Log scale

Examples of plots with logarithmic axes.

You can set the x/y axes to be logarithmic by passing "log" to set_xscale / set_yscale.

Convenience functions semilogx, semilogy, and loglog

Since plotting data on semi-logarithmic or double-logarithmic scales is very common, the functions semilogx, semilogy, and loglog are shortcuts for setting the scale and plotting data; e.g. ax.semilogx(x, y) is equivalent to ax.set_xscale('log'); ax.plot(x, y).

import matplotlib.pyplot as plt
import numpy as np

fig, (ax1, ax2, ax3) = plt.subplots(1, 3, layout='constrained', figsize=(7, 7/3))
# log x axis
t = np.arange(0.01, 10.0, 0.01)
ax1.semilogx(t, np.sin(2 * np.pi * t))
ax1.set(title='semilogx')
ax1.grid()
ax1.grid(which="minor", color="0.9")

# log y axis
x = np.arange(4)
ax2.semilogy(4*x, 10**x, 'o--')
ax2.set(title='semilogy')
ax2.grid()
ax2.grid(which="minor", color="0.9")

# log x and y axis
x = np.array([1, 10, 100, 1000])
ax3.loglog(x, 5 * x, 'o--')
ax3.set(title='loglog')
ax3.grid()
ax3.grid(which="minor", color="0.9")

Logarithms with other bases

By default, the log scale is to the base 10. One can change this via the base parameter.

fig, ax = plt.subplots()
ax.bar(["L1 cache", "L2 cache", "L3 cache", "RAM", "SSD"],
       [32, 1_000, 32_000, 16_000_000, 512_000_000])
ax.set_yscale('log', base=2)
ax.set_yticks([1, 2**10, 2**20, 2**30], labels=['kB', 'MB', 'GB', 'TB'])
ax.set_title("Typical memory sizes")
ax.yaxis.grid()

Dealing with negative values

Non-positive values cannot be displayed on a log scale. The scale has two options to handle these. Either mask the values so that they are ignored, or clip them to a small positive value. Which one is more suited depends on the type of the data and the visualization.

The following example contains errorbars going negative. If we mask these values, the bar vanishes, which is not desirable. In contrast, clipping makes the value small positive (but well below the used scale) so that the error bar is drawn to the edge of the Axes.

x = np.linspace(0.0, 2.0, 10)
y = 10**x
yerr = 1.75 + 0.75*y

fig, (ax1, ax2) = plt.subplots(1, 2, layout="constrained", figsize=(6, 3))
fig.suptitle("errorbars going negative")
ax1.set_yscale("log", nonpositive='mask')
ax1.set_title('nonpositive="mask"')
ax1.errorbar(x, y, yerr=yerr, fmt='o', capsize=5)

ax2.set_yscale("log", nonpositive='clip')
ax2.set_title('nonpositive="clip"')
ax2.errorbar(x, y, yerr=yerr, fmt='o', capsize=5)

plt.show()