1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
|
//Orthogonal decomposition - QR method
//reduce A to tridiagonal form
clc;
clear;
close();
format('v',7);
A1 = [1 4 2;-1 2 0;1 3 -1];
disp(A1, 'A = ');
// zero is created in lower triangle
//by taking the rotation matrix X1=[c s 0;-s c 0;0 0 1]; where c=cos and s=sin
//O is theta
Q = eye(3,3);
for i=2:3
for j=1:i-1
p=i;q=j;
O = -atan(A1(p,q)/(A1(q,q)));
c = cos(O);
s = sin(O);
X = eye(3,3);
X(p,p)=c;
X(q,q)=c;
X(p,q)=-s;
X(q,p)=s;
A1 = X'*A1;
Q = Q*X;
disp(A1,X,'The X and A matrix : ');
end
end
R = A1;
disp(R,Q,'Hence the original matrix can be decomposed as : ')
|
