/// <summary>
/// Samples an inverse Wishart distributed random variable by sampling
/// a Wishart random variable and inverting the matrix.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="nu">The degrees of freedom.</param>
/// <param name="s">The scale matrix.</param>
/// <returns>a sample from the distribution.</returns>
public static Matrix<double> Sample(Random rnd, double nu, Matrix<double> s)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
var r = Wishart.Sample(rnd, nu, s.Inverse());
return r.Inverse();
}
/// <summary>
/// Samples an inverse Wishart distributed random variable by sampling
/// a Wishart random variable and inverting the matrix.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="degreesOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
/// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
/// <returns>a sample from the distribution.</returns>
public static Matrix <double> Sample(System.Random rnd, double degreesOfFreedom, Matrix <double> scale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(degreesOfFreedom, scale))
{
throw new ArgumentException(Resource.InvalidDistributionParameters);
}
var r = Wishart.Sample(rnd, degreesOfFreedom, scale.Inverse());
return(r.Inverse());
}
public void CanCreateWishart(double nu, int order)
{
var matrix = Matrix<double>.Build.RandomPositiveDefinite(order, 1);
var d = new Wishart(nu, matrix);
Assert.AreEqual(nu, d.DegreesOfFreedom);
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
public void CanGetS()
{
const int Order = 2;
var matrix = Matrix<double>.Build.RandomPositiveDefinite(Order, 1);
var d = new Wishart(1.0, matrix);
for (var i = 0; i < Order; i++)
{
for (var j = 0; j < Order; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
public void CanGetNu(double nu)
{
var d = new Wishart(nu, Matrix<double>.Build.RandomPositiveDefinite(2, 1));
Assert.AreEqual(nu, d.DegreesOfFreedom);
}
public void ValidateVariance(double nu, int order)
{
var d = new Wishart(nu, Matrix<double>.Build.RandomPositiveDefinite(order, 1));
var variance = d.Variance;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(nu * ((d.Scale[i, j] * d.Scale[i, j]) + (d.Scale[i, i] * d.Scale[j, j])), variance[i, j]);
}
}
}
public void ValidateToString()
{
var d = new Wishart(1.0, Matrix<double>.Build.RandomPositiveDefinite(2, 1));
Assert.AreEqual("Wishart(DegreesOfFreedom = 1, Rows = 2, Columns = 2)", d.ToString());
}
public void ValidateMode(double nu, int order)
{
var d = new Wishart(nu, Matrix<double>.Build.RandomPositiveDefinite(order, 1));
var mode = d.Mode;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual((nu - d.Scale.RowCount - 1.0) * d.Scale[i, j], mode[i, j]);
}
}
}
public void ValidateDensity(double nu, double density)
{
const int Order = 1;
var matrix = new DenseMatrix(Order);
matrix[0, 0] = 1;
var x = new DenseMatrix(Order);
x[0, 0] = 5;
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqualRelative(density, d.Density(x), 16);
}
public void HasRandomSource()
{
var d = new Wishart(1.0, Matrix<double>.Build.RandomPositiveDefinite(2, 1));
Assert.IsNotNull(d.RandomSource);
}
public void FailSetRandomSourceWithNullReference()
{
var d = new Wishart(1.0, Matrix<double>.Build.RandomPositiveDefinite(2, 1));
Assert.Throws<ArgumentNullException>(() => d.RandomSource = null);
}
public void CanSample()
{
var d = new Wishart(1.0, Matrix<double>.Build.RandomPositiveDefinite(2, 1));
d.Sample();
}
public void ValidateDensity(double nu, double density)
{
var matrix = Matrix<double>.Build.Dense(1, 1, 1.0);
var x = Matrix<double>.Build.Dense(1, 1, 5.0);
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqualRelative(density, d.Density(x), 16);
}