This small package defines some implicit and TimeType-based moving window functions.
The methods here are intended to be simple and fast for AbstractVector, but the broader purpose is to define functions that we can later define even richer methods for (ie for richer data structures like from TimeBars.jl) in later pacakges.
At first I'm not focusing on higher dimensional arrays or non-unit strides, but they may be added at some point. However, windows/periods other than implicit-indexed based ones (eg time period windows for a time index) will be a focus.
Moving window function is the generic term I use for a function that is applied over a window via a stride, hence the package name. Time or progression is assumed to be ascending where it applies (eg the last value of an input is the latest value for time series inputs).
Moving window functions are either higher-order (generic) or pre-made (more optimized). Generic versions are named after their kind (eg slide) and expect a function as the first argument. These applicators are general, but may be less performant than lower level optimized moving window functions. Optimized moving window functions are named like slide{fn}. More on optimized moving window functions below.
A rolling window (roll) applies a fixed width moving window function. If the window size, w>1, the output will be truncated by w-1.
A sliding window (slide) is the same as a rolling window except there is no output truncation. In the generic slide function, the window is expanded for the first w-1 values until w is reached. In some optimized sliding window functions where it makes sense (see below), the first w-1 outputs may be copied over directly from the input.
An expanding window (expand) has an expanding length window that is expanded at each step of the input.
A partition window (part) partitions the input into n subsets.
In some cases, moving window function applications can be optimized for performance above the simple loop of applying the function and taking a step. For example, moving sum can be done in O(N) time by keeping track of an accumulated sum and just adding subtracting each step instead of applying sum in the generic way.
Optimized sliding window function examples:
slidesum: optimized sliding sum, Kahan corrected by default.slidemean: optimized sliding mean, Kahan corrected by default.slidemin: optimized sliding minimum, this just wraps sairus7's MaxMinFilters.movmin for convenienceslidemax: optimized sliding maximum, this just wraps sairus7's MaxMinFilters.movmax for convenienceslidedot: optimized sliding dot product, Kahan corrected by default. Firstw-1values are passed through without a dot product.
You can always use the unoptimized versions of these via slide(sum, ...), slide(maximum, ...), and so on.
regularity: check the completeness of aTimeTypevector at some minimum periodicity
Credit for slidemin, slidemax, and sliderange goes to sairus7's excellent MaxMinFilters.jl package. I decided to wrap these for my own convenience because they were already quite fast.