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I would like to create lines between subplots in pyplot as illustrated by the red dashed lines here (added in a pdf editor).

I've read documentation on connectionpatch, but I'm having difficulty making sense of the examples well enough to translate to my particular case. For my case, I've included a simplified version of my code, using the same axes structures in case that is relevant. How do I create these dashed lines between subplots?

import numpy as np
import matplotlib.pyplot as plt

# Create a 2 x 2 grid: (row, column) 
fig, ax = plt.subplots(2,2) 

# Create a subplot to share common x and y labels
fig.add_subplot(111, frameon=False)
plt.tick_params(
top='off', 
bottom='off', 
left='off', 
right='off')
plt.grid(False)
plt.xlabel('x')
plt.ylabel('function(x)')

# x-axis
x = np.linspace(0,2*np.pi,100)

# Top left
ax[0,0].tick_params(
axis='both', 
which='both', 
bottom=False, 
left=False,
top=False, 
right=False,
labelbottom=False, 
labelleft=False,)
ax[0,0].plot(x,np.sin(x),color='grey')

# Top Right
ax[0,1].tick_params(
axis='both', 
which='both', 
bottom=False, 
left=False,
top=False, 
right=False,
labelbottom=False, 
labelleft=False,)
ax[0,1].plot(x,np.sin(2*x),color='grey')


# Bottom Left
ax[1,0].tick_params(
axis='both', 
which='both', 
bottom=False, 
left=False,
top=False, 
right=False,
labelbottom=False, 
labelleft=False,)
ax[1,0].plot(x,np.cos(x), color='black')

# Bottom Right
ax[1,1].tick_params(
axis='both', 
which='both', 
bottom=False, 
left=False,
top=False, 
right=False,
labelbottom=False, 
labelleft=False,)
ax[1,1].plot(x,np.cos(2*x), color='black')

plt.tight_layout(h_pad=2.5)

The ConnectionPatch example shows how to use a ConnectionPatch to connect two axes. For your case you would do it like this:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import ConnectionPatch

fig, axes = plt.subplots(2,2) 

# Create a subplot to share common x and y labels
frameax = fig.add_subplot(111, frameon=False)
frameax.grid(False)
frameax.set_xlabel('x', labelpad=10)
frameax.set_ylabel('function(x)',labelpad=10)

for ax in list(axes.flat) + [frameax]:
 ax.tick_params(axis='both', which='both', 
 bottom=False, left=False, top=False, right=False,
 labelbottom=False, labelleft=False)

# x-axis
x = np.linspace(0,2*np.pi,100)

axes[0,0].plot(x,np.sin(x),color='grey')
axes[0,1].plot(x,np.sin(2*x),color='grey')
axes[1,0].plot(x,np.cos(x), color='black')
axes[1,1].plot(x,np.cos(2*x), color='black')

kw = dict(linestyle="--", color="red")
cp1 = ConnectionPatch((.5, 0), (.5, 1), "axes fraction", "axes fraction",
 axesA=axes[0,0], axesB=axes[1,0], **kw)
cp2 = ConnectionPatch((.5, 0), (.5, 1), "axes fraction", "axes fraction",
 axesA=axes[0,1], axesB=axes[1,1], **kw)

for cp in (cp1, cp2):
 axes[1,1].add_artist(cp)

plt.show()