/// <summary>
/// Householder Reflection: Evaluate symmetric? unitary Q such that Q*v = -sigma*||v||*e1
/// </summary>
public static ComplexMatrix Reflection(ComplexVector v)
{
Complex sigma = v[0].Sign;
ComplexVector u = v.Clone();
u[0] += sigma * v.Norm();
ComplexMatrix m = ComplexMatrix.Identity(v.Length, v.Length);
m.MultiplyAccumulateInplace(u.TensorMultiply(u), -2d / u.ScalarMultiply(u));
return m;
}
/// <summary>
/// Householder Reflection: Evaluate symmetric? unitary Q such that Q*v = -sigma*||v||*e1
/// </summary>
public static ComplexMatrix Reflection(ComplexVector v)
{
Complex sigma = v[0].Sign;
ComplexVector u = v.Clone();
u[0] += sigma * v.Norm();
ComplexMatrix m = ComplexMatrix.Identity(v.Length, v.Length);
m.MultiplyAccumulateInplace(u.TensorMultiply(u), -2d / u.ScalarMultiply(u));
return(m);
}
public void TestAlmostEquals_ComplexVector()
{
ComplexVector a1 = ComplexVector.Random(3, new ContinuousUniformDistribution());
ComplexVector a2 = a1.Clone();
ComplexVector b = -a1;
ComplexVector c = a1 * (1.0 + (1e+10 * Number.PositiveEpsilonOf(1.0)));
ComplexVector d = a1 * (1.0 + (2 * Number.PositiveEpsilonOf(1.0)));
Helper_TestAlmostEqualityForGenericType(a1, a2, b, c, d);
// Wrapper
Assert.That(ComplexVector.AlmostEqual(a1, c), Is.False);
Assert.That(ComplexVector.AlmostEqual(a1, c, 1e-10), Is.False);
Assert.That(ComplexVector.AlmostEqual(a1, c, 1e-2), Is.True);
// reference type -> no boxing
Assert.That(a1, Is.SameAs(a1));
}
