用数据评估未知函数的积分 table

Question

我想找到 2 个有界区域。但是，我不知道蓝色曲线的功能，但我确实有它的数据 table。我查找并发现了使用 scipy.integrate.simps 的可能性，但我不知道如何指定该区域以红线（上或下）为界而不是 x 轴为界。

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import matplotlib
from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,
                               AutoMinorLocator)
from sklearn.linear_model import LinearRegression
from scipy import interpolate
from scipy import integrate

%matplotlib inline

file = pd.read_excel("T8.xlsx","Phthalansäureanhydrid",usecols=[2,3])
X = file['Zeit(s)']
Y = file['Temperatur(Celcius Grad)']

fig, ax = plt.subplots()
ax.plot(X,Y,'-',color='#10A5F3', label="Phthalansäureanhydrid")
ax.grid(True, which='major', axis='both', color='#F19211', linestyle='-')
#ax.grid(True, which='minor', axis='both', color='#F19211', linestyle='--')
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
#ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
#ax.legend(loc='upper center', frameon=True)

#major & minor ticks
ax.xaxis.set_major_locator(MultipleLocator(100))
ax.xaxis.set_major_formatter(FormatStrFormatter('%d'))
ax.xaxis.set_minor_locator(MultipleLocator(10))

#extrapolation - first line
temp1 = []
time1 = []
xnew1 = []
for i in file.index:
    if i > 630:
        temp1.append(file['Temperatur(Celcius Grad)'][i])
        time1.append(file['Zeit(s)'][i])
    else:
        xnew1.append(file['Zeit(s)'][i])

extrapo1 = InterpolatedUnivariateSpline(time1, temp1, k=1)
ynew1 = extrapo1(xnew1)

#extrapolation - second line
temp2 = []
time2 = []
xnew2 = []
for i in file.index:
    if 100<i<400:
        temp2.append(file['Temperatur(Celcius Grad)'][i])
        time2.append(file['Zeit(s)'][i])
    if i>400:
        xnew2.append(file['Zeit(s)'][i])

ynew2 = np.polyval(z,xnew2)
z = np.polyfit(time2,temp2,1)

#horizontal line
def hori(x):
    a = xnew1.index(x)
    b = xnew2.index(x)
    return np.linspace(ynew2[b],ynew1[a])

#integral

plt.plot(xnew1,ynew1,'-',color='black')
plt.plot(xnew2,ynew2,'-',color='black')
plt.plot([470]*len(hori(470)),hori(470),'--',color='red')

plt.savefig('phth.pdf')

Link 到数据：https://docs.google.com/spreadsheets/d/1xznXj-aA-Szq2s4KWb-qPWYxZbQNrA5FgUCQT6i7oVo/edit?usp=sharing

Answer 1

我将编写一个基本的说明性示例，以便您了解如何处理此类问题。这不是针对您的数据，但应该对您有所帮助：

import matplotlib.pyplot as plt
import numpy as np

# Here are my curves
x = np.linspace(0, np.pi/2, num=100)
blue = np.sin(x)
orange = np.linspace(0.5, 0.8, num=100)
green = np.linspace(0.1, 0.2, num=100)

# Here is a plot to illustrate my example
plt.plot(x, blue, x, orange, x, green)
plt.show()

这个地块已经标注了我想要计算的区域；蓝色曲线下方但以绿色和橙色曲线为界的区域：

因此，为了解决这个问题，我们将解决以下问题：

当它高于绿色且低于橙色时在蓝色曲线下方

并将其添加到区域
低于蓝色时在橙色曲线下方

然后减去面积
低于蓝色时在绿色曲线下方

这有点复杂，但请尝试描绘这些区域，以便您可以弄清楚我们为什么要添加和减去这些区域。我们可以使用 np.trapz 函数计算出这些区域，并只屏蔽我们想要的区域：

mask = (blue > green) * (blue < orange)
first_bullet_area = np.trapz(blue[mask], x[mask])
mask = (orange < blue)
second_bullet_area = np.trapz(orange[mask], x[mask])
mask = (green < blue)
third_bullet_area = np.trapz(green[mask], x[mask])

然后我们只需要做加减法：

>>> first_bullet_area + second_bullet_area - third_bullet_area
0.6190953349008973

用数据评估未知函数的积分 table

Evaluate integral of unknown function with data table

python

integral