在不知道函数的情况下，计算给定一组坐标的曲线下面积

我有一个100个数字的列表，作为 Y 轴的高度，作为 X 轴的长度: 1到100，步长为5。我需要使用矩形和 Scipy 计算(x，y)点和 X 轴的曲线所包含的面积。我需要找到这条曲线的函数吗？还是不要？几乎我读过的所有例子都是关于 Y 轴的一个特定方程式。在我的例子中，没有等式，只有列表中的数据。经典的解决方案是加上或 Y 点和乘以步骤 X 的距离... 使用 Scipy 有什么想法吗？

请问，有没有人能推荐一本关于数值(有限基本)方法的书，使用 Scipy 和 Numpy? ..。

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You can use Simpsons rule or the Trapezium rule to calculate the area under a graph given a table of y-values at a regular interval.

Python script that calculates Simpsons rule:

def integrate(y_vals, h):
i = 1
total = y_vals[0] + y_vals[-1]
for y in y_vals[1:-1]:
if i % 2 == 0:
total += 2 * y
else:
total += 4 * y
i += 1
return total * (h / 3.0)

h is the offset (or gap) between y values, and y_vals is an array of well, y values.

Example (In same file as above function):

y_values = [13, 45.3, 12, 1, 476, 0]
interval = 1.2
area = integrate(y_values, interval)
print("The area is", area)
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The numpy and scipy libraries include the composite trapezoidal (numpy.trapz) and Simpson's (scipy.integrate.simpson) rules.

Here's a simple example. In both trapz and simpson, the argument dx=5 indicates that the spacing of the data along the x axis is 5 units.

import numpy as np
from scipy.integrate import simpson
from numpy import trapz




# The y values.  A numpy array is used here,
# but a python list could also be used.
y = np.array([5, 20, 4, 18, 19, 18, 7, 4])


# Compute the area using the composite trapezoidal rule.
area = trapz(y, dx=5)
print("area =", area)


# Compute the area using the composite Simpson's rule.
area = simpson(y, dx=5)
print("area =", area)

Output:

area = 452.5
area = 460.0
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If you have sklearn installed, a simple alternative is to use sklearn.metrics.auc

This computes the area under the curve using the trapezoidal rule given arbitrary x, and y array

import numpy as np
from sklearn.metrics import auc


dx = 5
xx = np.arange(1,100,dx)
yy = np.arange(1,100,dx)


print('computed AUC using sklearn.metrics.auc: {}'.format(auc(xx,yy)))
print('computed AUC using np.trapz: {}'.format(np.trapz(yy, dx = dx)))

both output the same area: 4607.5

the advantage of sklearn.metrics.auc is that it can accept arbitrarily-spaced 'x' array, just make sure it is ascending otherwise the results will be incorrect


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