resample().interpolate() should not fill pre-existing NaNs

[shoyer]

Currently, interpolate() as part of resample() currently fills in all existing NaN values:

import pandas as pd

all_times = pd.date_range('2016-01-01', '2016-01-8')
times = all_times[1:3].append(all_times[4:-2])  # time coord with some missing days
s = pd.Series(range(len(times)), index=times)

>>> s
2016-01-02    0
2016-01-03    1
2016-01-05    2
2016-01-06    3
dtype: int64

>>> s.reindex(all_times)
2016-01-01    NaN
2016-01-02    0.0
2016-01-03    1.0
2016-01-04    NaN
2016-01-05    2.0
2016-01-06    3.0
2016-01-07    NaN
2016-01-08    NaN
Freq: D, dtype: float64

>>> s.reindex(all_times).resample('12H').interpolate()
2016-01-01 00:00:00     NaN
2016-01-01 12:00:00     NaN
2016-01-02 00:00:00    0.00
2016-01-02 12:00:00    0.50
2016-01-03 00:00:00    1.00
2016-01-03 12:00:00    1.25
2016-01-04 00:00:00    1.50
2016-01-04 12:00:00    1.75
2016-01-05 00:00:00    2.00
2016-01-05 12:00:00    2.50
2016-01-06 00:00:00    3.00
2016-01-06 12:00:00    3.00
2016-01-07 00:00:00    3.00
2016-01-07 12:00:00    3.00
2016-01-08 00:00:00    3.00
Freq: 12H, dtype: float64

This is inconsistent with the other fill methods, which only fill in NaNs introduced by upsampling:

>>> s.reindex(all_times).resample('12H').ffill() 
2016-01-01 00:00:00    NaN
2016-01-01 12:00:00    NaN
2016-01-02 00:00:00    0.0
2016-01-02 12:00:00    0.0
2016-01-03 00:00:00    1.0
2016-01-03 12:00:00    1.0
2016-01-04 00:00:00    NaN
2016-01-04 12:00:00    NaN
2016-01-05 00:00:00    2.0
2016-01-05 12:00:00    2.0
2016-01-06 00:00:00    3.0
2016-01-06 12:00:00    3.0
2016-01-07 00:00:00    NaN
2016-01-07 12:00:00    NaN
2016-01-08 00:00:00    NaN
Freq: 12H, dtype: float64

I'd like to see resample's interpolate() switch its behavior to no longer fill pre-existing NaNs. If those NaNs are not meaningful, it is straightforward to .drop() them first if necessary. This behavior violates the model that upsampling should only depend on what index values are present, not the data values.

Some variation of this have come up in several other issues:

• Resample / upsample behavior diverges from pandas  pydata/xarray#1631 by @jhamman where I noticed this
• ENH: new interpolate kwarg to skip gaps #16457 by @naifrec
• Enhancement Request: control extrapolation on .interpolate #16284 by @WBare