Is there a package in Julia for interpolation using a **monotone** cubic spline interpolation on an **irregular** grid? I seem to be failing to find one.

Interpolations.jl does provide monotone option, but only on a regular grid. On irregular grids it only supports linear constant and linear interpolations.

BSplineKit.jl does provide even higher-order interpolations on irregular grids, but does not offer monotone option.

Dierckx.jl does not seem to fit either.

Anything else?

For illustration, here comes some data and cubic spline interpolation, but not monotone, using BSplineKit.jl

```
M = [0.0, 0.4, 0.8, 0.9, 1.0, 1.2, 1.4, 1.6, 1.8]
η = [0.54, 0.54, 0.54, 0.75, 0.79, 0.78, 0.89, 0.93, 0.93]
using BSplineKit
itp_η = interpolate(M2, η, BSplineOrder(4))
M_range = LinRange(0.0,1.8,100)
scatter(M,η,xlabel="M [-]",ylabel="η")
plot!(M_range,itp_η.(M_range))
```

And here comes a solution of the same problem in Matlab – this is what I need in Julia:

```
M = [0.0, 0.4, 0.8, 0.9, 1.0, 1.2, 1.4, 1.6, 1.8]
eta = [0.54, 0.54, 0.54, 0.75, 0.79, 0.78, 0.89, 0.93, 0.93]
M_range = linspace(0,1.8,100)
eta_pchip = pchip(M,eta,M_range);
plot(M,eta,'o',M_range,eta_pchip)
xlabel('M')
ylabel('eta')
```