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
self._inv_matrix = None
self._metric_tensor = None
self._diags = None
self._lll_matrix_mappings = {}
self._lll_inverse = None
self.is_orthogonal = all([abs(a - 90) < 1e-5 for a in self._angles])
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 __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
self._inv_matrix = None
self._metric_tensor = None
self._diags = None
self._lll_matrix_mappings = {}
self._lll_inverse = None
self.is_orthogonal = all([abs(a - 90) < 1e-5 for a in self._angles])
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 set_matrix(self,matrix):
'''
Set the values of the matrix of lattice vectors
and reset lengths and angles accordingly
Args:
matrix (list) of length n_dim x n_dim
'''
m = np.array(matrix, dtype=np.float64).reshape((self.n_dim, self.n_dim))
lengths = np.sqrt(np.sum(m ** 2, axis=1))
angles = np.zeros(self.n_dim)
for i in range(self.n_dim):
j = (i + 1) % self.n_dim
k = (i + 2) % self.n_dim
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
self._inv_matrix = None
self._metric_tensor = None
self._diags = None
self._lll_matrix_mappings = {}
self._lll_inverse = None
self.is_orthogonal = all([abs(a - 90) < 1e-5 for a in self._angles])
def from_parameters(
a: float,
b: float,
c: float,
alpha: float,
beta: float,
gamma: float,
vesta: bool = False,
):
"""
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.
vesta: True if you import Cartesian coordinates from VESTA.
Returns:
Lattice with the specified lattice parameters.
"""
alpha_r = radians(alpha)
beta_r = radians(beta)
gamma_r = radians(gamma)
if vesta:
cos_alpha = np.cos(alpha_r)
cos_beta = np.cos(beta_r)
cos_gamma = np.cos(gamma_r)
sin_gamma = np.sin(gamma_r)
c1 = c * cos_beta
c2 = (c * (cos_alpha - (cos_beta * cos_gamma))) / sin_gamma
vector_a = [float(a), 0.0, 0.0]
vector_b = [b * cos_gamma, b * sin_gamma, 0]
vector_c = [c1, c2, math.sqrt(c ** 2 - c1 ** 2 - c2 ** 2)]
else:
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 from_parameters(
a: float,
b: float,
c: float,
alpha: float,
beta: float,
gamma: float,
vesta: bool = False,
):
"""
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.
vesta: True if you import Cartesian coordinates from VESTA.
Returns:
Lattice with the specified lattice parameters.
"""
alpha_r = radians(alpha)
beta_r = radians(beta)
gamma_r = radians(gamma)
if vesta:
cos_alpha = np.cos(alpha_r)
cos_beta = np.cos(beta_r)
cos_gamma = np.cos(gamma_r)
sin_gamma = np.sin(gamma_r)
c1 = c * cos_beta
c2 = (c * (cos_alpha - (cos_beta * cos_gamma))) / sin_gamma
vector_a = [float(a), 0.0, 0.0]
vector_b = [b * cos_gamma, b * sin_gamma, 0]
vector_c = [c1, c2, math.sqrt(c**2 - c1**2 - c2**2)]
else:
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 get_angles(matrix, lengths=None):
"""Returns the angles (alpha, beta, gamma) of the lattice."""
if lengths is not None:
lengths = get_lengths(matrix)
m = matrix
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]))
angles = np.arccos(angles) * 180.0 / pi
return tuple(angles.tolist()) # type: ignore
def angles(self) -> Tuple[float]:
"""
Returns the angles (alpha, beta, gamma) of the lattice.
"""
m = self._matrix
lengths = self.lengths
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]))
angles = np.arccos(angles) * 180.0 / pi
return tuple(angles.tolist())
def angles(self) -> Tuple[float]:
"""
Returns the angles (alpha, beta, gamma) of the lattice.
"""
m = self._matrix
lengths = self.lengths
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]))
angles = np.arccos(angles) * 180.0 / pi
return tuple(angles.tolist())
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(acos(abs_cap(v)))
phi = sum(vals)
return phi + (3 - len(r)) * 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(acos(abs_cap(v)))
phi = sum(vals)
return phi + (3 - len(r)) * pi