Position colorbar inside figure

Question

I have a simple scatter plot where each point has a color given by a value between 0 and 1 set to a chosen colormap. Here's a MWE of my code:

import matplotlib.pyplot as plt 
import numpy as np
import matplotlib.gridspec as gridspec

x = np.random.randn(60) 
y = np.random.randn(60)
z = [np.random.random() for _ in range(60)]

fig = plt.figure()
gs = gridspec.GridSpec(1, 2)

ax0 = plt.subplot(gs[0, 0])
plt.scatter(x, y, s=20)

ax1 = plt.subplot(gs[0, 1])
cm = plt.cm.get_cmap('RdYlBu_r')
plt.scatter(x, y, s=20 ,c=z, cmap=cm)
cbaxes = fig.add_axes([0.6, 0.12, 0.1, 0.02]) 
plt.colorbar(cax=cbaxes, ticks=[0.,1], orientation='horizontal')

fig.tight_layout()
plt.show()

which looks like this:

The problem here is that I want the small horizontal colorbar position to the lower left of the plot but using the cax argument not only feels a bit hacky, it apparently conflicts with tight_layout which results in the warning:

/usr/local/lib/python2.7/dist-packages/matplotlib/figure.py:1533: UserWarning: This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.
  warnings.warn("This figure includes Axes that are not "

Isn't there a better way to position the colorbar, ie without getting a nasty warning thrown at you whenever you run the code?

---

Edit

I wanted the colorbar to show only the max and min values, ie: 0 and 1 and Joe helped me do that by adding vmin=0, vmax=1 to scatter like so:

plt.scatter(x, y, s=20, vmin=0, vmax=1)

so I'm removing this part of the question.

Answer 1

One may use a mpl_toolkits.axes_grid1.inset_locator.inset_axes to place an axes inside another axes. This axes can be used to host the colorbar. Its position is relative the the parent axes, similar to how legends are placed, using a loc argument (e.g. loc=3 means lower left). Its width and height can be specified in absolute numbers (inches) or relative to the parent axes (percentage).

cbaxes = inset_axes(ax1, width="30%", height="3%", loc=3) 

import matplotlib.pyplot as plt 
import numpy as np
import matplotlib.gridspec as gridspec
from mpl_toolkits.axes_grid1.inset_locator import inset_axes

x = np.random.randn(60) 
y = np.random.randn(60)
z = [np.random.random() for _ in range(60)]

fig = plt.figure()
gs = gridspec.GridSpec(1, 2)

ax0 = plt.subplot(gs[0, 0])
plt.scatter(x, y, s=20)

ax1 = plt.subplot(gs[0, 1])
cm = plt.cm.get_cmap('RdYlBu_r')
plt.scatter(x, y, s=20 ,c=z, cmap=cm)

fig.tight_layout()

cbaxes = inset_axes(ax1, width="30%", height="3%", loc=3) 
plt.colorbar(cax=cbaxes, ticks=[0.,1], orientation='horizontal')


plt.show()

Note that in order to suppress the warning, one might simply call tight_layout prior to adding the inset axes.