Area between two curves-CodePudding

I was able to plot the lines and fill the area in between, however, I'm trying to calculate the area between the two curves. I cant use the integral since I don't have the equation, I only have a bunch of points. How can I calculate the area in between?

fig,ax1= plt.subplots(figsize=(8,5))
plt.plot(Lag_Distance,True_Values,color='blue',label='Sampled Variogram'); plt.scatter(Lag_Distance,True_Values,color='blue',edgecolor='blue',zorder=10)
plt.plot(Lag_Distance,a['Variogram Value'],color='black',label='Estimated Variogram (P=1)'); plt.scatter(Lag_Distance,a['Variogram Value'],color='black',edgecolor='black',zorder=10) 
plt.fill_between(Lag_Distance,a['Variogram Value'],True_Values,color='red',alpha=0.2)
plt.legend(loc='lower right',fontsize=20)
ax1.set_xlabel('Lag Distance',fontsize=20);
ax1.set_ylabel('$^\gamma$',fontsize=30);
ax1.set_title(' Variogram in the major direction 160 (P =1) ',fontsize=20);
plt.subplots_adjust(left=0.0,bottom=0.0,right=1.0,top=1.1); plt.show() # set plot size

enter image description here

CodePudding user response：

Since all of the points are connected by lines, integrating using the trapezoid rule will give you the exact area.

The numpy library has a trapezoidal integration function so you can take the difference between the area under the estimated variogram and the area under the sampled variogram:

import numpy as np

area = np.trapz(y=a['Variogram Value'] - True_Values, x=Lag_Distance)