The package Interpolations.jl implements a variety of interpolation schemes for the Julia language. It has the goals of ease-of-use, broad algorithmic support, and exceptional performance.
Currently this package supports B-splines and irregular grids. The API has been designed with intent to support more options. Pull-requests are more than welcome! It should be noted that the API may continue to evolve over time.
There are many other interpolation packages implemented in Julia. For a listing, see Other Interpolation Packages.
Some of these packages support methods that
Interpolations does not, so if you can't find what you need here, check one of them or submit a pull request here.
Interpolations.jl can be installed via the following invocation since it is a registered Julia package.
using Pkg Pkg.add("Interpolations")
Create a grid
xs and an array
A of values to be interpolated
xs = 1:0.2:5 A = log.(xs)
Create linear interpolation object without extrapolation
interp_linear = linear_interpolation(xs, A) interp_linear(3) # exactly log(3) interp_linear(3.1) # approximately log(3.1) interp_linear(0.9) # outside grid: error
Create linear interpolation object with extrapolation
interp_linear_extrap = linear_interpolation(xs, A,extrapolation_bc=Line()) interp_linear_extrap(0.9) # outside grid: linear extrapolation
Performant Example Usage
The above use of
LinearInterpolation is actually a short hand for a composition of
extrapolate. You may not need all of the the scaling and extrapolation features.
interp_linear = extrapolate(scale(interpolate(A, BSpline(Linear())), xs))
If we know we do not need the extrapolation portion, we can use the following.
scaled_itp = scale(interpolate(A, BSpline(Linear())), xs)
We can also remove the scaling for further performance if integer valued knots and regular grids are sufficient.
itp = interpolate(A, BSpline(Linear()))
Removing the scaling or extrapolation will help accelerate interpolation by removing unneeded operations and branches. This can permit the use of advanced processor Single Instruction/Multiple Data (SIMD) capabilities.
Interpolations.jl is optimized for use with regular grids with uniform spacing. The highest performance is achieved when the knots are an
AbstractUnitRange such as
Base.OneTo(9). The default case if no knots are specified is to assign the knots as a
UnitRange starting at
If the knots are not unit spaced or start at a distinct value other than
1, then the
scale function can be used. While this increases the flexibility of the interpolation, some performance penalty is acquired. See Scaled BSplines for further information.
If the knots are irregularly spaced, then the ranges between knots will have to be scaled as in the
Gridded interpolation type. See Gridded interpolation for additional details.
Points outside the knots
For points not between knots, extrapolation can be used. This introduces a branch into the code that checks whether the point to be queried is inside or outside of the knots. This branch can inhibit the use of vectorized SIMD computation, resulting in a reduction of performance. See Extrapolation.