public static void ComputeEigenvalues(this SymmetricMatrix2 @this, out double low, out double high)
{
var halfTrace = @this.Trace() / 2;
var disc = BasicMath.Sqrt(halfTrace * halfTrace - @this.Det());
low = halfTrace - disc;
high = halfTrace + disc;
}
public void Eigenvectors_and_eigenvalues_of_satisfy_defining_equations
([Values(0.577, 0.577, 0.577, 0.577)] double xx,
[Values(2.718, 0.577, 0.577, 0.577)] double yy,
[Values(3.141, 0, 1e-40, 1e-60)] double xy)
{
var mat = new SymmetricMatrix2(xx, yy, xy);
var loVal = mat.LowEigenvalue();
var loVec = mat.LowEigenvector();
Expect((mat - SymmetricMatrix2.Scalar(loVal)).Det(), Is.EqualTo(0).Within(_tolerance));
Expect(Vector2.Distance(mat * loVec, loVal * loVec), Is.LessThan(_tolerance));
var hiVal = mat.HighEigenvalue();
var hiVec = mat.HighEigenvector();
Expect((mat - SymmetricMatrix2.Scalar(hiVal)).Det(), Is.EqualTo(0).Within(_tolerance));
Expect(Vector2.Distance(mat * hiVec, hiVal * hiVec), Is.LessThan(_tolerance));
Expect(loVal, Is.LessThan(hiVal + _tolerance));
Expect(loVal + hiVal, Is.EqualTo(mat.Trace()).Within(_tolerance));
}
public static double HighEigenvalue(this SymmetricMatrix2 @this)
{
var halfTrace = @this.Trace() / 2;
return(halfTrace + BasicMath.Sqrt(halfTrace * halfTrace - @this.Det()));
}