This package is the continuation of Tim Holy's work on Grid.jl, with the explicit goal of reaching feature parity for B-splines in the near future (PRs are more than welcome!).
Just
Pkg.add("Interpolations")
from the Julia REPL.
Note: the API might change in future versions, if necessary to accomodate new functionality.
using Interpolations
x = 1:5 # must be a unit range starting at 1
coarse = sin(x)
itp1 = Interpolation(coarse, Linear(OnGrid()), ExtrapPeriodic())
sinx = [itp1[x] for x in -pi:.01:3pi]
cosx = [gradient(itp,x)[1] for x in -pi:.1:3pi]
To interpolate this data using Interpolations.jl you provide the constructor with a few arguments that describe how the interpolation should be performed.
The first argument describes the interpolation type in terms of degree, grid behavior and, if necessary, boundary conditions. There are currently three degrees available: Constant, Linear and Quadratic, corresponding to B-splines of degree 0, 1 and 2, respectively.
You also have to specify what grid representation you want. There are currently two choices: OnGrid, in which the data points are assumed to lie on the boundaries of the interpolation interval, and OnCell in which the data points are assumed to lie on half-intervals between cell boundaries.
B-splines of quadratic or higher degree require solving an equation system to obtain the interpolation coefficients, and for that you must specify a boundary condition that is applied to close the system. The following boundary conditions are implemented: Flat, Line, Free, Periodic and Reflect; their mathematical implications are described in detail in the pdf document under /doc/latex.
The final argument to the Interpolation constructor describes what happens if you try to index into the interpolation object with coordinates outside of [1, size(data,d)] in any dimension d. The implemented boundary conditions are ExtrapError, ExtrapNaN, ExtrapConstant, ExtrapLinear, ExtrapPeriodic and ExtrapReflect.
Note that for extrapolating a periodic data set in a way that makes sense, you should specify both the Periodic boundary condition and the ExtrapPeriodic extrapolation behavior, and similarly for reflecting extrapolation. There might be API changes in the future to make these behaviors easier to specify.
There's an IJulia notebook that shows off some of the current functionality, and outlines where we're headed. I try to keep it up to date when I make any significant improvements and/or breaking changes, but if it's not, do file a PR.
Work is very much in progress, but and help is always welcome. If you want to help out but don't know where to start, take a look at issue #5 - our feature wishlist =)
Contributions in any form are appreciated, but my time is limited and your code is most likely to be included quickly in the library if it comes in a pull request with at least a few sanity tests (see the /test directory for some examples).