nodes = linspace(-2,4,7);

f=@(x)(x+1)./(3*x.^2+2*x+1);


#plot(nodes, f(nodes),'o');
#hold on


x=linspace(-2,4,500);


#plot(x,f(x));
hold on

lnf=lagrange_classic(nodes,f(nodes),x);

#plot(x,lnf)


boor = spline(nodes,f(nodes),x);

#plot(x,boor)

df = @(x)(-(3*x.^2+6*x+1)./(3*x.^2+2*x+1).^2);

herm = hermite(nodes,f(nodes), df(nodes),x)
#plot(x,herm)


f=@(x)(x.*sin(pi.*x));

nodes = [-1,-1/2,0,1/2,1,3/2];

x=linspace(-1,3/2,500);

boor = spline(nodes,f(nodes),x);
boor_comp = spline(nodes,[pi,f(nodes),-1],x)
piece = pchip(nodes,f(nodes),x)

#plot(nodes, f(nodes),'o');
#hold on
#plot(x,boor);
#plot(x, boor_comp);
#plot(x, piece);


nodes = [0.5,1.5,2,3,3.5,4.5,5,6,7,8];

f_nodes = [5,5.8,5.8,6.8,6.9,7.6,7.8,8.2,9.2,9.9];
x=linspace(0.5,8,500);

p = polyfit(nodes,f_nodes,1);
plot(nodes, f_nodes,'o');
hold on
plot(x, polyval(p,x))

norm(p)

polyval(p,4)