normal_pdf.h

// Description: Pdf of normal distribution

#ifndef PASTELSYS_NORMAL_PDF_H
#define PASTELSYS_NORMAL_PDF_H

#include "pastel/sys/random/normal_distribution.h"

#include <cmath>

namespace Pastel
{

    // Probability log-density of normal distribution.
    template <typename Real>
    Real logPdf(
        const Normal_Distribution<Real>& distribution,
        const arma::Col<Real>& x)
    {
        auto rotated = distribution.rotation() * (x - distribution.mean());

        return std::log(2 * constantPi<Real>()) * (-(Real)distribution.n() / 2) +
            std::log(distribution.detCovariance()) / 2 -
            trans(rotated) /
            distribution.scale() * 
            rotated / 2;
    }

    // Probability density of normal distribution.
    template <typename Real>
    Real pdf(
        const Normal_Distribution<Real>& distribution,
        const arma::Col<Real>& x)
    {
        return std::exp(logPdf(distribution, x));
    }

}

#endif