To install this package simply type in the REPL:

using Pkg
Pkg.add("PiecewiseLinearApprox")

The package performs piecewise linear interpolation over an arbitrary number of dimensions. There are only two functions that need mentioning. The first function computes a set of nodes spaced uniformly over a specified domain for a variable.

nodes = piecewise_linear_nodes(n,domain)

where n is an integer representing the desired number of nodes and domain is a 1D array containing the upper and lower values for the domain. If no domain is specified, then it defaults to [1.0,-1.0].

To evaluate the piecewise linear approximation at an arbitrary point in the domain we use the command

y_hat = piecewise_linear_evaluate(y,nodes,point)

where y is a multidimensional array, nodes is a tuple of 1D-arrays or an array of 1D-arrays, and point is a 1D array.

If point resides outside the domain in any dimension, then linear extrapolation in that dimension is performed.

• ChebyshevApprox.jl
• SmolyakApprox.jl
• HyperbolicCrossApprox.jl