// ---------------------------------------------------------
// Fonction base(j) de Lagrange. (0 =< j =< n)
// ---------------------------------------------------------
function p=lagrange(pts,j,X); 
x=poly(0,X); 
n=length(pts); 
j=j+1; 
xnj=pts((1:n)~=j); 
p=prod((x-xnj)./(pts(j)-xnj));
endfunction 
//
// ---------------------------------------------------------
// Fonction interpolation de Lagrange.
// ---------------------------------------------------------
function p=interp(ft,pts,X); 
x=poly(0,X); 
n=length(pts);  
for i=1:n
 ploc(i) = ft(pts(i))*lagrange(pts,i-1,'t');
end
p = sum(ploc(1:n));
endfunction
//
// ---------------------------------------------------------
// Fonction calcul des differences divisees.
// ---------------------------------------------------------
function D=diffdiv(pts,val); 
L = length(pts)
//
D(1:L,1) = val(1:L)';
//
for j=2:L
  for i = 1:(L-j+1)  
    D(i,j) = (D(i+1,j-1) - D(i,j-1))/(pts(i+j-1)-pts(i));
  end
end
//
endfunction 
//
// ---------------------------------------------------------
// Fonction test d'application des methodes d'interpolation.
// phenomene de Runge
// ---------------------------------------------------------
function y=ftest(x);
y = ( ones(length(x)) ./ (1 + 16*x.^2) );
endfunction 
//