Update secondary_axis tutorial when the second axis is interpolated from the first. In this case the interpolation must be defined outside the bounds of the data that is plotted. Moreover the tutorial in question has been simplified.

dkweiss31 · dkweiss31 · commit cd1c6cc2331b · 2024-11-04T19:35:07.000-05:00
diff --git a/galleries/examples/subplots_axes_and_figures/secondary_axis.py b/galleries/examples/subplots_axes_and_figures/secondary_axis.py
@@ -17,7 +17,6 @@
 import numpy as np
 
 import matplotlib.dates as mdates
-from matplotlib.ticker import AutoMinorLocator
 
 fig, ax = plt.subplots(layout='constrained')
 x = np.arange(0, 360, 1)
@@ -96,48 +95,50 @@ def one_over(x):
 plt.show()
 
 # %%
-# Sometime we want to relate the axes in a transform that is ad-hoc from
-# the data, and is derived empirically.  In that case we can set the
-# forward and inverse transforms functions to be linear interpolations from the
-# one data set to the other.
+# Sometime we want to relate the axes in a transform that is ad-hoc from the data, and
+# is derived empirically. Or, one axis could be a complicated nonlinear function of the
+# other. In these cases we can set the forward and inverse transform functions to be
+# linear interpolations from the one set of independent variables to the other.
 #
 # .. note::
 #
 #   In order to properly handle the data margins, the mapping functions
 #   (``forward`` and ``inverse`` in this example) need to be defined beyond the
-#   nominal plot limits.
-#
-#   In the specific case of the numpy linear interpolation, `numpy.interp`,
-#   this condition can be arbitrarily enforced by providing optional keyword
-#   arguments *left*, *right* such that values outside the data range are
-#   mapped well outside the plot limits.
+#   nominal plot limits. This condition can be enforced by extending the
+#   interpolation beyond the plotted values, both to the left and the right,
+#   see ``x1n`` and ``x2n`` below.
 
 fig, ax = plt.subplots(layout='constrained')
-xdata = np.arange(1, 11, 0.4)
-ydata = np.random.randn(len(xdata))
-ax.plot(xdata, ydata, label='Plotted data')
-
-xold = np.arange(0, 11, 0.2)
-# fake data set relating x coordinate to another data-derived coordinate.
-# xnew must be monotonic, so we sort...
-xnew = np.sort(10 * np.exp(-xold / 4) + np.random.randn(len(xold)) / 3)
-
-ax.plot(xold[3:], xnew[3:], label='Transform data')
-ax.set_xlabel('X [m]')
+x1_vals = np.arange(2, 11, 0.4)
+# second independent variable is a nonlinear function of the other.
+# this simple example can be more easily handled without interpolation, and is done
+# this way only for pedagogical purposes.
+x2_vals = x1_vals ** 2
+ydata = 50.0 + 20 * np.random.randn(len(x1_vals))
+ax.plot(x1_vals, ydata, label='Plotted data')
+ax.plot(x1_vals, x2_vals, label=r'$x_2(x_1)$')
+ax.set_xlabel(r'$x_1$')
 ax.legend()
 
+# need to define mapped values outside of plotted range to ensure the secondary
+# axis is plotted correctly
+x1n = np.concatenate(([0.0], x1_vals, [20]))
+x2n = np.concatenate(([0.0], x2_vals, [20**2]))
+
 
 def forward(x):
-    return np.interp(x, xold, xnew)
+    return np.interp(x, x1n, x2n)
 
 
 def inverse(x):
-    return np.interp(x, xnew, xold)
-
+    return np.interp(x, x2n, x1n)
 
+# use axvline to prove that the derived secondary axis is correctly plotted
+ax.axvline(np.sqrt(40), color="grey", ls="--")
+ax.axvline(10, color="grey", ls="--")
 secax = ax.secondary_xaxis('top', functions=(forward, inverse))
-secax.xaxis.set_minor_locator(AutoMinorLocator())
-secax.set_xlabel('$X_{other}$')
+secax.set_xticks([10, 20, 40, 60, 80, 100])
+secax.set_xlabel(r'$x_2$')
 
 plt.show()
 
