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

[Ron Boisvert <boisvert@nist.gov>]

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


Hi all,
  if you happen to need a full size Q matrix (as I have) from a QR 
factorization replace the getQ() method in QRfactorization.java,
with this code:

/** Generate and return the (economy-sized) orthogonal factor
  @return     Q
  */
 
  public Matrix getQ() {
     return getQ(true);
  }

  /** Generate and return the orthogonal factor
  @param economy If true the factor is economy sized
  @return     Q
  */

  public Matrix getQ(boolean economy) {
     Matrix X = new Matrix(m,economy?n:m);
     double[][] Q = X.getArray();
     if (!economy) {
        if (QR[n-1][n-1] != 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];
              }
           }
        }
     }
     for (int k = n-1-(economy?0:1); k >= 0; k--) {
        Q[k][k] = 1.0;
        for (int j = (economy?n:m)-1; j >=k; j--) {
           if (QR[k][k] != 0) {
              double s = 0.0;
              for (int i = k; i < m; i++) {
                 s += QR[i][k]*Q[i][j];
              }
              s = -s/QR[k][k];
              for (int i = k; i < m; i++) {
                 Q[i][j] += s*QR[i][k];
              }
           }
        }
     }
     return X;
  }

I have tested it with various sized matrices and the result look ok. But 
don't take my word for it, try it yourself :)

Cheers,
Andreas