[Fwd: correction to full size Q output from a QR factorization]

[Ron Boisvert <boisvert@nist.gov>]

Sender: Andreas Kyrmegalos <andreask1@vivodinet.gr>
Subject: correction to full size Q output from a QR factorization


Hello again,
 in the QRDecomposition code I have neglected to include the case when 
rank= n-1 and no householder vector has been calculated. I have an 
implementation of the QR algorithm that allows pivoting but I m 
skeptical about releasing it. This slight omission is a good example of 
why I refrain from its release.

Anyway here's the corrected code (the only change is the addition of the 
else clause):

     ....
     if (!economy) {
        if (QR[n-1][n-1] != 0.0) {
           for(int k = m-1; k >= n-1;k--) {
              Q[k][k] = 1.0;
              double s = 0.0;
               for (int i = n-1; i <=k; i++) {
                 s += QR[i][n-1]*Q[i][k];
              }
              s = -s/QR[n-1][n-1];
              Q[k][k] += s*QR[k][n-1];
              for (int i = m-1; i >k; i--) {
                 Q[i][k] += s*QR[i][n-1];
                 Q[k][i] = Q[i][k];
              }
           }
        }
        else {
           for(int k = m-1; k >= n-1;k--)
              Q[k][k] = 1.0;
        }
     } 
      ....

  I apologize to anyone who may have used the code but as I've pointed 
out before, please do test the code before using it.

Cheers,
Andreas