disp(' ')
disp('generate a matrix A')
disp(' ')
A = rand(5,3)
[Q,R] = qr(A);
disp(' ')
disp('The Q matrix in the QR decomposition')
disp(' ')
Q
disp(' ')
disp('The R matrix in the QR decomposition')
disp(' ')
R
disp(' ')
disp('Verify Q*R - A')
disp(' ')
clearzeros(Q*R-A,1.0e-10)
disp(' ')
disp('Verify Q transpose time Q as an identity matrix')
disp(' ')
B = clearzeros( Q'*Q, 1.0e-10 )
disp(' ')
disp('Verify Q times Q transpose as an identity matrix')
disp(' ')
C = clearzeros( Q*Q', 1.0e-10)
disp(' ')
disp(' ')
disp('Generate a linear system of known solution [1;...;1]')
disp(' ')
A = rand(5,5)
b = A*ones(5,1)
disp(' ')
disp('Step 1: QR decomposition of A')
disp(' ')
[Q,R] = qr(A)
disp(' ')
disp('Step 2: d as Q transpose time b')
disp(' ')
d = Q'*b
disp(' ')
disp('Step 3: backward substution for R*x = d')
disp(' ')
x = backsub(R,d)
disp(' ')
disp('Step 3: backward substution for R*x = d')
disp(' ')