Pandas Interpolate 'time' vs 'linear'

Question

In Pandas interpolate function, is method='time' equivalent to method='linear' when the time index is equally spaced?

A basic example suggests this is the case:

even_index = pd.date_range('2019-02-20 10:00 am', 
                           '2019-02-20 2:00 pm', freq='1 h')
values = [10, np.nan, 30, np.nan, 50]

pd.DataFrame(values, index=even_index).interpolate(method='time')

                        0
2019-02-20 10:00:00  10.0
2019-02-20 11:00:00  20.0
2019-02-20 12:00:00  30.0
2019-02-20 13:00:00  40.0
2019-02-20 14:00:00  50.0


pd.DataFrame(values, index=even_index).interpolate(method='linear')

                        0
2019-02-20 10:00:00  10.0
2019-02-20 11:00:00  20.0
2019-02-20 12:00:00  30.0
2019-02-20 13:00:00  40.0
2019-02-20 14:00:00  50.0

A difference between 'time' and 'linear' only seems to occur if the time index is not equally spaced:

uneven_index = pd.to_datetime(['2019-02-20 10:00 am', 
               '2019-02-20 10:30 am', '2019-02-20 12:30 pm', 
               '2019-02-20 1:30 pm', '2019-02-20 2:00 pm'])


pd.DataFrame(values, index=uneven_index).interpolate(method='time')

                             0
2019-02-20 10:00:00  10.000000
2019-02-20 10:30:00  14.000000
2019-02-20 12:30:00  30.000000
2019-02-20 13:30:00  43.333333
2019-02-20 14:00:00  50.000000

pd.DataFrame(values, index=uneven_index).interpolate(method='linear')

                        0
2019-02-20 10:00:00  10.0
2019-02-20 10:30:00  20.0
2019-02-20 12:30:00  30.0
2019-02-20 13:30:00  40.0
2019-02-20 14:00:00  50.0

My question is whether this always holds. Can it be assumed with an equally spaced time index, method='time' will always perform linear interpolation?

Answer 1

Yes it is

From the documentation:

‘linear’: Ignore the index and treat the values as equally spaced

Therefore, if your index is equally spaced and you use the proper method ('time' method for a time index in your example, but it could also be the 'index' method for a numeric index with equally spaced values), you will indeed get the same result.