/// <summary>
/// Samples a matrix normal distributed random variable.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="m">The mean of the matrix normal.</param>
/// <param name="v">The covariance matrix for the rows.</param>
/// <param name="k">The covariance matrix for the columns.</param>
/// <exception cref="ArgumentOutOfRangeException">If the dimensions of the mean and two covariance matrices don't match.</exception>
/// <returns>a sequence of samples from the distribution.</returns>
public static Matrix<double> Sample(System.Random rnd, Matrix<double> m, Matrix<double> v, Matrix<double> k)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(m, v, k))
{
throw new ArgumentException(Resources.InvalidDistributionParameters);
}
var n = m.RowCount;
var p = m.ColumnCount;
// Compute the Kronecker product of V and K, this is the covariance matrix for the stacked matrix.
var vki = v.KroneckerProduct(k.Inverse());
// Sample a vector valued random variable with VKi as the covariance.
var vector = SampleVectorNormal(rnd, new DenseVector(n*p), vki);
// Unstack the vector v and add the mean.
var r = m.Clone();
for (var i = 0; i < n; i++)
{
for (var j = 0; j < p; j++)
{
r.At(i, j, r.At(i, j) + vector[(j*n) + i]);
}
}
return r;
}
