如何通过python或numpy将两个四元数相乘 [英] How to multiply two quaternions by python or numpy

问题描述

我有两个四元数:Q1 = w0，x0，y0，z0和Q2 = w1，x1，y1，z1.我想通过使用NumPy或可以返回二维数组的Python函数将它们相乘.我在网上找到了一些由Christoph Gohlke编写的伪代码来进行这种乘法.我尝试了很多，但未能应用.有人可以帮我做这种乘法吗?伪代码在这里:`

I have two quaternions: Q1= w0, x0, y0, z0 and Q2 = w1, x1, y1, z1. I would like to multiply them by using NumPy or Python function which can return 2-d array. I found some pseudocodes on the internet which is written by Christoph Gohlke to do this kind of multiplication. I tried a lot but failed to apply it. Can anyone help me please to do this kind of multiplication? The pseudocodes are here: `

def quaternion_multiply(quaternion1, quaternion0):
w0, x0, y0, z0 = quaternion0
w1, x1, y1, z1 = quaternion1
return array([-x1*x0 - y1*y0 - z1*z0 + w1*w0,
                     x1*w0 + y1*z0 - z1*y0 + w1*x0,
                    -x1*z0 + y1*w0 + z1*x0 + w1*y0,
                     x1*y0 - y1*x0 + z1*w0 + w1*z0], dtype=float64)` 

推荐答案

以下是使用您的函数的一个小示例:

Here's a little example using your function:

import numpy as np
import random


def quaternion_multiply(quaternion1, quaternion0):
    w0, x0, y0, z0 = quaternion0
    w1, x1, y1, z1 = quaternion1
    return np.array([-x1 * x0 - y1 * y0 - z1 * z0 + w1 * w0,
                     x1 * w0 + y1 * z0 - z1 * y0 + w1 * x0,
                     -x1 * z0 + y1 * w0 + z1 * x0 + w1 * y0,
                     x1 * y0 - y1 * x0 + z1 * w0 + w1 * z0], dtype=np.float64)

N = 4
for i in range(N):
    q1 = np.random.rand(4)
    q2 = np.random.rand(4)
    q = quaternion_multiply(q1, q2)
    print("{0} x {1} = {2}".format(q1, q2, q))

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