differential_entropy_normal.h

// Description: Differential entropy of a normal distribution

#ifndef TIM_DIFFERENTIAL_ENTROPY_NORMAL_H
#define TIM_DIFFERENTIAL_ENTROPY_NORMAL_H

#include "tim/core/mytypes.h"

#include <pastel/sys/real/real_concept.h>
#include <cmath>

namespace Tim
{

    //! Differential entropy of a normal distribution.
    /*!
   Preconditions:
   dimension > 0
   covarianceDeterminant >= 0

   dimension:
   The dimension of the distribution.

   covarianceDeterminant:
   The determinant of the covariance matrix of the distribution.
   */
    template <typename Real>
    Real differentialEntropyNormal(
        integer dimension, 
        const NoDeduction<Real>& covarianceDeterminant)
    {
        PENSURE_OP(dimension, >, 0);
        PENSURE_OP(covarianceDeterminant, >=, 0);

        static const Real ConstantFactor = std::log(
            2 * constantPi<Real>()) + 1;

        return 0.5 * (
            std::log(covarianceDeterminant) + 
            dimension * ConstantFactor);
    }

}

#endif