Python: finding the intersection point of two gaussian curves

Question

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

Answer 1

Here's a solution based on purely numpy that is also applicable to curves other than Gaussian.

def get_intersection_locations(y1,y2,test=False,x=None): 
    """
    return indices of the intersection point/s.
    """
    idxs=np.argwhere(np.diff(np.sign(y1 - y2))).flatten()
    if test:
        x=range(len(y1)) if x is None else x
        plt.figure(figsize=[2.5,2.5])
        ax=plt.subplot()
        ax.plot(x,y1,color='r',label='line1',alpha=0.5)
        ax.plot(x,y2,color='b',label='line2',alpha=0.5)
        _=[ax.axvline(x[i],color='k') for i in idxs]
        _=[ax.text(x[i],ax.get_ylim()[1],f"{x[i]:1.1f}",ha='center',va='bottom') for i in idxs]
        ax.legend(bbox_to_anchor=[1,1])
        ax.set(xlabel='x',ylabel='density')
    return idxs

# single intersection
x = np.arange(-10, 10, 0.001)
y1=sc.stats.norm.pdf(x,-2,2)
y2=sc.stats.norm.pdf(x,2,3)
get_intersection_locations(y1=y1,y2=y2,x=x,test=True) # returns indice/s array([10173])

# double intersection
x = np.arange(-10, 10, 0.001)
y1=sc.stats.norm.pdf(x,-2,1)
y2=sc.stats.norm.pdf(x,2,3)
get_intersection_locations(y1=y1,y2=y2,x=x,test=True)

Based on an answer to a similar question.