Convenience function for polynomial interpolation
Constructs a polynomial that passes through a given set of points, then evaluates the polynomial. For reasons of numerical stability, this function does not compute the coefficients of the polynomial.
This function uses a “barycentric interpolation” method that treats the problem as a special case of rational function interpolation. This algorithm is quite stable, numerically, but even in a world of exact computation, unless the x coordinates are chosen very carefully - Chebyshev zeros (e.g. cos(i*pi/n)) are a good choice - polynomial interpolation itself is a very ill-conditioned process due to the Runge phenomenon.
Based on Berrut and Trefethen 2004, “Barycentric Lagrange Interpolation”.
xi : array-like of length N
yi : array-like N by R
x : scalar or array-like of length M
y : scalar or array-like of length R or length M or M by R
Construction of the interpolation weights is a relatively slow process. If you want to call this many times with the same xi (but possibly varying yi or x) you should use the class BarycentricInterpolator. This is what this function uses internally.