I attempted to create an example showing the behavior ofset_units when shared axes have units, but there are many problems.

1. The units examples rely onTaggedValue defined in basic_units.py.TaggedValue is a container based on numpy's dispatch mechanism where__array__ returns the underlying data as a base classndarray - no more units. This breaks plotting functions likeplot that, very early in execution, callscbook._check_1d that callsnp.atleast1d that calls__array__. Subsequent call toset_units then fails because the data, nowndarray has no units converter.
2. Plotting functions likebar andscatter don't assign a 'units' callback, so the call toAxis.set_units does nothing. Unlikeplot that does set a 'units' callback.
3. I can changeTaggedValue.__array__ to return an array ofTaggedValue objects, but this breaks the ellipse example.

@jklymak Is this proposed PR sufficient? Creating an example using the existing basic_units definition isn't going to work as discussed above. I read the unitsdiscourse and see that units has a rather long history. Is there any work on defining an interface layer between incoming data and plot function internals?