(60)
a2 = np.array([np.cos(theta), np.sin(theta), 0])
a3 = np.array([0, 0, 1])
pos = [[0, 0, 0], 1 / 3 * (a1 + a2)]
x = f * 90
orientations = np.deg2rad(np.array([-30 + x, 150 + x]))
orientations = [rowan.from_axis_angle(a3, t) for t in orientations]
return hoomd.lattice.unitcell(N,
a1,
a2,
a3,
dimensions=2,
position=pos,
orientation=orientations)
def test_distance_to_surface_unit_area_ngon_vertex_distance(shape, ):
"""Check that the actual distances are computed correctly."""
distances = np.linalg.norm(shape.vertices - shape.center, axis=-1)
theta = np.linspace(0, 2 * np.pi, shape.num_vertices + 1)
assert np.allclose(shape.distance_to_surface(theta)[:-1], distances)
# Try a positive rotation.
verts = rowan.rotate(rowan.from_axis_angle([0, 0, 1], 0.1), shape.vertices)
shape = ConvexPolygon(verts)
assert np.allclose(shape.distance_to_surface(theta + 0.1)[:-1], distances)
# Now try a negative rotation.
verts = rowan.rotate(rowan.from_axis_angle([0, 0, 1], -0.2),
shape.vertices)
shape = ConvexPolygon(verts)
assert np.allclose(shape.distance_to_surface(theta - 0.1)[:-1], distances)
def test_single(self):
"""Test rotation about an axis."""
v = np.array([1, 0, 0])
theta = np.pi
quats = rowan.from_axis_angle(v, theta)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(np.allclose(quats, np.array([0, 1, 0, 0])))
def quaternion_from_axis_angle(x, y, z, theta):
"""Generate a quaternion from axis [x, y, z] and angle theta."""
if x == y == z == 0:
return np.array([1, 0, 0, 0])
axis = np.array([x, y, z])
axis /= np.linalg.norm(axis)
return rowan.from_axis_angle(axis, theta)
def orbit(self, yaw=0, pitch=0, roll=0, factor=-0.0025, slight=False):
"""Orbit the camera about the look_at point."""
if slight:
factor = factor * 0.1
basis = numpy.array(self._start_camera.basis)
q1 = rowan.from_axis_angle(basis[1, :], factor * yaw)
q2 = rowan.from_axis_angle(basis[0, :], factor * pitch)
q3 = rowan.from_axis_angle(basis[2, :], factor * roll)
q = rowan.multiply(q2, rowan.multiply(q1, q3))
v = self._start_camera.position - self._start_camera.look_at
v = rowan.rotate(q, v)
self.camera.position = self._start_camera.look_at + v
self.camera.up = rowan.rotate(q, basis[1, :])
def test_ordered(self):
# do not need positions, just orientations
N = 1000
axes = np.zeros(shape=(N, 3), dtype=np.float32)
angles = np.zeros(shape=N, dtype=np.float32)
axes[:, 2] = 1.0
# generate similar angles
np.random.seed(1030)
angles = np.random.uniform(low=0.0, high=0.05, size=N)
orientations = rowan.from_axis_angle(axes, angles)
# create cubatic object
t_initial = 5.0
t_final = 0.001
scale = 0.95
n_replicates = 10
cop = freud.order.Cubatic(t_initial, t_final, scale, n_replicates)
# Test access
with self.assertRaises(AttributeError):
cop.order
with self.assertRaises(AttributeError):
cop.orientation
with self.assertRaises(AttributeError):
cop.particle_order
with self.assertRaises(AttributeError):
cop.global_tensor
with self.assertRaises(AttributeError):
cop.cubatic_tensor
cop.compute(orientations)
# Test access
cop.order
cop.orientation
cop.particle_order
cop.global_tensor
cop.cubatic_tensor
# Test values of the OP
self.assertAlmostEqual(cop.order,
1,
places=2,
msg="Cubatic Order is not approx. 1")
self.assertGreater(np.nanmin(cop.particle_order),
0.9,
msg="Per particle order parameter value is too low")
# Test attributes
self.assertAlmostEqual(cop.t_initial, t_initial)
self.assertAlmostEqual(cop.t_final, t_final)
self.assertAlmostEqual(cop.scale, scale)
# Test shapes for the tensor since we can't ensure values.
self.assertEqual(cop.orientation.shape, (4, ))
self.assertEqual(cop.cubatic_tensor.shape, (3, 3, 3, 3))
self.assertEqual(cop.global_tensor.shape, (3, 3, 3, 3))
def test_multiple_vectors(self):
"""Test multiple vectors against an angle."""
v = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
theta = np.pi
quats = rowan.from_axis_angle(v, theta)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(
np.allclose(quats,
np.array([[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])))
def get_bin(query_point, point, query_point_angle, point_angle):
r_ij = point - query_point
orientation = rowan.from_axis_angle([0, 0, 1], -point_angle)
rot_r_ij = rowan.rotate(orientation, r_ij)
xy_bins = np.floor(
(rot_r_ij[:2] + [maxX, maxY]) / [dx, dy]).astype(np.int32)
angle_bin = np.floor(
((query_point_angle - np.arctan2(-r_ij[1], -r_ij[0])) %
(2. * np.pi)) / dT).astype(np.int32)
return [xy_bins[0], xy_bins[1], angle_bin]
def test_ordered(self):
# do not need positions, just orientations
N = 1000
axes = np.zeros(shape=(N, 3), dtype=np.float32)
angles = np.zeros(shape=N, dtype=np.float32)
axes[:, 2] = 1.0
# generate similar angles
np.random.seed(1030)
angles = np.random.uniform(low=0.0, high=0.05, size=N)
orientations = rowan.from_axis_angle(axes, angles)
# create cubatic object
t_initial = 5.0
t_final = 0.001
scale = 0.95
n_replicates = 10
cop = freud.order.Cubatic(t_initial, t_final, scale, n_replicates)
# Test access
with pytest.raises(AttributeError):
cop.order
with pytest.raises(AttributeError):
cop.orientation
with pytest.raises(AttributeError):
cop.particle_order
with pytest.raises(AttributeError):
cop.global_tensor
with pytest.raises(AttributeError):
cop.cubatic_tensor
cop.compute(orientations)
# Test access
cop.order
cop.orientation
cop.particle_order
cop.global_tensor
cop.cubatic_tensor
# Test values of the OP
assert round(abs(cop.order - 1),
2) == 0, "Cubatic Order is not approx. 1"
assert (np.nanmin(cop.particle_order) >
0.9), "Per particle order parameter value is too low"
# Test attributes
assert round(abs(cop.t_initial - t_initial), 7) == 0
assert round(abs(cop.t_final - t_final), 7) == 0
assert round(abs(cop.scale - scale), 7) == 0
# Test shapes for the tensor since we can't ensure values.
assert cop.orientation.shape == (4, )
assert cop.cubatic_tensor.shape == (3, 3, 3, 3)
assert cop.global_tensor.shape == (3, 3, 3, 3)
def gen_sym_quats(group):
"""Generate symmetric quaternions for a set of point groups."""
operations = symgroups[group]
quats = []
for operation in operations:
qtemp = rowan.from_axis_angle(axes=operation[1],
angles=2 * np.pi / operation[0])
quats.append(qtemp.tolist())
quats.append(rowan.multiply([-1, 0, 0, 0], qtemp).tolist())
return quats
def test_multiple(self):
"""Test multiple vectors against multiple angles"""
v = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
theta = np.array([np.pi, np.pi / 2, np.pi / 3])
quats = rowan.from_axis_angle(v, theta)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(
np.allclose(
quats,
np.array([[0, 1, 0, 0], [np.sqrt(2) / 2, 0,
np.sqrt(2) / 2, 0],
[np.sqrt(3) / 2, 0, 0, 1 / 2]])))
def test_inertia_tensor(square):
"""Test the inertia tensor calculation."""
square.center = (0, 0, 0)
assert np.sum(square.inertia_tensor > 1e-6) == 1
assert square.inertia_tensor[2, 2] == 1 / 6
# Validate yz plane.
rotation = rowan.from_axis_angle([0, 1, 0], np.pi / 2)
rotated_verts = rowan.rotate(rotation, square.vertices)
rotated_square = ConvexPolygon(rotated_verts)
assert np.sum(rotated_square.inertia_tensor > 1e-6) == 1
assert rotated_square.inertia_tensor[0, 0] == 1 / 6
# Validate xz plane.
rotation = rowan.from_axis_angle([1, 0, 0], np.pi / 2)
rotated_verts = rowan.rotate(rotation, square.vertices)
rotated_square = ConvexPolygon(rotated_verts)
assert np.sum(rotated_square.inertia_tensor > 1e-6) == 1
assert rotated_square.inertia_tensor[1, 1] == 1 / 6
# Validate translation along each axis.
delta = 2
area = square.area
for i in range(3):
translation = [0] * 3
translation[i] = delta
translated_verts = square.vertices + translation
translated_square = ConvexPolygon(translated_verts)
offdiagonal_tensor = translated_square.inertia_tensor.copy()
diag_indices = np.diag_indices(3)
offdiagonal_tensor[diag_indices] = 0
assert np.sum(offdiagonal_tensor > 1e-6) == 0
expected_diagonals = [0, 0, 1 / 6]
for j in range(3):
if i != j:
expected_diagonals[j] += area * delta * delta
assert np.allclose(
np.diag(translated_square.inertia_tensor), expected_diagonals
)
def test_complex(self):
"""Test higher dimensions and broadcasting."""
# Various ways of producing the same output
expected_output = (np.array([
[0, 1, 0, 0],
[np.sqrt(2) / 2, 0, np.sqrt(2) / 2, 0],
[np.sqrt(3) / 2, 0, 0, 1 / 2],
])[np.newaxis, np.newaxis, ...].repeat(2, axis=0).repeat(2, axis=1))
# Matching array shapes (no broadcasing at all)
v = (np.array([[1, 0, 0], [0, 1, 0],
[0, 0, 1]])[np.newaxis, np.newaxis,
...].repeat(2, axis=0).repeat(2, axis=1))
theta = (np.array([np.pi, np.pi / 2,
np.pi / 3])[np.newaxis, np.newaxis,
...].repeat(2, axis=0).repeat(2,
axis=1))
quats = rowan.from_axis_angle(v, theta)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(np.allclose(quats, expected_output))
# Broadcasting in theta
theta_reduced = theta[0, :, ...]
quats = rowan.from_axis_angle(v, theta_reduced)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(np.allclose(quats, expected_output))
# Broadcasting in v
v_reduced = v[:, 0, ...]
quats = rowan.from_axis_angle(v_reduced, theta)
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(np.allclose(quats, expected_output))
# Broadcasting in both
quats = rowan.from_axis_angle(v_reduced[:, np.newaxis, ...],
theta_reduced[np.newaxis, :, ...])
self.assertTrue(quats.shape[:-1] == v.shape[:-1])
self.assertTrue(np.allclose(quats, expected_output))
def test_quaternions(self):
"""Test that using quaternions as angles works."""
boxSize = 8
box = freud.box.Box.square(boxSize)
points = np.array([[0, 0, 0]], dtype=np.float32)
query_points = np.array([[1.1, 0.0, 0.0], [-1.2, 0.0, 0.0],
[0.0, 1.3, 0.0], [0.0, -1.4, 0.0]],
dtype=np.float32)
angles = np.array([0.0] * points.shape[0], dtype=np.float32)
query_angles = np.array([0.0] * query_points.shape[0],
dtype=np.float32)
orientations = rowan.from_axis_angle([0, 0, 1], angles)
query_orientations = rowan.from_axis_angle([0, 0, 1], query_angles)
max_width = 3
nbins = 3
pmft = freud.pmft.PMFTXY(max_width, max_width, nbins)
pmft.compute((box, points),
orientations,
query_points,
neighbors={
'mode': 'nearest',
'num_neighbors': 1
})
# Now every point in query_points will find the origin as a neighbor.
npt.assert_array_equal(pmft.bin_counts,
[[0, 1, 0], [1, 0, 1], [0, 1, 0]])
# Now there will be only one neighbor for the single point.
pmft.compute((box, query_points),
query_orientations,
points,
neighbors={
'mode': 'nearest',
'num_neighbors': 1
})
npt.assert_array_equal(pmft.bin_counts,
[[0, 0, 0], [0, 0, 0], [0, 1, 0]])
def test_perfect(self):
"""Test perfectly aligned systems with different molecular axes"""
N = 10000
axes = np.zeros(shape=(N, 3), dtype=np.float32)
angles = np.zeros(shape=N, dtype=np.float32)
axes[:, 0] = 1.0
orientations = rowan.from_axis_angle(axes, angles)
# Test for parallel to molecular axis
u = np.array([1, 0, 0])
op_parallel = freud.order.Nematic(u)
# Test access
with self.assertRaises(AttributeError):
op_parallel.order
with self.assertRaises(AttributeError):
op_parallel.director
with self.assertRaises(AttributeError):
op_parallel.particle_tensor
with self.assertRaises(AttributeError):
op_parallel.nematic_tensor
op_parallel.compute(orientations)
# Test access
op_parallel.order
op_parallel.director
op_parallel.particle_tensor
op_parallel.nematic_tensor
self.assertTrue(op_parallel.order == 1)
npt.assert_equal(op_parallel.director, u)
npt.assert_equal(
op_parallel.nematic_tensor, np.diag([1, -0.5, -0.5]))
npt.assert_equal(
op_parallel.nematic_tensor, np.mean(
op_parallel.particle_tensor, axis=0))
# Test for perpendicular to molecular axis
u = np.array([0, 1, 0])
op_perp = freud.order.Nematic(u)
op_perp.compute(orientations)
self.assertEqual(op_perp.order, 1)
npt.assert_equal(op_perp.director, u)
npt.assert_equal(
op_perp.nematic_tensor, np.diag([-0.5, 1, -0.5]))
def test_orientation_with_fewer_query_points(self):
"""The orientations should be associated with the query points if they
are provided. Ensure that this works when the number of points and
query points differ."""
L = 8
box = freud.box.Box.cube(L)
# Don't place the points at exactly distances of 0/1 apart to avoid any
# ambiguity when the distances fall on the bin boundaries.
points = np.array([[0.1, 0.1, 0], [0.89, 0.89, 0]], dtype=np.float32)
points2 = np.array([[1, 0, 0]], dtype=np.float32)
angles = np.array([np.deg2rad(0)] * points.shape[0], dtype=np.float32)
quats = rowan.from_axis_angle([0, 0, 1], angles)
angles2 = np.array([np.deg2rad(0)] * points2.shape[0],
dtype=np.float32)
quats2 = rowan.from_axis_angle([0, 0, 1], angles2)
def points_to_set(bin_counts):
"""Extract set of unique occupied bins from pmft bin counts."""
return set(zip(*np.asarray(np.where(bin_counts)).tolist()))
max_width = 3
cells_per_unit_length = 4
nbins = max_width * cells_per_unit_length
pmft = freud.pmft.PMFTXYZ(max_width, max_width, max_width, nbins)
# There should be two nonzero bins:
# dx=-0.9, dy=0.1: bin (4, 6).
# dx=-0.11, dy=0.89: bin (5, 7).
pmft.compute(
(box, points),
quats2,
points2,
neighbors={
"mode": "nearest",
"num_neighbors": 2
},
)
npt.assert_array_equal(points_to_set(pmft.bin_counts), {(4, 6, 6),
(5, 7, 6)})
# Now the sets of points are swapped, so:
# dx=0.9, dy=-0.1: bin (7, 5).
# dx=0.11, dy=-0.89: bin (6, 4).
pmft.compute(
(box, points2),
quats,
points,
neighbors={
"mode": "nearest",
"num_neighbors": 2
},
)
npt.assert_array_equal(points_to_set(pmft.bin_counts), {(7, 5, 6),
(6, 4, 6)})
# Apply a rotation to whichever point is provided as a query_point by
# 45 degrees (easiest to picture if you think of each point as a
# square).
angles2 = np.array([np.deg2rad(45)] * points2.shape[0],
dtype=np.float32)
quats2 = rowan.from_axis_angle([0, 0, 1], angles2)
# Determine the relative position of the point when points2 is rotated
# by 45 degrees. Since we're undoing the orientation of the orientation
# of the particle, we have to conjugate the quaternion.
bond_vector = rowan.rotate(rowan.conjugate(quats2), points - points2)
bins = ((bond_vector + max_width) * cells_per_unit_length /
2).astype(int)
bins = {tuple(x) for x in bins}
pmft.compute(
(box, points),
quats2,
points2,
neighbors={
"mode": "nearest",
"num_neighbors": 2
},
)
npt.assert_array_equal(points_to_set(pmft.bin_counts), bins)
def test_orientation_with_query_points(self):
"""The orientations should be associated with the query points if they
are provided."""
L = 8
box = freud.box.Box.cube(L)
# Don't place the points at exactly distances of 0/1 apart to avoid any
# ambiguity when the distances fall on the bin boundaries.
points = np.array([[0.1, 0.1, 0]], dtype=np.float32)
points2 = np.array([[1, 0, 0]], dtype=np.float32)
angles = np.array([np.deg2rad(0)] * points2.shape[0], dtype=np.float32)
quats = rowan.from_axis_angle([0, 0, 1], angles)
max_width = 3
cells_per_unit_length = 4
nbins = max_width * cells_per_unit_length
pmft = freud.pmft.PMFTXYZ(max_width, max_width, max_width, nbins)
# In this case, the only nonzero bin should be in the bin corresponding
# to dx=-0.9, dy=0.1, which is (4, 6).
pmft.compute(
(box, points),
quats,
points2,
neighbors={
"mode": "nearest",
"num_neighbors": 1
},
)
npt.assert_array_equal(
np.asarray(np.where(pmft.bin_counts)).squeeze(), (4, 6, 6))
# Now the sets of points are swapped, so dx=0.9, dy=-0.1, which is
# (7, 5).
pmft.compute(
(box, points2),
quats,
points,
neighbors={
"mode": "nearest",
"num_neighbors": 1
},
)
npt.assert_array_equal(
np.asarray(np.where(pmft.bin_counts)).squeeze(), (7, 5, 6))
# Apply a rotation to whichever point is provided as a query_point by
# 45 degrees (easiest to picture if you think of each point as a
# square).
angles = np.array([np.deg2rad(45)] * points2.shape[0],
dtype=np.float32)
quats = rowan.from_axis_angle([0, 0, 1], angles)
# Determine the relative position of the point when points2 is rotated
# by 45 degrees. Since we're undoing the orientation of the orientation
# of the particle, we have to conjugate the quaternion.
bond_vector = rowan.rotate(rowan.conjugate(quats), points - points2)
bins = ((bond_vector + max_width) * cells_per_unit_length /
2).astype(int)
pmft.compute(
(box, points),
quats,
points2,
neighbors={
"mode": "nearest",
"num_neighbors": 1
},
)
npt.assert_array_equal(
np.asarray(np.where(pmft.bin_counts)).squeeze(), bins.squeeze())
# If we swap the order of the points, the angle should no longer
# matter.
bond_vector = rowan.rotate(rowan.conjugate(quats), points2 - points)
bins = ((bond_vector + max_width) * cells_per_unit_length /
2).astype(int)
pmft.compute(
(box, points2),
quats,
points,
neighbors={
"mode": "nearest",
"num_neighbors": 1
},
)
npt.assert_array_equal(
np.asarray(np.where(pmft.bin_counts)).squeeze(), bins.squeeze())
(-3, [0, 0, 1]),
(2, [1, 0, 0]),
(2, [np.cos(np.pi / 3), np.sin(np.pi / 3), 0]),
(2, [-np.cos(np.pi / 3), np.sin(np.pi / 3), 0]),
]
# http://www-history.mcs.st-and.ac.uk/~john/geometry/Lectures/L10.html
# Generated by hand
# Some variables to clean up the icosohedral group
icodi = np.pi - np.arctan(2) # the dihedral angle
picodi = -np.pi / 2 + np.arctan(2) # pi/2 - the dihedral angle
# a face vector that will be used a lot
face1 = [np.cos(picodi), 0, -np.sin(picodi)]
# the vector to the crown edges
lat_edge = rowan.rotate(
rowan.from_axis_angle(axes=[0, 1, 0], angles=icodi / 2), [0, 0, 1])
# the vector to the mid-latitude edges
crown_edge = rowan.rotate(
rowan.from_axis_angle(axes=face1, angles=2 * 2 * np.pi / 5), lat_edge)
crown_vert = [-0.850651, 0.0, 1.11352] # A vertex in the top pentagon
equi_vert = rowan.rotate(
rowan.from_axis_angle(axes=face1, angles=1 * 2 * np.pi / 5), crown_vert)
icosohedral = [
(1, [1, 0, 0]),
# first face pair
(5, [0, 0, 1]),
(5 / 2, [0, 0, 1]),
(5 / 3, [0, 0, 1]),
(5 / 4, [0, 0, 1]),
# second face pair
omega = np.radians(np.arange(0,365,5))
ro_y = {}
yi = 0
for v in tqdm(pf_xyz):
ro_h = {}
for fi,fam in enumerate(pf.symHKL):
axis = np.cross(fam,v)
angle = np.arccos(np.dot(fam,v))
q0 = rowan.from_axis_angle(axis, angle)
q0_n = rowan.normalize(q0)
q1_n = [rowan.normalize(rowan.from_axis_angle(h, omega)) for h in fam]
# eu = np.zeros((len(omega),3,fam.shape[0]))
eu = []
for i,(qA,qB) in enumerate(zip(q0_n,q1_n)):
qF = rowan.multiply(qA, qB)
with np.errstate(divide='ignore'):
temp = np.array((qF[:,1]/qF[:,0],qF[:,2]/qF[:,0],qF[:,3]/qF[:,0])).T
ax = ro2ax(temp)
def initialize(job):
import hoomd
import hoomd.hpmc
import scipy.spatial
"""Sets up the system and sets default values for writers and stuf
"""
# get sp params
f = job.sp.patch_offset
n_e = job.sp.n_edges
n_ge = job.sp.n_guest_edges
gar = job.sp.guest_aspect_ratio
host_guest_area_ratio = job.sp.host_guest_area_ratio
n_repeats = job.sp.n_repeats
seed = job.sp.replica
# initialize the hoomd context
msg_fn = job.fn('init-hoomd.log')
hoomd.context.initialize('--mode=cpu --msg-file={}'.format(msg_fn))
# figure out shape vertices and patch locations
xs = np.array([np.cos(n * 2 * np.pi / n_e) for n in range(n_e)])
ys = np.array([np.sin(n * 2 * np.pi / n_e) for n in range(n_e)])
zs = np.zeros_like(ys)
vertices = np.vstack((xs, ys, zs)).T
A_particle = scipy.spatial.ConvexHull(vertices[:, :2]).volume
vertices = vertices - np.mean(vertices, axis=0)
vertex_vertex_vectors = np.roll(vertices, -1, axis=0) - vertices
half_edge_locations = vertices + 0.5 * vertex_vertex_vectors
patch_locations = half_edge_locations + f * (vertices -
half_edge_locations)
# make the guest particles
xs = np.array([np.cos(n * 2 * np.pi / n_ge) for n in range(n_ge)])
ys = np.array([np.sin(n * 2 * np.pi / n_ge) for n in range(n_ge)])
zs = np.zeros_like(ys)
guest_vertices = np.vstack((xs, ys, zs)).T
rot_quat = rowan.from_axis_angle([0, 0, 1], 2 * np.pi / n_ge / 2)
guest_vertices = rowan.rotate(rot_quat, guest_vertices)
guest_vertices[:, 0] *= gar
target_guest_area = A_particle * host_guest_area_ratio
current_guest_area = scipy.spatial.ConvexHull(guest_vertices[:, :2]).volume
guest_vertices *= np.sqrt(target_guest_area / current_guest_area)
# save everything into the job doc that we need to
if hoomd.comm.get_rank() == 0:
job.doc.vertices = vertices
job.doc.patch_locations = patch_locations
job.doc.A_particle = A_particle
job.doc.guest_vertices = guest_vertices
hoomd.comm.barrier()
# build the system
if job.sp.initial_config in ('open', 's3'):
uc = job._project.s3_unitcell(job.sp.patch_offset)
system = hoomd.init.create_lattice(uc, n_repeats)
else:
raise NotImplementedError('Initialization not implemented.')
# restart writer; period=None since we'll just call write_restart() at end
restart_writer = hoomd.dump.gsd(filename=job.fn('restart.gsd'),
group=hoomd.group.all(),
truncate=True,
period=None,
phase=0)
# set up the integrator with the shape info
mc = hoomd.hpmc.integrate.convex_polygon(seed=seed, d=0, a=0)
mc.shape_param.set('A', vertices=vertices[:, :2])
total_particle_area = len(system.particles) * A_particle
phi = total_particle_area / system.box.get_volume()
sf = np.sqrt(phi / job.sp.phi)
hoomd.update.box_resize(
Lx=system.box.Lx * sf,
Ly=system.box.Ly * sf,
period=None,
)
restart_writer.dump_shape(mc)
restart_writer.dump_state(mc)
mc.set_params(d=0.1, a=0.5)
# save everything into the job doc that we need to
if hoomd.comm.get_rank() == 0:
job.doc.mc_d = {x: 0.05 for x in system.particles.types}
job.doc.mc_a = {x: 0.1 for x in system.particles.types}
job.doc.vertices = vertices
job.doc.patch_locations = patch_locations
job.doc.A_particle = A_particle
for k, v in job._project.required_defaults:
job.doc.setdefault(k, v)
os.system('cp {} {}'.format(job.fn('restart.gsd'), job.fn('init.gsd')))
hoomd.comm.barrier()
restart_writer.write_restart()
if hoomd.comm.get_rank() == 0:
os.system('cp {} {}'.format(job.fn('restart.gsd'), job.fn('init.gsd')))
hoomd.comm.barrier()
return
fibre_e[fi] = {}
fibre_q[fi] = {}
nn_gridPts[fi] = {}
nn_gridDist[fi] = {}
for yi in trange(len(xyz_pf)):
y = xyz_pf[yi]
# for fi,fam in enumerate(pf.symHKL):
axis = np.cross(fam, y)
angle = np.arccos(np.dot(fam, y))
q0 = quat.from_axis_angle(axis, angle)
q0_n = quat.normalize(q0)
q1_n = [quat.normalize(quat.from_axis_angle(h, omega)) for h in fam]
# eu = np.zeros((len(omega),3,fam.shape[0]))
eu2 = []
qfib = np.zeros((len(q1_n[0]), len(q0_n), 4))
for sym_eq, (qA, qB) in enumerate(zip(q0_n, q1_n)):
temp = quat.multiply(qA, qB)
qfib[:, sym_eq, :] = temp
def calcFibre(symHKL, yset, qgrid, omega, rad, tree, euc_rad):
fibre_e = {}
fibre_q = {}
nn_gridPts = {}
nn_gridDist = {}
egrid_trun = {}
for fi, fam in enumerate(tqdm(symHKL)):
fibre_e[fi] = {}
fibre_q[fi] = {}
nn_gridPts[fi] = {}
nn_gridDist[fi] = {}
egrid_trun[fi] = {}
""" set proper iterator """
if isinstance(yset, dict): it = yset[fi]
else: it = yset
q1_n = [quat.from_axis_angle(h, omega) for h in fam]
for yi, y in enumerate(it):
axis = np.cross(fam, y)
angle = np.arccos(np.dot(fam, y))
q0_n = quat.from_axis_angle(axis, angle)
# q0_n = quat.normalize(q0)
qfib = np.zeros((len(q1_n[0]), len(q0_n), 4))
for sym_eq, (qA, qB) in enumerate(zip(q0_n, q1_n)):
temp = quat.multiply(qA, qB)
qfib[:, sym_eq, :] = temp
phi1, Phi, phi2 = quat2eu(qfib)
phi1 = np.where(phi1 < 0, phi1 + 2 * np.pi,
phi1) #brnng back to 0 - 2pi
Phi = np.where(Phi < 0, Phi + np.pi, Phi) #brnng back to 0 - pi
phi2 = np.where(phi2 < 0, phi2 + 2 * np.pi,
phi2) #brnng back to 0 - 2pi
eu_fib = np.stack((phi1, Phi, phi2), axis=2)
eu_fib = np.reshape(eu_fib, (eu_fib.shape[0] * eu_fib.shape[1],
eu_fib.shape[2])) #new method
fz = (eu_fib[:, 0] <= od._phi1max) & (
eu_fib[:, 1] <= od._Phimax) & (eu_fib[:, 2] <= od._phi2max)
fz_idx = np.nonzero(fz)
fibre_e[fi][yi] = eu_fib[fz]
fib_idx = np.unravel_index(fz_idx[0],
(qfib.shape[0], qfib.shape[1]))
fibre_q[fi][yi] = qfib[fib_idx]
# """ reduce geodesic query size """
# qfib_pos = np.copy(qfib[fib_idx])
# qfib_pos[qfib_pos[:,0] < 0] *= -1
# query = np.concatenate(tree.query_radius(qfib_pos,euc_rad))
# query_uni = np.unique(query)
# qgrid_trun = qgrid[query_uni]
# qgrid_trun_idx = np.arange(len(qgrid))[query_uni] #store indexes to retrieve original grid pts later
""" distance calc """
temp = quatMetricNumba(qgrid, qfib[fib_idx])
""" find tube """
tube = (temp <= rad)
temp = np.column_stack((np.argwhere(tube)[:, 0], temp[tube]))
""" round very small values """
temp = np.round(temp, decimals=7)
""" move values at zero to very small (1E-5) """
temp[:, 1] = np.where(temp[:, 1] == 0, 1E-5, temp[:, 1])
""" sort by min distance """
temp = temp[np.argsort(temp[:, 1], axis=0)]
""" return unique pts (first in list) """
uni_pts = np.unique(temp[:, 0], return_index=True)
nn_gridPts[fi][yi] = uni_pts[0].astype(int)
nn_gridDist[fi][yi] = temp[uni_pts[1], 1]
# egrid_trun[fi][yi] = bungeAngs[query_uni]
return nn_gridPts, nn_gridDist, fibre_e
def _calcFibreHDF5(hfam, yset, omega, qgrid, od, h5fname, h5gname):
fibre_e = {}
fibre_q = {}
nn_gridPts = {}
nn_gridDist = {}
f = _h5.File(h5fname, 'r+')
grp = f.create_group(h5gname)
fib_grp = grp.create_group('fibre')
dist_grp = grp.create_group('dist')
for yi, y in enumerate(yset):
axis = _np.cross(hfam, y)
angle = _np.arccos(_np.dot(hfam, y))
q0 = _quat.from_axis_angle(axis, angle)
q1 = [_quat.from_axis_angle(h, omega) for h in hfam]
qfib = _np.zeros((len(q1[0]), len(q0), 4))
for sym_eq, (qA, qB) in enumerate(zip(q0, q1)):
temp = _quat.multiply(qA, qB)
qfib[:, sym_eq, :] = temp
phi1, Phi, phi2 = _quat2eu(qfib)
phi1 = _np.where(phi1 < 0, phi1 + 2 * _np.pi,
phi1) #brnng back to 0 - 2pi
Phi = _np.where(Phi < 0, Phi + _np.pi, Phi) #brnng back to 0 - pi
phi2 = _np.where(phi2 < 0, phi2 + 2 * _np.pi,
phi2) #brnng back to 0 - 2pi
eu_fib = _np.stack((phi1, Phi, phi2), axis=2)
eu_fib = _np.reshape(
eu_fib,
(eu_fib.shape[0] * eu_fib.shape[1], eu_fib.shape[2])) #new method
fz = (eu_fib[:, 0] < od._phi1max) & (eu_fib[:, 1] < od._Phimax) & (
eu_fib[:, 2] < od._phi2max)
fz_idx = _np.nonzero(fz)
fibre_e[yi] = eu_fib[fz]
fib_idx = _np.unravel_index(fz_idx[0], (qfib.shape[0], qfib.shape[1]))
fibre_q[yi] = qfib[fib_idx]
""" distance calc """
temp = quatMetricNumba(qgrid, qfib[fib_idx])
fib_grp.create_dataset(str(yi),
data=fibre_q[yi],
compression="gzip",
compression_opts=9)
dist_grp.create_dataset(str(yi),
data=temp,
compression="gzip",
compression_opts=9)
# """ find tube """
# tube = (temp <= rad)
# temp = _np.column_stack((_np.argwhere(tube)[:,0],temp[tube]))
# """ round very small values """
# temp = _np.round(temp, decimals=7)
# """ move values at zero to very small (1E-5) """
# temp[:,1] = _np.where(temp[:,1] == 0, 1E-5, temp[:,1])
# """ sort by min distance """
# temp = temp[_np.argsort(temp[:,1],axis=0)]
# """ return unique pts (first in list) """
# uni_pts = _np.unique(temp[:,0],return_index=True)
# nn_gridPts[yi] = uni_pts[0]
# nn_gridDist[yi] = temp[uni_pts[1],1]
# return nn_gridPts, nn_gridDist, fibre_e, fibre_q
f.close()
return
azi = np.linspace(0,2*pi,azi_n)
pol = np.ones((len(azi)))*pol
x = np.sin(pol) * np.cos(azi)
y = np.sin(pol) * np.sin(azi)
z = np.cos(pol)
pts.append(np.array((x,y,z)).T)
xyz_sphere = np.vstack(pts)
# %%
## secondary rotations
# offset_rots = quat.from_euler(np.deg2rad([0,0,0,0,0]), np.deg2rad([0,2,2,2,2]), np.deg2rad([0,5,10,15,20]),convention='zxz',axis_type='intrinsic')
offset_rots = quat.from_axis_angle(np.array(([-1,1,0],[-1,1,0],[1,-1,0],[-1,-1,2])), np.deg2rad([0,8,8,-8]))
cphi = np.cos(phi/2)
sphi = np.sin(phi/2)
q0 = {}
q = {}
qf = {}
fibre_e = {}
fibre_q = {}
tube_e = {}
nn_gridPts = {}
nn_gridDist = {}