Python:在x中以不均匀的步长积分曲线下面积 [英] Python: integrating area under curve with uneven steps in x

问题描述

我有一个 y 值列表和一个 x 值列表.我想找到由这些点定义的曲线下的面积.对于具有均匀间距的 x 值，我找到了几个解决此问题的方法:

1) 给定一组坐标，在不知道函数的情况下计算曲线下的面积

2) 使用scipy对样本进行离散积分

但是当 x 值不均匀分布时，这两种方法都不起作用.

例如:

<预><代码>>>>从 scipy.integrate 导入 simps>>>y = np.array([1,1,1,1])>>>x = np.array([0,5,20,30])>>>辛普斯(y，x)-inf

当然，在上面的代码中使用 x = np.array([0,10,20,30]) 返回 30.0，正如预期的那样.

谁能建议一种方法来找到 x 间距不均匀的曲线下的面积?

解决方案

我只想找一个简单的梯形规则:

将 numpy 导入为 npx = np.array([0,5,20,30])y = np.array([1,1,1,1])s = np.sum((x[1:] - x[:-1]) * (y[1:] + y[:-1])/2)# 和...一样# s = 0.0# 对于范围内的 k(len(x) - 1):# s += (x[k+1] - x[k]) * (y[k+1] + y[k])/2印刷)

30.0

I have a list of y values and a list of x values. I would like to find the area under the curve defined by these points. I have found a couple of solutions to this problem for x values with even spacing:

1) Calculating the area under a curve given a set of coordinates, without knowing the function

2) Using scipy to perform discrete integration of the sample

But neither of these works when the x values are not evenly spaced.

For example:

>>> from scipy.integrate import simps
>>> y = np.array([1,1,1,1])
>>> x = np.array([0,5,20,30])
>>> simps(y,x)
-inf

Of course, using x = np.array([0,10,20,30]) in the above code returns 30.0, as expected.

Can anyone suggest a way to find the area under a curve with uneven x-spacing?

解决方案

I'd just go for a simple trapezoidal rule:

import numpy as np

x = np.array([0,5,20,30])
y = np.array([1,1,1,1])

s = np.sum((x[1:] - x[:-1]) * (y[1:] + y[:-1]) / 2)
# same as
# s = 0.0
# for k in range(len(x) - 1):
#    s += (x[k+1] - x[k]) * (y[k+1] + y[k]) / 2

print(s)

30.0

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