// ---------------------------------------------------------
// Calculs de polynomes orthogonaux.
// ---------------------------------------------------------
exec tp4_orthopol.sci;
N = 6;
a = 2*ones(N,1);
b = 0*ones(N,1);
c = -1*ones(N,1);
a(1) = 1;
b(1) = 0;
c(1) = 1;
PN1 = orthopol(N,a,b,c,'toto')  // (Polynomes de Chebyshev)
//
a = 2*ones(N,1);
b = 0*ones(N,1);
c = -1*ones(N,1);
a(1) = 2;
b(1) = 0;
c(1) = 1;
PN2 = orthopol(N,a,b,c,'X')  // (Polynomes de Chebyshev de 2e espece)
//
vectN = [1:N]';
a = -1*ones(N,1)./vectN;
b = (2*vectN - 1) ./ vectN;
c = (-vectN+1)./vectN;
a(1) = -1;
b(1) = 1;
c(1) = 1;
PNL = orthopol(N,a,b,c,'X')  // (Polynomes de Laguerre)
//
x=linspace(0,5,10000); clf; 
plot2d(x', horner(PNL,x)')