Cubic spline interpolation in Julia with irregular grids

Question

I'm porting some code from R to Julia, and struggling with translating R's spline function. I need a Julia function:

function spline_j(x,y,xout)

that yields the same return as calling the R function:

spline(x,y,,"fmm",,,xout)

i.e. using the method of Forsyth, Malcolm and Moler, which is the default method in R.

My x and y are always 1-dimensional, but the points of x are not regularly spaced. That non-regularity seems to rule out using the pure-Julia Interpolations package as the documentation states "presently only LinearInterpolation supports irregular grids".

The Dierckx package supports irregular x, so a candidate for spline_j is:

using Dierckx

function spline_j(x, y, xout)
    spl = Dierckx.Spline1D(x, y)
    spl(xout)
end

which matches R's spline function if method is "natural".

Is it possible to replicate R's "fmm" method in Julia?

Answer 1

Following this PR https://github.com/JuliaMath/Interpolations.jl/pull/238 (merged as #243), Interpolations.jl actually has a number of excellent monotonic spline interpolation algorithms that support irregular grids, including Fritsch-Carlson (1980), Fritsch-Butland (1984), and Steffen (1990).

It doesn't seem to be reflected in the docs yet, but the options are visible in the following git diff

For example:

using Interpolations, Plots
x = sort(2*rand(10))
y = x.^2 .+ rand.()

itp = interpolate(x,y,FritschCarlsonMonotonicInterpolation())
xq = minimum(x):0.01:maximum(x)

plot(x,y, seriestype=:scatter, label="Data", legend=:topleft, framestyle=:box)
plot!(xq, itp.(xq), label="Interpolation")

If you prefer different interpolation methods, you can also substitute FiniteDifferenceMonotonicInterpolation,FritschButlandMonotonicInterpolation, or SteffenMonotonicInterpolation for FritschCarlsonMonotonicInterpolation.