REF/ENH: Refactor NDFrame finalization
In preperation for https://github.com/pandas-dev/pandas/issues/27108
(disallowing duplicates), we need to enhance our metadata propagation.

*We need a way for a particiular attribute to deterimine how it's
propagated for a particular method*. Our current method of metadata
propagation lacked two features

1. It only copies an attribute from a source NDFrame to a new NDFrame.
   There is no way to propagate metadata from a collection of NDFrames
   (say from `pd.concat`) to a new NDFrame.
2. It only and always copies the attribute. This is not always
   appropriate when dealing with a collection of input NDFrames, as the
   source attributes may differ. The resolution of conflicts will differ
   by attribute (for `Series.name` we might throw away the name. For
   `Series.allow_duplicates`, any Series disallowing duplicates should
   mean the output disallows duplicates)

- [ ] Closes https://github.com/pandas-dev/pandas/issues/8572
- [ ] Update existing calls to `__finalize__ ` to pass through `method`
- [ ] profile / Run ASV

cc @jreback @jbrockmendel, this is the start of what I need for https://github.com/pandas-dev/pandas/issues/27108#issuecomment-527633246. Briefly, adding a `.allows_duplicate_labels` attribute to NDFrame, which will be propagated through all operations. That already works for most things, but it's dropped for operations involving multiple inputs (concat, binops, etc.).

This PR puts the infrastructure in place to support this. We aren't using it yet (outside of tests), but will when I make the duplicate labels PR.

```python
duplicate_labels_meta = PandasMetadata("allows_duplicates")


@duplicate_labels_meta.register(pd.concat)
def _(new, concatenater):
    new.allows_duplicate_labels = all(x.allows_duplicate_labels for x in concatenater.objs)

@duplicate_labels_meta.register(Series.__array_ufunc__)
def _(new, inputs):
    new.allows_duplicate_labels = ...
```

But I split this off so that PR will be smaller. Not necessarily a precursor to this, but it would be nice if we had a systematic way to make sure we were using `_constructor` and `__finalize__` in all the appropriate places. > it would be nice if we had a systematic way to make sure we were using _constructor and __finalize__ in all the appropriate places.

I refactored to use a class-based approach, rather than decorators. The weirdest thing is that users need to actually create an instance of their subclass so that we know about it, but don't actually do anything with it.

```python
>>> mymeta = MyMeta("mymeta")
```

Now that I think about it, I guess that we could have a class decorator for registering. So then they do something like

```python

@register_metadata
class MyMeta(PandasMetadata):
    name = "mymeta"
```

And then we just instantiate it when we need it, rather than relying on singletons per `name`.

Edit: If we prefer this class-based approach, then I'll need to write out additional `finalize_*` methods, one per method calling finalize. This will give a nice API on what calls `__finalize__` with which types. > The weirdest thing is that users need to actually create an instance of their subclass so that we know about it, but don't actually do anything with it.

Yah, this is a little confusing.  What if my Meta subclass can take on multiple values, I'd assume I'd need multiple instances of it. > What if my Meta subclass can take on multiple values

Do you mean refer to multiple attributes? If so, then yes, that would get strange.


```python
class MyMetaBase(PandasMetadata):
    ...

@register_metdata
class MyMyetaA(MyMetaBase):
    name = 'a'

@register_metadata
class MyMetaB(MyMetaBase):
    name = 'b
```

versus

```python
my_meta_a = MyMetaBase(name='a')
my_meta_b = MyMetaBase(name='b')
```

neither is great. > Do you mean refer to multiple attributes? If so, then yes, that would get strange.

I mean different values that a single attribute can take.  e.g.

```
class AllowsDuplicateLabels(PandasMetadata):
    def __init__(self, allows):
        self.allows = allows

    def __bool__(self):
        return self.allows

    [...]


ser = pd.Series(range(3)
ser._metadata["allows"] = AllowsDuplicateLabels(False)

ser2 = pd.Series(range(4))
ser2._metadata["allows"] = AllowsDuplicateLabels(True)

>>> ser.index = [1, 1, 1]
ValueError: Series does not allow duplicate labels.
``` Hmm OK. Not sure I fully understand, but let me try to clarify.

Everything I've put up here as to do with metadata *resolution*: How do we transfer metadata from the source object(s) to the new object. It looks like your example is getting into specifying metadata values, though I may be misunderstanding. I haven't thought much about changing `NDFrame._metadata` from a list of strings specifying attributes. > I haven't thought much about changing NDFrame._metadata from a list of strings specifying attributes.

That part of my example was probably unhelpful.  If it makes it any clearer, pretend I use something other than `_metadata` that doesn't already exist. Sorry, I'm still not following your example. Changed my mind one more time. I started down a class based approach where we define

```
class PandasMeta:
    def copy(self, new, other):
    def concat(self, new, other):
    def sort_index(self, new, other):
```

While that's nice, since it gives a well-defined API for what finalize does, it complicates the implementation of the common case a decent amount. You can see it at https://github.com/pandas-dev/pandas/compare/master...TomAugspurger:metadata-dispatch+complex?expand=1

So I've backed off that and simplified this to get things working for my short-term needs (disallow_duplicates). A piece of metadata still has per-method control (pandas will need to be updated to pass `method=` in more places).

Doing some perf checks now. Do we need this class-based approach? What can you not do with the current implementation?

> It only copies an attribute from a source NDFrame to a new NDFrame.
    There is no way to propagate metadata from a collection of NDFrames
    (say from pd.concat) to a new NDFrame.

This is already possible, as `__finalize__` gets passed the `_concatenator` object, which has access to all frames passed to concat. 
This is what we do in geopandas (https://github.com/geopandas/geopandas/blob/29add0a735b00dc20c79e0fccc8e6a775c4997b0/geopandas/geodataframe.py#L561-L574)

>It only and always copies the attribute. This is not always
    appropriate when dealing with a collection of input NDFrames, as the
    source attributes may differ. The resolution of conflicts will differ
    by attribute

In principle, you can do this in `__finalize__` as well. You have access to the name of the attribute, so you can implement different logic for different attributes. It might not necessarily nice to have to put this all in `__finalize__`, and another approach could be cleaner. But I don't fully understand what *functionality* you are trying to add.



 To be clear, I am not opposed to making the implementation nicer, or making it more easily extensible to add custom logic, etc. I just first want to understand the constraints / needed functionality, before forming my opinion on the new implementation.

An easier way for external people to define custom behaviour for metadata without clashing with pandas (eg currently by overriding `__finalize__`, if pandas would add custom logic for an `allow_duplicates`, the current implementation of geopandas would override that I think), would certainly be very valuable! Class-based isn't necessary.

The root thing that I'd like to see is a way for a specific piece of
metadata (`Series.name`, `NDFrame.allows_duplicates`) to dictate how it's
resolved. Right now, all attributes are handled the same (copy from the source
to the new when the source is an `NDFrame`).

Since we (pandas) are the one adding `NDFrame.allows_duplicates`, we can of
course just do that handling ourself in `NDFrame.__finalize__`. Roughly

```diff
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 68308b2f83..5d63105335 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -5174,7 +5174,11 @@ class NDFrame(PandasObject, SelectionMixin):
         """
         if isinstance(other, NDFrame):
             for name in self._metadata:
-                object.__setattr__(self, name, getattr(other, name, None))
+                if name == 'allows_duplicates':
+                    allows_duplicates = all(getattr(x, name, None) for x in other)
+                    object.__setattr__(self, name, allows_duplicates)
+                else:
+                    object.__setattr__(self, name, getattr(other, name, None))
         return self
 
     def __getattr__(self, name):
```

I'll have a few more changes propagating metdata for things like _Concatenator,
and I'll want to pass different metadata in places (`Series.__array_ufunc__`
should pass `inputs`). But that's the basic idea.

Given that I'd *like* to do this for 1.0, should we avoid the larger changes here?
Certainly, adding special handling for `allows_duplicates` will let us establish
the desired behavior on master, guiding a later refactor. @jorisvandenbossche I put up https://github.com/pandas-dev/pandas/pull/28394 for ease of comparison. That'll be the "minimal" approach (no general changes to `NDArray.__finalize__`) Right now, I'm going to push forward on https://github.com/pandas-dev/pandas/pull/28394. That may give some guidance on how to design a metadata finalization API. Apologies for the wasted review time.