import numpy as np
try:
from scipy.spatial.distance import cdist
scipy_present = True
except ImportError:
scipy_present = False
from scm.plams.tools.units import Units
__all__ = [
"rotation_matrix",
"axis_rotation_matrix",
"distance_array",
"angle",
"dihedral",
"cell_shape",
"cellvectors_from_shape",
]
[docs]def rotation_matrix(vec1, vec2):
"""
Calculate the rotation matrix rotating *vec1* to *vec2*. Vectors can be any containers with 3 numerical values. They don't need to be normalized. Returns 3x3 numpy array.
"""
vec1, vec2 = np.array(vec1), np.array(vec2)
a = vec1 / np.linalg.norm(vec1)
b = vec2 / np.linalg.norm(vec2)
# avoid division by zero in case of antiparallel vectors
if abs(1 + np.dot(a, b)) < 1e-8:
return -np.eye(3)
v1, v2, v3 = np.cross(a, b)
M = np.array([[0, -v3, v2], [v3, 0, -v1], [-v2, v1, 0]])
return np.identity(3) + M + np.dot(M, M) / (1 + np.dot(a, b))
[docs]def axis_rotation_matrix(vector, angle, unit="radian"):
"""
Calculate the rotation matrix rotating along the *vector* by *angle* expressed in *unit*.
*vector* can be any container with 3 numerical values. They don't need to be normalized. A positive angle denotes counterclockwise rotation, when looking along *vector*. Returns 3x3 numpy array.
"""
vector /= np.linalg.norm(vector)
v0, v1, v2 = vector
W = np.array([[0, -v2, v1], [v2, 0, -v0], [-v1, v0, 0]])
angle = Units.convert(angle, unit, "radian")
a1 = np.sin(angle)
a2 = 1.0 - np.cos(angle)
return np.identity(3) + a1 * W + a2 * W @ W
[docs]def distance_array(array1, array2):
"""Calculates distance between each pair of points in *array1* and *array2*. Returns 2D ``numpy`` array.
Uses fast ``cdist`` function if ``scipy`` is present, otherwise falls back to slightly slower ``numpy`` loop. Arguments should be 2-dimensional ``numpy`` arrays with the same second dimension. If *array1* is A x N and *array2* is B x N, the returned array is A x B.
"""
return cdist(array1, array2) if scipy_present else np.array([np.linalg.norm(i - array2, axis=1) for i in array1])
[docs]def angle(vec1, vec2, result_unit="radian"):
"""Calculate an angle between vectors *vec1* and *vec2*.
*vec1* and *vec2* should be iterable containers of length 3 (for example: tuple, list, numpy array). Values stored in them are expressed in Angstrom. Returned value is expressed in *result_unit*.
This method requires all atomic coordinates to be numerical values, :exc:`~exceptions.TypeError` is raised otherwise.
"""
vec1 = np.array([*vec1], dtype=float)
vec2 = np.array([*vec2], dtype=float)
num = np.dot(vec1, vec2)
den = np.sqrt(((vec1) ** 2).sum()) * np.sqrt(((vec2) ** 2).sum())
return Units.convert(np.arccos(num / den), "radian", result_unit)
[docs]def dihedral(p1, p2, p3, p4, unit="radian"):
"""Calculate the value of diherdal angle formed by points *p1*, *p2*, *p3* and *p4* in a 3D space. Arguments can be any containers with 3 numerical values, also instances of |Atom|. Returned value is always non-negative, measures the angle clockwise (looking along *p2-p3* vector) and is expressed in *unit*."""
p1 = np.array([*p1], dtype=float)
p2 = np.array([*p2], dtype=float)
p3 = np.array([*p3], dtype=float)
p4 = np.array([*p4], dtype=float)
b0 = p1 - p2
b1 = p3 - p2
b2 = p4 - p3
b1 /= np.linalg.norm(b1)
v = b0 - np.dot(b0, b1) * b1
w = b2 - np.dot(b2, b1) * b1
x = np.dot(v, w)
y = np.dot(np.cross(b1, v), w)
ret = np.arctan2(y, x)
ret = 2 * np.pi + ret if ret < 0 else ret
return Units.convert(ret, "radian", unit)
[docs]def cell_shape(lattice):
"""
Converts lattice vectors to lengths and angles (in radians)
Sets internal cell size data, based on set of cell vectors.
*cellvectors* is list containing three cell vectors (a 3x3 matrix)
"""
lattice = np.asarray(lattice)
a, b, c = np.sqrt((lattice**2).sum(axis=1))
if a == 0.0 and b == 0.0 and c == 0.0:
return
alpha, beta, gamma = (90.0, 90.0, 90.0)
if c != 0:
alpha = angle(lattice[1], lattice[2])
beta = angle(lattice[0], lattice[2])
if b != 0:
gamma = angle(lattice[0], lattice[1])
return [a, b, c, alpha, beta, gamma]
def cell_lengths(lattice, unit="angstrom"):
"""Return the lengths of the lattice vector. Returns a list with the same length as the number of lattice vector."""
if lattice is None or len(lattice) == 0:
raise ValueError("Cannot calculate cell_lengths for nonperiodic system")
lattice = np.asarray(lattice)
ret = np.sqrt((lattice**2).sum(axis=1)) * Units.conversion_ratio("angstrom", unit)
return ret.tolist()
def cell_angles(lattice, unit="degree"):
"""Return the angles between lattice vectors.
unit : str
output unit
For 2D systems, returns a list [gamma]
For 3D systems, returns a list [alpha, beta, gamma]
"""
ndim = len(lattice)
if ndim < 2:
raise ValueError(
"Cannot calculate cell_angles for fewer than 2 lattice vectors. Tried with {} lattice vectors".format(ndim)
)
gamma = angle(lattice[0], lattice[1], result_unit=unit)
if ndim == 2:
return [gamma]
if ndim >= 3:
alpha = angle(lattice[1], lattice[2], result_unit=unit)
beta = angle(lattice[0], lattice[2], result_unit=unit)
return [alpha, beta, gamma]
[docs]def cellvectors_from_shape(box):
"""
Converts lengths and angles (in radians) of lattice vectors to the lattice vectors
"""
a = box[0]
b = box[1]
c = box[2]
alpha, beta, gamma = 90.0, 90.0, 90
if len(box) == 6:
alpha = box[3] # *np.pi/180.
beta = box[4] # *np.pi/180.
gamma = box[5] # *np.pi/180.
va = [a, 0.0, 0.0]
vb = [b * np.cos(gamma), b * np.sin(gamma), 0.0]
cx = c * np.cos(beta)
cy = (np.cos(alpha) - np.cos(beta) * np.cos(gamma)) * c / np.sin(gamma)
volume = 1 - np.cos(alpha) ** 2 - np.cos(beta) ** 2 - np.cos(gamma) ** 2
volume += 2 * np.cos(alpha) * np.cos(beta) * np.cos(gamma)
volume = np.sqrt(volume)
cz = c * volume / np.sin(gamma)
vc = [cx, cy, cz]
lattice = [va, vb, vc]
return lattice
