renyi_entropy_normal.h

// Description: Analytical solutions for Renyi entropies
// Documentation: renyi_entropy_analytic.txt

#ifndef TIM_RENYI_ENTROPY_NORMAL_H
#define TIM_RENYI_ENTROPY_NORMAL_H

#include "tim/core/mytypes.h"
#include "tim/core/differential_entropy_normal.h"

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

#include <cmath>

namespace Tim
{

    //! Renyi entropy of a gaussian distribution.
    /*!
   Preconditions:
   dimension > 0
   covarianceDeterminant >= 0

   q:
   The power in the definition of Renyi entropy.
   If q = 1, differentialEntropyNormal() is returned
   instead.

   dimension:
   The dimension of the distribution.

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

        if (q == 1)
        {
            return differentialEntropyNormal<Real>(
                dimension,
                covarianceDeterminant);
        }

        // H_q^*(X) = (n / 2)[log(2 pi) - (log(q) / (1 - q))] + 
        //            (1 / 2)log(det(C))

        return ((Real)dimension / 2) * 
            (std::log(2 * constantPi<Real>()) - std::log(q) / (1 - q)) +
            std::log(covarianceDeterminant) / 2;
    }

}

#endif