python - 在圆内生成均匀分布的点

Question

''' 我试图在一个应该均匀分布的圆圈中生成点，但我得到了一个奇怪的模式。如果我将半径 R 增加到一个非常大的值，则分布看起来是正常的，但 R 值较小时会产生螺旋。有什么改进代码的建议吗？'''

from numpy.random import uniform
#from scipy.stats import uniform
import matplotlib.pyplot as plt
import numpy as np
import math  

R = 5
# Generate uniformly distributed random numbers.
rand_num = []
for i in range(30000):
    rand_num.append(np.random.uniform(0,1))

# Use these generated numbers to obtain the CDF of the radius which is the true radius i.e. r = R*sqrt(random()).
radius = []
for n,data in enumerate(rand_num):
    radius.append(R*math.sqrt(data))

# Generate the angle using the same uniformly distributed random numbers.
theta2 = []
for n, k in enumerate(radius):
    theta2.append(2*math.pi*radius[n])

# Calculate the corresponding x-coordinate.
x = []
for j,v in enumerate(radius):
    x.append(radius[j]*math.cos(theta2[j]))
x = np.array(x)   

# Calculate the correspoding y-coordinate.
y = []    
for j,v in enumerate(radius):
    y.append(radius[j]*math.sin(theta2[j]))
y = np.array(y)

# Finally plot the coordinates.
plt.figure(figsize=(10,10))
plt.scatter(x, y, marker='o')

Answer 1

是的，代码应该给你一个螺旋，因为两者都theta与radius成正比rand_num。相反，您应该theta独立生成radius。此外，使用 numpy 的矢量化运算符而不是数学的

R = 5
num_points = 10000

np.random.seed(1)
theta = np.random.uniform(0,2*np.pi, num_points)
radius = np.random.uniform(0,R, num_points) ** 0.5

x = radius * np.cos(theta)
y = radius * np.sin(theta)

# visualize the points:
plt.scatter(x,y, s=1)

输出：