OctaveFunctions/LagrangePolynomial.m

function [Lnk] = LagrangePolynomial(x_data, k, x)
%LagrangePolynomial evaluates a single Lagrange polynomial
%
%   Input
%       - x_data: One-dimensional list of x-coordinates of poins through
%       which the interpolating polynomial will pass. The degree of the
%       interpolating polynomial, n, will be inferred from the number
%       entries in x_data
%       - k: The interpolating polynomial will equal one at x_data(k + 1)
%       and be zero for other entries in x_data. 0 <= k <= n
%        - x: One-dimensional list of values for which the Lagrange
%        polynomial will be evaluted
%   Output
%       - Lnk: Value of the Lagrange polynomial of degree n, index k, at x

n = length(x_data) - 1;

%Make x a row vector. As noted above, it is assumed to be a single row or
%column
x = x(:)';

Lnk = 1;
for(m = 0:n)
    if(m ~= k)
        Lnk = Lnk.*(x - x_data(m + 1))/(x_data(k + 1) - x_data(m +1));
    end
end
end