Exemple #1
0
bool QRDecomposition<T>::set(const MatrixT& A)
{
  QR.copy(A);
  tau.resize(Min(A.m,A.n));

  for (int i=0;i<Min(A.m,A.n);i++) {
    /* Compute the Householder transformation to reduce the j-th
       column of the matrix to a multiple of the j-th unit vector */
    
    VectorT c_full,c;
    QR.getColRef(i,c_full);
    c.setRef(c_full,i);
    T tau_i = HouseholderTransform (c);
    tau(i)=tau_i;
    
    /* Apply the transformation to the remaining columns and
       update the norms */
    
    if (i+1 < A.n) {
      MatrixT m;
      m.setRef(QR,i,i+1);
      HouseholderPreMultiply (tau_i, c, m);
    }
  }
  return true;
}
Exemple #2
0
void QRDecomposition<T>::getQ(MatrixT& Q) const
{
  Assert(tau.n == Min(QR.m,QR.n));
  Q.resize(QR.m,QR.m);

  int i;
  Q.setIdentity();
  for (i=Min(QR.m,QR.n);i>0 && i--;) {
    VectorT c,h;
    QR.getColRef(i,c);
    h.setRef(c,i);
    MatrixT m;
    m.setRef(Q,i,i);
    HouseholderPreMultiply(tau(i),h,m);
  }
}
Exemple #3
0
void QRDecomposition<T>::leastSquares(const VectorT& b, VectorT& x, VectorT& residual) const
{
  if(x.n == 0) x.resize(QR.n);
  Assert(QR.m >= QR.n);
  Assert(QR.m == b.n);
  Assert(QR.n == x.n);
  Assert(QR.m == residual.n);

  MatrixT R;
  R.setRef(QR,0,0,1,1,QR.n,QR.n);
  VectorT c;
  c.setRef(residual,0,1,QR.n);

  /* compute rhs = Q^T b */ 
  QtMul(b,residual);
  
  /* Solve R x = rhs */
  UBackSubstitute(R,c,x);
  
  /* Compute residual = b - A x = Q (Q^T b - R x) */
  c.setZero();
  QMul(residual,residual);
}