mindscience.e3nn.o3.Irrep

class mindscience.e3nn.o3.Irrep(l, p=None)[source]

Irreducible representation of O(3). This class does not contain any data, it is a structure that describe the representation. It is typically used as argument of other classes of the library to define the input and output representations of functions. The irrep is labeled by a non-negative integer l (the degree) and a parity p (1 for even, -1 for odd). Common aliases: "e" for even parity, "o" for odd parity, "y" for parity (-1)^l.

Parameters

l (Union[int, str]) – non-negative integer, the degree of the representation, \(l = 0, 1, \dots\). Alternatively, a string such as "1o" or "2e" encoding both degree and parity.
p (int, optional) – the parity of the representation, \(p \in \{1, -1\}\). Ignored when l is a string. Default: None.

Raises

NotImplementedError – If method is not implemented.
ValueError – If l is negative or p is not in {1, -1}.
ValueError – If l cannot be converted to an Irrep.
TypeError – If l is not int or str.

Examples

>>> from mindscience.e3nn.o3 import Irrep
>>> Irrep(0, 1)
0e
>>> Irrep("1y")
1o
>>> Irrep("2o").dim
5
>>> Irrep("2e") in Irrep("1o") * Irrep("1o")
True
>>> Irrep("1o") + Irrep("2o")
1x1o+1x2o

is_scalar()[source]

Check whether this irrep is the trivial (scalar) representation.

Returns: bool, True if l = 0 and parity p = 1, False otherwise.

wigD_from_angles(alpha, beta, gamma, k=None)[source]

Compute the Wigner-D matrix representation of O(3) from the three Euler angles \((\alpha, \beta, \gamma)\) that describe the rotation sequence:

Rotate by \(\gamma\) around the original Y axis.
Rotate by \(\beta\) around the new X axis.
Rotate by \(\alpha\) around the newest Y axis.

Parameters

alpha (Union[Tensor[float32], list[float], tuple[float], ndarray[np.float32], float]) – Rotation \(\alpha\) around Y axis, applied third.
beta (Union[Tensor[float32], list[float], tuple[float], ndarray[np.float32], float]) – Rotation \(\beta\) around X axis, applied second.
gamma (Union[Tensor[float32], list[float], tuple[float], ndarray[np.float32], float]) – Rotation \(\gamma\) around Y axis, applied first.
k (Union[None, Tensor[float32], list[float], tuple[float], ndarray[np.float32], float], optional) – How many times the parity is applied. Default: None .

Returns

Tensor, representation wigner D matrix of O(3). The shape of Tensor is \((..., 2l+1, 2l+1)\) .

Examples

>>> m = Irrep(1, -1).wigD_from_angles(0, 0 ,0, 1)
>>> print(m)
[[-1,  0,  0],
[ 0, -1,  0],
[ 0,  0, -1]]

wigD_from_matrix(R)[source]

Compute the Wigner-D matrix representation of O(3) from rotation matrices.

Parameters: R (Tensor) – Rotation matrices. The shape of Tensor is \((..., 3, 3)\).
Returns: Tensor, representation wigner D matrix of O(3). The shape of Tensor is \((..., 2l+1, 2l+1)\).
Raises: TypeError – If R is not a Tensor.

Examples

>>> from mindspore import ops
>>> m = Irrep(1, -1).wigD_from_matrix(-ops.eye(3))
>>> print(m)
[[-1,  0,  0],
[ 0, -1,  0],
[ 0,  0, -1]]