def test_bounding_circle_radius_random_hull_rotation(points, rotation):
"""Test that rotating vertices does not change the bounding radius."""
assume(not np.all(rotation == 0))
hull = ConvexHull(points)
poly = Polygon(points[hull.vertices])
rotation = rowan.normalize(rotation)
rotated_vertices = rowan.rotate(rotation, poly.vertices)
poly_rotated = Polygon(rotated_vertices)
circle = poly.minimal_bounding_circle
rotated_circle = poly_rotated.minimal_bounding_circle
assert np.isclose(circle.radius, rotated_circle.radius)
def test_ap(self):
"""Test finding quaternion to rotate antiparallel vectors onto each
other"""
# For this test, there are multiple quaternions that would effect the
# correct rotation, so rather than checking for a specific one we check
# that the appropriate rotation results from applying the quaternion
vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(
rowan.rotate(quat, vec1),
vec2/np.linalg.norm(vec2, axis=-1)
))
vec1 = np.array([1, 0, 0])
vec2 = np.array([[0, 1, 0],
[2, 0, 0],
[-2, 0, 0]])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(
rowan.rotate(quat, vec1),
vec2/np.linalg.norm(vec2, axis=-1)[:, np.newaxis]
))
vec1 = np.array([0, 1, 0])
vec2 = np.array([[0, 0, 1],
[0, 2, 0],
[0, -2, 0]])
quat = rowan.vector_vector_rotation(vec1, vec2)
self.assertTrue(
np.allclose(
rowan.rotate(quat, vec1),
vec2/np.linalg.norm(vec2, axis=-1)[:, np.newaxis]
))
def testfun(random_quat):
assume(not np.all(random_quat == 0))
random_quat = rowan.normalize(random_quat)
rotated_points = rowan.rotate(random_quat, square_points)
r = 1
poly = ConvexSpheropolygon(rotated_points, radius=r)
hull = ConvexHull(square_points[:, :2])
cap_area = np.pi * r * r
edge_area = np.sum(
np.linalg.norm(square_points - np.roll(square_points, 1, 0), axis=1), axis=0
)
sphero_area = cap_area + edge_area
assert np.isclose(poly.signed_area, hull.volume + sphero_area)
def _calc_shift(orientations: np.ndarray, molecule: Molecule) -> np.ndarray:
"""A function to calculate the shift of large particle positions to COM positions.
The positions defined in the Trimer classes are for the center of the 'large' particle since
this was the output from the packing algorithm. This offsets these values to be on the center of
mass, taking into account the orientation of the molecule.
Args:
orientations: Orientation of particles in degrees
molecule: The molecule for which the shift is occurring.
"""
pos_shift = molecule.get_relative_positions()[0]
orient_quat = rowan.from_euler(np.deg2rad(orientations), 0, 0)
return rowan.rotate(orient_quat, pos_shift)
def get_bin(self, query_point, point, query_point_orientation,
point_orientation):
r_ij = point - query_point
rot_r_ij = rowan.rotate(rowan.conjugate(query_point_orientation), r_ij)
limits = np.asarray(self.limits)
xy_bins = tuple(
np.floor((rot_r_ij[:2] + limits) * np.asarray(self.bins[:2]) /
(2 * limits)).astype(np.int32))
point_angle = rowan.geometry.angle(point_orientation)
angle_bin = np.floor(
((point_angle - np.arctan2(-r_ij[1], -r_ij[0])) % TWO_PI) *
self.bins[2] / TWO_PI).astype(np.int32)
return xy_bins + (angle_bin, )
def test_rotational_invariance(self):
classes = [[(-1., 0, 0), (1., 0, 0)], [(0, 1, 0), (0, -1, 0)]]
num_classes = len(classes)
num_data = 128
train_ins = np.tile(classes, (num_data, 1, 1))
train_ins += np.random.normal(scale=.1, size=train_ins.shape)
# sort by R to learn permutation invariance
rsqs = np.linalg.norm(train_ins, axis=-1)
for (neighborhood, rsq) in zip(train_ins, rsqs):
neighborhood[:] = neighborhood[np.argsort(rsq)]
train_ins, test_ins = train_ins[:num_data], train_ins[num_data:]
train_outs = np.tile(np.arange(num_classes), num_data // 2)
quats = rowan.random.rand(test_ins.shape[0])
test_ins = rowan.rotate(quats[:, np.newaxis], test_ins)
model = keras.models.Sequential()
model.add(
pythia.learned.bonds.InertiaRotation(
4, input_shape=train_ins.shape[1:]))
model.add(pythia.learned.spherical_harmonics.SphericalHarmonics(2))
model.add(pythia.learned.spherical_harmonics.NeighborAverage())
model.add(
pythia.learned.spherical_harmonics.ComplexProjection(4, 'abs'))
model.add(keras.layers.Activation('relu'))
model.add(keras.layers.Flatten())
model.add(keras.layers.BatchNormalization())
model.add(keras.layers.Dense(num_classes, activation='softmax'))
model.compile('sgd', 'categorical_crossentropy', metrics=['accuracy'])
net_train_outs = keras.utils.to_categorical(train_outs, num_classes)
train_history = model.fit(train_ins,
net_train_outs,
validation_data=(test_ins, net_train_outs),
epochs=100,
verbose=0,
shuffle=True)
self.assertLess(np.mean(train_history.history['val_accuracy']), .55)
def to_view(bod, view_orientation, image_size):
lin_grid = np.linspace(-1, 1, image_size)
x, y = np.meshgrid(lin_grid, lin_grid)
y = -y
r2 = x**2 + y**2
z = np.sqrt(np.clip(1 - r2, 0, None))
xyz = np.dstack((x, y, z))
xyz = rowan.rotate(rowan.inverse(view_orientation), xyz)
x, y, z = xyz[:, :, 0], xyz[:, :, 1], xyz[:, :, 2]
view = np.zeros((image_size, image_size))
phi = np.arccos(z)
theta = np.arctan2(y, x) % (2 * np.pi)
num_theta_bins, num_phi_bins = bod.nbins
theta_bin_edges, phi_bin_edges = bod.bin_edges
theta_bins = np.trunc(theta / (2 * np.pi) * num_theta_bins).astype(int)
phi_bins = np.trunc(phi / np.pi * num_phi_bins).astype(int)
view = bod.bond_order[theta_bins, phi_bins]
view[r2 > 1] = np.nan
return view
def test_rotational_invariance(self):
box = freud.box.Box.cube(10)
positions = np.array([[0, 0, 0], [-1, -1, 0], [-1, 1, 0], [1, -1, 0],
[1, 1, 0], [-1, 0, -1], [-1, 0, 1], [1, 0, -1],
[1, 0, 1], [0, -1, -1], [0, -1, 1], [0, 1, -1],
[0, 1, 1]])
query_point_indices = np.zeros(len(positions) - 1)
point_indices = np.arange(1, len(positions))
nlist = freud.locality.NeighborList.from_arrays(
len(positions), len(positions), query_point_indices, point_indices,
np.full(len(query_point_indices), np.sqrt(2)))
q6 = freud.order.Steinhardt(6)
w6 = freud.order.Steinhardt(6, wl=True)
q6.compute((box, positions), neighbors=nlist)
q6_unrotated_order = q6.particle_order[0]
w6.compute((box, positions), neighbors=nlist)
w6_unrotated_order = w6.particle_order[0]
for i in range(10):
np.random.seed(i)
quat = rowan.random.rand()
positions_rotated = rowan.rotate(quat, positions)
# Ensure Q6 is rotationally invariant
q6.compute((box, positions_rotated), neighbors=nlist)
npt.assert_allclose(q6.particle_order[0],
q6_unrotated_order,
rtol=1e-5)
npt.assert_allclose(q6.particle_order[0],
PERFECT_FCC_Q6,
rtol=1e-5)
# Ensure W6 is rotationally invariant
w6.compute((box, positions_rotated), neighbors=nlist)
npt.assert_allclose(w6.particle_order[0],
w6_unrotated_order,
rtol=1e-5)
npt.assert_allclose(w6.particle_order[0],
PERFECT_FCC_W6,
rtol=1e-5)
def transform(self, coords, sensor_labels):
sensor_order = {s: idx for idx, s in enumerate(sensor_labels)}
ref_cols = [
sensor_order[self._nasion],
sensor_order[self._right],
sensor_order[self._left]
]
if len(coords.shape) == 2:
coords = np.expand_dims(coords, axis=0)
for n in np.arange(coords.shape[0]):
try:
q, t = rowan.mapping.davenport(
coords[n, ref_cols, :],
self.fixed_ref
)
coords[n,:,:] = rowan.rotate(q, coords[n,:,:]) + t
except Exception as e:
warnings.warn(
'Caught an error and emitting NaNs.\nError message:\n' + \
str(e)
)
coords[n,:,:] = np.nan
return coords
def test_init_crystal_position(crystal_params):
if isinstance(crystal_params.crystal, (TrimerP2)):
return
with crystal_params.temp_context(cell_dimensions=1):
snap = init_from_crystal(crystal_params,
equilibration=False,
minimize=False)
crys = crystal_params.crystal
num_mols = get_num_mols(snap)
mol_positions = crystal_params.molecule.get_relative_positions()
positions = np.concatenate([
pos + rowan.rotate(orient, mol_positions)
for pos, orient in zip(crys.positions, crys.get_orientations())
])
box = np.array([snap.box.Lx, snap.box.Ly, snap.box.Lz])
if crys.molecule.rigid:
sim_pos = snap.particles.position[num_mols:] % box
else:
sim_pos = snap.particles.position % box
init_pos = positions % box
assert_allclose(sim_pos, init_pos)
def f(self, s, a):
# input:
# s, nd array, (n,)
# a, nd array, (m,1)
# output
# dsdt, nd array, (n,1)
dsdt = np.zeros(self.n)
q = s[6:10]
omega = s[10:]
# get input
a = np.reshape(a, (self.m, ))
eta = np.dot(self.B0, a)
f_u = np.array([0, 0, eta[0]])
tau_u = np.array([eta[1], eta[2], eta[3]])
# dynamics
# dot{p} = v
dsdt[0:3] = s[3:6]
# mv = mg + R f_u
dsdt[3:6] = self.g + rowan.rotate(q, f_u) / self.mass
# dot{R} = R S(w)
# to integrate the dynamics, see
# https://www.ashwinnarayan.com/post/how-to-integrate-quaternions/, and
# https://arxiv.org/pdf/1604.08139.pdf
qnew = rowan.calculus.integrate(q, omega, self.ave_dt)
qnew = rowan.normalize(qnew)
if qnew[0] < 0:
qnew = -qnew
# transform qnew to a "delta q" that works with the usual euler integration
dsdt[6:10] = (qnew - q) / self.ave_dt
# mJ = Jw x w + tau_u
dsdt[10:] = self.inv_J * (np.cross(self.J * omega, omega) + tau_u)
return dsdt.reshape((len(dsdt), 1))
def render(self, rotation=(1, 0, 0, 0), **kwargs):
positions = rowan.rotate(rotation, self.positions)
orientations = rowan.multiply(rotation,
rowan.normalize(self.orientations))
rotations = np.degrees(rowan.to_euler(orientations))
lines = []
for (pos, rot, col, alpha) in zip(positions, rotations,
self.colors[:, :3],
1 - self.colors[:, 3]):
lines.append(
'sphere {{ '
'0, 1 scale<{a}, {b}, {c}> '
'rotate <{rot[2]}, {rot[1]}, {rot[0]}> '
'translate <{pos[0]}, {pos[1]}, {pos[2]}> '
'pigment {{ color <{col[0]}, {col[1]}, {col[2]}> transmit {alpha} }} '
'}}'.format(a=self.a,
b=self.b,
c=self.c,
pos=pos,
rot=rot,
col=col,
alpha=alpha))
return lines
def test_single_quaternion(self):
"""Testing trivial rotations"""
self.assertTrue(np.all(rowan.rotate(one, one_vector) == one_vector))
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
(3, [0, 0, 1]),
(-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
def update_arrays(self):
if not self._dirty_attributes:
return
# TODO make number of facets a configurable attribute
thetas = np.linspace(0, 2 * np.pi, 10, endpoint=False)
# to begin, pretend we are constructing a unit circle in the
# xy plane; multiply xy by each line radius and z by each line
# length before rotating and translating appropriately
image = np.array(
[np.cos(thetas),
np.sin(thetas),
np.zeros_like(thetas)]).T
image = np.concatenate([image, image + (0, 0, 1)], axis=0)
# indices to make all triangles for a given Line object
image_indices = np.tile(
np.arange(2 * len(thetas))[:, np.newaxis], (1, 3))
image_indices[:len(thetas), 1] += 1
image_indices[:len(thetas), 2] += len(thetas)
image_indices[len(thetas):, 1] += 1 - len(thetas)
image_indices[len(thetas):, 2] += 1
image_indices[len(thetas) - 1, 1] -= len(thetas)
image_indices[-1, 1:] -= len(thetas)
cap_indices = np.array(
list(
geometry.fanTriangleIndices(
np.arange(len(thetas))[np.newaxis])))
image_indices = np.concatenate(
[image_indices, cap_indices[:, ::-1],
len(thetas) + cap_indices],
axis=0)
# normal vectors for each Line segment
normals = self.end_points - self.start_points
lengths = np.linalg.norm(normals, axis=-1, keepdims=True)
normals /= lengths
# find quaternion to rotate (0, 0, 1) into the direction each
# Line is pointing
quats = rowan.vector_vector_rotation(
np.array([0, 0, 1.])[np.newaxis, :], normals)
# Nlines*Nvertices*3
vertices = np.tile(image[np.newaxis], (len(quats), 1, 1))
# set xy according to line width
vertices[:, :, :2] *= self.widths[:, np.newaxis, np.newaxis] * 0.5
# set z according to line length
vertices[:, :, 2] *= lengths[:, np.newaxis, 0]
# rotate appropriately
vertices = rowan.rotate(quats[:, np.newaxis], vertices)
# translation by start_points will happen in _finalize_primitive_arrays
# these are incorrect normals, but this looks to be the most
# straightforward way to have the normals get serialized
normals = vertices - self.start_points[:, np.newaxis]
colors = np.tile(self.colors[:, np.newaxis], (1, len(image), 1))
positions = np.tile(self.start_points[:, np.newaxis],
(1, len(image), 1))
self._finalize_primitive_arrays(positions, None, colors, vertices,
normals, image_indices)
def write(self, trajectory, file=sys.stdout):
"""Serialize a trajectory into pos-format and write it to file.
:param trajectory: The trajectory to serialize
:type trajectory: :class:`~garnett.trajectory.Trajectory`
:param file: A file-like object."""
def _write(msg, end='\n'):
file.write(msg + end)
for i, frame in enumerate(trajectory):
# data section
if frame.data is not None:
header_keys = frame.data_keys
_write('#[data] ', end='')
_write(' '.join(header_keys))
columns = list()
for key in header_keys:
columns.append(frame.data[key])
rows = np.array(columns).transpose()
for row in rows:
_write(' '.join(row))
_write('#[done]')
# boxMatrix and rotation
box_matrix = np.array(frame.box.get_box_matrix())
if self._rotate and frame.view_rotation is not None:
for i in range(3):
box_matrix[:, i] = rowan.rotate(frame.view_rotation,
box_matrix[:, i])
if frame.view_rotation is not None and not self._rotate:
angles = rowan.to_euler(frame.view_rotation,
axis_type='extrinsic',
convention='xyz') * 180 / math.pi
_write('rotation ' + ' '.join((str(_num(_)) for _ in angles)))
_write('boxMatrix ', end='')
_write(' '.join((str(_num(v)) for v in box_matrix.flatten())))
# shape defs
try:
if len(frame.types) != len(frame.type_shapes):
raise ValueError(
"Unequal number of types and type_shapes.")
for name, type_shape in zip(frame.types, frame.type_shapes):
_write('def {} "{}"'.format(name, type_shape.pos_string))
except AttributeError:
# If AttributeError is raised because the frame does not contain
# shape information, fill them all with the default shape
for name in frame.types:
logger.info("No shape defined for '{}'. "
"Using fallback definition.".format(name))
_write('def {} "{}"'.format(
name, DEFAULT_SHAPE_DEFINITION.pos_string))
# Orientations must be provided for all particles
# If the frame does not have orientations, identity quaternions are used
orientation = getattr(frame, 'orientation',
np.array([[1, 0, 0, 0]] * frame.N))
for typeid, pos, rot in zip(frame.typeid, frame.position,
orientation):
name = frame.types[typeid]
_write(name, end=' ')
try:
shapedef = frame.shapedef.get(name)
except AttributeError:
shapedef = DEFAULT_SHAPE_DEFINITION
if self._rotate and frame.view_rotation is not None:
pos = rowan.rotate(frame.view_rotation, pos)
rot = rowan.multiply(frame.view_rotation, rot)
if isinstance(shapedef, SphereShape):
_write(' '.join((str(_num(v)) for v in pos)))
elif isinstance(shapedef, ArrowShape):
# The arrow shape actually has two position vectors of
# three elements since it has start.{x,y,z} and end.{x,y,z}.
# That is, "rot" is not an accurate variable name, since it
# does not represent a quaternion.
_write(' '.join(
(str(_num(v)) for v in chain(pos, rot[:3]))))
else:
_write(' '.join((str(_num(v)) for v in chain(pos, rot))))
_write('eof')
logger.debug("Wrote frame {}.".format(i + 1))
logger.info("Wrote {} frames.".format(i + 1))
def translation(self, value):
controls = self._backend_objects['controls']
value = np.asarray(value) - (0, 0, self.z_offset)
value = rowan.rotate(rowan.conjugate(self.rotation), value)
controls.target = (-value).tolist()
controls.exec_three_obj_method('update')
def check_rotation_invariance(quat):
rotated_poly = ConvexPolyhedron(rowan.rotate(quat, poly.vertices))
assert sphere_isclose(poly_insphere, rotated_poly.insphere, atol=1e-4)
def quatrot(q, v):
"""Rotates the given vector array v by the quaternions in the array
q"""
return rowan.rotate(q, v)
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())
def calculateNematicAndPlot(orientations,points,clusterOrient,latent, name):
# To show orientations, we use arrows rotated by the quaternions.
arrowheads = rowan.rotate(orientations, [1, 0, 0])
(a,b,c)=(np.min(points[:,0]), np.min(points[:,1]), np.min(points[:,2]))
(x,y,z)=(np.max(points[:,0]), np.max(points[:,1]), np.max(points[:,2]))
boxSize=(x-a)*(y-b)*(z-c)
ls=boxSize**(1/3.0)
fig = plt.figure(figsize=(8,4))
ax = fig.add_subplot(121, projection='3d')
ax.plot(centroids[:,0],centroids[:,1],centroids[:,2],'k.',ms=0.5)
ax.plot(points[:,0],points[:,1],points[:,2],'b.')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.view_init(elev=105., azim=165)
ax = fig.add_subplot(122, projection='3d')
factor=1
ax.quiver3D(points[:, 0], points[:, 1], points[:, 2],
factor*arrowheads[:, 0], factor*arrowheads[:, 1], factor*arrowheads[:, 2],length=ls/5.0, arrow_length_ratio=0.4, color='b', lw=1)
nop = freud.order.Nematic([1, 0, 0])
nop.compute(orientations)
#print("The value of the order parameter is {}.".format(nop.order))
center=np.mean(points,axis=0)
'''
eig = np.linalg.eig(nop.nematic_tensor)
rotation=R.from_dcm(eig[1])
arrowheads = rowan.rotate(rotation.as_quat(), [1, 0, 0])
#ax.quiver3D(center[0], center[1], center[2],arrowheads[0], arrowheads[1], arrowheads[2],length=20, color='k', lw=2)
print(name, np.max(eig[0]),eig[1], rotation.as_dcm())
'''
'''
arrowheads = rowan.rotate(clusterOrient[[0,1,2,3]], [1, 0, 0])
factor=ls/50.0
latent=[12,6,3]
ax.quiver3D(center[0], center[1], center[2],arrowheads[0], arrowheads[1], arrowheads[2],length=latent[0]*factor, color='b', lw=1)
ax.quiver3D(center[0], center[1], center[2],-arrowheads[0], -arrowheads[1], -arrowheads[2],length=latent[0]*factor, color='b', lw=1)
arrowheads = rowan.rotate(clusterOrient[[4,5,6,7]], [1, 0, 0])
ax.quiver3D(center[0], center[1], center[2],arrowheads[0], arrowheads[1], arrowheads[2],length=latent[1]*factor, color='m', lw=1)
ax.quiver3D(center[0], center[1], center[2],-arrowheads[0], -arrowheads[1], -arrowheads[2],length=latent[1], color='m', lw=1)
arrowheads = rowan.rotate(clusterOrient[[8,9,10,11]], [1, 0, 0])
ax.quiver3D(center[0], center[1], center[2],arrowheads[0], arrowheads[1], arrowheads[2],length=latent[2]*factor, color='k', lw=1)
ax.quiver3D(center[0], center[1], center[2],-arrowheads[0], -arrowheads[1], -arrowheads[2],length=latent[2]*factor, color='k', lw=1)
'''
t=' ['
t1=[]
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 0], [1, 0, 1], [0, 1, 1], [1, 1, 1]]
for ax1 in axes:
nop = freud.order.Nematic(ax1)
nop.compute(orientations)
#print("For axis {}, the value of the order parameter is {:0.3f}.".format(ax1, nop.order))
t=t+' %0.2f,'%nop.order
t1.append(nop.order)
t=t[0:-1]+']'
fig.suptitle("Cluster "+str(name)+''+'', fontsize=16);
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.view_init(elev=105., azim=165)
plt.savefig('Nematic/cluster'+str(name)+'.png')
#plt.show()
plt.close()
return t1
def f(self, X, Z, A, t, logentry=None):
# x = X[0]
# y = X[1]
# z = X[2]
# xdot = X[3]
# ydot = X[4]
# zdot = X[5]
# qw = X[6]
# qx = X[7]
# qy = X[8]
# qz = X[9]
# wx = X[10]
# wy = X[11]
# wz = X[12]
a = Z**2
# a = A
J = self.J
dxdt = np.zeros(13)
q = X[6:10]
q = rowan.normalize(q)
omega = X[10:]
B0 = self.B0 * self.params['C_T']
# B0 = self.B0
eta = np.dot(B0, a)
f_u = np.array([0, 0, eta[0]])
tau_u = np.array([eta[1], eta[2], eta[3]])
dxdt[0:3] = X[3:6]
# dxdt[3:6] = -9.81 + rowan.rotate(q, f_u) / self.params['m']
dxdt[3:6] = np.array([0., 0., -9.81
]) + rowan.rotate(q, f_u) / self.params['m']
Vinf = self.params['Vwind_mean'] - np.linalg.norm(X[3:6])
Vinf_B = rowan.rotate(rowan.inverse(q), Vinf)
Vz_B = np.array([0.0, 0.0, Vinf_B[2]])
Vs_B = Vinf_B - Vz_B
alpha = np.arcsin(np.linalg.norm(Vz_B) / np.linalg.norm(Vinf_B))
n = np.sqrt(
np.multiply(a, self.B0[0, :]) /
(self.params['C_T'] * self.params['rho'] * self.params['D']**4))
Fs_B = (Vs_B / np.linalg.norm(Vs_B)
) * self.params['C_s'] * self.params['rho'] * sum(
n**self.params['k1']) * (np.linalg.norm(Vinf)**(
2 - self.params['k1'])) * (self.params['D']**(
2 + self.params['k1'])) * (
(np.pi / 2)**2 -
alpha**2) * (alpha + self.params['k2'])
# Fs_B = [0,0,0]
dxdt[3:6] += rowan.rotate(q, Fs_B) / self.mass
qnew = rowan.calculus.integrate(q, omega, self.ave_dt)
if qnew[0] < 0:
qnew = -qnew
dxdt[6:10] = (qnew - q) / self.ave_dt
dxdt[10:] = 1 / J * (np.cross(J * omega, omega) + tau_u)
dxdt[10:] += 1 / J * np.cross(
np.array([0.0, 0.0, self.params['D'] / 4]), Fs_B)
euler_o = rowan.to_euler(q, 'xyz')
if logentry is not None:
logentry['f_u'] = f_u
logentry['tau'] = tau_u
logentry['euler_o'] = euler_o
return dxdt.reshape((len(dxdt), 1))
def render(self):
"""Render this Scene object."""
# Remove existing fresnel geometries from the scene
for geometry in self._geometries:
geometry.remove()
# Clear the list of fresnel geometries
self._geometries = []
# Add fresnel scene geometries from plato scene primitives
for prim in self._primitives:
geometry = prim.render(self._fresnel_scene)
self._geometries.append(geometry)
# Set up the camera
camera_up = rowan.rotate(rowan.conjugate(self.rotation), [0, 1, 0])
camera_position = rowan.rotate(rowan.conjugate(self.rotation), -self.translation)
camera_look_at = camera_position + rowan.rotate(rowan.conjugate(self.rotation), [0, 0, -1])
camera_height = self.size[1]/self.zoom
try:
orthographic_camera = fresnel.camera.Orthographic
except AttributeError:
# Support fresnel < 0.13.0
orthographic_camera = fresnel.camera.orthographic
self._fresnel_scene.camera = orthographic_camera(
position=camera_position,
look_at=camera_look_at,
up=camera_up,
height=camera_height)
# Set up lights
lights = []
if 'ambient_light' in self.enabled_features:
config = self.get_feature_config('ambient_light')
magnitude = config.get('value', 0.25)
if magnitude > 0:
lights.append(fresnel.light.Light(direction=(0, 0, 1),
color=(magnitude, magnitude, magnitude),
theta=np.pi))
if 'directional_light' in self.enabled_features:
config = self.get_feature_config('directional_light')
directions = config.get('value', (.25, .5, -1))
directions = np.atleast_2d(directions).astype(np.float32)
for direction in directions:
magnitude = np.linalg.norm(direction)
if magnitude > 0:
lights.append(fresnel.light.Light(direction=-direction,
color=(magnitude, magnitude, magnitude),
theta=0.7))
if len(lights) > 0:
self._fresnel_scene.lights = lights
# Set up tracer
if 'pathtracer' in self.enabled_features:
# Use path tracer if enabled
config = self.get_feature_config('pathtracer')
tracer = self._path_tracer
samples = config.get('samples', 64)
def render_function(scene, **kwargs):
return tracer.sample(scene, samples, **kwargs)
else:
# Use preview tracer by default
tracer = self._preview_tracer
tracer.anti_alias = 'antialiasing' in self.enabled_features
render_function = tracer.render
self._output = render_function(self._fresnel_scene)
def translation(self):
controls = self._backend_objects['controls']
translation = -np.array(controls.target)
translation = rowan.rotate(self.rotation, translation)
translation[2] += self.z_offset
return translation
def check_position(central_position, central_orientation,
constituent_position, local_position):
d_pos = rowan.rotate(central_orientation, local_position)
assert np.allclose(central_position + d_pos, constituent_position)
def test_zero_beta(self):
"""Check cases where beta is 0."""
# Since the Euler calculations are all done using matrices, it's easier
# to construct the test cases by directly using matrices as well. We
# assume gamma is 0 since, due to gimbal lock, only either alpha+gamma
# or alpha-gamma is a relevant parameter, and we just scan the other
# possible values. The actual function is defined such that gamma will
# always be zero in those cases. We define the matrices using lambda
# functions to support sweeping a range of values for alpha and beta,
# specifically to test cases where signs flip e.g. cos(0) vs cos(pi).
# These sign flips lead to changes in the rotation angles that must be
# tested.
mats_euler_intrinsic = [
('xzx', 'intrinsic', lambda alpha, beta:
[[np.cos(beta), 0, 0],
[0, np.cos(beta) * np.cos(alpha), -np.sin(alpha)],
[0, np.cos(beta) * np.sin(alpha),
np.cos(alpha)]]),
('xyx', 'intrinsic', lambda alpha, beta:
[[np.cos(beta), 0, 0],
[0, np.cos(alpha), -np.cos(beta) * np.sin(alpha)],
[0, np.sin(alpha),
np.cos(beta) * np.cos(alpha)]]),
('yxy', 'intrinsic', lambda alpha, beta:
[[np.cos(alpha), 0,
np.cos(beta) * np.sin(alpha)], [0, np.cos(beta), 0],
[-np.sin(alpha), 0,
np.cos(beta) * np.cos(alpha)]]),
('yzy', 'intrinsic', lambda alpha, beta:
[[np.cos(beta) * np.cos(alpha), 0,
np.sin(alpha)], [0, np.cos(beta), 0],
[-np.cos(beta) * np.sin(alpha), 0,
np.cos(alpha)]]),
('zyz', 'intrinsic', lambda alpha, beta: [[
np.cos(beta) * np.cos(alpha), -np.sin(alpha), 0
], [np.cos(beta) * np.sin(alpha),
np.cos(beta), 0], [0, 0, np.cos(beta)]]),
('zxz', 'intrinsic', lambda alpha, beta:
[[np.cos(alpha), -np.cos(beta) * np.sin(alpha), 0],
[np.sin(alpha), np.cos(beta) * np.cos(beta), 0],
[0, 0, np.cos(beta)]]),
]
mats_tb_intrinsic = [
('xzy', 'intrinsic', lambda alpha, beta: [[0, -np.sin(
beta), 0], [np.sin(beta) * np.cos(alpha), 0, -np.sin(
alpha)], [np.sin(beta) * np.sin(alpha), 0,
np.cos(alpha)]]),
('xyz', 'intrinsic',
lambda alpha, beta: [[0, 0, np.sin(
beta)], [np.sin(beta) * np.sin(alpha),
np.cos(alpha), 0
], [-np.sin(beta) * np.cos(alpha),
np.sin(alpha), 0]]),
('yxz', 'intrinsic', lambda alpha, beta:
[[np.cos(alpha), np.sin(beta) * np.sin(alpha), 0],
[0, 0, -np.sin(beta)],
[-np.sin(alpha), np.sin(beta) * np.cos(alpha), 0]]),
('yzx', 'intrinsic', lambda alpha, beta:
[[0, -np.sin(beta) * np.cos(alpha),
np.sin(alpha)], [np.sin(beta), 0, 0],
[0, np.sin(beta) * np.sin(alpha),
np.cos(alpha)]]),
('zyx', 'intrinsic', lambda alpha, beta: [[
0, -np.sin(alpha),
np.sin(beta) * np.cos(alpha)
], [0, np.cos(alpha),
np.sin(beta) * np.sin(alpha)], [-np.sin(beta), 0, 0]]),
('zxy', 'intrinsic', lambda alpha, beta: [[
np.cos(alpha), 0,
np.sin(beta) * np.sin(alpha)
], [np.sin(alpha), 0, -np.sin(beta) * np.cos(alpha)], [0, -1, 0]]),
]
# Extrinsic rotations can be tested identically to intrinsic rotations
# in the case of proper Euler angles.
mats_euler_extrinsic = [(m[0], 'extrinsic', m[2])
for m in mats_euler_intrinsic]
# For Tait-Bryan angles, extrinsic rotations axis order must be
# reversed (since axes 1 and 3 are not identical), but more
# importantly, due to the sum/difference of alpha and gamma that
# arises, we need to test the negative of alpha to catch the dangerous
# cases. In practice we get the same results since we're sweeping alpha
# values in the tests below, but it's useful to set this up precisely.
mats_tb_extrinsic = [(m[0][::-1], 'extrinsic', lambda alpha, beta: m[2]
(-alpha, beta)) for m in mats_tb_intrinsic]
# Since angle representations may not be unique, checking that
# quaternions are equal may not work. Instead we perform rotations and
# check that they are identical. For simplicity, we rotate the
# simplest vector with all 3 components (otherwise tests won't catch
# the problem because there's no component to rotate).
test_vector = [1, 1, 1]
mats_intrinsic = (mats_euler_intrinsic, mats_tb_intrinsic)
mats_extrinsic = (mats_euler_extrinsic, mats_tb_extrinsic)
# The beta angles are different for proper Euler angles and Tait-Bryan
# angles because the relevant beta terms will be sines and cosines,
# respectively.
all_betas = ((0, np.pi), (np.pi / 2, -np.pi / 2))
alphas = (0, np.pi / 2, np.pi, 3 * np.pi / 2)
for mats in (mats_intrinsic, mats_extrinsic):
for betas, mat_set in zip(all_betas, mats):
for convention, axis_type, mat_func in mat_set:
quaternions = []
for beta in betas:
for alpha in alphas:
mat = mat_func(alpha, beta)
if np.linalg.det(mat) == -1:
# Some of these will be improper rotations.
continue
quat = rowan.from_matrix(mat)
quaternions.append(quat)
euler = rowan.to_euler(quat, convention, axis_type)
converted = rowan.from_euler(*euler,
convention=convention,
axis_type=axis_type)
correct_rotation = rowan.rotate(quat, test_vector)
test_rotation = rowan.rotate(
converted, test_vector)
self.assertTrue(np.allclose(correct_rotation,
test_rotation,
atol=1e-6),
msg="""
Failed for convention {},
axis type {},
alpha = {},
beta = {}.
Expected quaternion: {}.
Calculated: {}.
Expected vector: {}.
Calculated vector: {}.""".format(
convention, axis_type, alpha,
beta, quat, converted,
correct_rotation,
test_rotation))
# For completeness, also test with broadcasting.
quaternions = np.asarray(quaternions).reshape(-1, 4)
all_euler = rowan.to_euler(quaternions, convention,
axis_type)
converted = rowan.from_euler(all_euler[...,
0], all_euler[...,
1],
all_euler[..., 2], convention,
axis_type)
self.assertTrue(
np.allclose(rowan.rotate(quaternions, test_vector),
rowan.rotate(converted, test_vector),
atol=1e-6))
def rotate_vectors(quaternion, vector):
return rowan.rotate(quaternion, vector)
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 read(self):
"Read the frame data from the stream."
self.stream.seek(self.start)
i = line = None
def _assert(assertion):
assert i is not None
assert line is not None
if not assertion:
raise ParserError("Failed to read line #{}: {}.".format(
i, line))
monotype = False
raw_frame = _RawFrameData()
raw_frame.view_rotation = None
for i, line in enumerate(self.stream):
if _is_comment(line):
continue
if line.startswith('#'):
if line.startswith('#[data]'):
_assert(raw_frame.data is None)
raw_frame.data_keys, raw_frame.data, j = \
self._read_data_section(line, self.stream)
i += j
else:
raise ParserError(line)
else:
tokens = line.rstrip().split()
if not tokens:
continue # empty line
elif tokens[0] in TOKENS_SKIP:
continue # skip these lines
if tokens[0] == 'eof':
logger.debug("Reached end of frame.")
break
elif tokens[0] == 'def':
definition, data, end = line.strip().split('"')
_assert(len(end) == 0)
name = definition.split()[1]
type_shape = self._parse_shape_definition(data)
if name not in raw_frame.types:
raw_frame.types.append(name)
raw_frame.type_shapes.append(type_shape)
else:
typeid = raw_frame.type_shapes.index(name)
raw_frame.type_shapes[typeid] = type_shape
warnings.warn(
"Redefinition of type '{}'.".format(name))
elif tokens[0] == 'shape': # monotype
data = line.strip().split('"')[1]
raw_frame.types.append(self.default_type)
type_shape = self._parse_shape_definition(data)
raw_frame.type_shapes.append(type_shape)
_assert(len(raw_frame.type_shapes) == 1)
monotype = True
elif tokens[0] in ('boxMatrix', 'box'):
if len(tokens) == 10:
raw_frame.box = np.array(
[self._num(v) for v in tokens[1:]]).reshape((3, 3))
elif len(tokens) == 4:
raw_frame.box = np.array([[self._num(tokens[1]), 0, 0],
[0,
self._num(tokens[2]), 0],
[0, 0,
self._num(tokens[3])]
]).reshape((3, 3))
elif tokens[0] == 'rotation':
euler_angles = np.array([float(t) for t in tokens[1:]])
euler_angles *= np.pi / 180
raw_frame.view_rotation = rowan.from_euler(
*euler_angles, axis_type='extrinsic', convention='xyz')
else:
# assume we are reading positions now
if not monotype:
name = tokens[0]
if name not in raw_frame.types:
raw_frame.types.append(name)
type_shape = self._parse_shape_definition(' '.join(
tokens[:3]))
raw_frame.type_shapes.append(type_shape)
else:
name = self.default_type
typeid = raw_frame.types.index(name)
type_shape = raw_frame.type_shapes[typeid]
if len(tokens) == 7 and isinstance(type_shape, ArrowShape):
xyz = tokens[-6:-3]
quat = tokens[-3:] + [0]
elif len(tokens) >= 7:
xyz = tokens[-7:-4]
quat = tokens[-4:]
elif len(tokens) >= 3:
xyz = tokens[-3:]
quat = None
else:
raise ParserError(line)
raw_frame.typeid.append(typeid)
raw_frame.position.append([self._num(v) for v in xyz])
if quat is None:
raw_frame.orientation.append(quat)
else:
raw_frame.orientation.append(
[self._num(v) for v in quat])
# Perform inverse rotation to recover original coordinates
if raw_frame.view_rotation is not None:
pos = rowan.rotate(rowan.inverse(raw_frame.view_rotation),
raw_frame.position)
else:
pos = np.asarray(raw_frame.position)
# If all the z coordinates are close to zero, set box dimension to 2
if np.allclose(pos[:, 2], 0.0, atol=1e-7):
raw_frame.box_dimensions = 2
# If no valid orientations have been added, the array should be empty
if all([quat is None for quat in raw_frame.orientation]):
raw_frame.orientation = []
else:
# Replace values of None with an identity quaternion
for i in range(len(raw_frame.orientation)):
if raw_frame.orientation[i] is None:
raw_frame.orientation[i] = [1, 0, 0, 0]
return raw_frame