/// <summary>
/// Samples a Dirichlet distributed random vector.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="alpha">The Dirichlet distribution parameter.</param>
/// <returns>a sample from the distribution.</returns>
public static double[] Sample(System.Random rnd, double[] alpha)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(alpha))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
var n = alpha.Length;
var gv = new double[n];
var sum = 0.0;
for (var i = 0; i < n; i++)
{
if (alpha[i] == 0.0)
{
gv[i] = 0.0;
}
else
{
gv[i] = Gamma.Sample(rnd, alpha[i], 1.0);
}
sum += gv[i];
}
for (var i = 0; i < n; i++)
{
gv[i] /= sum;
}
return(gv);
}
/// <summary>
/// Samples the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="degreesOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
/// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
/// <param name="chol">The cholesky decomposition to use.</param>
/// <returns>a random number from the distribution.</returns>
static Matrix <double> DoSample(System.Random rnd, double degreesOfFreedom, Matrix <double> scale, Cholesky <double> chol)
{
var count = scale.RowCount;
// First generate a lower triangular matrix with Sqrt(Chi-Squares) on the diagonal
// and normal distributed variables in the lower triangle.
var a = new DenseMatrix(count, count);
for (var d = 0; d < count; d++)
{
a.At(d, d, Math.Sqrt(Gamma.Sample(rnd, (degreesOfFreedom - d) / 2.0, 0.5)));
}
for (var i = 1; i < count; i++)
{
for (var j = 0; j < i; j++)
{
a.At(i, j, Normal.Sample(rnd, 0.0, 1.0));
}
}
var factor = chol.Factor;
return(factor * a * a.Transpose() * factor.Transpose());
}
/// <summary>
/// Generates a sequence of samples from the NormalGamma distribution
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="meanLocation">The location of the mean.</param>
/// <param name="meanScale">The scale of the mean.</param>
/// <param name="precisionShape">The shape of the precision.</param>
/// <param name="precisionInvScale">The inverse scale of the precision.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable <MeanPrecisionPair> Samples(System.Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInvScale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInvScale))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
while (true)
{
var mp = new MeanPrecisionPair();
// Sample the precision.
mp.Precision = double.IsPositiveInfinity(precisionInvScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInvScale);
// Sample the mean.
mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0 / (meanScale * mp.Precision)));
yield return(mp);
}
}
/// <summary>
/// Generates a sample from the distribution.
/// </summary>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sample from the distribution.</returns>
public static double Sample(int shape, double rate)
{
return(Gamma.Sample(shape, rate));
}
/// <summary>
/// Generates a sample from the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="shape">The shape (k) of the Erlang distribution. Range: k ≥ 0.</param>
/// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.</param>
/// <returns>a sample from the distribution.</returns>
public static double Sample(System.Random rnd, int shape, double rate)
{
return(Gamma.Sample(rnd, shape, rate));
}
