% Sin curve using Lagrange Interpolation Method ...
% Author : Saket Soni
% Description : Numerical Assignment for plotting a sin curve using
%               Lagrange's Interpolation Method.

a = 0;                  %   boundary values
b = 7;                  %

x = a : 1 : b;          %   actual values x
y = sin(x);             %   actual values y

n = 8;                  %   no of actual values
en = 71;                %   no of emperical values to be generated

ex = a : 0.1 : b       %   x for emperical values
ey = zeros(1,en);       %   y for emperical values

num = 1;                %   for numerator
den = 1;                %   for denominator

z = 0;                  %   for printing the x axis

for k = 1 : en
%    ex(k) = (a+b)/2 +(a-b)/2*cos(((2*k-1)*3.1415)/(2*n));
    ey(k) = 0;
    for j = 1 : n
        num = 1;
        den = 1;
        for i = 1 : j-1
            num = num * (ex(k)-x(i));
            den = den * (x(j)-x(i));
        end
        for i = j+1 : n
            num = num * (ex(k)-x(i));
            den = den * (x(j)-x(i));
        end
        ey(k) = ey(k) + (y(j)*num)/den;
    end
end

plot(x,y,ex,ey,ex,z);
end