python - 使用 NumPy 和 matplotlib 绘制的图形上未显示某些点

Question

对于下面的代码，其工作是对函数 f 执行蒙特卡罗积分，我想知道如果我将 f 定义为 y = sqrt(1-x^2)，这是单位四分之一圆的方程，并且指定一个大于 1 的端点，因为我们知道 f 仅定义为 0 import numpy as np
import matplotlib.pyplot as plt

def definite_integral_show(f, x0, x1, N):
"""Approximate the definite integral of f(x)dx between x0 and x1 using
N random points

Arguments:
f -- a function of one real variable, must be nonnegative on [x0, x1]
N -- the number of random points to use


"""
#First, let's compute fmax. We do that by evaluating f(x) on a grid
#of points between x0 and x1
#This assumes that f is generally smooth. If it's not, we're in trouble!
x = np.arange(x0, x1, 0.01)

y = f(x)
print(y)
f_max = max(y)


#Now, let's generate the random points. The x's should be between
#x0 and x1, so we first create points beterrm 0 and (x1-x0), and
#then add x0
#The y's should be between 0 and fmax
#
# 0...(x1-x0)
x_rand = x0 + np.random.random(N)*(x1-x0)
print(x_rand)

y_rand = 0 + np.random.random(N)*f_max



#Now, let's find the indices of the poitns above and below
#the curve. That is, for points below the curve, let's find
# i s.t. y_rand[i] < f(x_rand)[i]
#And for points above the curve, find
# i s.t. y_rand[i] >= f(x_rand)[i]
ind_below = np.where(y_rand < f(x_rand))
ind_above = np.where(y_rand >= f(x_rand))


#Finally, let's display the results
plt.plot(x, y, color = "red")
pts_below = plt.scatter(x_rand[ind_below[0]], y_rand[ind_below[0]], color = "green")
pts_above = plt.scatter(x_rand[ind_above[0]], y_rand[ind_above[0]], color = "blue")
plt.legend((pts_below, pts_above),
('Pts below the curve', 'Pts above the curve'),
loc='lower left',
ncol=3,
fontsize=8)


def f1(x):
    return np.sqrt(1-x**2)

definite_integral_show(f1, 0, 6, 200)

令我惊讶的是，该程序仍然有效，并为我提供了以下图片。

我怀疑它有效，因为在 NumPy 中，在对数组执行操作时，数组中的 nan 会被忽略。但是，我不明白为什么图片只包含 x 和 y 坐标都在 0 到 1 之间的点。不在此范围内的点在哪里，但其值由

x_rand = x0 + np.random.random(N)*(x1-x0)
y_rand = 0 +  np.random.random(N)*f_max

Answer 1

您可以只打印出数组(例如只生成一个随机点)，然后查看它们都不会进入 ind_below也不是 ind_above ...
那是因为所有涉及 nan 的比较返回 False . (另见: What is the rationale for all comparisons returning false for IEEE754 NaN values? )。 (所以 y_rand < nan 和 y_rand >= nan 都计算为 False )
更改代码的最简单方法是

ind_below = np.where(y_rand < f(x_rand))
ind_above = np.where(~(y_rand < f(x_rand)))

(可选地只计算一次数组)