GridInterpolations

This package performs multivariate interpolation on a rectilinear grid. At the moment, it provides implementations of multilinear, simplex, and nearest neighbor interpolation.

For a description of multilinear and simplex interpolation see: Scott Davies, Multidimensional Triangulation and Interpolation for Reinforcement Learning, Advances in Neural Information Processing Systems, Cambridge, MA: MIT Press, 1997. pdf

There are some related packages, such as Grid.jl and Interpolations.jl.

Installation

Start Julia and run the following command:

Pkg.add("GridInterpolations")

Usage

To use the GridInterpolations module, begin your code with

using GridInterpolations

Interpolation

Create two-dimensional rectangular and simplex interpolation grids, a data array, and a point of interest:

grid = RectangleGrid([0., 0.5, 1.],[0., 0.5, 1.])  	# rectangular grid
sGrid = SimplexGrid([0., 0.5, 1.],[0., 0.5, 1.])	# simplex grid
nGrid = NearestGrid([0., 0.5, 1.],[0., 0.5, 1.])   	# nearest neighbor grid 
gridData = [8., 1., 6., 3., 5., 7., 4., 9., 2.]   	# vector of value data at each cut
x = [0.25, 0.75]  									# point at which to perform interpolation

Perform interpolation on the rectangular grid:

julia> interpolate(grid,gridData,x)
5.25

Or interpolate on the simplex grid:

julia> interpolate(sGrid,gridData,x)
6.0

Or interpolate on the nearest neighbor grid:

julia> interpolate(nGrid,gridData,x)
1.0 

Compute interpolants for the rectangular, simplex, and nearest neighbor grids:

julia> sGrid = SimplexGrid([0., 0.5, 1.],[0., 0.5, 1.])
[[0.0,0.5,1.0],[0.0,0.5,1.0]]

julia> interpolants(sGrid, x)
([4,5,8],[0.5,0.0,0.5])

Convert an index to a Grid coordinate:

julia> ind2x(grid, 3)
2-element Array{Float64,1}:
 1.0
 0.0

Number of verticies in the grid:

julia> length(grid)
9

Number of dimensions:

julia> dimensions(grid)
2

Credits

Contributors to this package include Maxim Egorov, Eric Mueller, Alex Gao, and Mykel Kochenderfer.