% feladat: adott:
% alappontok        x : 0 0.5 1 1.5 2 2.5 3 3.5 4
% fuggvenyertekek : y : 2  3  1 −4 −2  1  3  10 4
% kell: f(2.6) kozelitese, 3-adfoku Lagrange polival
% 4 legkozelebbi pont: szimmetrikusan korulotte
px = [2 2.5 3 3.5]
py = [-2 1 3 10]
% mikor eloszor elrontottuk a 4 pontot...
%px = [1.5 2 2.5 3]
%py = [-4 -2 1 3 ]
p1 = [1 -px(1)] % [1 -2]
p2 = [1 -px(2)]
p3 = [1 -px(3)]
p4 = [1 -px(4)]
l1 = conv( conv(p2,p3), p4)
l1 /= polyval(l1,px(1))
% ekvivalens: l1 = l1 / polyval(l1,2)
l2 = conv( conv(p1,p3), p4)
l2 /= polyval(l2,px(2))
l3 = conv( conv(p1,p2), p4)
l3 /= polyval(l3,px(3))
l4 = conv( conv(p1,p2), p3)
l4 /= polyval(l4,px(4))
L = py(1)*l1 + py(2)*l2 + py(3)*l3 + py(4)*l4
% -2*l1 + 1*l2 + 3*l3 + 10*l4
x = 1:0.1:4
plot(x,0*x,x,polyval(L,x),px,py,'*','markersize',15)
polyval(L,2.6)