/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[][] Generate(int samples, double[][] result, Random source)
{
double[] z = new double[Dimension];
double[] u = Mean;
if (leftTriangularFactor == null)
{
if (svd != null)
{
leftTriangularFactor = new double[Dimension, Dimension];
double[,] V = svd.RightSingularVectors;
for (int i = 0; i < svd.Diagonal.Length; i++)
{
double d = Math.Sqrt(svd.Diagonal[i]);
for (int j = 0; j < Dimension; j++)
{
leftTriangularFactor[j, i] = d * V[j, i];
}
}
}
else
{
leftTriangularFactor = chol.LeftTriangularFactor;
}
}
for (int i = 0; i < samples; i++)
{
NormalDistribution.Random(Dimension, result: z, source: source);
leftTriangularFactor.Dot(z, result: result[i]);
result[i].Add(u, result: result[i]);
}
return(result);
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="dimension">The number of dimensions in the n-dimensional sphere.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public static double[][] Random(int samples, int dimension, double[][] result, Random source)
{
for (int i = 0; i < result.Length; i++)
{
// Generate independent normally-distributed vectors
NormalDistribution.Random(dimension, result: result[i], source: source);
result[i].Normalize(inPlace: true); // make unit norm
}
return(result);
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[][] Generate(int samples, double[][] result, Random source)
{
double[] normal = new double[Dimension + 2];
for (int i = 0; i < result.Length; i++)
{
// Generate n + 2 independent normal distributed values
NormalDistribution.Random(normal.Length, result: normal, source: source);
normal.Normalize(inPlace: true); // make unit norm
for (int j = 0; j < Dimension; j++) // take n dimensions
{
result[i][j] = normal[j] * radius + center[j];
}
}
return(result);
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[][] Generate(int samples, double[][] result)
{
if (chol == null)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive definite.");
}
double[,] A = chol.LeftTriangularFactor;
double[] z = new double[Dimension];
double[] u = Mean;
for (int i = 0; i < samples; i++)
{
NormalDistribution.Random(Dimension, result: z);
Matrix.Dot(A, z, result: result[i]);
Elementwise.Add(result[i], u, result: result[i]);
}
return(result);
}