function f=mnhf_lagrangeP(xt,ft,x)
%MNHF_LAGRANGEP contructs a Lagrange polynomial from discrete data.
%
% (xt,ft) - discrete data (xt unequally-spaced)
% x - x-coordinate of interpolated values.
% f - y-coordinate of interpolated values.
%
% Usage:  mnhf_lagrangeP([1,2,3.5,5],[1,4,3.5^2,25],[3,4])

nx = length(xt);
ny = length(ft);
m =  length(x);

if nx~=ny 
  error(' (xt,ft) do not have the same number of values') 
end

% Initialize.
delt = zeros(1,nx);
f    = zeros(1,m);

for k=1:m
 sum = 0;
 for i=1:nx
  delt(i)=1;
  for j=1:nx
   if j~=i
     delt(i) = delt(i)*(x(k)-xt(j))/(xt(i)-xt(j));
   end
  end
  sum = sum + ft(i) * delt(i) ;
 end
 f(k) = sum;
end