Gaussian Density eval and comparison using Infer.NET

GuassianDensity eval

using Microsoft.ML.Probabilistic.Math;
using Vector = Microsoft.ML.Probabilistic.Math.Vector;

class Program
{
    static void Main(string[] args)
    {
        Vector x = Vector.FromArray(new double[] { 0, 1 });
        //Vector x = new Vector();
        //Vector mean = new Vector(new double[] { 0.1, 1.1 });
        Vector mean = Vector.FromArray(new double[] { 0.1, 1.1 });
        PositiveDefiniteMatrix variance = new PositiveDefiniteMatrix(new double[,] { { 0.1, 0.1 }, { 0.1, 0.5 } });
        int d = x.Count;
        double logProb;

        // evaluate the Gaussian density via direct matrix inverse and determinant.
        Microsoft.ML.Probabilistic.Math.Vector dx = x - mean;
        logProb = -0.5 * variance.LogDeterminant() - d * MMath.LnSqrt2PI - 0.5 * dx.Inner(variance.Inverse() * dx);
        Console.WriteLine("log p(x|m,V) = {0}", logProb);

        // evaluate the Gaussian density using Cholesky decomposition.
        LowerTriangularMatrix varianceChol = new LowerTriangularMatrix(d, d);
        varianceChol.SetToCholesky(variance);
        dx.PredivideBy(varianceChol);
        // new dx = inv(chol(v))*dx so that
        // (new dx)'*(new dx) = dx'*inv(chol(v))'*inv(chol(v))*dx 
        // = dx'*inv(chol(v)*chol(v)')*dx
        // = dx'*inv(v)*dx
        logProb = -varianceChol.TraceLn() - d * MMath.LnSqrt2PI - 0.5 * dx.Inner(dx);
        Console.WriteLine("log p(x|m,V) = {0}", logProb);
        Console.ReadKey();
    }
}