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DOC: add scales to Axes docs
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‎galleries/examples/scales/custom_scale.py

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"""
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.. _custom_scale:
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============
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Custom scale
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============

‎galleries/users_explain/axes/index.rst

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@@ -36,6 +36,7 @@ annotations like x- and y-labels, titles, and legends.
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arranging_axes
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colorbar_placement
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Autoscaling axes <autoscale>
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scales
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Legends <legend_guide>
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Subplot mosaic <mosaic>
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Constrained layout guide <constrainedlayout_guide>

‎galleries/users_explain/axes/scales.py

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"""
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===========
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Axis scales
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===========
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By default Matplotlib displays data on axis objects that have linear scales.
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This behavior can be changed, usually directly by using the
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`~.axes.Axes.set_xscale` or `~.axes.Axes.set_yscale` methods.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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import matplotlib.scale as mscale
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from matplotlib.ticker import FixedLocator, NullFormatter
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fig, axs = plt.subplot_mosaic([['linear', 'linear-log'],
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['log-linear', 'log-log']], layout='constrained')
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x = np.arange(0, 3*np.pi, 0.1)
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y = 2 * np.sin(x) + 3
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ax = axs['linear']
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ax.plot(x, y)
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ax.set_xlabel('linear')
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ax.set_ylabel('linear')
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ax = axs['linear-log']
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ax.plot(x, y)
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ax.set_yscale('log')
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ax.set_xlabel('linear')
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ax.set_ylabel('log')
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ax = axs['log-linear']
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ax.plot(x, y)
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ax.set_xscale('log')
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ax.set_xlabel('log')
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ax.set_ylabel('linear')
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ax = axs['log-log']
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ax.plot(x, y)
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ax.set_xscale('log')
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ax.set_yscale('log')
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ax.set_xlabel('log')
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ax.set_ylabel('log')
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# %%
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# loglog and semilogx/y
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# =====================
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#
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# The logarithmic axis is used so often that there are a set
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# helper functions, that do the same thing: `~.axes.Axes.semilogy`,
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# `~.axes.Axes.semilogx`, and `~.axes.Axes.loglog`.
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fig, axs = plt.subplot_mosaic([['linear', 'linear-log'],
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['log-linear', 'log-log']], layout='constrained')
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x = np.arange(0, 3*np.pi, 0.1)
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y = 2 * np.sin(x) + 3
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ax = axs['linear']
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ax.plot(x, y)
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ax.set_xlabel('linear')
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ax.set_ylabel('linear')
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ax.set_title('plot(x, y)')
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ax = axs['linear-log']
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ax.semilogy(x, y)
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ax.set_xlabel('linear')
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ax.set_ylabel('log')
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ax.set_title('semilogy(x, y)')
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ax = axs['log-linear']
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ax.semilogx(x, y)
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ax.set_xlabel('log')
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ax.set_ylabel('linear')
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ax.set_title('semilogx(x, y)')
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ax = axs['log-log']
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ax.loglog(x, y)
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ax.set_xlabel('log')
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ax.set_ylabel('log')
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ax.set_title('loglog(x, y)')
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# %%
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# Other built-in scales
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# =====================
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#
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# There are other scales that can be used. The list of registered
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# scales can be returned from `.scales.get_scale_names`:
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print(mscale.get_scale_names())
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# %%
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#
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todo = ['asinh', 'symlog', 'log', 'logit', ]
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fig, axs = plt.subplot_mosaic([['asinh', 'symlog'],
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['log', 'logit']], layout='constrained')
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x = np.arange(0, 1000)
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for td in todo:
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ax = axs[td]
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if td in ['asinh', 'symlog']:
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yy = x - np.mean(x)
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elif td in ['logit']:
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yy = (x-np.min(x))
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yy = yy / np.max(np.abs(yy))
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else:
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yy = x
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ax.plot(yy, yy)
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ax.set_yscale(td)
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ax.set_title(td)
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# %%
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# Optional arguments for scales
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# =============================
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#
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# Some of the default scales have optional arguments. These are
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# documented in the API reference for the respective scales at
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# `~.matplotlib.scales`. One can change the base of the logarithm
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# being plotted (eg 2 below) or the linear threshold range
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# for ``'symlog'``.
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fig, axs = plt.subplot_mosaic([['log', 'symlog']], layout='constrained',
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figsize=(6.4, 3))
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for td in axs:
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ax = axs[td]
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if td in ['log']:
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ax.plot(x, x)
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ax.set_yscale('log', base=2)
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ax.set_title('log base=2')
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else:
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ax.plot(x - np.mean(x), x - np.mean(x))
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ax.set_yscale('symlog', linthresh=100)
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ax.set_title('symlog linthresh=100')
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# %%
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#
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# Arbitrary function scales
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# ============================
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#
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# Users can define a full scale class and pass that to `~.axes.Axes.set_xscale`
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# and `~.axes.Axes.set_yscale` (see :ref:`custom_scale`). A short cut for this
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# is to use the 'function' scale, and pass as extra arguments a ``forward`` and
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# an ``inverse`` function. The following performs a `Mercator transform
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# <https://en.wikipedia.org/wiki/Mercator_projection>`_ to the y-axis.
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# Function Mercator transform
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def forward(a):
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a = np.deg2rad(a)
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return np.rad2deg(np.log(np.abs(np.tan(a) + 1.0 / np.cos(a))))
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def inverse(a):
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a = np.deg2rad(a)
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return np.rad2deg(np.arctan(np.sinh(a)))
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t = np.arange(0, 170.0, 0.1)
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s = t / 2.
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fig, ax = plt.subplots(layout='constrained')
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ax.plot(t, s, '-', lw=2)
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ax.set_yscale('function', functions=(forward, inverse))
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ax.set_title('function: Mercator')
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ax.grid(True)
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ax.set_xlim([0, 180])
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ax.yaxis.set_minor_formatter(NullFormatter())
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ax.yaxis.set_major_locator(FixedLocator(np.arange(0, 90, 10)))
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# %%
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#
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# What is a "scale"?
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# ==================
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#
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# A scale is an object that gets attached to an axis. The class documentation
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# is at `~.scale`. `~.axes.Axes.set_xscale` and `~.axes.Axes.set_yscale` are
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# helper methods for `~.axis.Axis.set_scale`. You can also determine the scale
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# on an axis with:
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fig, ax = plt.subplots(layout='constrained',
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figsize=(3.2, 3))
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ax.semilogy(x, x)
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print(ax.xaxis.get_scale())
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print(ax.yaxis.get_scale())
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# %%
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#
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# Setting a scale does three things. First it defines a transform on the axis
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# that maps between data values to position along the axis. This transform can
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# be accessed via `~.axis.Axis.get_transform`.
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print(ax.yaxis.get_transform())
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# %%
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#
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# Transforms on the axis are a relatively low-level concept, but is one of the
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# important roles played by ``set_scale``.
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#
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# Setting the scale also sets default tick locators (`~.ticker`) and tick
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# formatters appropriate for the scale. An axis with a 'log' scale has a
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# `~.ticker.LogLocator` to pick ticks at decade intervals, and a
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# `~.ticker.LogFormatter` to use scientific notation on the decades.
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print('X axis')
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print(ax.xaxis.get_major_locator())
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print(ax.xaxis.get_major_formatter())
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print('Y axis')
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print(ax.yaxis.get_major_locator())
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print(ax.yaxis.get_major_formatter())

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