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Merge #460 which adds new sampling approaches
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pc494 authored Mar 29, 2024
2 parents 1adb75f + b45df09 commit e658e7b
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5 changes: 5 additions & 0 deletions .zenodo.json
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"name": "Anders Christian Mathisen",
"affiliation": "Norwegian University of Science and Technology"
},
{
"name": "Carter Francis",
"orcid": "0000-0003-2564-1851",
"affiliation": "University of Wisconsin Madison"
},
{
"name": "Simon Høgås"
},
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3 changes: 3 additions & 0 deletions CHANGELOG.rst
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Expand Up @@ -31,6 +31,9 @@ Added
- The ``random()`` methods of ``Orientation`` and ``Misorientation`` now accept
``symmetry``. A ``random()`` method is also added to ``Vector3d`` and ``Miller``, the
latter accepting a ``phase``.
- ``Added orix.sampling.get_sample_zone_axis`` for getting zone axes for some point group.
- ``Added orix.sampling.get_sample_reduced_fundamental`` for getting reduced
fundamental zone for some point group.

Changed
-------
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47 changes: 47 additions & 0 deletions examples/rotations/sampling_rotations.py
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"""
==================
Sampling rotations
==================
This example shows how to sample some phase object in Orix. We will
get both the zone axis and the reduced fundamental zone rotations for
the phase of interest.
"""

from diffpy.structure import Atom, Lattice, Structure

from orix.crystal_map import Phase
from orix.sampling import get_sample_reduced_fundamental, get_sample_zone_axis
from orix.vector import Vector3d

a = 5.431
latt = Lattice(a, a, a, 90, 90, 90)
atom_list = []
for coords in [[0, 0, 0], [0.5, 0, 0.5], [0, 0.5, 0.5], [0.5, 0.5, 0]]:
x, y, z = coords[0], coords[1], coords[2]
atom_list.append(Atom(atype="Si", xyz=[x, y, z], lattice=latt)) # Motif part A
atom_list.append(
Atom(atype="Si", xyz=[x + 0.25, y + 0.25, z + 0.25], lattice=latt)
) # Motif part B
struct = Structure(atoms=atom_list, lattice=latt)
p = Phase(structure=struct, space_group=227)
reduced_fun = get_sample_reduced_fundamental(resolution=4, point_group=p.point_group)

vect_rot = (
reduced_fun * Vector3d.zvector()
) # get the vector representation of the rotations
vect_rot.scatter(grid=True) # plot the stereographic projection of the rotations

# %%

zone_axis_rot, directions = get_sample_zone_axis(
phase=p, density="7", return_directions=True
) # get the zone axis rotations
zone_vect_rot = (
zone_axis_rot * Vector3d.zvector()
) # get the vector representation of the rotations
zone_vect_rot.scatter(
grid=True, vector_labels=directions, text_kwargs={"size": 8, "rotation": 0}
) # plot the stereographic projection of the rotations

# %%
9 changes: 8 additions & 1 deletion orix/sampling/__init__.py
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Expand Up @@ -29,11 +29,18 @@
)
from orix.sampling.S2_sampling import sampling_methods as sample_S2_methods
from orix.sampling.SO3_sampling import uniform_SO3_sample
from orix.sampling.sample_generators import get_sample_fundamental, get_sample_local
from orix.sampling.sample_generators import (
get_sample_fundamental,
get_sample_local,
get_sample_reduced_fundamental,
get_sample_zone_axis,
)

__all__ = [
"get_sample_fundamental",
"get_sample_reduced_fundamental",
"get_sample_local",
"get_sample_zone_axis",
"sample_S2",
"sample_S2_methods",
"uniform_SO3_sample",
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127 changes: 126 additions & 1 deletion orix/sampling/sample_generators.py
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Expand Up @@ -20,10 +20,13 @@

import numpy as np

from orix.quaternion import OrientationRegion, Rotation, Symmetry
from orix.crystal_map import Phase
from orix.quaternion import OrientationRegion, Rotation, Symmetry, symmetry
from orix.quaternion.symmetry import get_point_group
from orix.sampling import sample_S2
from orix.sampling.SO3_sampling import _three_uniform_samples_method, uniform_SO3_sample
from orix.sampling._cubochoric_sampling import cubochoric_sampling
from orix.vector import Vector3d


def get_sample_fundamental(
Expand Down Expand Up @@ -165,3 +168,125 @@ def _remove_larger_than_angle(rot: Rotation, max_angle: Union[int, float]) -> Ro
mask = half_angles < half_angle
rot_out = rot[mask]
return rot_out


def get_sample_reduced_fundamental(
resolution: float,
mesh: str = None,
point_group: Symmetry = None,
) -> Rotation:
"""Produces rotations to align various crystallographic directions with
the z-axis, with the constraint that the first Euler angle phi_1=0.
The crystallographic directions sample the fundamental zone, representing
the smallest region of symmetrically unique directions of the relevant
crystal system or point group.
Parameters
----------
resolution
An angle in degrees representing the maximum angular distance to a
first nearest neighbor grid point.
mesh
Type of meshing of the sphere that defines how the grid is created. See
orix.sampling.sample_S2 for all the options. A suitable default is
chosen depending on the crystal system.
point_group
Symmetry operations that determines the unique directions. Defaults to
no symmetry, which means sampling all 3D unit vectors.
Returns
-------
Rotation
(N, 3) array representing Euler angles for the different orientations
"""
if point_group is None:
point_group = symmetry.C1

if mesh is None:
s2_auto_sampling_map = {
"triclinic": "icosahedral",
"monoclinic": "icosahedral",
"orthorhombic": "spherified_cube_edge",
"tetragonal": "spherified_cube_edge",
"cubic": "spherified_cube_edge",
"trigonal": "hexagonal",
"hexagonal": "hexagonal",
}
mesh = s2_auto_sampling_map[point_group.system]

s2_sample = sample_S2(resolution, method=mesh)
fundamental = s2_sample[s2_sample <= point_group.fundamental_sector]

phi = fundamental.polar
phi2 = (np.pi / 2 - fundamental.azimuth) % (2 * np.pi)
phi1 = np.zeros(phi2.shape[0])
euler_angles = np.vstack([phi1, phi, phi2]).T

return Rotation.from_euler(euler_angles, degrees=False)


def _corners_to_centroid_and_edge_centers(corners):
"""
Produces the midpoints and center of a trio of corners
Parameters
----------
corners : list of lists
Three corners of a streographic triangle
Returns
-------
list_of_corners : list
Length 7, elements ca, cb, cc, mean, cab, cbc, cac where naming is such that
ca is the first corner of the input, and cab is the midpoint between
corner a and corner b.
"""
ca, cb, cc = corners[0], corners[1], corners[2]
mean = tuple(np.add(np.add(ca, cb), cc))
cab = tuple(np.add(ca, cb))
cbc = tuple(np.add(cb, cc))
cac = tuple(np.add(ca, cc))
return [ca, cb, cc, mean, cab, cbc, cac]


def get_sample_zone_axis(
density: str = "3",
phase: Phase = None,
return_directions: bool = False,
) -> Rotation:
"""Produces rotations to align various crystallographic directions with
the sample zone axes.
Parameters
----------
density
Either '3' or '7' for the number of directions to return.
phase
The phase for which the zone axis rotations are required.
return_directions
If True, returns the directions as well as the rotations.
"""
system = phase.point_group.system
corners_dict = {
"cubic": [(0, 0, 1), (1, 0, 1), (1, 1, 1)],
"hexagonal": [(0, 0, 1), (2, 1, 0), (1, 1, 0)],
"orthorhombic": [(0, 0, 1), (1, 0, 0), (0, 1, 0)],
"tetragonal": [(0, 0, 1), (1, 0, 0), (1, 1, 0)],
"trigonal": [(0, 0, 1), (-1, -2, 0), (1, -1, 0)],
"monoclinic": [(0, 0, 1), (0, 1, 0), (0, -1, 0)],
}
if density == "3":
direction_list = corners_dict[system]
elif density == "7":
direction_list = _corners_to_centroid_and_edge_centers(corners_dict[system])
else:
raise ValueError("Density must be either 3 or 7")

# rotate the directions to the z axis
rots = np.stack(
[
Rotation.from_align_vectors(v, Vector3d.zvector()).data
for v in direction_list
]
)
rotations = Rotation(rots)
if return_directions:
return rotations, direction_list
else:
return rotations
56 changes: 54 additions & 2 deletions orix/tests/sampling/test_sampling.py
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Expand Up @@ -16,12 +16,20 @@
# You should have received a copy of the GNU General Public License
# along with orix. If not, see <http://www.gnu.org/licenses/>.

from diffpy.structure import Atom, Lattice, Structure
import numpy as np
import pytest

from orix.crystal_map import Phase
from orix.quaternion import Rotation
from orix.quaternion.symmetry import C2, C6, D6, get_point_group
from orix.sampling import get_sample_fundamental, get_sample_local, uniform_SO3_sample
from orix.quaternion.symmetry import C1, C2, C4, C6, D6, get_point_group
from orix.sampling import (
get_sample_fundamental,
get_sample_local,
get_sample_reduced_fundamental,
get_sample_zone_axis,
uniform_SO3_sample,
)
from orix.sampling.SO3_sampling import _resolution_to_num_steps
from orix.sampling._polyhedral_sampling import (
_get_angles_between_nn_gridpoints,
Expand Down Expand Up @@ -175,3 +183,47 @@ def test_get_sample_fundamental_space_group(self, C6_sample):
C2_sample = get_sample_fundamental(4, space_group=3, method="haar_euler")
ratio = C2_sample.size / C6_sample.size
assert np.isclose(ratio, 3, atol=0.2)

def test_get_sample_reduced_fundamental(self):
rotations = get_sample_reduced_fundamental(resolution=4)
rotations2 = get_sample_reduced_fundamental(resolution=4, point_group=C2)
rotations4 = get_sample_reduced_fundamental(resolution=4, point_group=C4)
rotations6 = get_sample_reduced_fundamental(resolution=4, point_group=C4)

assert (
np.abs(rotations.size / rotations2.size) - 2 < 0.1
) # about 2 times more rotations
assert (
np.abs(rotations2.size / rotations4.size) - 2 < 0.1
) # about 2 times more rotations
assert (
np.abs(rotations.size / rotations6.size) - 6 < 0.1
) # about 6 times more rotations

@pytest.mark.parametrize("density", ("3", "7", "5"))
@pytest.mark.parametrize("get_directions", (True, False))
def test_get_zone_axis(self, density, get_directions):
a = 5.431
latt = Lattice(a, a, a, 90, 90, 90)
atom_list = []
for coords in [[0, 0, 0], [0.5, 0, 0.5], [0, 0.5, 0.5], [0.5, 0.5, 0]]:
x, y, z = coords[0], coords[1], coords[2]
atom_list.append(
Atom(atype="Si", xyz=[x, y, z], lattice=latt)
) # Motif part A
atom_list.append(
Atom(atype="Si", xyz=[x + 0.25, y + 0.25, z + 0.25], lattice=latt)
) # Motif part B
struct = Structure(atoms=atom_list, lattice=latt)
p = Phase(structure=struct, space_group=227)
if density == "5":
with pytest.raises(ValueError):
get_sample_zone_axis(phase=p, density=density)
else:
if get_directions:
rot, _ = get_sample_zone_axis(
phase=p, density=density, return_directions=True
)
else:
rot = get_sample_zone_axis(phase=p, density=density)
assert isinstance(rot, Rotation)

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