四元数奇异值分解 matlab代码
时间: 2023-11-25 10:07:22 浏览: 47
以下是 MATLAB 代码,用于计算四元数的奇异值分解:
```matlab
function [U,S,V] = quat_svd(q)
% QUAT_SVD Compute Singular Value Decomposition (SVD) of a Quaternion
% [U,S,V] = quat_svd(q) calculates the Singular Value Decomposition of a
% quaternion q, where q is a 4x1 vector [w x y z], and returns the left
% singular vectors U, singular values S, and right singular vectors V.
%
% See also SVD.
% Convert quaternion to 3x3 rotation matrix
R = quat2rotm(q);
% Calculate SVD of rotation matrix
[U,S,V] = svd(R);
end
```
注意:在使用此代码之前,需要先安装 Robotics System Toolbox。
相关问题
四元数奇异值分解 Python代码
以下是使用Python实现四元数奇异值分解(Quaternion Singular Value Decomposition)的代码:
```python
import numpy as np
from scipy.linalg import sqrtm
def quaternion_svd(Q):
"""
Perform Quaternion Singular Value Decomposition (QSVD) on a quaternion matrix Q.
Args:
Q (np.array): A 4x4 quaternion matrix.
Returns:
U (np.array): A 4x4 unitary quaternion matrix.
sigma (np.array): A 4x1 vector of singular values.
V (np.array): A 4x4 unitary quaternion matrix.
"""
# Construct the Hermitian matrix H from Q
H = np.zeros((4, 4), dtype=np.complex64)
H[:3, :3] = Q[1:, 1:] - Q[0, 0] * np.identity(3)
H[:3, 3] = Q[1:, 0]
H[3, :3] = np.conj(Q[1:, 0])
H[3, 3] = Q[0, 0]
# Compute the eigenvectors and eigenvalues of H
eigvals, eigvecs = np.linalg.eig(H)
# Sort the eigenvectors based on the magnitude of their eigenvalues
idx = np.argsort(np.abs(eigvals))[::-1]
eigvecs = eigvecs[:, idx]
# Compute the left and right singular vectors of Q
U = np.zeros((4, 4), dtype=np.complex64)
V = np.zeros((4, 4), dtype=np.complex64)
for i in range(4):
v = eigvecs[:, i]
u = Q @ v
U[:, i] = u / np.linalg.norm(u)
V[:, i] = v / np.linalg.norm(v)
# Compute the singular values of Q
sigma = np.sqrt(np.abs(eigvals[idx]))
return U, sigma, V
```
这个函数接受一个 $4 \times 4$ 的四元数矩阵作为输入,返回左奇异向量矩阵 $U$,奇异值向量 $\sigma$ 和右奇异向量矩阵 $V$。其中,左奇异向量矩阵和右奇异向量矩阵都是 $4 \times 4$ 的 unitary quaternion 矩阵,而奇异值向量是一个 $4 \times 1$ 的向量。
注意,这个代码依赖于 NumPy 和 SciPy 库。
对偶四元数转XYZ欧拉角Matlab代码
对偶四元数转XYZ欧拉角的Matlab代码如下:
```matlab
function euler = dualQuaternionToEuler(dq)
q1 = dq.q1;
q2 = dq.q2;
q3 = dq.q3;
q4 = dq.q4;
R = [q1^2 + q2^2 - q3^2 - q4^2, 2*(q2*q3 - q1*q4), 2*(q2*q4 + q1*q3);
2*(q2*q3 + q1*q4), q1^2 - q2^2 + q3^2 - q4^2, 2*(q3*q4 - q1*q2);
2*(q2*q4 - q1*q3), 2*(q3*q4 + q1*q2), q1^2 - q2^2 - q3^2 + q4^2];
euler = [atan2(R(3, 2), R(3, 3));
atan2(-R(3, 1), sqrt(R(3, 2)^2 + R(3, 3)^2));
atan2(R(2, 1), R(1, 1))];
end
```