lagrange_poly.m

function p = lagrange_poly(knots, data)
%LAGRANGE_POLY  Lagrange interpolation polynomial.
%   P = LAGRANGE_POLY(KNOTS, DATA) returns a vector containing the
%   coefficients of the Lagrange polynomial for the function
%   values in the vector DATA evaluated at the points KNOTS.
%
%   The N coefficients are ordered so that P(1) is the
%   coefficient corresponding to x^(N-1) and P(N) is the
%   coefficient for x^0, i.e., the polynomial l(x) is defined
%   by l(x) = P(1)x^(N-1) + P(2)x^(N-2) + ... + P(N)x^0.
%
%   The function computes the coefficients of the Lagrange
%   polynomial using the constructive method shown in lectures.
%   (This is not the most efficient or most stable approach, just
%   for demo, see homework for Barycentric form).

  p = 0;
  for k = 1:length(knots)
    p = p + generate_L(k, knots)*data(k);
  end
end


% Subfunction for generating the individual components
function Lk = generate_L(k, knots)
  these_points = knots([1:(k-1) (k+1):end]);
  Lk = poly(these_points);
  the_scale_factor = prod(knots(k) - these_points);
  Lk = Lk/the_scale_factor;
end