Python在4维球体上的点的均匀分布 [英] Python Uniform distribution of points on 4 dimensional sphere

问题描述

我需要在4维球体上均匀分布点.我知道这并不像选择3个角度并使用极坐标那样简单.

I need a uniform distribution of points on a 4 dimensional sphere. I know this is not as trivial as picking 3 angles and using polar coordinates.

我使用的3维尺寸

from random import random

u=random()
costheta = 2*u -1 #for distribution between -1 and 1
theta = acos(costheta)
phi = 2*pi*random

x=costheta
y=sin(theta)*cos(phi)
x=sin(theta)*sin(phi)

这给出了x，y和z的均匀分布.

This gives a uniform distribution of x, y and z.

如何获得4维的相似分布?

How can I obtain a similar distribution for 4 dimensions?

推荐答案

一种标准方式，也许不是最快的，是使用穆勒方法在N-球形:

A standard way, though, perhaps not the fastest, is to use Muller's method to generate uniformly distributed points on an N-sphere:

import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d.axes3d as axes3d

N = 600
dim = 3

norm = np.random.normal
normal_deviates = norm(size=(dim, N))

radius = np.sqrt((normal_deviates**2).sum(axis=0))
points = normal_deviates/radius

fig, ax = plt.subplots(subplot_kw=dict(projection='3d'))
ax.scatter(*points)
ax.set_aspect('equal')
plt.show()

只需将dim = 3更改为dim = 4即可在4个球体上生成点.

Simply change dim = 3 to dim = 4 to generate points on a 4-sphere.

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