# Copyright 2021-2023 @ Shenzhen Bay Laboratory &
# Peking University &
# Huawei Technologies Co., Ltd
#
# This code is a part of MindSPONGE:
# MindSpore Simulation Package tOwards Next Generation molecular modelling.
#
# MindSPONGE is open-source software based on the AI-framework:
# MindSpore (https://www.mindspore.cn/)
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ============================================================================
"""
Quaternion
"""
from mindspore import numpy as msnp
from mindspore import ops
[文档]def hamiltonian_product(quaternion_1, tensor_2):
""" Get the Hamiltonian-product of the given quaternion and tensor.
Args:
quaternion_1 (Tensor): A tensor to calculate.
tensor_2 (Tensor): A tensor to calculate.
Returns:
The hamiltonian product result.
"""
if quaternion_1.ndim == 1:
quaternion_1 = quaternion_1[None, :]
if tensor_2.ndim == 1:
tensor_2 = tensor_2[None, :]
inverse_quaternion = quaternion_inverse(quaternion_1)
op1 = quaternion_multiply(tensor_2, inverse_quaternion)
res = quaternion_multiply(quaternion_1, op1)
return res
[文档]def quaternion_multiply(tensor_1, tensor_2):
""" Get the quaternion multiplication of the given tensor.
Args:
tensor_1 (Tensor): A tensor to calculate.
tensor_2 (Tensor): The other tensor to calculate.
Returns:
The multiplication result.
"""
if tensor_1.ndim == 1:
tensor_1 = tensor_1[None, :]
if tensor_2.ndim == 1:
tensor_2 = tensor_2[None, :]
if tensor_1.shape[-1] == 1 and tensor_2.shape[-1] == 4:
return _constant_multiply(tensor_2, tensor_1)
if tensor_2.shape[-1] == 1 and tensor_1.shape[-1] == 4:
return _constant_multiply(tensor_1, tensor_2)
if tensor_1.shape[-1] == 3:
tensor_1 = msnp.pad(tensor_1, ((0, 0), (1, 0)), mode='constant', constant_value=0)
return quaternion_multiply(tensor_1, tensor_2)
if tensor_2.shape[-1] == 3:
tensor_2 = msnp.pad(tensor_2, ((0, 0), (1, 0)), mode='constant', constant_value=0)
return quaternion_multiply(tensor_1, tensor_2)
return _quaternion_multiply(tensor_1, tensor_2)
[文档]def quaternion_inverse(tensor_1):
""" Get the quaternion conjugate of the given tensor.
Args:
tensor_1 (Tensor): A tensor to calculate.
Returns:
tensor_2(Tensor), The multiplication result with shape (B, 4).
"""
if tensor_1.ndim == 1:
tensor_1 = tensor_1[None, :]
if tensor_1.shape[-1] == 1:
return msnp.pad(tensor_1, ((0, 0), (0, 3)), mode='constant', constant_value=0)
if tensor_1.shape[-1] == 3:
return -msnp.pad(tensor_1, ((0, 0), (0, 3)), mode='constant', constant_value=0) / (msnp.norm(
tensor_1, axis=-1
)[:, None] ** 2)
return msnp.hstack((tensor_1[:, 0][:, None], -tensor_1[:, 1:])) / (msnp.norm(
tensor_1, axis=-1
)[:, None] ** 2)
def _quaternion_multiply(tensor_1, tensor_2):
""" Get the quaternion multiplication of the given tensor.
Args:
tensor_1 (Tensor): A tensor with shape (B, 4).
tensor_2 (Tensor): A tensor with shape (B, 4).
Returns:
q(Tensor), A tensor with shape (B, 4).
"""
if tensor_1.shape[-1] != 4 or tensor_2.shape[-1] != 4:
raise ValueError('The input tensor shape for quaternion_multiply should be like (B, 4) or (4, ).')
s_1 = tensor_1[:, 0]
s_2 = tensor_2[:, 0]
v_1 = tensor_1[:, 1:]
v_2 = tensor_2[:, 1:]
s = s_1 * s_2
d = ops.batch_dot(v_1, v_2, axes=-1)
s -= d
v = msnp.zeros_like(v_1)
v += s_1 * v_2
v += v_1 * s_2
v += msnp.cross(v_1, v_2, axisc=-1)
q = msnp.hstack((s, v))
return q
def _constant_multiply(tensor_1, constant):
""" Get the quaternion multiplication of the given tensor and constant.
Args:
tensor_1 (Tensor): A tensor with shape (B, 4).
constant (Tensor): A tensor with shape (B, 1).
Returns:
A tensor with shape (B, 4).
"""
return tensor_1 * constant