Creating a log-linear plot in matplotlib using hist2d

The reason it's not working correctly is that plt.hist2d uses the pcolorfast method, which is much more efficient for large images, but doesn't support log axes.

To have a 2D histogram that works correctly on log axes, you'll need to make it yourself using np.histogram2d and ax.pcolor. However, it's only one extra line of code.

To start with, let's use exponentially spaced bins on a linear axis:

import numpy as np
import matplotlib.pyplot as plt

x, y = np.random.random((2, 1000))
x = 10**x

xbins = 10**np.linspace(0, 1, 10)
ybins = np.linspace(0, 1, 10)

fig, ax = plt.subplots()
ax.hist2d(x, y, bins=(xbins, ybins))

plt.show()

Okay, all well and good. Let's see what happens if we make the x-axis use a log scale:

import numpy as np
import matplotlib.pyplot as plt

x, y = np.random.random((2, 1000))
x = 10**x

xbins = 10**np.linspace(0, 1, 10)
ybins = np.linspace(0, 1, 10)

fig, ax = plt.subplots()
ax.hist2d(x, y, bins=(xbins, ybins))

ax.set_xscale('log') # <-- Only difference from previous example

plt.show()

Notice that the log scaling seems to have been applied, but the colored image (the histogram) isn't reflecting it. The bins should appear square! They're not because the artist created by pcolorfast doesn't support log axes.

To fix this, let's make the histogram using np.histogram2d (what plt.hist2d uses behind-the-scenes), and then plot it using pcolormesh (or pcolor), which does support log axes:

import numpy as np
import matplotlib.pyplot as plt
np.random.seed(1977)

x, y = np.random.random((2, 1000))
x = 10**x

xbins = 10**np.linspace(0, 1, 10)
ybins = np.linspace(0, 1, 10)

counts, _, _ = np.histogram2d(x, y, bins=(xbins, ybins))

fig, ax = plt.subplots()
ax.pcolormesh(xbins, ybins, counts.T)

ax.set_xscale('log')

plt.show()

(Note that we have to transpose counts here, because pcolormesh expects the axes to be in the order of (Y, X).)

Now we get the result we'd expect: