This PR adds support for period-filling interpolation. From the docstring:
Perform a period-filling linear interpolation between the two neighboring points.
This interpolation is period-filling because it ensures that there is no gap on input data
larger than the given period.
This interpolation method is best explained with an example. Let us assume data is defined
on 03/01/1985, 05/01/1985, 11/02/1985, ... 17/12/1985, 07/01/1995, 11/01/1995, 14/02/1995,
..., 19/12/1995. In this case, data is defined every 10 years (date format is DD/MM/YYYY).
You can think of LinearPeriodFillingInterpolation as first filling the years in between by
performing linear interpolation across years, then performs a second linear interpolation
for the specific day (in actuality, the order of operations is reversed). In this example,
suppose first we want to evaluate the input on 04/01/1985. Since we have data for 1985, we
simply perform linear interpolation between 03/01/1985 and 05/01/1985. Suppose now, we want
to evaluate on 08/01/1987. We do not have data for the year 1987, so, we perform three
linear interpolations, first to evaluate the data on 08/01/1985 and 08/01/1995 (using the
neighboring points), and then between the resulting two values.
extrapolation_bc specifies how to deal with out of boundary values. The default value is
Throw, meaning that extrapolation is not allowed.
When is this interpolation method useful?
This interpolation method is useful when certain variations are more important than others.
For example, suppose you have hourly data defined once a month, on the 15th. A naive
interpolation method would interpolate use data from 15 Jan at 23.00 and 15 Feb at 00.00 to
interpolate on any day/hour of the days in between 15 Jan and 15 Feb. However, this would be
remove the diurnal cycle. LinearPeriodFillingInterpolation solves this problem.
Implementation details
How is LinearPeriodFillingInterpolation actually implemented?
First, let get a high level perspective. Let us continue with the example above.
There are two cases:
First, the target date falls within other dates that are boundary dates for the two
neighboring years. An example is 08/01/1986 because both 08/01/1985 and 08/01/1995 have two
neighboring dates (05/01/1985, 11/02/1985 and 07/01/1995, 11/01/1995). This is the easy
case: we interpolate 05/01/1985 and 11/02/1985 to get 08/01/1985, and 07/01/1995 and
11/01/1995 to get 08/01/1995, and interpolate the two results to get 08/01/1986.
Second, the other cases, when the target date does not have two boundary dates defined in
An example is 04/01/1986 because 07/01/1995 is the earliest date available on that
year. We have to be careful with this interpolation because we do not want to mix December
1985 with January 1995. In this case, we perform another interpolation to obtain a date in
December 1994 and reduce to the first case using this date as second half of the
interpolation bracket. To find what date to interpolate to, we walk the available dates
backwards in time at find the first date that we can interpolate because it falls into the
first case. In this example, it is 11/02/1994 (which we can obtain because we have data for
11/12/1985 and we can interpolate data on 11/12/1995).
This PR adds support for period-filling interpolation. From the docstring:
Closes #74