lagrange-interpolation

Author: Jonah Miller (jonah.maxwell.miller@gmail.com)

Simple library for Lagrange Interpolation in 1D, 2D, and 3D on a
Cartesian product grid. Written in C for maximum compatibility. The
plot below shows the error for piecewise 2nd-order interpolation using this library:

The plot blow shows the error (rescaled by the grid spacing) for
piecewise fourth-order interpolation of the function sin(5x) on the
evenly-spaced interval [-pi,pi] using this library:

The plot below shows the norm of the error for the interpolation of
the function sin(5x)cos(3y) on the evenly spaced domain [-pi,pi]^2
using 2nd, 4th, and 6th order interpolation.

Installation

This code is simple enough that you can just copy-paste lagrange.c
and lagrange.h into your project. At the moment, that’s the only
installation method.

Use

The header file should provide the interface for the functions you are
interested in. Most interesting, probably, are the
lagrange_interp_NDfo functions, where you specify an order of
interpolating polynomial in each dimension and the library evaluates a
piecewise interpolating polynomial of that order over the grid. The
lagrange_interp_ND series of functions are global interpolators and
should be used only if your grid points are stable for high-order
interpolation.

Testing

You can test the code by cloning the directory, entering it, and
typing make test. You can also generate a nice plot with make plot. The plotting functionality requires the scientific python
stack.

git cone git@github.com:Yurlungur/lagrange-interpolation.git
cd lagrange-interpolation
make test