Lab 4 19.04

function Hermitescript
%% reprezentarea grafica a pol
fp=inline('2*exp(2*x)','x');
f=inline('exp(2*x)','x');
fprintf('Functia interpolata este: \n')
disp(f);
fprintf('Nodurile de interpolare sunt: \n')
disp (x); disp(Y);
n=2;
X=linspace(-1,1,n+1);
Y=f(X);
Yp=fp(X);
x=linspace(-1,1,100);

for i=1:100
    Her(i)=Hermite(X,Y,Yp,x(i));
end

plot(X,Y,'o','MarkerFaceColor','g');
hold on;
plot(x,Her);

%% Reprez. grafica a derivatei H2n+1
figure (2)
dher=diff(Her)./diff(x);
plot(x(1:length(x)-1),dher);
hold on
plot(X,Yp,'o');

function y=SplineL(X,Y,x)
n=length(X);
for j=1:(n-1)
    a(j)=Y(j);
    b(j)=(Y(j+1)-Y(j))/(X(j+1)-X(j));
end
for j=1:(n-1)
    if x>=X(j) & x<=X(j+1)
        S=a(j)+b(j)*(x-X(j));
        break;
    end
end
y=S;
end

%% metoda hermite de determinare a polinomului H2n+1
function y = Hermite(X,Y,Yp,x)

n = length(X)-1;
Her=0;

for k=1:(n+1)
    L=1;Lp=0;
    for j=1:(n+1)
         if j~=k
         L=L*(x-X(j))/(X(k)-X(j));
         Lp=Lp+1/(X(k)-X(j));
end
end

H=L*L*(1-2*Lp*(x-X(k)));
K=L*L*(x-X(k));
Her=Her+H*Y(k)+K*Yp(k);

end

y=Her;

end

%in loc de Hermite(...) ii dam apel cu functia asta
function y=SplineL(X,Y,x)
n=length(X);

for j=1:(n-1)
    a(j)=Y(j);
    b(j)=(Y(j+1)-Y(j))/(X(j+1)-X(j));
end

for j=1:(n-1)
    if x>=X(j) & x<=X(j+1)
        S=a(j)+b(j)*(x-X(j));
        break;
    end
end

y=S;

end

end