LinearInterpolations
Why?
There are many excellent packages for interpolation in Julia. For instance:
All packages I am aware of assume, that the objects being interpolated implement addition and scalar multiplication. However mathematically only a notion of weighted average is required for linear interpolation. Examples of objects that support weighted average, but not addition and/or scalar multiplication are:
- Probability distributions
- Rotations and various other Lie groups
This package works with any notion of weighted average.
Usage
julia> using LinearInterpolations
julia> xs = 1:3; ys=[10, 100, 1000]; # 1d
julia> interpolate(xs, ys, 1)
10.0
julia> interpolate(xs, ys, 1.5)
55.0
julia> pt = [1.5]; interpolate(xs, ys, pt)
55.0
julia> itp = Interpolate(xs, ys); # construct a callable for convenience
julia> itp(1.5)
55.0
julia> grid=(1:3, [10, 15]); vals = [1 2; 3 4; 5 6]; pt=[1,10]; # multi dimensional
julia> interpolate(grid, vals, pt)
1.0
julia> function winner_takes_it_all(wts, objs)
# custom notion of weighted average
I = argmax(wts)
return objs[I]
end
julia> xs = 1:4; ys=[:no, :addition, :or, :multiplication];
julia> interpolate(xs, ys, 1.1, combine=winner_takes_it_all)
:no
julia> interpolate(xs, ys, 1.9, combine=winner_takes_it_all)
:addition
julia> interpolate(xs, ys, 3.7, combine=winner_takes_it_all)
:multiplicationDesign goals
- Lightweight and simple
- Support interpolation of objects that don't define
+,* - Reasonable performance