/// <summary>
/// Constructs and returns a new QR decomposition object; computed by Householder reflections;
/// The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
/// Return a decomposition object to access <i>R</i> and the Householder vectors <i>H</i>, and to compute <i>Q</i>.
/// </summary>
/// <param name="A">A rectangular matrix.</param>
/// <exception cref="ArgumentException">if <i>A.Rows < A.Columns</i>.</exception>
public QRDecomposition(DoubleMatrix2D A)
{
Property.DEFAULT.CheckRectangular(A);
Functions F = Functions.functions;
// Initialize.
QR = A.Copy();
m = A.Rows;
n = A.Columns;
Rdiag = A.Like1D(n);
//Rdiag = new double[n];
DoubleDoubleFunction hypot = Algebra.HypotFunction();
// precompute and cache some views to avoid regenerating them time and again
DoubleMatrix1D[] QRcolumns = new DoubleMatrix1D[n];
DoubleMatrix1D[] QRcolumnsPart = new DoubleMatrix1D[n];
for (int k = 0; k < n; k++)
{
QRcolumns[k] = QR.ViewColumn(k);
QRcolumnsPart[k] = QR.ViewColumn(k).ViewPart(k, m - k);
}
// Main loop.
for (int k = 0; k < n; k++)
{
//DoubleMatrix1D QRcolk = QR.ViewColumn(k).ViewPart(k,m-k);
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
//if (k<m) nrm = QRcolumnsPart[k].aggregate(hypot,F.identity);
for (int i = k; i < m; i++)
{ // fixes bug reported by [email protected]
nrm = Algebra.Hypot(nrm, QR[i, k]);
}
if (nrm != 0.0)
{
// Form k-th Householder vector.
if (QR[k, k] < 0)
{
nrm = -nrm;
}
QRcolumnsPart[k].Assign(F2.Div(nrm));
/*
* for (int i = k; i < m; i++) {
* QR[i][k] /= nrm;
* }
*/
QR[k, k] = QR[k, k] + 1;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
DoubleMatrix1D QRcolj = QR.ViewColumn(j).ViewPart(k, m - k);
double s = QRcolumnsPart[k].ZDotProduct(QRcolj);
/*
* // fixes bug reported by John Chambers
* DoubleMatrix1D QRcolj = QR.ViewColumn(j).ViewPart(k,m-k);
* double s = QRcolumnsPart[k].ZDotProduct(QRcolumns[j]);
* double s = 0.0;
* for (int i = k; i < m; i++) {
* s += QR[i][k]*QR[i][j];
* }
*/
s = -s / QR[k, k];
//QRcolumnsPart[j].Assign(QRcolumns[k], F.PlusMult(s));
for (int i = k; i < m; i++)
{
QR[i, j] = QR[i, j] + s * QR[i, k];
}
}
}
Rdiag[k] = -nrm;
}
}
/// <summary>
/// Construct and returns a new empty matrix <i>of the same dynamic type</i> as the receiver, having the specified size.
/// For example, if the receiver is an instance of type <see cref="DenseDoubleMatrix1D"/> the new matrix must also be of type <see cref="DenseDoubleMatrix1D"/>,
/// if the receiver is an instance of type <see cref="SparseDoubleMatrix1D"/> the new matrix must also be of type <see cref="SparseDoubleMatrix1D"/>, etc.
/// In general, the new matrix should have internal parametrization as similar as possible.
/// </summary>
/// <param name="size">the number of cell the matrix shall have.</param>
/// <returns>a new empty matrix of the same dynamic type.</returns>
public override DoubleMatrix1D Like(int size)
{
return(content2D.Like1D(size));
}
