def test_barycentric(self):
#2d test
simplex1 = np.array([[0.3, 0.1], [0.2, -1.2], [1.3, 2.3]])
pts1 = np.array([[0.6, 0.1], [1.3, 2.3], [0.5, 0.5], [.7, 1]])
output1 = barycentric_coords(pts1, simplex1)
#do back conversion to cartesian
o_dot_s = np.sum(output1[:, :, None] * simplex1[None, :, :], axis=1)
self.assertTrue(np.allclose(pts1, o_dot_s))
#do 3d tests
simplex2 = np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 0, 0]])
pts2 = np.array([[0, 0, 1], [0, 0.5, 0.5], [1./3, 1./3, 1./3]])
output2 = barycentric_coords(pts2, simplex2)
self.assertTrue(np.allclose(output2[1], [0.5, 0.5, 0, 0]))
#do back conversion to cartesian
o_dot_s = np.sum(output2[:, :, None] * simplex2[None, :, :], axis=1)
self.assertTrue(np.allclose(pts2, o_dot_s))
#test single point
self.assertTrue(np.allclose(output2[2],
barycentric_coords(pts2[2], simplex2)))
def _voronoi_points(self, structure):
"""
returns the voronoi points for a structure. returns in the
format of a list of lists, where the first index corresponds
to the index of the site in the original structure that neighbors
the point. I.e. simplices[0] is the list of points around the site
structure[0]
"""
all_coords = self._fake_periodic(structure)
logging.debug("Starting calculating Voronoi points")
vt = VoronoiTess(all_coords)
simplices = []
# only return the coordinates associated with the
# points in the original structure
for i, r in enumerate(vt.regions[: len(structure)]):
points = []
for v in r:
if self._interior:
new_site = PeriodicSite("X", vt.vertices[v], structure.lattice, coords_are_cartesian=True)
d = structure[i].distance(new_site)
s_points = structure.get_neighbors_in_shell(new_site.coords, d, 0.01)
s_points = map(lambda x: x[0].coords, s_points)
# brute force check that point is in its polyhedron
# (len(s_points) should usually be 4, except in high
# symmetry cases)
for simplex in itertools.combinations(s_points, 4):
try:
bcs = barycentric_coords(vt.vertices[v], np.array(simplex))
if np.min(bcs) > 0:
points.append(vt.vertices[v])
break
except np.linalg.LinAlgError as err:
if "Singular matrix" not in err.message:
raise
else:
points.append(vt.vertices[v])
simplices.append(points)
logging.debug("Finished calculating Voronoi points")
return simplices