Index

DataInteprolationsND.jl is a library for interpolating arbitrarily high dimensional array data. The domain of this interpolation is a (hyper)rectangle. Support is included for efficient evaluation at multiple points in the domain through KernelAbstractions.jl.

For one dimensional interpolation see also DataInterpolations.jl.

API

An NDInterpolation is defined by a tuple of interpolation dimensions and the data u to interpolate.

using DataInterpolationsND

t1 = cumsum(rand(5))
t2 = cumsum(rand(7))

interpolation_dimensions = (
    LinearInterpolationDimension(t1),
    LinearInterpolationDimension(t2)
)

# The outputs will be vectors of length 2
u = rand(5, 7, 2)

interp = NDInterpolation(u, interpolation_dimensions)

Evaluation of this vector valued interpolation can be done in place or out of place.

interp(0.5, 0.5)

out = zeros(2)
interp(out, 0.5, 0.5)

If we provide t_eval for the interpolation dimensions, we can evaluate at these points either 'zipped' (where all t_eval must be of the same length) or as a grid defined by the Cartesian product of the t_eval.

interpolation_dimensions = (
    LinearInterpolationDimension(t1; t_eval = range(first(t1), last(t1); length = 100)),
    LinearInterpolationDimension(t2; t_eval = range(first(t2), last(t2); length = 100))
)

interp = NDInterpolation(u, interpolation_dimensions)

# Out of place zipped evaluation
eval_unstructured(interp) # Yields Matrix of size (100, 2)

# In place grid evaluation
out = zeros(100, 100, 2)
eval_grid!(out, interp)

This is particularly efficient for evaluating the interpolation for the same t_eval multiple times with different values for u, because the indices (and basis functions if applicable) for the t_eval are cached during the interpolation dimension construction.

Available interpolations

The interpolation types are given by the corresponding interpolation dimension type.

LinearInterpolationDimension(t): Linear interpolation in the sense of bilinear, trilinear interpolation etc.
ConstantInterpolationDimension(t): An interpolation with a constant value in each interval between t points. The Boolean option left (default true) can be used to indicate which side of the interval in which the input lies determines the output value.
BSplineInterpolationDimension(t, degree): Interpolation using BSpline basis functions. The input values t are interpreted as knots, and optionally knot multiplicities can be supplied. Per dimension a degree can be specified. Note that for an NDInterpolation of this type, the size of u for a certain dimension is equal to sum(multiplicities) - degree - 1. This interpolation dimension type can also be used to define NURBS, by passing cache = NURBSWeights(weights) to the NDInterpolation constructor.