API: dispatch to EA.astype
Closes https://github.com/pandas-dev/pandas/issues/21296

split from https://github.com/pandas-dev/pandas/pull/22325

Note that this is just a partial fix to get sparse working. We have some issues:

for better or worse, categorical is still special cased. `Series[EA].astype('category')` will not yet dispatch to `EA.astype`. That's good non-pandas EAs won't have to worry about specially handling categorical. It's bad, since it's a special case.

And that's the second issue, in general, how should we handle astyping from EA1 -> EA2? In principle, we always have `ndarray[object]` as the lowest common denominator. So something like `EA2(EA.astype(object))` may work. But that won't necessarily be efficient. I'm not sure what's best here.

cc @xhochy 
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22343?src=pr&el=h1) Report
> Merging [#22343](https://codecov.io/gh/pandas-dev/pandas/pull/22343?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/cf70d11a25ec59a5b630921d86759c7fa49884db?src=pr&el=desc) will **increase** coverage by `<.01%`.
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```diff
@@            Coverage Diff             @@
##           master   #22343      +/-   ##
==========================================
+ Coverage   92.05%   92.05%   +<.01%     
==========================================
  Files         169      169              
  Lines       50709    50712       +3     
==========================================
+ Hits        46679    46682       +3     
  Misses       4030     4030
```

| Flag | Coverage Δ | |
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| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/22343?src=pr&el=tree) | Coverage Δ | |
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| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/22343/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.24% <0%> (ø)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/22343/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `93.72% <0%> (ø)` | :arrow_up: |

------

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 Code changes look good!

Regarding the discussion items you mention, I am wondering if we need some kind of "negotation protocol" between (EA) dtypes for this. Basically something like:

- consider ``Series(EA).astype(dtype)``
- first try ``EA.astype(dtype)`` -> if the EA knows how to handle the specific `dtype`, return a new EA/array; if it does not know how to convert itself to `dtype`, return NotImplemented
- if the above returned NotImplemented, ask `dtype` if it knows how to convert the `EA` values to its own dtype -> if it knows, return a new EA/array; otherwise return NotImplemented
- if both don't know (above return NotImplemented again), either raise an error or fall back to the base implementation (`np.array(self, dtype=dtype,`, which might also raise an error)

That would in principle enable `EA.astype(EA2)`, and might also mitigate the 'category' problem you mention. Your negotiation seems sensible I think. I worry a bit about a divergence between `Series.astype(dtype)` and `Series.values.astype(dtype)`, but that's maybe unavoidable.

edit: though it would be strange (wrong) for a method like `ExtensionArray.astype` to return NotImplemented, so this would have to be a back-channel like `ExtensionArray._astype`, which is the same as astype, but can return NotImplemented? This seems messy. > I worry a bit about a divergence between Series.astype(dtype) and Series.values.astype(dtype)

That's a good point, yeah, that would be strange. Such a negotiation does not really fit for a method, only for functions probably .. > Such a negotiation does not really fit for a method, only for functions probably...

How about raising (and catching) an `UnsupportedConversionError` (but letting other errors pass through)?  That should easily be compatible with method calls. Perhaps. We'll leave that for another issue though I think, if we discover a need for it in practice. Fixed the referenced issue. That's the same issue as for https://github.com/pandas-dev/pandas/pull/22345? Ugh, too early. https://github.com/pandas-dev/pandas/issues/21296 is the one. @jreback was your comment about the wrong issue number all that was left from your point of view? If so, this should be good to go. thanks @TomAugspurger 

maybe need to modify text in pandas/arrays/base/ExtensionArray (the doc-string) to add astype)?