tsallis_entropy_uniform.h

// Description: Tsallis entropy of a uniform distribution
// Documentation: tsallis_entropy_analytic.txt

#ifndef TIM_TSALLIS_ENTROPY_UNIFORM_H
#define TIM_TSALLIS_ENTROPY_UNIFORM_H

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

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

namespace Tim
{

    //! Tsallis entropy of a uniform distribution.
    /*!
   Preconditions:
   supportVolume >= 0

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

   supportVolume:
   The measure m of the support of the probability density
   function p: m({x in R^n: p(x) != 0})
   */
    template <typename Real>
    Real uniformTsallisEntropy(
        const NoDeduction<Real>& q,
        const NoDeduction<Real>& supportVolume)
    {
        PENSURE_OP(supportVolume, >, 0);

        if (q == 1)
        {
            return differentialEntropyUniform<Real>(supportVolume);
        }

        // I = 1 / m(S)^(q - 1)

        Real I = inverse(std::pow(supportVolume, q - 1));

        // H_q(X) = (1 - I) / (q - 1)

        return (1 - I) / (q - 1);
    }

}

#endif