function [Ln] = LagrangePolynomials(x_data, x)
%LagrangePolynomials evaluates the entire collection of Lagrange
%polynomials
%
%   Input:
%       - x_data: One-dimensional list of x-coordinates of points through
%       which the interpolating polynomial will pass. The degree of the
%       interpolating polynomial, n, will be inferred from the number of
%       entries in x_data
%       - x: One-dimensional list of values for which the Lagrange
%       polynomial will be evaluated
%
%   Output:
%       -Ln: Matrix of values of Lagrange polynomials of degree n. The
%       matrix has a row for each polynomial and a column for each value of
%       x

    %Allocate space for the output matrix by initializing it to zero

    value_count = length(x);
    n = length(x_data) - 1;
    Ln = zeros(n + 1, value_count);

    %Build each row of the output matrix by evaluating the corresponding
    %polynomial at the x value(s)
    for(k = 0:n)
        Ln(k + 1, :) = LagrangePolynomial(x_data, k, x);
    end
end