/// <summary>
/// Computes the Householder vector.
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
private static MatrixQ[] HouseholderVector(MatrixQ x)
{
//throw new NotImplementedException("Supposingly buggy!");
//if (!x.IsReal())
// throw new ArgumentException("Cannot compute housholder vector of non-real vector.");
int n = x.VectorLength();
if (n == 0)
throw new InvalidOperationException("Expected vector as argument.");
MatrixQ y = x / x.Norm();
MatrixQ buf = y.Extract(2, n, 1, 1);
Complex s = Dot(buf, buf);
MatrixQ v = Zeros(n, 1);
v[1] = Complex.One;
v.Insert(2, 1, buf);
double beta = 0;
if (s != 0) {
Complex mu = Complex.Sqrt(y[1] * y[1] + s);
if (y[1].Re <= 0)
v[1] = y[1] - mu;
else
v[1] = -s / (y[1] + mu);
beta = 2 * v[1].Re * v[1].Re / (s.Re + v[1].Re * v[1].Re);
v = v / v[1];
}
return new MatrixQ[] { v, new MatrixQ(beta) };
}
