python 中圆圈内除外的随机数生成器

Question

我想在二维数据x(0,1)和y(0,1)中生成750个随机数

X1 = np.random.random((750,2))

但是，我想确保我在圆形区域中没有任何值，例如

我可以删除该值，但我想将随机数固定为 750。生成此类列表的最佳方法是什么？

Answer 1

你可以直接应用毕达哥拉斯定理。这是我的代码

import numpy as np
import matplotlib.pyplot as plt

dist = 0.2

X1 = np.random.random((750,2))
X2 = [x for x in X1 if (x[0]-0.5)**2 + (x[1]-0.5)**2 > dist**2] # filter values that are to close to center

# for plotting
x = [x[0] for x in X2]
y = [y[1] for y in X2]
plt.scatter(x,y)
plt.show()

Answer 2

import random
points = []
radius = 1
num_points=1500
index = 0
max_coord = 750
while index < num_points:
  x=random.random()*max_coord
  y=random.random()*max_coord
  if x**2 + y**2 > radius**2:
    points = points + [[x,y]]
    index = index + 1
print(points)

更改max_coor以获得更大的数字。这只会给您在给定半径 = 1 的圆之外的 1500 个点。每个坐标在 0 和 750 之间变化

Answer 3

您可以使用一种名为 rejection sampling. Generate candidate values and see if they meet your constraints. If so, accept them, otherwise reject and repeat. With 2-d sampling, the probability of acceptance on a given trial is P{Accept} = Area(acceptance region) / Area(generating region). Repetitions due to rejection are independent, so the number of trials has a geometric distribution 且参数为 p = P{Accept} 的著名技术来执行此操作和 Expected # trials = 1 / P{Accept}。例如，如果拒绝区域是一个以单位正方形为中心的半径为 1/2 的圆，P{Accept} = (4 - Pi)/4 平均每个生成的值需要 4/(4 - Pi) (approximately 4.66) 次尝试。显然，如果半径 >= sqrt(2)/2，这将不起作用，并且当您接近该限制时会变得昂贵。

请注意，拒绝圆不需要以正方形为中心，您只需拒绝距离圆心小于半径的任何候选人。

代码如下：

import numpy as np

def generate_pt(exclusion_radius):
    while True:
        candidate = np.random.sample(2)
        # The following assumes the rejection circle is centered at (0.5, 0.5).
        # Adjust by subtracting individual x/y coordinates for the center of
        # the circle if you don't want it centered.  Acceptance/rejection
        # distance is determined by Pythagorean theorem.
        if np.sum(np.square(candidate - 0.5)) >= exclusion_radius * exclusion_radius:
            return candidate

# Generate 750 points outside the centered circle of radius 0.3.
data = np.array([generate_pt(0.3) for _ in range(750)])

python 中圆圈内除外的随机数生成器

random numer generation except inside of the circle in python

python

database

random

training-data