levy_distribution.hpp

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//============================================================================
// vSMC/include/vsmc/rng/levy_distribution.hpp
//----------------------------------------------------------------------------
//                         vSMC: Scalable Monte Carlo
//----------------------------------------------------------------------------
// Copyright (c) 2013-2015, Yan Zhou
// All rights reserved.
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//============================================================================

#ifndef VSMC_RNG_LEVY_DISTRIBUTION_HPP
#define VSMC_RNG_LEVY_DISTRIBUTION_HPP

#include <vsmc/rng/internal/common.hpp>
#include <vsmc/rng/normal_distribution.hpp>

namespace vsmc
{

namespace internal
{

template <typename RealType>
inline bool levy_distribution_check_param(RealType, RealType b)
{
    return b > 0;
}

} // namespace vsmc::internal

template <typename RealType>
class LevyDistribution
{
    VSMC_DEFINE_RNG_DISTRIBUTION_2(
        Levy, levy, RealType, result_type, a, 0, result_type, b, 1)
    VSMC_DEFINE_RNG_DISTRIBUTION_OPERATORS

    public:
    result_type min VSMC_MNE() const { return a(); }

    result_type max VSMC_MNE() const
    {
        return std::numeric_limits<result_type>::max VSMC_MNE();
    }

    void reset() { normal_ = NormalDistribution<RealType>(0, 1); }

    private:
    NormalDistribution<RealType> normal_;

    template <typename RNGType>
    result_type generate(RNGType &rng, const param_type &param)
    {
        result_type r = normal_(rng);

        return param.a() + param.b() / (r * r);
    }
}; // class LevyDistribution

namespace internal
{

template <std::size_t K, typename RealType, typename RNGType>
inline void levy_distribution_impl(
    RNGType &rng, std::size_t n, RealType *r, RealType a, RealType b)
{
    normal_distribution(
        rng, n, r, static_cast<RealType>(0), static_cast<RealType>(1));
    sqr(n, r, r);
    inv(n, r, r);
    fma(n, b, r, a, r);
}

} // namespace vsmc::internal

template <typename RealType, typename RNGType>
inline void levy_distribution(
    RNGType &rng, std::size_t n, RealType *r, RealType a, RealType b)
{
    const std::size_t k = 1000;
    const std::size_t m = n / k;
    const std::size_t l = n % k;
    for (std::size_t i = 0; i != m; ++i)
        internal::levy_distribution_impl<k>(rng, k, r + i * k, a, b);
    internal::levy_distribution_impl<k>(rng, l, r + m * k, a, b);
}

template <typename RealType, typename RNGType>
inline void rng_rand(
    RNGType &rng, LevyDistribution<RealType> &dist, std::size_t n, RealType *r)
{
    dist(rng, n, r);
}

} // namespace vsmc

#endif // VSMC_RNG_LEVY_DISTRIBUTION_HPP