void SingularValueDecomposition<Real>::HouseholderQR (
const GMatrix<Real>& A, GMatrix<Real>& Q, GMatrix<Real>& R)
{
// The matrix R gets a copy of A, and is then overwritten during the
// algorithm with the correct entries to be upper triangular.
R = A;
int numRows = R.GetNumRows();
int numCols = R.GetNumColumns();
assertion(numRows >= numCols, "Too many columns (use transpose)\n");
int row, col;
GVector<Real> V(numRows);
std::vector<GVector<Real> > VSave;
for (col = 0; col < numCols; ++col)
{
// Create the Householder vector for the partial column of A.
for (row = 0; row < col; ++row)
{
V[row] = (Real)0;
}
Real length = (Real)0;
for (row = col; row < numRows; ++row)
{
V[row] = R[row][col];
length += V[row]*V[row];
}
length = Math<Real>::Sqrt(length);
Real beta = V[col] + Math<Real>::Sign(V[col])*length;
if (beta != (Real)0)
{
Real invBeta = ((Real)1)/beta;
for (int i = col + 1; i < numRows; ++i)
{
V[i] *= invBeta;
}
}
V[col] = (Real)1;
// Premultiply A by the V-reflection matrix.
HouseholderPremultiply(V, R);
// Save the Householder vectors.
VSave.push_back(V);
}
// First, make Q the identity. Second, extract the Householder vectors
// and premultiply by the V-reflections to build Q.
memset(Q.GetElements(), 0, Q.GetNumElements()*sizeof(Real));
for (row = 0; row < numRows; ++row)
{
Q[row][row] = (Real)1;
}
for (col = numCols - 1; col >= 0; --col)
{
// Get the Householder vector.
V = VSave[col];
// Premultiply Q by the V-reflection matrix.
HouseholderPremultiply(V, Q);
}
}
