matplotlib · QuLogic · Feb 16, 2022 · Sep 26, 2021 · Sep 26, 2021 · Sep 26, 2021
diff --git a/doc/api/colors_api.rst b/doc/api/colors_api.rst
@@ -21,6 +21,7 @@ Classes
    :toctree: _as_gen/
    :template: autosummary.rst
 
+   AsinhNorm
    BoundaryNorm
    Colormap
    CenteredNorm

diff --git a/doc/users/next_whats_new/asinh_scale.rst b/doc/users/next_whats_new/asinh_scale.rst
@@ -0,0 +1,32 @@
+New axis scale ``asinh`` (experimental)
+---------------------------------------
+
+The new ``asinh`` axis scale offers an alternative to ``symlog`` that
+smoothly transitions between the quasi-linear and asymptotically logarithmic
+regions of the scale. This is based on an arcsinh transformation that
+allows plotting both positive and negative values that span many orders
+of magnitude.
+
+.. plot::
+
+    import matplotlib.pyplot as plt
+    import numpy as np
+
+    fig, (ax0, ax1) = plt.subplots(1, 2, sharex=True)
+    x = np.linspace(-3, 6, 100)
+
+    ax0.plot(x, x)
+    ax0.set_yscale('symlog')
+    ax0.grid()
+    ax0.set_title('symlog')
+
+    ax1.plot(x, x)
+    ax1.set_yscale('asinh')
+    ax1.grid()
+    ax1.set_title(r'$sinh^{-1}$')
+
+    for p in (-2, 2):
+        for ax in (ax0, ax1):
+            c = plt.Circle((p, p), radius=0.5, fill=False,
+                           color='red', alpha=0.8, lw=3)
+            ax.add_patch(c)
diff --git a/examples/images_contours_and_fields/colormap_normalizations_symlognorm.py b/examples/images_contours_and_fields/colormap_normalizations_symlognorm.py
@@ -1,42 +1,84 @@
 """
 ==================================
-Colormap Normalizations Symlognorm
+Colormap Normalizations SymLogNorm
 ==================================
 
 Demonstration of using norm to map colormaps onto data in non-linear ways.
 
 .. redirect-from:: /gallery/userdemo/colormap_normalization_symlognorm
 """
 
+###############################################################################
+# Synthetic dataset consisting of two humps, one negative and one positive,
+# the positive with 8-times the amplitude.
+# Linearly, the negative hump is almost invisible,
+# and it is very difficult to see any detail of its profile.
+# With the logarithmic scaling applied to both positive and negative values,
+# it is much easier to see the shape of each hump.
+#
+# See `~.colors.SymLogNorm`.
+
 import numpy as np
 import matplotlib.pyplot as plt
 import matplotlib.colors as colors
 
-"""
-SymLogNorm: two humps, one negative and one positive, The positive
-with 5-times the amplitude. Linearly, you cannot see detail in the
-negative hump.  Here we logarithmically scale the positive and
-negative data separately.
 
-Note that colorbar labels do not come out looking very good.
-"""
+def rbf(x, y):
+    return 1.0 / (1 + 5 * ((x ** 2) + (y ** 2)))
 
-N = 100
+N = 200
+gain = 8
 X, Y = np.mgrid[-3:3:complex(0, N), -2:2:complex(0, N)]
-Z1 = np.exp(-X**2 - Y**2)
-Z2 = np.exp(-(X - 1)**2 - (Y - 1)**2)
-Z = (Z1 - Z2) * 2
+Z1 = rbf(X + 0.5, Y + 0.5)
+Z2 = rbf(X - 0.5, Y - 0.5)
+Z = gain * Z1 - Z2
+
+shadeopts = {'cmap': 'PRGn', 'shading': 'gouraud'}
+colormap = 'PRGn'
+lnrwidth = 0.5
 
-fig, ax = plt.subplots(2, 1)
+fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)
 
 pcm = ax[0].pcolormesh(X, Y, Z,
-                       norm=colors.SymLogNorm(linthresh=0.03, linscale=0.03,
-                                              vmin=-1.0, vmax=1.0, base=10),
-                       cmap='RdBu_r', shading='nearest')
+                       norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
+                                              vmin=-gain, vmax=gain, base=10),
+                       **shadeopts)
 fig.colorbar(pcm, ax=ax[0], extend='both')
+ax[0].text(-2.5, 1.5, 'symlog')
 
-pcm = ax[1].pcolormesh(X, Y, Z, cmap='RdBu_r', vmin=-np.max(Z),
-                       shading='nearest')
+pcm = ax[1].pcolormesh(X, Y, Z, vmin=-gain, vmax=gain,
+                       **shadeopts)
 fig.colorbar(pcm, ax=ax[1], extend='both')
+ax[1].text(-2.5, 1.5, 'linear')
+
+
+###############################################################################
+# In order to find the best visualization for any particular dataset,
+# it may be necessary to experiment with multiple different color scales.
+# As well as the `~.colors.SymLogNorm` scaling, there is also
+# the option of using `~.colors.AsinhNorm` (experimental), which has a smoother
+# transition between the linear and logarithmic regions of the transformation
+# applied to the data values, "Z".
+# In the plots below, it may be possible to see contour-like artifacts
+# around each hump despite there being no sharp features
+# in the dataset itself. The ``asinh`` scaling shows a smoother shading
+# of each hump.
+
+fig, ax = plt.subplots(2, 1, sharex=True, sharey=True)
+
+pcm = ax[0].pcolormesh(X, Y, Z,
+                       norm=colors.SymLogNorm(linthresh=lnrwidth, linscale=1,
+                                              vmin=-gain, vmax=gain, base=10),
+                       **shadeopts)
+fig.colorbar(pcm, ax=ax[0], extend='both')
+ax[0].text(-2.5, 1.5, 'symlog')
+
+pcm = ax[1].pcolormesh(X, Y, Z,
+                       norm=colors.AsinhNorm(linear_width=lnrwidth,
+                                             vmin=-gain, vmax=gain),
+                       **shadeopts)
+fig.colorbar(pcm, ax=ax[1], extend='both')
+ax[1].text(-2.5, 1.5, 'asinh')
+
 
 plt.show()
diff --git a/examples/scales/asinh_demo.py b/examples/scales/asinh_demo.py
@@ -0,0 +1,109 @@
+"""
+============
+Asinh Demo
+============
+
+Illustration of the `asinh <.scale.AsinhScale>` axis scaling,
+which uses the transformation
+
+.. math::
+
+    a \\rightarrow a_0 \\sinh^{-1} (a / a_0)
+
+For coordinate values close to zero (i.e. much smaller than
+the "linear width" :math:`a_0`), this leaves values essentially unchanged:
+
+.. math::
+
+    a \\rightarrow a + {\\cal O}(a^3)
+
+but for larger values (i.e. :math:`|a| \\gg a_0`, this is asymptotically
+
+.. math::
+
+    a \\rightarrow a_0 \\, {\\rm sgn}(a) \\ln |a| + {\\cal O}(1)
+
+As with the `symlog <.scale.SymmetricalLogScale>` scaling,
+this allows one to plot quantities
+that cover a very wide dynamic range that includes both positive
+and negative values. However, ``symlog`` involves a transformation
+that has discontinuities in its gradient because it is built
+from *separate* linear and logarithmic transformations.
+The ``asinh`` scaling uses a transformation that is smooth
+for all (finite) values, which is both mathematically cleaner
+and reduces visual artifacts associated with an abrupt
+transition between linear and logarithmic regions of the plot.
+
+.. note::
+   `.scale.AsinhScale` is experimental, and the API may change.
+
+See `~.scale.AsinhScale`, `~.scale.SymmetricalLogScale`.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Prepare sample values for variations on y=x graph:
+x = np.linspace(-3, 6, 500)
+
+###############################################################################
+# Compare "symlog" and "asinh" behaviour on sample y=x graph,
+# where there is a discontinuous gradient in "symlog" near y=2:
+fig1 = plt.figure()
+ax0, ax1 = fig1.subplots(1, 2, sharex=True)
+
+ax0.plot(x, x)
+ax0.set_yscale('symlog')
+ax0.grid()
+ax0.set_title('symlog')
+
+ax1.plot(x, x)
+ax1.set_yscale('asinh')
+ax1.grid()
+ax1.set_title('asinh')
+
+
+###############################################################################
+# Compare "asinh" graphs with different scale parameter "linear_width":
+fig2 = plt.figure(constrained_layout=True)
+axs = fig2.subplots(1, 3, sharex=True)
+for ax, (a0, base) in zip(axs, ((0.2, 2), (1.0, 0), (5.0, 10))):
+    ax.set_title('linear_width={:.3g}'.format(a0))
+    ax.plot(x, x, label='y=x')
+    ax.plot(x, 10*x, label='y=10x')
+    ax.plot(x, 100*x, label='y=100x')
+    ax.set_yscale('asinh', linear_width=a0, base=base)
+    ax.grid()
+    ax.legend(loc='best', fontsize='small')
+
+
+###############################################################################
+# Compare "symlog" and "asinh" scalings
+# on 2D Cauchy-distributed random numbers,
+# where one may be able to see more subtle artifacts near y=2
+# due to the gradient-discontinuity in "symlog":
+fig3 = plt.figure()
+ax = fig3.subplots(1, 1)
+r = 3 * np.tan(np.random.uniform(-np.pi / 2.02, np.pi / 2.02,
+                                 size=(5000,)))
+th = np.random.uniform(0, 2*np.pi, size=r.shape)
+
+ax.scatter(r * np.cos(th), r * np.sin(th), s=4, alpha=0.5)
+ax.set_xscale('asinh')
+ax.set_yscale('symlog')
+ax.set_xlabel('asinh')
+ax.set_ylabel('symlog')
+ax.set_title('2D Cauchy random deviates')
+ax.set_xlim(-50, 50)
+ax.set_ylim(-50, 50)
+ax.grid()
+
+plt.show()
+
+###############################################################################
+#
+# .. admonition:: References
+#
+#    - `matplotlib.scale.AsinhScale`
+#    - `matplotlib.ticker.AsinhLocator`
+#    - `matplotlib.scale.SymmetricalLogScale`
diff --git a/examples/scales/symlog_demo.py b/examples/scales/symlog_demo.py
@@ -33,3 +33,17 @@
 
 fig.tight_layout()
 plt.show()
+
+###############################################################################
+# It should be noted that the coordinate transform used by ``symlog``
+# has a discontinuous gradient at the transition between its linear
+# and logarithmic regions. The ``asinh`` axis scale is an alternative
+# technique that may avoid visual artifacts caused by these disconinuities.
+
+###############################################################################
+#
+# .. admonition:: References
+#
+#    - `matplotlib.scale.SymmetricalLogScale`
+#    - `matplotlib.ticker.SymmetricalLogLocator`
+#    - `matplotlib.scale.AsinhScale`
diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
@@ -1680,6 +1680,38 @@ def linthresh(self, value):
         self._scale.linthresh = value
 
 
+@make_norm_from_scale(
+    scale.AsinhScale,
+    init=lambda linear_width=1, vmin=None, vmax=None, clip=False: None)
+class AsinhNorm(Normalize):
+    """
+    The inverse hyperbolic sine scale is approximately linear near
+    the origin, but becomes logarithmic for larger positive
+    or negative values. Unlike the `SymLogNorm`, the transition between
+    these linear and logarithmic regions is smooth, which may reduce
+    the risk of visual artifacts.
+
+    .. note::
+
+       This API is provisional and may be revised in the future
+       based on early user feedback.
+
+    Parameters
+    ----------
+    linear_width : float, default: 1
+        The effective width of the linear region, beyond which
+        the transformation becomes asymptotically logarithmic
+    """
+
+    @property
+    def linear_width(self):
+        return self._scale.linear_width
+
+    @linear_width.setter
+    def linear_width(self, value):
+        self._scale.linear_width = value
+
+
 class PowerNorm(Normalize):
     """
     Linearly map a given value to the 0-1 range and then apply