def test_periodic():
""" Test periodic images. """
from pylada.crystal.utilities import are_periodic_images
from numpy import array, dot
from numpy.linalg import inv
from random import randint, random
cell = array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]])
invcell = inv(cell)
for i in range(10):
vec = dot(cell, array([random(), random(), random()]))
for j in range(10):
vec2 = vec + dot(cell, array([randint(-10, 11), randint(-10, 11), randint(-10, 11)]))
assert are_periodic_images(vec, vec2, invcell)
vec3 = vec2 + dot(cell, array([random() + 0.0001, random(), random()]))
assert not are_periodic_images(vec, vec3, invcell)
def test_zero_centered():
""" Test that vector is folded to fractional coordinates >= -0.5 and < 0.5. """
from pylada.crystal.utilities import are_periodic_images, zero_centered
from numpy import array, dot, all
from numpy.linalg import inv
from random import uniform
cell = array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]])
invcell = inv(cell)
for i in range(100):
vec = dot(cell, array([uniform(-10, 10), uniform(-10, 10), uniform(-10, 10)]))
vec2 = zero_centered(vec, cell, invcell)
assert are_periodic_images(vec, vec2, invcell)
assert all(dot(invcell, vec2) >= -0.5) and all(dot(invcell, vec2) < 0.5)
def test_into_voronoi():
""" Test that vector is folded into first Brillouin zone. """
from pylada.crystal.utilities import are_periodic_images, into_voronoi
from numpy import array, dot
from numpy.linalg import inv
from random import uniform
cell = array([[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]])
invcell = inv(cell)
for i in range(100):
vec = dot(cell, array([uniform(-10, 10), uniform(-10, 10), uniform(-10, 10)]))
vec2 = into_voronoi(vec, cell, invcell)
assert are_periodic_images(vec, vec2, invcell)
n = dot(vec2, vec2)
assert dot(vec, vec) >= n
for j in range(-3, 4):
for k in range(-3, 4):
for l in range(-3, 4):
o = vec2 + dot(cell, [j, k, l])
assert dot(o, o) >= n