clear
clc

%----------------------------- Exercise 3.7 -----------------------------------%

% Dados
x = [1965 1970 1980 1985 1990 1991];
y = [17769 24001 25961 34336 29036 33417];


L62  = Intpol_Lagrange(x,y,1962);
S62  = spline(x, y, 1962);

L77  = Intpol_Lagrange(x,y,1977);
S77  = spline(x, y, 1977);

L92  = Intpol_Lagrange(x,y,1992);
S92  = spline(x, y, 1992);

printf('Ano 1962: \n Lagrange: %d \n Spline: %d \n Valor real: %d \n', L62, S62, 12380)

printf('Ano 1977: \n Lagrange: %d \n Spline: %d \n Valor real: %d \n', L77, S77, 27403)

printf('Ano 1992: \n Lagrange: %d \n Spline: %d \n Valor real: %d \n', L92, S92, 32059)

% Calculos para o plot

z =[1962:0.1:1992];

for i = 1:length(z)
  yl(i) = Intpol_Lagrange(x,y,z(i));
end

s3 = spline(x, y, z);

figure
set(gcf, 'color', [1 1 1]);
plot(x,y,'*k',z,yl,'--',z,s3,'-')
legend('Dados','Lagrange','Spline')