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Merge pull request #21178 from rwpenney/feature/asinh-scale
Add asinh axis scaling (*smooth* symmetric logscale)
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‎doc/api/colors_api.rst

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:toctree: _as_gen/
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:template: autosummary.rst
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AsinhNorm
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BoundaryNorm
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Colormap
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CenteredNorm

‎doc/users/next_whats_new/asinh_scale.rst

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New axis scale ``asinh`` (experimental)
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---------------------------------------
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The new ``asinh`` axis scale offers an alternative to ``symlog`` that
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smoothly transitions between the quasi-linear and asymptotically logarithmic
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regions of the scale. This is based on an arcsinh transformation that
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allows plotting both positive and negative values that span many orders
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of magnitude.
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.. plot::
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import matplotlib.pyplot as plt
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import numpy as np
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fig, (ax0, ax1) = plt.subplots(1, 2, sharex=True)
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x = np.linspace(-3, 6, 100)
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ax0.plot(x, x)
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ax0.set_yscale('symlog')
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ax0.grid()
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ax0.set_title('symlog')
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ax1.plot(x, x)
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ax1.set_yscale('asinh')
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ax1.grid()
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ax1.set_title(r'$sinh^{-1}$')
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for p in (-2, 2):
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for ax in (ax0, ax1):
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c = plt.Circle((p, p), radius=0.5, fill=False,
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color='red', alpha=0.8, lw=3)
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ax.add_patch(c)

‎examples/images_contours_and_fields/colormap_normalizations_symlognorm.py

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"""
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==================================
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Colormap Normalizations Symlognorm
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Colormap Normalizations SymLogNorm
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==================================
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Demonstration of using norm to map colormaps onto data in non-linear ways.
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.. redirect-from:: /gallery/userdemo/colormap_normalization_symlognorm
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"""
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###############################################################################
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# Synthetic dataset consisting of two humps, one negative and one positive,
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# the positive with 8-times the amplitude.
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# Linearly, the negative hump is almost invisible,
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# and it is very difficult to see any detail of its profile.
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# With the logarithmic scaling applied to both positive and negative values,
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# it is much easier to see the shape of each hump.
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#
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# See `~.colors.SymLogNorm`.
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.colors as colors
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"""
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SymLogNorm: two humps, one negative and one positive, The positive
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with 5-times the amplitude. Linearly, you cannot see detail in the
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negative hump. Here we logarithmically scale the positive and
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negative data separately.
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Note that colorbar labels do not come out looking very good.
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"""
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def rbf(x, y):
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return 1.0 / (1 + 5 * ((x ** 2) + (y ** 2)))
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N = 100
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N = 200
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gain = 8
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X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)]
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Z1 = np.exp(-X**2 - Y**2)
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Z2 = np.exp(-(X - 1)**2 - (Y - 1)**2)
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Z = (Z1 - Z2) * 2
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Z1 = rbf(X + 0.5, Y + 0.5)
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Z2 = rbf(X - 0.5, Y - 0.5)
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Z = gain * Z1 - Z2
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shadeopts = {'cmap': 'PRGn', 'shading': 'gouraud'}
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colormap = 'PRGn'
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lnrwidth = 0.5
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fig, ax = plt.subplots(2, 1)
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fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)
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pcm = ax[0].pcolormesh(X, Y, Z,
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norm=colors.SymLogNorm(linthresh=0.03, linscale=0.03,
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vmin=-1.0, vmax=1.0, base=10),
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cmap='RdBu_r', shading='nearest')
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norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
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vmin=-gain, vmax=gain, base=10),
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**shadeopts)
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fig.colorbar(pcm, ax=ax[0], extend='both')
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ax[0].text(-2.5, 1.5, 'symlog')
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pcm = ax[1].pcolormesh(X, Y, Z, cmap='RdBu_r', vmin=-np.max(Z),
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shading='nearest')
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pcm = ax[1].pcolormesh(X, Y, Z, vmin=-gain, vmax=gain,
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**shadeopts)
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fig.colorbar(pcm, ax=ax[1], extend='both')
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ax[1].text(-2.5, 1.5, 'linear')
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###############################################################################
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# In order to find the best visualization for any particular dataset,
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# it may be necessary to experiment with multiple different color scales.
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# As well as the `~.colors.SymLogNorm` scaling, there is also
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# the option of using `~.colors.AsinhNorm` (experimental), which has a smoother
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# transition between the linear and logarithmic regions of the transformation
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# applied to the data values, "Z".
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# In the plots below, it may be possible to see contour-like artifacts
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# around each hump despite there being no sharp features
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# in the dataset itself. The ``asinh`` scaling shows a smoother shading
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# of each hump.
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fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)
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pcm = ax[0].pcolormesh(X, Y, Z,
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norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
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vmin=-gain, vmax=gain, base=10),
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**shadeopts)
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fig.colorbar(pcm, ax=ax[0], extend='both')
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ax[0].text(-2.5, 1.5, 'symlog')
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pcm = ax[1].pcolormesh(X, Y, Z,
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norm=colors.AsinhNorm(linear_width=lnrwidth,
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vmin=-gain, vmax=gain),
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**shadeopts)
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fig.colorbar(pcm, ax=ax[1], extend='both')
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ax[1].text(-2.5, 1.5, 'asinh')
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plt.show()

‎examples/scales/asinh_demo.py

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"""
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============
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Asinh Demo
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============
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Illustration of the `asinh <.scale.AsinhScale>` axis scaling,
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which uses the transformation
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.. math::
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a \\rightarrow a_0 \\sinh^{-1} (a / a_0)
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For coordinate values close to zero (i.e. much smaller than
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the "linear width" :math:`a_0`), this leaves values essentially unchanged:
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.. math::
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a \\rightarrow a + {\\cal O}(a^3)
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but for larger values (i.e. :math:`|a| \\gg a_0`, this is asymptotically
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.. math::
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a \\rightarrow a_0 \\, {\\rm sgn}(a) \\ln |a| + {\\cal O}(1)
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As with the `symlog <.scale.SymmetricalLogScale>` scaling,
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this allows one to plot quantities
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that cover a very wide dynamic range that includes both positive
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and negative values. However, ``symlog`` involves a transformation
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that has discontinuities in its gradient because it is built
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from *separate* linear and logarithmic transformations.
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The ``asinh`` scaling uses a transformation that is smooth
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for all (finite) values, which is both mathematically cleaner
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and reduces visual artifacts associated with an abrupt
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transition between linear and logarithmic regions of the plot.
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.. note::
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`.scale.AsinhScale` is experimental, and the API may change.
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See `~.scale.AsinhScale`, `~.scale.SymmetricalLogScale`.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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# Prepare sample values for variations on y=x graph:
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x = np.linspace(-3, 6, 500)
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###############################################################################
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# Compare "symlog" and "asinh" behaviour on sample y=x graph,
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# where there is a discontinuous gradient in "symlog" near y=2:
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fig1 = plt.figure()
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ax0, ax1 = fig1.subplots(1, 2, sharex=True)
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ax0.plot(x, x)
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ax0.set_yscale('symlog')
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ax0.grid()
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ax0.set_title('symlog')
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ax1.plot(x, x)
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ax1.set_yscale('asinh')
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ax1.grid()
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ax1.set_title('asinh')
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###############################################################################
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# Compare "asinh" graphs with different scale parameter "linear_width":
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fig2 = plt.figure(constrained_layout=True)
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axs = fig2.subplots(1, 3, sharex=True)
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for ax, (a0, base) in zip(axs, ((0.2, 2), (1.0, 0), (5.0, 10))):
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ax.set_title('linear_width={:.3g}'.format(a0))
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ax.plot(x, x, label='y=x')
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ax.plot(x, 10*x, label='y=10x')
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ax.plot(x, 100*x, label='y=100x')
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ax.set_yscale('asinh', linear_width=a0, base=base)
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ax.grid()
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ax.legend(loc='best', fontsize='small')
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###############################################################################
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# Compare "symlog" and "asinh" scalings
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# on 2D Cauchy-distributed random numbers,
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# where one may be able to see more subtle artifacts near y=2
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# due to the gradient-discontinuity in "symlog":
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fig3 = plt.figure()
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ax = fig3.subplots(1, 1)
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r = 3 * np.tan(np.random.uniform(-np.pi / 2.02, np.pi / 2.02,
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size=(5000,)))
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th = np.random.uniform(0, 2*np.pi, size=r.shape)
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ax.scatter(r * np.cos(th), r * np.sin(th), s=4, alpha=0.5)
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ax.set_xscale('asinh')
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ax.set_yscale('symlog')
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ax.set_xlabel('asinh')
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ax.set_ylabel('symlog')
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ax.set_title('2D Cauchy random deviates')
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ax.set_xlim(-50, 50)
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ax.set_ylim(-50, 50)
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ax.grid()
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plt.show()
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###############################################################################
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#
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# .. admonition:: References
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#
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# - `matplotlib.scale.AsinhScale`
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# - `matplotlib.ticker.AsinhLocator`
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# - `matplotlib.scale.SymmetricalLogScale`

‎examples/scales/symlog_demo.py

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fig.tight_layout()
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plt.show()
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###############################################################################
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# It should be noted that the coordinate transform used by ``symlog``
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# has a discontinuous gradient at the transition between its linear
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# and logarithmic regions. The ``asinh`` axis scale is an alternative
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# technique that may avoid visual artifacts caused by these disconinuities.
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###############################################################################
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#
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# .. admonition:: References
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#
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# - `matplotlib.scale.SymmetricalLogScale`
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# - `matplotlib.ticker.SymmetricalLogLocator`
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# - `matplotlib.scale.AsinhScale`

‎lib/matplotlib/colors.py

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self._scale.linthresh = value
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@make_norm_from_scale(
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scale.AsinhScale,
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init=lambda linear_width=1, vmin=None, vmax=None, clip=False: None)
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class AsinhNorm(Normalize):
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"""
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The inverse hyperbolic sine scale is approximately linear near
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the origin, but becomes logarithmic for larger positive
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or negative values. Unlike the `SymLogNorm`, the transition between
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these linear and logarithmic regions is smooth, which may reduce
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the risk of visual artifacts.
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.. note::
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This API is provisional and may be revised in the future
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based on early user feedback.
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Parameters
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----------
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linear_width : float, default: 1
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The effective width of the linear region, beyond which
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the transformation becomes asymptotically logarithmic
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"""
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@property
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def linear_width(self):
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return self._scale.linear_width
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@linear_width.setter
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def linear_width(self, value):
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self._scale.linear_width = value
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class PowerNorm(Normalize):
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"""
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Linearly map a given value to the 0-1 range and then apply

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