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//Eg-10.10
//pg-449
clear
clc
x = [1 2 4];
y = [5 8.6 3.1];
//Refer to pg-448 for these conditions
//condition 1 gives
// 4a1 + 2b1 + c1 = 8.6
//condition 2 gives
// 16a1 + 4b1+c1 = 3.1
//condition 3 gives
// 4a0 + b0 = 4a1 + b1
//condition 4 gives
// a0 = 0
A = [2 1 0 0 0;0 0 4 2 1;1 1 0 0 0;0 0 16 4 1;1 0 -4 -1 0];
B = [8.6;8.6;5;3.1;0];
//The above conditions repesented in matrix equation form Ax = B can be solved for x as
//x = [b0;c0;a1;b1;c1]
x = inv(A)*B;
b0 = x(1);
c0 = x(2);
a1 = x(3);
b1 = x(4);
c1 = x(5);
x = poly(0,'x');
printf('The expressions for the splines are \n')
p = b0*x + c0;
q = a1*x^2 + b1*x + c1;
disp(p,q)
x1 = 1:0.01:2;
x2 = 2:0.01:4;
y1 = horner(p,x1);
y2 = horner(q,x2);
plot(x1,y1,x2,y2)
xlabel('x')
ylabel('y')
legend('Spline 1','Spline 2')
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