/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(params double[] x)
{
// http://www.buch-kromann.dk/tine/nonpar/Nonparametric_Density_Estimation_multidim.pdf
// http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode18.html
double sum = 0;
double[] delta = new double[Dimension];
if (type == WeightType.None)
{
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < x.Length; j++)
{
delta[j] = (x[j] - samples[i][j]);
}
sum += kernel.Function(chol.Solve(delta));
}
return(sum / (samples.Length * determinant));
}
if (type == WeightType.Repetition)
{
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < x.Length; j++)
{
delta[j] = (x[j] - samples[i][j]);
}
sum += kernel.Function(chol.Solve(delta)) * repeats[i];
}
return(sum / (numberOfSamples * determinant));
}
if (type == WeightType.Fraction)
{
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < x.Length; j++)
{
delta[j] = (x[j] - samples[i][j]);
}
sum += kernel.Function(chol.Solve(delta)) * weights[i];
}
return(sum / (sumOfWeights * determinant));
}
throw new InvalidOperationException();
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(double[] x)
{
// http://www.buch-kromann.dk/tine/nonpar/Nonparametric_Density_Estimation_multidim.pdf
// http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode18.html
double sum = 0;
CholeskyDecomposition chol = new CholeskyDecomposition(smoothing);
double[] delta = new double[Dimension];
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < x.Length; j++)
{
delta[j] = (x[j] - samples[i][j]);
}
sum += kernel.Function(chol.Solve(delta));
}
return(sum / (samples.Length * determinant));
}