WIP features (so far: Flat BC, Constant extrap)

[tomasaschan]

Constant extrapolation, such that itp[1-x] == itp[1] and itp[n+x] == itp[n] for any x >= 0 (after interpolating a 1D array of length n).

Note that this doesn't necessarily mean that itp[1] == A[1], since some boundary conditions invalidate that assumption; I figured it was better to enforce continuity at the domain edges:

using Gadfly, Interpolations
A = rand(15)
itp = Interpolation(A, Quadratic(ExtendInner(), OnCell()), ExtrapConstant())
plot(
    layer(x=[1:15], y=A, Geom.point),
    layer(x=[-1:.1:17], y=[itp[x] for x in -1:.1:17], Geom.path)
)

[timholy]

Grid (with itp = InterpGrid(A, BCnearest, InterpQuadratic)) definitely doesn't do that weird thing at x=15:

[tomasaschan]

I found a bug in my quadratic implementation that hopefully fixes this; the index was clamped by size(itp,d)-2 in the upper end, rather than size(itp,d)-1. Bugfix coming...

[tomasaschan]

I just pushed a fix to master; now Interpolations doesn't either =)

Well, at least not as weird. Grid.jl still seems to match up the data array's outermost data points with the interpolation, with Interpolations.jl doesn't; since the type here is OnCell, ExtendInner, the interpolation centered at x = 2 (thus valid for all x in [1.5,2.5]) is continued to x=1, and it doesn't actually go through that data point. I'll take a look and see what Grid does differently, but I suspect it's with a different BC.

[tomasaschan]

Yup, as I suspected: Grid implicitly uses a flat boundary condition for BCnearest, so the plot above isn't actually supposed to be a reproduction of Grid's behavior. I'll take a stab at implementing the flat BC for Interpolations next, to make comparison easier.

[timholy]

Nice!

[tomasaschan]

There! Flat BC with constant extrapolation seems to reproduce the results from Grid.

Interpolations:

Grid:

[timholy]

Very sweet! This is clearly coming along nicely.

[tomasaschan]

That's what happens when I suddenly have time to spend on this :)