ENH: Add func norm

[jklymak]

PR Summary

Derives a func norm from func scale. From the example:

###############################################################################
# FuncNorm: Arbitrary function normalization
# ------------------------------------------
#
# If the above norms do not provide the normalization you want, and you
# can express your normalization in terms of function, you can use
# `~.colors.FuncNorm`.  Note that this example is the same as
# `PowerNorm` with a power of 0.5:

def _forward(x):
    return np.sqrt(x)


def _inverse(x):
    return x**2

N = 100
X, Y = np.mgrid[0:3:complex(0, N), 0:2:complex(0, N)]
Z1 = (1 + np.sin(Y * 10.)) * X**2
fig, ax = plt.subplots()

norm = colors.FuncNorm((_forward, _inverse), vmin=0, vmax=20)
pcm = ax.pcolormesh(X, Y, Z1, norm=norm, cmap='PuBu_r', shading='auto')
ax.set_title('FuncNorm(x)')
fig.colorbar(pcm, shrink=0.6)
plt.show()

PR Checklist

• Has pytest style unit tests (and pytest passes).
• Is Flake 8 compliant (run flake8 on changed files to check).
• New features are documented, with examples if plot related.
• Documentation is sphinx and numpydoc compliant (the docs should build without error).
• Conforms to Matplotlib style conventions (install flake8-docstrings and pydocstyle<4 and run flake8 --docstring-convention=all).
• New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
• API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).

[timhoffm]

Minor style comments.

[QuLogic]

Did you not want to assert the inverse here as well?

[jklymak]

Yeah I wasn't going to but it does drop our test coverage, so added...

Interestingly the _make_norm_from_scale inverse doesn't work on a list of floats (i.e. [1, 2, 3]), but only on a numpy array (np.array([1, 2, 3])) whereas the forward works on a bare list. Not sure if that is a bug. @anntzer ?

[QuLogic]

Probably because inverse doesn't pass value through process_value like __call__ does. Something like:

diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
index e417b8178d..b37ec947fa 100644
--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -1449,12 +1449,14 @@ def _make_norm_from_scale(scale_cls, base_norm_cls=None, *, init=None):
             t_vmin, t_vmax = self._trf.transform([self.vmin, self.vmax])
             if not np.isfinite([t_vmin, t_vmax]).all():
                 raise ValueError("Invalid vmin or vmax")
+            value, is_scalar = self.process_value(value)
             rescaled = value * (t_vmax - t_vmin)
             rescaled += t_vmin
-            return (self._trf
-                    .inverted()
-                    .transform(rescaled)
-                    .reshape(np.shape(value)))
+            t_value = (self._trf
+                       .inverted()
+                       .transform(rescaled)
+                       .reshape(np.shape(value)))
+            return t_value[0] if is_scalar else t_value
 
     Norm.__name__ = base_norm_cls.__name__
     Norm.__qualname__ = base_norm_cls.__qualname__

Maybe it also needs the masking?

[jklymak]

Looks right. But maybe orthogonal to this PR. I opened an issue in #19239 just to keep them separate...

[QuLogic]

Since that is now fixed, do you want to remove the np.array from the inverse check?

[jklymak]

@timhoffm I think I addressed your concern above? Thanks!

[QuLogic]

Feel free to merge after.

[QuLogic]

Since that is now fixed, do you want to remove the np.array from the inverse check?