CLN: Make ufunc works for Index
closes #9966, #9974 (PR)

I understand these are never used because `Index` is no longer the subclass of `np.array`. Correct?
- [x] Add tests for ~~all~~ almost ufuncs
  - http://docs.scipy.org/doc/numpy/reference/ufuncs.html
- ~~CategoricalIndex~~: Needs to be done separately to fix `Categorical`, because number of categories can be changed.

```
np.sin(pd.Categorical([1, 2, 3]))
array([ 0.84147098,  0.90929743,  0.14112001])
```
- [x] MultiIndex: Raise `TypeError` or `AttributeError`, as ufuncs are performed to array of tuples.

yep I _think_ you could take them out. as `np.array(index)` will coerce to a ndarray (and not an index sub-class). This is done by `_shallow_copy` in any event.
 No, we need this. Otherwise `np.sin(idx)` returns an ndarray.

It's not documented, but `__array_finalize__` works even on non-subclasses. 
 ok let's add some tests and clean up the code
I suspect this should be in core/base then

eg to support the example above 
 IIRC there is another issue where for example (#9966 with a PR #9974) : 

```
In [22]: np.sin(Index(range(5)))
Out[22]: Int64Index([0.0, 0.841470984808, 0.909297426826, 0.14112000806, -0.756802495308], dtype='float64')
```

which is wrong, this needs to be created w/o slightly differently, e.g.

```
Index(func(...), **self._get_attributes_dict())
```

so that the attributes get propogates AND the correct type gets inferred (e.g. this would return a `FloatI64Index` in this case)

maybe  you want to supersede #9974 
 Thanks. I'll fix `Index.__array_wraps__` to make `ufunc` work. 

https://github.com/pydata/pandas/blob/master/pandas/core/index.py#L253

Am I correct that defining `__array_finalize__` is not needed if `__array_wraps__` is defined? Looks `__array_finalize__` is not defined in normal `Index`.

http://docs.scipy.org/doc/numpy/reference/arrays.classes.html
 This is correct -- **array_wraps** is what we need.

On Tue, Jul 21, 2015 at 5:44 AM, Sinhrks notifications@github.com wrote:

> Thanks. I'll fix `Index.__array_wraps__` to make `ufunc` work. 
> https://github.com/pydata/pandas/blob/master/pandas/core/index.py#L253
> Am I correct that defining `__array_finalize__` is not needed if `__array_wraps__` is defined? Looks `__array_finalize__` is not defined in normal `Index`.
> 
> ## http://docs.scipy.org/doc/numpy/reference/arrays.classes.html
> 
> Reply to this email directly or view it on GitHub:
> https://github.com/pydata/pandas/pull/10638#issuecomment-123293039
 Let me confirm 2 points:
1. Invalid ops for datetime-like indexes. 
   
   I understand numeric ufuncs (like `np.sin`) for datetime-like is almost meaningless. `PeriodIndex` is likely to return unexpected result because of current `__array__` definition. One idea is to raise error when `PeriodIndex` get float (invalid) result.
   
   ```
   import pandas as pd
   
   # OK
   np.sin(pd.DatetimeIndex(['2015-07', '2015-08']))
   # TypeError: ufunc 'sin' not supported for the input types, and the inputs could not be safely coerced to   any supported types according to the casting rule ''safe''
   
   # NG
   pidx = pd.PeriodIndex(['2015-07', '2015-08'], freq='M')
   np.sin(pidx)
   # Float64Index([-0.594884318359, 0.354966539136], dtype='float64')
   
   # ufunc is applied to i8 values
   pidx.__array__()
   # array([546, 547])
   ```
2. Some ufunc returns bool dtype. In such cases, it should return bool array as it is (like `Index.duplicated`)
   
   ```
   np.isnan(pidx)
   # Index([False, False], dtype='object')
   ```
 @sinhrks both of those points look right
 Yes, agreed

On Thu, Jul 23, 2015 at 4:14 AM, jreback notifications@github.com wrote:

> ## @sinhrks both of those points look right
> 
> Reply to this email directly or view it on GitHub:
> https://github.com/pydata/pandas/pull/10638#issuecomment-124060978
 @sinhrks you might want to steal tests from #9974 
 @sinhrks how's this coming along?
 @sinhrks how's this coming?
 @sinhrks if you can get to this in the next couple of days gr8, otherwise will defer this.
 I've looked through [`_add_numeric_operations`](https://github.com/pydata/pandas/blob/master/pandas/core/generic.py#L4324). You mean to define `PeriodIndex.sin` and so on used by `np.sin` and raise error? 
 @sinhrks I think `PeriodIndex` needs to override `__array_wrap__`. and raise if `context is not None` (I think). This is the return call from a ufunc type of operation, so it will 'succed' but we should raise an error. I don't know if their is a way to intercept it up front (their is if you are sub-class I think), but not sure about a duck-like
 @jreback Thanks, will check this.
 Updated and now green. 
 this doesn't seeem to close #9966 ?

```
In [9]: df = pd.DataFrame({'i': np.linspace(0, 5, 6).astype(np.int64), 
               'j': np.linspace(2, 3, 6)}).set_index('i')

In [10]: df
Out[10]: 
     j
i     
0  2.0
1  2.2
2  2.4
3  2.6
4  2.8
5  3.0

In [11]: df.index
Out[11]: Int64Index([0, 1, 2, 3, 4, 5], dtype='int64', name=u'i')

In [12]: df.index = df.index / 10.

In [13]: df.index
Out[13]: Int64Index([0.0, 0.1, 0.2, 0.3, 0.4, 0.5], dtype='float64', name=u'i')

```
 @jreback Standard arithmetic is handled by `_numeric_binop`. Now fixed.

```
df.index / 2.
# Float64Index([0.0, 0.5, 1.0, 1.5, 2.0, 2.5], dtype='float64', name=u'i')

np.divide(df.index, 2.)
# Float64Index([0.0, 0.5, 1.0, 1.5, 2.0, 2.5], dtype='float64', name=u'i')
```
 Failed in `Timedelta` ops. On current master, `mult` and `div` doesn't affect to existing freq, but it should?

```
import pandas as pd
idx = pd.timedelta_range('2 days', periods=3, freq='2D')

idx * 2
# TimedeltaIndex(['4 days', '8 days', '12 days'], dtype='timedelta64[ns]', freq='2D')
# -> freq should be "4D"?

idx / 2
# TimedeltaIndex(['1 days', '2 days', '3 days'], dtype='timedelta64[ns]', freq='2D')
# -> freq should be "D"?
```
 @sinhrks hmm I think you need to set the `freq=None` so it get's reinferred (or maybe can et it to 'infer')
 @sinhrks thanks!
