% Interpolating by lagrange's polynomials. 
function lagrange
% set up interpolation points
xi=[-1:1:1];
yi=f(xi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% graph both functions to compare
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1);
clf;
n=100;
x=-1:2/n:1;
y_exact=f(x);
y_interp=[];
for k=1:101 
y_interp=[y_interp, lagr_polyn(xi,yi,x(k))];
end
plot(x,y_exact,'r-',x,y_interp,'b-');


% n-th Lagrange's interpolating polynomial 
% xi, yi - are the arrays of interpolating points x_i, f(x_i)
% x is the point where the lagrange polynomial needs to be computed 
function y=lagr_polyn(xi,yi,x);
% determine the size of a == number of interpolating points
n=size(xi);
n=n(2);
% calculate the polynomial
y=0;
for j=1:n
  % Compute Lagrange's interpolating multiplier L_n,k
  L=1;
  for k=1:n
   if k~=j 
      L=L*(x - xi(k))/(xi(j)-xi(k));
   end    
  end
  y=y+yi(j)*L;
end
  
  
function y=f(x)
y=exp(x);