def test_abs_cap(self):
self.assertEqual(abs_cap(1.000000001), 1.0)
self.assertEqual(abs_cap(-1.000000001), -1.0)
v = random.uniform(-1, 1)
self.assertEqual(abs_cap(v), v)
self.assertEqual(abs_cap(1.000000001, 2), 1.000000001)
self.assertEqual(abs_cap(-2.000000001, 2), -2.0)
def test_abs_cap(self):
self.assertEqual(abs_cap(1.000000001), 1.0)
self.assertEqual(abs_cap(-1.000000001), -1.0)
v = random.uniform(-1, 1)
self.assertEqual(abs_cap(v), v)
self.assertEqual(abs_cap(1.000000001, 2), 1.000000001)
self.assertEqual(abs_cap(-2.000000001, 2), -2.0)
def __init__(self, matrix):
"""
Create a lattice from any sequence of 9 numbers. Note that the sequence
is assumed to be read one row at a time. Each row represents one
lattice vector.
Args:
matrix: Sequence of numbers in any form. Examples of acceptable
input.
i) An actual numpy array.
ii) [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
iii) [1, 0, 0 , 0, 1, 0, 0, 0, 1]
iv) (1, 0, 0, 0, 1, 0, 0, 0, 1)
Each row should correspond to a lattice vector.
E.g., [[10, 0, 0], [20, 10, 0], [0, 0, 30]] specifies a lattice
with lattice vectors [10, 0, 0], [20, 10, 0] and [0, 0, 30].
"""
m = np.array(matrix, dtype=np.float64).reshape((3, 3))
lengths = np.sqrt(np.sum(m ** 2, axis=1))
angles = np.zeros(3)
for i in range(3):
j = (i + 1) % 3
k = (i + 2) % 3
angles[i] = abs_cap(dot(m[j], m[k]) / (lengths[j] * lengths[k]))
self._angles = np.arccos(angles) * 180. / pi
self._lengths = lengths
self._matrix = m
# The inverse matrix is lazily generated for efficiency.
self._inv_matrix = None
self._metric_tensor = None
def from_parameters(a, b, c, alpha, beta, gamma):
"""
Create a Lattice using unit cell lengths and angles (in degrees).
Args:
a (float): *a* lattice parameter.
b (float): *b* lattice parameter.
c (float): *c* lattice parameter.
alpha (float): *alpha* angle in degrees.
beta (float): *beta* angle in degrees.
gamma (float): *gamma* angle in degrees.
Returns:
Lattice with the specified lattice parameters.
"""
alpha_r = radians(alpha)
beta_r = radians(beta)
gamma_r = radians(gamma)
val = (np.cos(alpha_r) * np.cos(beta_r) - np.cos(gamma_r))\
/ (np.sin(alpha_r) * np.sin(beta_r))
#Sometimes rounding errors result in values slightly > 1.
val = abs_cap(val)
gamma_star = np.arccos(val)
vector_a = [a * np.sin(beta_r), 0.0, a * np.cos(beta_r)]
vector_b = [-b * np.sin(alpha_r) * np.cos(gamma_star),
b * np.sin(alpha_r) * np.sin(gamma_star),
b * np.cos(alpha_r)]
vector_c = [0.0, 0.0, float(c)]
return Lattice([vector_a, vector_b, vector_c])
def solid_angle(center, coords):
"""
Helper method to calculate the solid angle of a set of coords from the
center.
Args:
center (3x1 array): Center to measure solid angle from.
coords (Nx3 array): List of coords to determine solid angle.
Returns:
The solid angle.
"""
o = np.array(center)
r = [np.array(c) - o for c in coords]
r.append(r[0])
n = [np.cross(r[i + 1], r[i]) for i in range(len(r) - 1)]
n.append(np.cross(r[1], r[0]))
vals = []
for i in range(len(n) - 1):
v = -np.dot(n[i], n[i + 1]) / (np.linalg.norm(n[i]) * np.linalg.norm(n[i + 1]))
vals.append(math.acos(abs_cap(v)))
phi = sum(vals)
return phi + (3 - len(r)) * math.pi
def solid_angle(center, coords):
"""
Helper method to calculate the solid angle of a set of coords from the
center.
Args:
center (3x1 array): Center to measure solid angle from.
coords (Nx3 array): List of coords to determine solid angle.
Returns:
The solid angle.
"""
o = np.array(center)
r = [np.array(c) - o for c in coords]
r.append(r[0])
n = [np.cross(r[i + 1], r[i]) for i in range(len(r) - 1)]
n.append(np.cross(r[1], r[0]))
vals = []
for i in range(len(n) - 1):
v = -np.dot(n[i], n[i + 1])\
/ (np.linalg.norm(n[i]) * np.linalg.norm(n[i + 1]))
vals.append(math.acos(abs_cap(v)))
phi = sum(vals)
return phi + (3 - len(r)) * math.pi
