Golub and van Loan's algorithm 5.4.1 for QR factorization is suitable as a rank revealing algorithm. The results are R, Q with the subdiagonal elements stored in "factored form" and the column ordering. Now can anyone help in the technique to take the Q from factored form to complete matrix. To give some additional information.
I used the following data (in Matlab style)
data= [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18];
Matlab call [Q R P]=qr(data,0)
produces
Q = -0.1048 -0.7161 0.6559 -0.2097 -0.5013 -0.5460 -0.3145 -0.2864 -0.4138 -0.4193 -0.0716 -0.0753 -0.5241 0.1432 0.2966 -0.6290 0.3581 0.0827 R = -28.6182 -24.2154 -26.4168 0 2.1483 1.0742 0 0 0.0000 p = 3 1 2
but my own attempt to implement this produces
Q= 0.10483 0 0 0.209657 0.0025 0 0.314485 0.184241 0.81162 0.419314 0.365981 0.398879 0.524142 0.54772 -0.0138585 0.628971 0.729459 -0.426595
while the R matches
-28.6182 -24.2154 -26.4168 0 2.1483 1.0742 0 0 0
The 2nd and 3rd columns of my Q seem to show a linear relationship with those from Matlab. Is there a way the Q results can be transformed to match those of Matlab ?