random_generalizedgaussian.h

// Description: Generalized-Gaussian-distributed random numbers

#ifndef PASTELSYS_RANDOM_GENERALIZEDGAUSSIAN_H
#define PASTELSYS_RANDOM_GENERALIZEDGAUSSIAN_H

#include "pastel/sys/mytypes.h"
#include "pastel/sys/vector.h"

namespace Pastel
{

    //! Returns a generalized-gaussian-distributed random real.
    /*!
   Preconditions:
   shape > 0

   This function assumes that the scale-parameter is 1.
   The Generalized Gaussian distribution corresponds
   to some well-known distributions on specific values
   of 'shape'. These are:
   * shape = 1: Laplace distribution.
   * shape = 2: Gaussian distribution (deviation 1 / sqrt(2)).
   * shape -> oo: Uniform distribution on [-1, 1] in limit.
   */
    template <typename Real>
    Real randomGeneralizedGaussian(
        const NoDeduction<Real>& shape);

    //! Returns a generalized-gaussian-distributed random real.
    /*!
   Preconditions:
   shape > 0
   scale >= 0

   This is a convenience function that calls:
   randomGeneralizedGaussian<Real>(shape) * scale.
   
   See the documentation for that function.
   */
    template <typename Real>
    Real randomGeneralizedGaussian(
        const NoDeduction<Real>& shape, 
        const NoDeduction<Real>& scale);

    //! Converts variance to Generalized Gaussian scale parameter.
    /*!
   Preconditions:
   shape > 0
   variance >= 0
   */
    template <typename Real>
    Real varianceToGeneralizedGaussianScale(
        const NoDeduction<Real>& shape,
        const NoDeduction<Real>& variance);

    //! Returns a vector of Generalized Gaussian random numbers.
    /*!
   Preconditions:
   shape > 0
   scale >= 0
   */
    template <typename Real, integer N>
    Vector<Real, N> randomGeneralizedGaussianVector(
        const NoDeduction<Real>& shape, 
        const NoDeduction<Real>& scale);

    //! Returns a vector of Generalized Gaussian random numbers.
    /*!
   Preconditions:
   dimension > 0
   shape > 0
   scale >= 0
   */
    template <typename Real, integer N>
    Vector<Real, N> randomGeneralizedGaussianVector(
        integer dimension,
        const NoDeduction<Real>& shape, 
        const NoDeduction<Real>& scale);

    //! Probability density function of the Generalized Gaussian Distribution.
    /*!
   Preconditions:
   shape > 0
   scale >= 0
   */
    template <typename Real>
    Real generalizedGaussianPdf(
        const NoDeduction<Real>& x,
        const NoDeduction<Real>& shape,
        const NoDeduction<Real>& scale);

    //! Probability density function of the Generalized Gaussian Distribution.
    /*!
   Preconditions:
   shape > 0
   */
    template <typename Real>
    Real generalizedGaussianPdf(
        const NoDeduction<Real>& x,
        const NoDeduction<Real>& shape);

}

#include "pastel/sys/random/random_generalizedgaussian.hpp"

#endif