/// <summary>
/// Evaluates the probability density function for the Wishart distribution.
/// </summary>
/// <param name="x">The matrix at which to evaluate the density at.</param>
/// <exception cref="ArgumentOutOfRangeException">If the argument does not have the same dimensions as the scale matrix.</exception>
/// <returns>the density at <paramref name="x"/>.</returns>
public double Density(Matrix <double> x)
{
var p = _scale.RowCount;
if (x.RowCount != p || x.ColumnCount != p)
{
throw Matrix.DimensionsDontMatch <ArgumentOutOfRangeException>(x, _scale, "x");
}
var dX = x.Determinant();
var siX = _chol.Solve(x);
// Compute the multivariate Gamma function.
var gp = Math.Pow(Constants.Pi, p * (p - 1.0) / 4.0);
for (var j = 1; j <= p; j++)
{
gp *= SpecialFunctions.Gamma((_degreesOfFreedom + 1.0 - j) / 2.0);
}
return(Math.Pow(dX, (_degreesOfFreedom - p - 1.0) / 2.0)
* Math.Exp(-0.5 * siX.Trace())
/ Math.Pow(2.0, _degreesOfFreedom * p / 2.0)
/ Math.Pow(_chol.Determinant, _degreesOfFreedom / 2.0)
/ gp);
}
/// <summary>
/// Evaluates the probability density function for the Wishart distribution.
/// </summary>
/// <param name="x">The matrix at which to evaluate the density at.</param>
/// <exception cref="ArgumentOutOfRangeException">If the argument does not have the same dimensions as the scale matrix.</exception>
/// <returns>the density at <paramref name="x"/>.</returns>
public double Density(Matrix <double> x)
{
var p = _s.RowCount;
if (x.RowCount != p || x.ColumnCount != p)
{
throw new ArgumentOutOfRangeException("x", Resources.ArgumentMatrixDimensions);
}
var dX = x.Determinant();
var siX = _chol.Solve(x);
// Compute the multivariate Gamma function.
var gp = Math.Pow(Constants.Pi, p * (p - 1.0) / 4.0);
for (var j = 1; j <= p; j++)
{
gp *= SpecialFunctions.Gamma((_nu + 1.0 - j) / 2.0);
}
return(Math.Pow(dX, (_nu - p - 1.0) / 2.0)
* Math.Exp(-0.5 * siX.Trace())
/ Math.Pow(2.0, _nu * p / 2.0)
/ Math.Pow(_chol.Determinant, _nu / 2.0)
/ gp);
}
public void ShouldSolve()
{
var a = new double[, ]
{
{ 6.0, 15.0, 55.0 },
{ 15.0, 55.0, 225.0 },
{ 55.0, 225.0, 979.0 }
};
var rhs = new double[] { 9.5, 50.0, 237.0 };
var solution = Cholesky.Solve(a, rhs);
var expected = new double[] { -0.5, -1.0, 0.5 };
Assert.AreEqual(expected.Length, solution.Length);
for (var i = 0; i < solution.Length; ++i)
{
Assert.AreEqual(expected[i], solution[i], 0.000001);
}
}