Python: finding the intersection point of two gaussian curves

问题

I have two gaussian plots:

x = np.linspace(-5,9,10000)
plot1=plt.plot(x,mlab.normpdf(x,2.5,1))
plot2=plt.plot(x,mlab.normpdf(x,5,1))

and I want to find the point at where the two curves intersect. Is there a way of doing this? In particular I want to find the value of the x-coordinate where they meet.

回答1:

You want to find the x's such that both gaussian functions have the same height.(i.e intersect)

You can do so by equating two gaussian functions and solve for x. In the end you will get a quadratic equation with coefficients relating to the gaussian means and variances. Here is the final result:

import numpy as np

def solve(m1,m2,std1,std2):
  a = 1/(2*std1**2) - 1/(2*std2**2)
  b = m2/(std2**2) - m1/(std1**2)
  c = m1**2 /(2*std1**2) - m2**2 / (2*std2**2) - np.log(std2/std1)
  return np.roots([a,b,c])

m1 = 2.5
std1 = 1.0
m2 = 5.0
std2 = 1.0

result = solve(m1,m2,std1,std2)

The output is :

array([ 3.75])

You can plot the found intersections:

x = np.linspace(-5,9,10000)
plot1=plt.plot(x,mlab.normpdf(x,m1,std1))
plot2=plt.plot(x,mlab.normpdf(x,m2,std2))
plot3=plt.plot(result,mlab.normpdf(result,m1,std1),'o')

The plot will be:

If your gaussians have multiple intersections, the code will also find all of them(say m1=2.5, std1=3.0, m2=5.0, std2=1.0):

来源：https://stackoverflow.com/questions/22579434/python-finding-the-intersection-point-of-two-gaussian-curves