BUG/API: allow TimeGrouper with other columns in a groupby (GH3794)
closes #3794

```
In [3]: df
Out[3]: 
  Branch Buyer                Date  Quantity
0      A  Carl 2013-01-01 13:00:00         1
1      A  Mark 2013-01-01 13:05:00         3
2      A  Carl 2013-10-01 20:00:00         5
3      A  Carl 2013-10-02 10:00:00         1
4      A   Joe 2013-10-01 20:00:00         8
5      A   Joe 2013-10-02 10:00:00         1
6      A   Joe 2013-12-02 12:00:00         9
7      B  Carl 2013-12-02 14:00:00         3

[8 rows x 4 columns]

In [4]:    df.groupby([pd.Grouper(freq='1M',key='Date'),'Buyer']).sum()
Out[4]: 
                  Quantity
Date       Buyer          
2013-01-31 Carl          1
           Mark          3
2013-10-31 Carl          6
           Joe           9
2013-12-31 Carl          3
           Joe           9

[6 rows x 1 columns]

In [5]:    df = df.set_index('Date')

In [6]:    df['Date'] = df.index + pd.offsets.MonthEnd(2)

In [9]:    df.groupby([pd.Grouper(freq='6M',key='Date'),'Buyer']).sum()
Out[9]: 
                  Quantity
Date       Buyer          
2013-02-28 Carl          1
           Mark          3
2014-02-28 Carl          9
           Joe          18

[4 rows x 1 columns]

In [10]:    df.groupby([pd.Grouper(freq='6M',level='Date'),'Buyer']).sum()
Out[10]: 
                  Quantity
Date       Buyer          
2013-01-31 Carl          1
           Mark          3
2014-01-31 Carl          9
           Joe          18

[4 rows x 1 columns]

```

@cpcloud @hayd @jorisvandenbossche 
cc @TomAugspurger 

lmk what you think about the way to specify what the TimeGrouper applies (as maybe we should use this elsewhere), eg #5677
 maybe what would resolve both of these is to allow something like a `G` (which is essentially a generalizeation of `TimeGrouper`)

where this example could be written as:
`df.reset_index().groupby([pd.G('Date',freq='1M'),'Buyer']).sum()`

so if you want to specify something:

```
class G(object):
    def __init__(self, name=None, level=None, freq=None):
               # allow name=None only of freq is not None or level is not None          
```

```
df.groupby([G(level='foo'),G('bar'),'bah',G('Date',freq='6M')]).sum()
```

you would groupby: a level named `foo`, a column `bar`, a column `bah`, and a column named `Date` with 6M freq

so `column_name` is equiv to `G(column_name)`
- I think this wouldn't break back compat
- allows us to 'hide' `TimeGrouper`
- makes ability to groupby with an arbitrary object a bit easier
- this would not preclude the #5677 modification (and specifying `level` may not even be
  necessary if you search first the index then the columns)
 This looks very useful.  Just to make sure, you've only got the grouping by index level and column name working with the special case of a time grouper right?

I made some progress on https://github.com/pydata/pandas/issues/5677, but it's really messy. IIRC, the code for determining the grouping is really tightly tied to building the groups. Maybe I'll look at that again today and push something up. Then we can think about out to handle this also.
 tom that's right

a construct like G solves the problem and/or can try to figure it out 

but for TimeGrouper it's necessary (you can figure it out too but it's more ambiguous and should be explicitly specified)
 @TomAugspurger @hayd anybody like/dislike the `G` syntax?
 I really like the syntax. Only issue I see is if G is too short/not descriptive...
 `Grouper`? `Grouping` (can alias `G` too)
 annoyingly both these already exist in groupby
 I know, but they are internal, so could rename

how about just `pd.Group(...)` (rememeber this is only needed in some limited circumstances)
 I was thinking `pd.Group()`.
 The functionality here would really be a big improvement!
- Isn't `Grouper` a little bit more correct in meaning than `Group`? As is the specifies the grouper, by which column/index level/... groups are made? If I am correctly understanding it, I would be in favor of `Grouper`.
- For the docs, we could maybe recommend using `from pandas import Group(er) as G`? 
- The use of the `name` arg: any reason not to use `column=`? Or is there some similar functionalitiy that uses `name`?

I was wondering, are there other places users would at the moment use `TimeGrouper`? Or only in groupby? 
 This is going to become the base class of TimeGrouper; its not really any different, but would allow one to disambiguate things.

`Grouper` is correct, but exists as a 'private' class in groupby.py
 updated....

@TomAugspurger @jorisvandenbossche @hayd @cpcloud 

take a look when you have a chance (top section is updated)

This is actually not a very big change in implementation (e.g. determining how to group is still very complicate). But a bit cleaner I think. Could be cleaned up a bit more, e.g. a Categorical could be integrated into the Grouper hierarchy now (i'll open an issue for that),
 Looks good.

When I groupby by _just_ a `pd.Grouper`, I get a `TypeError: axis must be a DatetimeIndex, but got an instance of 'Int64Index'`.

```
In [19]: df
Out[19]: 
                 Date Branch Buyer  Quantity
0 2013-10-01 13:00:00      A  Carl         1
1 2013-10-01 13:05:00      A  Mark         3
2 2013-10-01 20:00:00      A  Carl         5
3 2013-10-02 10:00:00      A  Carl         1
4 2013-10-01 20:00:00      A   Joe         8
5 2013-10-02 10:00:00      A   Joe         1
6 2013-10-02 12:00:00      A   Joe         9
7 2013-10-02 14:00:00      B  Carl         3

[8 rows x 4 columns]

In [20]: df.groupby(pd.Grouper(freq='1M', key='Date'))
```

I think we want to support this case, right?
Passing the `Grouper` inside a list works correctly. Does it get sent down a Series path with just the one grouper?
 that's a bug
 I really like this change.
 well....turns out had to refactor a bit to get a nice inteface, whoosh. Upside is I actually understand grouping now. I put in lots of comments to explain, so should be easy to build on this (hopefully).

@TomAugspurger I think #5677 should be very straightforward on top of this and/or may not be necessary (as you can do it now, maybe just expand the docs section a tiny bit).
 @TomAugspurger if prob could but just catching an invalid level that is passed str a multi-index
the next case catches a invalid for an index

prob could be combined
 Some after merge comments:
- Since `pd.Grouper` is used now in the docs and so a public object, the docstring of it should also be included in the api docs I think (in groupby section)
- However that will mean, as it is a class and not a function, that all methods will also be added to the docs, which is maybe not really desirable. Are there any methods of pd.Grouper that a user would ever have to use? If not, maybe make them private?
- I think the docstring could also be a bit clearer (eg more explanation of what arguments `key` and `level` exactly mean)
 i'll fix the docs....regarding your 2nd point.

none of the methods are meant to be public, but this is a 'private' class except for the actual constructor, so not sure what to do about that.

any suggestions?
 just make all methods `_...`? So they don't appear in the docs/are user visible. Or is this tedious to always have to use `_..` methods internally?
 ```
object?   -> Details about 'object', use 'object??' for extra details.
pd.Grouper
In [1]: pd.Grouper?
Type:       type
String Form:<class 'pandas.core.groupby.Grouper'>
File:       /mnt/home/jreback/pandas/pandas/core/groupby.py
Docstring:
A Grouper allows the user to specify a groupby instruction for a target object,
e.g. the DataFrame that is being grouped.

This specification will select a column via the key parameter, or if the level and/or
axis parameters are given, a level of the index of the target object.

These are local specifications and will override 'global' settings, that is the parameters
axis and level which are passed to the groupby itself.

Parameters
----------
key : groupby key, which selects the grouping column of the target,
      defaults to None
level : name/number of the level for the target index, defaults to None
freq : string / freqency object, defaults to None
       This will groupby the specified frequency if the target selection (via key or level) is
       a datetime-like object
axis : number/name of the axis, defaults to None
sort : boolean, whether to sort the resulting labels, defaults to False

Returns
-------
A specification for a groupby instruction

Examples
--------
df.groupby(Grouper(key='A')) : syntatic sugar for df.groupby('A')
df.groupby(Grouper(key='date',freq='60s')) : specify a resample on the column 'date'
df.groupby(Grouper(level='date',freq='60s',axis=1)) :
   specify a resample on the level 'date' on the columns axis with a frequency of 60s
Constructor information:
 Definition:pd.Grouper(self, key=None, level=None, freq=None, axis=None, sort=False)
```
 Can you try to keep to the numpydoc format?

```
arg : type, default ... .
    Explanation.
```

The examples will also be rendered nicely (on the html pages) if you do eg:

```
Specify a resample on the column 'date':

>>> df.groupby(Grouper(key='date',freq='60s'))

```
 don't want to make any methods internal. They are all 'internal' for the most part. I guess this could be changed but its a bit of a project in itself.
 ```
A Grouper allows the user to specify a groupby instruction for a target object,
e.g. the DataFrame that is being grouped.

This specification will select a column via the key parameter, or if the level and/or
axis parameters are given, a level of the index of the target object.

These are local specifications and will override 'global' settings, that is the parameters
axis and level which are passed to the groupby itself.

Parameters
----------
key : string, defaults to None
      groupby key, which selects the grouping column of the target
level : name/number, defaults to None
        the level for the target index
freq : string / freqency object, defaults to None
       This will groupby the specified frequency if the target selection (via key or level) is
       a datetime-like object
axis : number/name of the axis, defaults to None
sort : boolean, default to False
       whether to sort the resulting labels

Returns
-------
A specification for a groupby instruction

Examples
--------
>>> df.groupby(Grouper(key='A')) : syntatic sugar for df.groupby('A')
>>> df.groupby(Grouper(key='date',freq='60s')) : specify a resample on the column 'date'
>>> df.groupby(Grouper(level='date',freq='60s',axis=1)) :
    specify a resample on the level 'date' on the columns axis with a frequency of 60s
```
 What do you mean with 'make' them internal? What I meant was just simply renaming them eg `Grouper.get_grouper()` to `Grouper._get_grouper()`. But I don't know how much they are used/to what extent they are new, so can't judge how much work this is / worth the trouble.
 Another formatting comment: the explanation in 

```
arg : type, default ... .
    Explanation.
```

does not have to be aligned with `type`, it is just intended 4 spaces from arg.

Something else, in `A Grouper allows the user to specify a groupby instruction for a target object, e.g. the DataFrame that is being grouped.`, that last part `eg the DataFrame ...` is not really clear to me. Maybe just leave that out? (first part of the sentence is clear to me)
 addressed in #6655
 @jreback Something else, `TimeGrouper` has still some more functionality than the new `Grouper` I think (eg the `closed='left'` as in http://stackoverflow.com/questions/14569223/timegrouper-pandas). So `Grouper` does not fully replace `TimeGrouper` usage (for users)? So should we still add `TimeGrouper` to the docs? or add this to `Grouper`?
 no 

Grouper will create a TimeGrouper if passed a freq

and TimeGrouper is a subclass of Grouper

so any kw args are passed thru

their are some more args that are mainly used by resample but I am not sure that you care about for grouping

eg base,loffset don't matter when grouping

closed might though - if so I will add to Grouping docs 
