<p>埃德的回答很好。但是,我注意到当有两个或无限(完全重叠)的接触点时,它不起作用。下面是处理这两种情况的代码版本。</p>
<p>如果您还想继续查看分布图,可以使用Ed的代码。</p>
<pre><code>import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
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)
# 'lower' and 'upper' represent the lower and upper bounds of the space within which we are computing the overlap
if(len(result)==0): # Completely non-overlapping
overlap = 0.0
elif(len(result)==1): # One point of contact
r = result[0]
if(m1>m2):
tm,ts=m2,std2
m2,std2=m1,std1
m1,std1=tm,ts
if(r<lower): # point of contact is less than the lower boundary. order: r-l-u
overlap = (norm.cdf(upper,m1,std1)-norm.cdf(lower,m1,std1))
elif(r<upper): # point of contact is more than the upper boundary. order: l-u-r
overlap = (norm.cdf(r,m2,std2)-norm.cdf(lower,m2,std2))+(norm.cdf(upper,m1,std1)-norm.cdf(r,m1,std1))
else: # point of contact is within the upper and lower boundaries. order: l-r-u
overlap = (norm.cdf(upper,m2,std2)-norm.cdf(lower,m2,std2))
elif(len(result)==2): # Two points of contact
r1 = result[0]
r2 = result[1]
if(r1>r2):
temp=r2
r2=r1
r1=temp
if(std1>std2):
tm,ts=m2,std2
m2,std2=m1,std1
m1,std1=tm,ts
if(r1<lower):
if(r2<lower): # order: r1-r2-l-u
overlap = (norm.cdf(upper,m1,std1)-norm.cdf(lower,m1,std1))
elif(r2<upper): # order: r1-l-r2-u
overlap = (norm.cdf(r2,m2,std2)-norm.cdf(lower,m2,std2))+(norm.cdf(upper,m1,std1)-norm.cdf(r2,m1,std1))
else: # order: r1-l-u-r2
overlap = (norm.cdf(upper,m2,std2)-norm.cdf(lower,m2,std2))
elif(r1<upper):
if(r2<upper): # order: l-r1-r2-u
print norm.cdf(r1,m1,std1), "-", norm.cdf(lower,m1,std1), "+", norm.cdf(r2,m2,std2), "-", norm.cdf(r1,m2,std2), "+", norm.cdf(upper,m1,std1), "-", norm.cdf(r2,m1,std1)
overlap = (norm.cdf(r1,m1,std1)-norm.cdf(lower,m1,std1))+(norm.cdf(r2,m2,std2)-norm.cdf(r1,m2,std2))+(norm.cdf(upper,m1,std1)-norm.cdf(r2,m1,std1))
else: # order: l-r1-u-r2
overlap = (norm.cdf(r1,m1,std1)-norm.cdf(lower,m1,std1))+(norm.cdf(upper,m2,std2)-norm.cdf(r1,m2,std2))
else: # l-u-r1-r2
overlap = (norm.cdf(upper,m1,std1)-norm.cdf(lower,m1,std1))
</code></pre>