mindchemistry.e3.o3.Irreps

class mindchemistry.e3.o3.Irreps(irreps=None)[source]

Direct sum of irreducible representations 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.

Parameters

irreps (Union[str, Irrep, Irreps, List[Tuple[int]]]) – a string to represent the direct sum of irreducible representations.

Raises

ValueError – If irreps cannot be converted to an Irreps.
ValueError – If the mul part of irreps part is negative.
TypeError – If the mul part of irreps part is not int.

Supported Platforms:: Ascend

Examples

>>> from mindchemistry.e3.o3 import Irreps
>>> x = Irreps([(100, (0, 1)), (50, (1, 1))])
100x0e+50x1e
>>> x.dim
250
>>> Irreps("100x0e+50x1e+0x2e")
100x0e+50x1e+0x2e
>>> Irreps("100x0e+50x1e+0x2e").lmax
1
>>> Irrep("2e") in Irreps("0e+2e")
True
>>> Irreps(), Irreps("")
(, )
>>> Irreps('2x1o+1x0o') * Irreps('2x1o+1x0e')
4x0e+1x0o+2x1o+4x1e+2x1e+4x2e

count(ir)[source]

Multiplicity of ir.

Parameters: ir (Irrep) – Irrep
Returns: int, total multiplicity of ir.

Examples

>>> Irreps("1o + 3x2e").count("2e")
3

decompose(v, batch=False)[source]

Decompose a vector by Irreps.

Parameters

v (Tensor) – the vector to be decomposed.
batch (bool) – whether reshape the result such that there is at least a batch dimension. Default: False.

Returns

List of Tensors, the decomposed vectors by Irreps.

Raises

TypeError – If v is not Tensor.
ValueError – If length of the vector v is not matching with dimension of Irreps.

Examples

>>> import mindspore as ms
>>> input = ms.Tensor([1, 2, 3])
>>> m = Irreps("1o").decompose(input)
>>> print(m)
[Tensor(shape=[1,3], dtype=Int64, value=
[[1,2,3]])]

filter(keep=None, drop=None)[source]

Filter the Irreps by either keep or drop.

Parameters

keep (Union[str, Irrep, Irreps, List[str, Irrep]]) – list of irrep to keep. Default: None.
drop (Union[str, Irrep, Irreps, List[str, Irrep]]) – list of irrep to drop. Default: None.

Returns

Irreps, filtered irreps.

Raises

ValueError – If both keep and drop are not None.

Examples

>>> Irreps("1o + 2e").filter(keep="1o")
1x1o
>>> Irreps("1o + 2e").filter(drop="1o")
1x2e

randn(*size, normalization='component')[source]

Random tensor.

Parameters

*size (List[int]) – size of the output tensor, needs to contains a -1.
normalization (str) – {'component', 'norm'}, type of normalization method.

Returns

Tensor, the shape is size where -1 is replaced by self.dim.

Examples

>>> Irreps("5x0e + 10x1o").randn(5, -1, 5, normalization='norm').shape
(5, 35, 5)

remove_zero_multiplicities()[source]

Remove any irreps with multiplicities of zero.

Returns: Irreps

Examples

>>> Irreps("4x0e + 0x1o + 2x3e").remove_zero_multiplicities()
4x0e+2x3e

simplify()[source]

Simplify the representations.

Returns: Irreps

Examples

>>> Irreps("1e + 1e + 0e").simplify()
2x1e+1x0e
>>> Irreps("1e + 1e + 0e + 1e").simplify()
2x1e+1x0e+1x1e

sort()[source]

Sort the representations by increasing degree.

Returns

irreps (Irreps) - sorted Irreps

p (tuple[int]) - permute orders. p[old_index] = new_index

inv (tuple[int]) - inversed permute orders. p[new_index] = old_index

Examples

>>> Irreps("1e + 0e + 1e").sort().irreps
1x0e+1x1e+1x1e
>>> Irreps("2o + 1e + 0e + 1e").sort().p
(3, 1, 0, 2)
>>> Irreps("2o + 1e + 0e + 1e").sort().inv
(2, 1, 3, 0)

static spherical_harmonics(lmax, p=- 1)[source]

Representation of the spherical harmonics.

Parameters

lmax (int) – maximum of l.
p (int) – {1, -1}, the parity of the representation.

Returns

Irreps, representation of \((Y^0, Y^1, \dots, Y^{\mathrm{lmax}})\).

Examples

>>> Irreps.spherical_harmonics(3)
1x0e+1x1o+1x2e+1x3o
>>> Irreps.spherical_harmonics(4, p=1)
1x0e+1x1e+1x2e+1x3e+1x4e

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

Representation wigner D matrices of O(3) from Euler angles.

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]) – 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 = Irreps("1o").wigD_from_angles(0, 0 ,0, 1)
>>> print(m)
[[-1,  0,  0],
[ 0, -1,  0],
[ 0,  0, -1]]

wigD_from_matrix(R)[source]

Representation wigner D matrices 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

>>> m = Irreps("1o").wigD_from_matrix(-ops.eye(3))
>>> print(m)
[[-1,  0,  0],
[ 0, -1,  0],
[ 0,  0, -1]]