/// <summary>
/// Computes the QR decomposition.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <param name="q">The Q matrix.</param>
/// <param name="r">The R matrix.</param>
private static void Compute(Matrix matrix, out Matrix q, out Matrix r)
{
// source: Rosetta Code, http://rosettacode.org/wiki/QR_decomposition
q = MatrixFactory.CreateIdentity(matrix.NumberOfRows);
r = new Matrix(matrix);
for (Int32 i = 0; i < matrix.NumberOfRows - 1 && i < matrix.NumberOfColumns; i++)
{
Vector v = new Vector(matrix.NumberOfRows - i);
for (Int32 j = i; j < matrix.NumberOfRows; j++)
{
v[j - i] = r[j, i];
}
Matrix h = HouseholderTransformation.Transform(v);
Matrix hFull = MatrixFactory.CreateIdentity(matrix.NumberOfRows);
for (Int32 j = i; j < matrix.NumberOfRows; j++)
{
for (Int32 k = i; k < matrix.NumberOfColumns; k++)
{
hFull[j, k] = h[j - i, k - i];
}
}
q = q * hFull;
r = hFull * r;
}
}
/// <summary>
/// Transforms the specified vector.
/// </summary>
/// <param name="vector">The vector.</param>
/// <returns>The Householder matrix of the <paramref name="vector" />.</returns>
/// <exception cref="System.ArgumentNullException">The vector is null.</exception>
public static Matrix Transform(Double[] vector)
{
HouseholderTransformation transformation = new HouseholderTransformation(vector);
transformation.Compute();
return(transformation.H);
}