//Redduction to upper Hessenberg form and calculating eigen values
clc;
clear;
close();
format('v',7);
A1 = [4 2 1 -3;2 4 1 -3;3 2 2 -3;1 2 1 0];
//the element with largest modulus below diagonal in first column need to be at the top and then similarly for column 2
A1=gsort(A1,'lr');
temp = A1(:,3);
A1(:,3) = A1(:,2);
A1(:,2) = temp;
M1 = eye(4,4);
M1(3,2) = A1(3,1)/A1(2,1);
M1(4,2) = A1(4,1)/A1(2,1);
A2 = inv(M1)*A1*M1;

A2=gsort(A2,'lr');
temp = A2(:,3);
A2(:,3) = A2(:,4);
A2(:,4) = temp;
M2 = eye(4,4);
M2(4,3) = A2(4,2)/A2(3,2);
A3 = inv(M2)*A2*M2;
H = A3;
disp(H,'Upper Hessenberg Matrix :')
l =0;
for i=4:-1:1
    K =H(1:i,1:i);
    while abs(K(i,i)-l)>0.005
        l=K(i,i);
        [Q,R]=qr(K-K(i,i)*eye(i,i));
        K = R*Q + K(i,i)*eye(i,i);
    end
    l = 0;
    EV(i) = K(i,i);
end
disp(EV,'Eigen Values : ')