Enable add/sub operations involving a CFTimeIndex and a TimedeltaIndex

[spencerkclark]

In [1]: import xarray as xr

In [2]: start_dates = xr.cftime_range('1999-12', periods=12, freq='M')

In [3]: end_dates = start_dates.shift(1, 'M')

In [4]: end_dates - start_dates
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-43c24409020b> in <module>()
----> 1 end_dates - start_dates

/Users/spencerclark/xarray-dev/xarray/xarray/coding/cftimeindex.pyc in __sub__(self, other)
    365
    366     def __sub__(self, other):
--> 367         return CFTimeIndex(np.array(self) - other)
    368
    369

TypeError: unsupported operand type(s) for -: 'numpy.ndarray' and 'CFTimeIndex'

Problem description

Subtracting one DatetimeIndex from another produces a TimedeltaIndex:

In [5]: import pandas as pd

In [6]: start_dates = pd.date_range('1999-12', periods=12, freq='M')

In [7]: end_dates = start_dates.shift(1, 'M')

In [8]: end_dates - start_dates
Out[8]:
TimedeltaIndex(['31 days', '29 days', '31 days', '30 days', '31 days',
                '30 days', '31 days', '31 days', '30 days', '31 days',
                '30 days', '31 days'],
               dtype='timedelta64[ns]', freq=None)

This should also be straightforward to enable for CFTimeIndexes and would be useful, for example, in the problem described in #2481 (comment).

Expected Output

In [1]: import xarray as xr

In [2]: start_dates = xr.cftime_range('1999-12', periods=12, freq='M')

In [3]: end_dates = start_dates.shift(1, 'M')

In [4]: end_dates - start_dates
Out[4]:
TimedeltaIndex(['31 days', '29 days', '31 days', '30 days', '31 days',
                '30 days', '31 days', '31 days', '30 days', '31 days',
                '30 days', '31 days'],
               dtype='timedelta64[ns]', freq=None)

[spencerkclark]

Adding a TimedeltaIndex to a CFTimeIndex would also make sense:

In [1]: import xarray as xr; import pandas as pd

In [2]: a = xr.cftime_range('2000', periods=5)

In [3]: deltas = pd.TimedeltaIndex([pd.Timedelta(days=1) for _ in range(5)])

In [4]: a + deltas
Out[4]:
CFTimeIndex([2000-01-02 00:00:00, 2000-01-03 00:00:00, 2000-01-04 00:00:00,
             2000-01-05 00:00:00, 2000-01-06 00:00:00],
            dtype='object')

In [5]: deltas + a
Out[5]:
CFTimeIndex([2000-01-02 00:00:00, 2000-01-03 00:00:00, 2000-01-04 00:00:00,
             2000-01-05 00:00:00, 2000-01-06 00:00:00],
            dtype='object')

So would subtracting a TimedeltaIndex from a CFTimeIndex:

In [6]: a - deltas
Out[6]:
CFTimeIndex([1999-12-31 00:00:00, 2000-01-01 00:00:00, 2000-01-02 00:00:00,
             2000-01-03 00:00:00, 2000-01-04 00:00:00],
            dtype='object')