%% feladat: 3-adfoku Lagrange polinommal f(0.4) kozelitese
%% adott: x : 0 0.5 1 1.5  2 2.5 3 3.5 4
%% hozza: y : 2  3  1  −4 −2  1  3  10 4
%% valasszuk ki a 4 legkozelebbit
px = [0 0.5 1 1.5]
py = [2 3 1 -4]
p1 = [1 -px(1)]
p2 = [1 -px(2)]
p3 = [1 -px(3)]
p4 = [1 -px(4)]
l1 = conv( conv(p2,p3) ,p4) %% l1 szamlaloja,
% gyoktenyezok szorzata
l1 = l1 / polyval(l1,px(1)) % skalazas,
% ekvivalens: l1 = l1 / polyval(l1,0)
% ugyanez analog modon a tobbi l2, l3, l4-re
l2 = conv( conv(p1,p3) ,p4)
l2 = l2 / polyval(l2,px(2))
l3 = conv( conv(p1,p2) ,p4)
l3 = l3 / polyval(l3,px(3))
l4 = conv( conv(p1,p2) ,p3)
l4 = l4 / polyval(l4,px(4))
x = -.5:0.1:2
plot(x,0*x,x,polyval(p3,x))
L = 2*l1 + 3*l2 + 1*l3 -4*l4
plot(x,0*x,x,polyval(L,x),px,py,'*') % onellenorzesre
polyval(L,px) == py % onellenorzesre
polyfit(px,py,3) % onellenorzesre
%% tenyleges kerdesre valasz: f(0.4) = ?
% kozelites:
polyval(L,0.4)