Main figure legend outside of subplots

Question

I have a number of subplots within a single figure. Each figure plots multiple lines that represent the same thing (represented by color) but in different situations (different subplots). I would like to create a legend at the base of the figure showing what the color of the line means. However, I running into a problem with getting the legend to not overlap the subplots and if I can adjust the axes, getting the legend to save.

I have tried a few different solutions with some help here but have been unable to adapt to subplots. Below is an example code that I am working with.

import numpy as np
import matplotlib.pyplot as plt

m1=1
m2=10

x=np.linspace(0,100,num=101,endpoint=True)
y1m1=m1*x**2
y2m1=m1*x**0.5
y1m2=m2*x**2
y2m2=m2*x**0.5

fig=plt.figure(figsize=(4,4))
ax1=fig.add_subplot(211)
ax1.plot(x,y1m1,'b',label=r'$x^2$')
ax1.plot(x,y2m1,'r',label=r'$\sqrt{x}$')
ax2=fig.add_subplot(212)
ax2.plot(x,y1m2,'b')
ax2.plot(x,y2m2,'r')
fig.legend(loc='lower center',ncol=2)
fig.tight_layout()
fig.savefig('examplefig.png',dpi=300)
plt.show()

My goal is to save the output to a png for a good figure.

Answer 1

This is one way of doing it using the suggestion provided here. The idea is to add the legend at position with respect to a given axis object. In your case, since you want to add the legend at the base, it is preferred you specify the position relative to ax2. Using ncol=2 is a matter of personal choice.

fig=plt.figure(figsize=(4,4))
ax1=fig.add_subplot(211)
l1, = ax1.plot(x,y1m1,'b')
l2, = ax1.plot(x,y2m1,'r')
ax2=fig.add_subplot(212)
ax2.plot(x,y1m2, 'b')
ax2.plot(x,y2m2, 'r')

ax2.legend(handles = [l1,l2] , labels=[r'$x^2$', r'$\sqrt{x}$'],
           bbox_to_anchor=(0.7, -0.2), ncol=2)

fig.tight_layout()