/// <summary>Eigen Decomposition.</summary>
/// <param name="A">Input Matrix.</param>
/// <returns>Tuple(Eigen Values, Eigen Vectors)</returns>
public static Tuple <Vector, Matrix> Evd(Matrix A)
{
Evd eigs = new Evd(A);
eigs.Compute();
return(new Tuple <Vector, Matrix>(eigs.Eigenvalues, eigs.Eigenvectors));
}
public void CanFactorizeRandomSymmetricMatrix(int order, bool diagonal)
{
// create random matrix
var rand = Matrix.Rand(order, 1.13);
// create a symmetric positive definite matrix
var A = rand.T * rand;
if (diagonal)
{
var diag = A[0, 0];
for (var i = 1; i < order; i++)
A[i, i] = diag;
}
var evd = new Evd(A);
// compute eigenvalues/eigenvectors
evd.Compute();
var eigenvectors = evd.Eigenvectors;
var eigenvalues = evd.Eigenvalues;
foreach (var e in eigenvalues)
Assert.False(double.IsNaN(e));
Assert.Equal(order, eigenvectors.Rows);
Assert.Equal(order, eigenvectors.Cols);
Assert.Equal(order, eigenvalues.Length);
// make sure that A = V*λ*VT
var computed = eigenvectors * eigenvalues.Diag() * eigenvectors.T;
Assert.True(A.Equals(computed, 1e-10));
}
public void CanFactorizeRandomSymmetricMatrix(int order)
{
// create random matrix
var rand = Matrix.Rand(order, 1.13);
// create a symmetric positive definite matrix
var A = rand.T * rand;
var evd = new Evd(A);
// compute eigenvalues/eigenvectors
evd.compute();
var eigenvectors = evd.Eigenvectors;
var eigenvalues = evd.Eigenvalues;
Assert.AreEqual(order, eigenvectors.Rows);
Assert.AreEqual(order, eigenvectors.Cols);
Assert.AreEqual(order, eigenvalues.Length);
// make sure that A = V*λ*VT
var computed = eigenvectors * eigenvalues.Diag() * eigenvectors.T;
Assert.IsTrue(A.Equals(computed, 1e-10));
}
/// <summary>Eigen Decomposition.</summary>
/// <param name="A">Input Matrix.</param>
/// <returns>Tuple(Eigen Values, Eigen Vectors)</returns>
public static Tuple<Vector, Matrix> Evd(Matrix A)
{
var eigs = new Evd(A);
eigs.compute();
return new Tuple<Vector, Matrix>(eigs.Eigenvalues, eigs.Eigenvectors);
}