close all

%vstupom su: hodnota x, pre ktoru to pocitame, a polia X a fX (zadane hodnoty x a zadane f(x) k danym x )
%vystupom je suma (podla vzorca)
function sum = lagrange(x, X, fX)
  sum = 0;
  ord = size(X)(2);
  for i = 1:ord
    res = fX(i);
    for j = 1:ord
      if j ~= i
        numerator = (x - X(j));
        denominator = (X(i) - X(j));
        if denominator ~= 0
          res .*= (numerator / denominator);
        end
      end
    end
    sum += res;
  end
end

%vstupy zo zadania
input_X = [1 2 4 8 16];
input_fX = [0 1 2 3 4];

%aby plot vzdy ukazal, vstupy + nieco malo navyse
step = 0.1;
from = input_X(1) - 10*step;
to = input_X(end) + 10*step;

%vykreslenie
n = from:0.1:to;    %% TOTO su tie x co davas do L ..
plot(n, lagrange(n, input_X, input_fX))
hold on
plot(input_X,input_fX, '*')