ENH: Allow to register standalone figures with pyplot

It may be fundamentally nice not to have to create the figure
though pyplot to be able to use it in pyplot afterwards. You can now do

```
from matplotlib.figure import Figure
import matplotlib.pyplot as plt

fig = Figure()
fig.subplots().plot([1, 3, 2])

plt.figure(fig)  # fig is now tracked in pyplot
plt.show()
```

This also opens up the possibility to more dynamically track
and untrack figures in pyplot, which opens up the road to
optimized figure tracking in pyplot (matplotlib#29849)

Author: timhoffm

lib/matplotlib/pyplot.py

@@ -990,21 +990,32 @@ def figure(
     in the matplotlibrc file.
     """
     allnums = get_fignums()
+    next_num = max(allnums) + 1 if allnums else 1
 
     if isinstance(num, FigureBase):
         # type narrowed to `Figure | SubFigure` by combination of input and isinstance
+        has_figure_property_parameters = (
+            any(param is not None for param in [figsize, dpi, facecolor, edgecolor])
+            or not frameon or kwargs
+        )
+
         root_fig = num.get_figure(root=True)
         if root_fig.canvas.manager is None:
-            raise ValueError("The passed figure is not managed by pyplot")
-        elif (any(param is not None for param in [figsize, dpi, facecolor, edgecolor])
-              or not frameon or kwargs) and root_fig.canvas.manager.num in allnums:
+            if has_figure_property_parameters:
+                raise ValueError(
+                    "You cannot pass figure properties when calling figure() with "
+                    "an existing Figure instance")
+            backend = _get_backend_mod()
+            manager_ = backend.new_figure_manager_given_figure(next_num, root_fig)
+            _pylab_helpers.Gcf._set_new_active_manager(manager_)
+            return manager_.canvas.figure
+        elif has_figure_property_parameters and root_fig.canvas.manager.num in allnums:
             _api.warn_external(
                 "Ignoring specified arguments in this call because figure "
                 f"with num: {root_fig.canvas.manager.num} already exists")
         _pylab_helpers.Gcf.set_active(root_fig.canvas.manager)
         return root_fig
 
-    next_num = max(allnums) + 1 if allnums else 1
     fig_label = ''
     if num is None:
         num = next_num

lib/matplotlib/tests/test_pyplot.py

@@ -470,6 +470,30 @@ def test_multiple_same_figure_calls():
     assert fig is fig3
 
 
+def test_register_existing_figure_with_pyplot():
+    from matplotlib.figure import Figure
+    # start with a standalone figure
+    fig = Figure()
+    assert fig.canvas.manager is None
+    with pytest.raises(AttributeError):
+        # Heads-up: This will change to returning None in the future
+        # See docstring for the Figure.number property
+        fig.number
+    # register the Figure with pyplot
+    plt.figure(fig)
+    assert fig.number == 1
+    # the figure can now be used in pyplot
+    plt.suptitle("my title")
+    assert fig.get_suptitle() == "my title"
+    # it also has a manager that is properly wired up in the pyplot state
+    assert plt._pylab_helpers.Gcf.get_fig_manager(fig.number) is fig.canvas.manager
+    # and we can regularly switch the pyplot state
+    fig2 = plt.figure()
+    assert fig2.number == 2
+    assert plt.figure(1) is fig
+    assert plt.gcf() is fig
+
+
 def test_close_all_warning():
     fig1 = plt.figure()