Axis scales#

By default Matplotlib displays data on the axis using a linear scale. Matplotlib also supports logarithmic scales, and other less common scales as well. Usually this can be done directly by using the set_xscale or set_yscale methods.

import matplotlib.pyplot as plt
import numpy as np

import matplotlib.scale as mscale
from matplotlib.ticker import FixedLocator, NullFormatter

fig, axs = plt.subplot_mosaic([['linear', 'linear-log'],
                               ['log-linear', 'log-log']], layout='constrained')

x = np.arange(0, 3*np.pi, 0.1)
y = 2 * np.sin(x) + 3

ax = axs['linear']
ax.plot(x, y)
ax.set_xlabel('linear')
ax.set_ylabel('linear')

ax = axs['linear-log']
ax.plot(x, y)
ax.set_yscale('log')
ax.set_xlabel('linear')
ax.set_ylabel('log')

ax = axs['log-linear']
ax.plot(x, y)
ax.set_xscale('log')
ax.set_xlabel('log')
ax.set_ylabel('linear')

ax = axs['log-log']
ax.plot(x, y)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('log')
ax.set_ylabel('log')

[axes scales]

loglog and semilogx/y#

The logarithmic axis is used so often that there are a set helper functions, that do the same thing: semilogy, semilogx, and loglog.

fig, axs = plt.subplot_mosaic([['linear', 'linear-log'],
                               ['log-linear', 'log-log']], layout='constrained')

x = np.arange(0, 3*np.pi, 0.1)
y = 2 * np.sin(x) + 3

ax = axs['linear']
ax.plot(x, y)
ax.set_xlabel('linear')
ax.set_ylabel('linear')
ax.set_title('plot(x, y)')

ax = axs['linear-log']
ax.semilogy(x, y)
ax.set_xlabel('linear')
ax.set_ylabel('log')
ax.set_title('semilogy(x, y)')

ax = axs['log-linear']
ax.semilogx(x, y)
ax.set_xlabel('log')
ax.set_ylabel('linear')
ax.set_title('semilogx(x, y)')

ax = axs['log-log']
ax.loglog(x, y)
ax.set_xlabel('log')
ax.set_ylabel('log')
ax.set_title('loglog(x, y)')

[plot(x, y), semilogy(x, y), semilogx(x, y), loglog(x, y)]

Other built-in scales#

There are other scales that can be used. The list of registered scales can be returned from scale.get_scale_names:

print(mscale.get_scale_names())

['asinh', 'function', 'functionlog', 'linear', 'log', 'logit', 'symlog']

fig, axs = plt.subplot_mosaic([['asinh', 'symlog'],
                               ['log', 'logit']], layout='constrained')

x = np.arange(0, 1000)

for name, ax in axs.items():
    if name in ['asinh', 'symlog']:
        yy = x - np.mean(x)
    elif name in ['logit']:
        yy = (x-np.min(x))
        yy = yy / np.max(np.abs(yy))
    else:
        yy = x

    ax.plot(yy, yy)
    ax.set_yscale(name)
    ax.set_title(name)

[asinh, symlog, log, logit]

Optional arguments for scales#

Some of the default scales have optional arguments. These are documented in the API reference for the respective scales at scale. One can change the base of the logarithm being plotted (eg 2 below) or the linear threshold range for 'symlog'.

fig, axs = plt.subplot_mosaic([['log', 'symlog']], layout='constrained',
                              figsize=(6.4, 3))

for name, ax in axs.items():
    if name in ['log']:
        ax.plot(x, x)
        ax.set_yscale('log', base=2)
        ax.set_title('log base=2')
    else:
        ax.plot(x - np.mean(x), x - np.mean(x))
        ax.set_yscale('symlog', linthresh=100)
        ax.set_title('symlog linthresh=100')

[log base=2, symlog linthresh=100]

Arbitrary function scales#

Users can define a full scale class and pass that to set_xscale and set_yscale (see Custom scale). A short cut for this is to use the 'function' scale, and pass as extra arguments a forward and an inverse function. The following performs a Mercator transform to the y-axis.

# Function Mercator transform
def forward(a):
    a = np.deg2rad(a)
    return np.rad2deg(np.log(np.abs(np.tan(a) + 1.0 / np.cos(a))))


def inverse(a):
    a = np.deg2rad(a)
    return np.rad2deg(np.arctan(np.sinh(a)))


t = np.arange(0, 170.0, 0.1)
s = t / 2.

fig, ax = plt.subplots(layout='constrained')
ax.plot(t, s, '-', lw=2)

ax.set_yscale('function', functions=(forward, inverse))
ax.set_title('function: Mercator')
ax.grid(True)
ax.set_xlim(0, 180)
ax.yaxis.set_minor_formatter(NullFormatter())
ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 90, 10)))

[function: Mercator]

What is a "scale"?#

A scale is an object that gets attached to an axis. The class documentation is at scale. set_xscale and set_yscale set the scale on the respective Axis objects. You can determine the scale on an axis with get_scale:

fig, ax = plt.subplots(layout='constrained',
                              figsize=(3.2, 3))
ax.semilogy(x, x)

print(ax.xaxis.get_scale())
print(ax.yaxis.get_scale())

[axes scales]

linear
log

Setting a scale does three things. First it defines a transform on the axis that maps between data values to position along the axis. This transform can be accessed via get_transform:

print(ax.yaxis.get_transform())

LogTransform(base=10, nonpositive='clip')

Transforms on the axis are a relatively low-level concept, but is one of the important roles played by set_scale.

Setting the scale also sets default tick locators (ticker) and tick formatters appropriate for the scale. An axis with a 'log' scale has a LogLocator to pick ticks at decade intervals, and a LogFormatter to use scientific notation on the decades.

print('X axis')
print(ax.xaxis.get_major_locator())
print(ax.xaxis.get_major_formatter())

print('Y axis')
print(ax.yaxis.get_major_locator())
print(ax.yaxis.get_major_formatter())

X axis
<matplotlib.ticker.AutoLocator object at 0x735ee6011430>
<matplotlib.ticker.ScalarFormatter object at 0x735ee62deb10>
Y axis
<matplotlib.ticker.LogLocator object at 0x735ee6254a40>
<matplotlib.ticker.LogFormatterSciNotation object at 0x735ee5fd9c10>

Total running time of the script: (0 minutes 11.011 seconds)

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