NormalExp.h

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#ifndef EIGENRAND_DISTS_NORMAL_EXP_H
#define EIGENRAND_DISTS_NORMAL_EXP_H
 
namespace Eigen
{
    namespace Rand
    {
        template<typename _Scalar>
        class StdNormalGen : OptCacheStore, public GenBase<StdNormalGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "normalDist needs floating point types.");
            bool valid = false;
            UniformRealGen<_Scalar> ur;
            
        public:
            using Scalar = _Scalar;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                if (valid)
                {
                    valid = false;
                    return OptCacheStore::get<_Scalar>();
                }
                valid = true;
 
                _Scalar v1, v2, sx;
                while (1)
                {
                    v1 = 2 * ur(rng) - 1;
                    v2 = 2 * ur(rng) - 1;
                    sx = v1 * v1 + v2 * v2;
                    if (sx && sx < 1) break;
                }
                _Scalar fx = std::sqrt((_Scalar)-2.0 * std::log(sx) / sx);
                OptCacheStore::get<_Scalar>() = fx * v2;
                return fx * v1;
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                if (valid)
                {
                    valid = false;
                    return OptCacheStore::template get<Packet>();
                }
                valid = true;
                Packet u1 = ur.template packetOp<Packet>(rng),
                    u2 = ur.template packetOp<Packet>(rng);
 
                u1 = psub(pset1<Packet>(1), u1);
 
                auto radius = psqrt(pmul(pset1<Packet>(-2), plog(u1)));
                auto theta = pmul(pset1<Packet>(2 * constant::pi), u2);
                Packet sintheta, costheta;
 
                psincos(theta, sintheta, costheta);
                OptCacheStore::template get<Packet>() = pmul(radius, costheta);
                return pmul(radius, sintheta);
            }
        };
 
        template<typename _Scalar>
        class NormalGen : public GenBase<NormalGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "normalDist needs floating point types.");
            StdNormalGen<_Scalar> stdnorm;
            _Scalar mean = 0, stdev = 1;
        
        public:
            using Scalar = _Scalar;
 
            NormalGen(_Scalar _mean = 0, _Scalar _stdev = 1)
                : mean{ _mean }, stdev{ _stdev }
            {
            }
 
            NormalGen(const NormalGen&) = default;
            NormalGen(NormalGen&&) = default;
 
            NormalGen& operator=(const NormalGen&) = default;
            NormalGen& operator=(NormalGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return stdnorm(std::forward<Rng>(rng)) * stdev + mean;
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                return padd(pmul(
                    stdnorm.template packetOp<Packet>(std::forward<Rng>(rng)),
                    pset1<Packet>(stdev)
                ), pset1<Packet>(mean));
            }
        };
 
        template<typename _Scalar>
        class LognormalGen : public GenBase<LognormalGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "lognormalDist needs floating point types.");
            NormalGen<_Scalar> norm;
 
        public:
            using Scalar = _Scalar;
 
            LognormalGen(_Scalar _mean = 0, _Scalar _stdev = 1)
                : norm{ _mean, _stdev }
            {
            }
 
            LognormalGen(const LognormalGen&) = default;
            LognormalGen(LognormalGen&&) = default;
 
            LognormalGen& operator=(const LognormalGen&) = default;
            LognormalGen& operator=(LognormalGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return std::exp(norm(std::forward<Rng>(rng)));
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                return pexp(norm.template packetOp<Packet>(std::forward<Rng>(rng)));
            }
        };
 
        template<typename _Scalar>
        class StudentTGen : public GenBase<StudentTGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "studentT needs floating point types.");
            UniformRealGen<_Scalar> ur;
            _Scalar n;
 
        public:
            using Scalar = _Scalar;
 
            StudentTGen(_Scalar _n = 1)
                : n{ _n }
            {
            }
 
            StudentTGen(const StudentTGen&) = default;
            StudentTGen(StudentTGen&&) = default;
 
            StudentTGen& operator=(const StudentTGen&) = default;
            StudentTGen& operator=(StudentTGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                _Scalar v1, v2, sx;
                while (1)
                {
                    v1 = 2 * ur(rng) - 1;
                    v2 = 2 * ur(rng) - 1;
                    sx = v1 * v1 + v2 * v2;
                    if (sx && sx < 1) break;
                }
 
                _Scalar fx = std::sqrt(n * (std::pow(sx, -2 / n) - 1) / sx);
                return fx * v1;
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                Packet u1 = ur.template packetOp<Packet>(rng),
                    u2 = ur.template packetOp<Packet>(rng);
 
                u1 = psub(pset1<Packet>(1), u1);
                auto pn = pset1<Packet>(n);
                auto radius = psqrt(pmul(pn,
                    psub(pexp(pmul(plog(u1), pset1<Packet>(-2 / n))), pset1<Packet>(1))
                ));
                auto theta = pmul(pset1<Packet>(2 * constant::pi), u2);
                //Packet sintheta, costheta;
                //psincos(theta, sintheta, costheta);
                return pmul(radius, psin(theta));
            }
        };
 
        template<typename> class GammaGen;
 
        template<typename _Scalar>
        class ExponentialGen : public GenBase<ExponentialGen<_Scalar>, _Scalar>
        {
            friend GammaGen<_Scalar>;
            static_assert(std::is_floating_point<_Scalar>::value, "expDist needs floating point types.");
            UniformRealGen<_Scalar> ur;
            _Scalar lambda = 1;
 
        public:
            using Scalar = _Scalar;
 
            ExponentialGen(_Scalar _lambda = 1)
                : lambda{ _lambda }
            {
            }
            
            ExponentialGen(const ExponentialGen&) = default;
            ExponentialGen(ExponentialGen&&) = default;
 
            ExponentialGen& operator=(const ExponentialGen&) = default;
            ExponentialGen& operator=(ExponentialGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return -std::log(1 - ur(std::forward<Rng>(rng))) / lambda;
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                return pnegate(pdiv(plog(
                    psub(pset1<Packet>(1), ur.template packetOp<Packet>(std::forward<Rng>(rng)))
                ), pset1<Packet>(lambda)));
            }
        };
 
        template<typename> class NegativeBinomialGen;
 
        template<typename _Scalar>
        class GammaGen : OptCacheStore, public GenBase<GammaGen<_Scalar>, _Scalar>
        {
            template<typename _Ty>
            friend class NegativeBinomialGen;
            static_assert(std::is_floating_point<_Scalar>::value, "gammaDist needs floating point types.");
            int cache_rest_cnt = 0;
            ExponentialGen<_Scalar> expon;
            _Scalar alpha, beta, px, sqrt;
 
        public:
            using Scalar = _Scalar;
 
            GammaGen(_Scalar _alpha = 1, _Scalar _beta = 1)
                : alpha{ _alpha }, beta{ _beta }
            {
                px = constant::e / (alpha + constant::e);
                sqrt = std::sqrt(2 * alpha - 1);
            }
 
            GammaGen(const GammaGen&) = default;
            GammaGen(GammaGen&&) = default;
 
            GammaGen& operator=(const GammaGen&) = default;
            GammaGen& operator=(GammaGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                if (alpha < 1)
                {
                    _Scalar ux, vx, xx, qx;
                    while (1)
                    {
                        ux = expon.ur(rng);
                        vx = expon.ur.nzur_scalar(rng);
 
                        if (ux < px)
                        {
                            xx = std::pow(vx, 1 / alpha);
                            qx = std::exp(-xx);
                        }
                        else
                        {
                            xx = 1 - std::log(vx);
                            qx = std::pow(xx, alpha - 1);
                        }
 
                        if (expon.ur(rng) < qx)
                        {
                            return beta * xx;
                        }
                    }
                }
                if (alpha == 1)
                {
                    return beta * expon(rng);
                }
                int count;
                if ((count = alpha) == alpha && count < 20)
                {
                    _Scalar yx;
                    yx = expon.ur.nzur_scalar(rng);
                    while (--count)
                    {
                        yx *= expon.ur.nzur_scalar(rng);
                    }
                    return -beta * std::log(yx);
                }
 
                while (1)
                {
                    _Scalar yx, xx;
                    yx = std::tan(constant::pi * expon.ur(rng));
                    xx = sqrt * yx + alpha - 1;
                    if (xx <= 0) continue;
                    if (expon.ur(rng) <= (1 + yx * yx)
                        * std::exp((alpha - 1) * std::log(xx / (alpha - 1)) - sqrt * yx))
                    {
                        return beta * xx;
                    }
                }
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                using RUtils = RandUtils<Packet, Rng>;
                auto& cm = Rand::detail::CompressMask<sizeof(Packet)>::get_inst();
 
                RUtils ru;
                if (alpha < 1)
                {
                    while (1)
                    {
                        Packet ux = ru.uniform_real(rng);
                        Packet vx = ru.nonzero_uniform_real(rng);
 
                        Packet xx = pexp(pmul(pset1<Packet>(1 / alpha), plog(vx)));
                        Packet qx = pexp(pnegate(xx));
 
                        Packet xx2 = psub(pset1<Packet>(1), plog(vx));
                        Packet qx2 = pexp(pmul(plog(xx2), pset1<Packet>(alpha - 1)));
 
                        auto c = pcmplt(ux, pset1<Packet>(px));
                        xx = pblendv(c, xx, xx2);
                        qx = pblendv(c, qx, qx2);
 
                        ux = ru.uniform_real(rng);
                        Packet cands = pmul(pset1<Packet>(beta), xx);
                        bool full = false;
                        cache_rest_cnt = cm.compress_append(cands, pcmplt(ux, qx),
                            OptCacheStore::template get<Packet>(), cache_rest_cnt, full);
                        if (full) return cands;
                    }
                }
                if (alpha == 1)
                {
                    return pmul(pset1<Packet>(beta),
                        expon.template packetOp<Packet>(rng)
                    );
                }
                int count;
                if ((count = alpha) == alpha && count < 20)
                {
                    RUtils ru;
                    Packet ux, yx;
                    yx = ru.nonzero_uniform_real(rng);
                    while (--count)
                    {
                        yx = pmul(yx, ru.nonzero_uniform_real(rng));
                    }
                    return pnegate(pmul(pset1<Packet>(beta), plog(yx)));
                }
                else
                {
                    while (1)
                    {
                        Packet alpha_1 = pset1<Packet>(alpha - 1);
                        Packet ys, yc;
                        psincos(pmul(pset1<Packet>(constant::pi), ru.uniform_real(rng)), ys, yc);
                        Packet yx = pdiv(ys, yc);
                        Packet xx = padd(pmul(pset1<Packet>(sqrt), yx), alpha_1);
                        auto c = pcmplt(pset1<Packet>(0), xx);
                        Packet ux = ru.uniform_real(rng);
                        Packet ub = pmul(padd(pmul(yx, yx), pset1<Packet>(1)),
                            pexp(psub(
                                pmul(alpha_1, plog(pdiv(xx, alpha_1))),
                                pmul(yx, pset1<Packet>(sqrt))
                            ))
                        );
                        c = pand(c, pcmple(ux, ub));
                        Packet cands = pmul(pset1<Packet>(beta), xx);
                        bool full = false;
                        cache_rest_cnt = cm.compress_append(cands, c,
                            OptCacheStore::template get<Packet>(), cache_rest_cnt, full);
                        if (full) return cands;
                    }
                }
            }
        };
 
        template<typename _Scalar>
        class WeibullGen : public GenBase<WeibullGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "weilbullDist needs floating point types.");
            UniformRealGen<_Scalar> ur;
            _Scalar a = 1, b = 1;
 
        public:
            using Scalar = _Scalar;
 
            WeibullGen(_Scalar _a = 1, _Scalar _b = 1)
                : a{ _a }, b{ _b }
            {
            }
            
            WeibullGen(const WeibullGen&) = default;
            WeibullGen(WeibullGen&&) = default;
 
            WeibullGen& operator=(const WeibullGen&) = default;
            WeibullGen& operator=(WeibullGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return std::pow(-std::log(1 - ur(std::forward<Rng>(rng))), 1 / a) * b;
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                return pmul(pexp(pmul(plog(pnegate(plog(
                    psub(pset1<Packet>(1), ur.template packetOp<Packet>(std::forward<Rng>(rng)))
                ))), pset1<Packet>(1 / a))), pset1<Packet>(b));
            }
        };
 
        template<typename _Scalar>
        class ExtremeValueGen : public GenBase<ExtremeValueGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "extremeValueDist needs floating point types.");
            UniformRealGen<_Scalar> ur;
            _Scalar a = 0, b = 1;
 
        public:
            using Scalar = _Scalar;
 
            ExtremeValueGen(_Scalar _a = 0, _Scalar _b = 1)
                : a{ _a }, b{ _b }
            {
            }
 
            ExtremeValueGen(const ExtremeValueGen&) = default;
            ExtremeValueGen(ExtremeValueGen&&) = default;
 
            ExtremeValueGen& operator=(const ExtremeValueGen&) = default;
            ExtremeValueGen& operator=(ExtremeValueGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return (a - b * std::log(-std::log(ur.nzur_scalar(std::forward<Rng>(rng)))));
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                using RUtils = RandUtils<Packet, Rng>;
                return psub(pset1<Packet>(a),
                    pmul(plog(pnegate(plog(RUtils{}.nonzero_uniform_real(std::forward<Rng>(rng))))), pset1<Packet>(b))
                );
            }
        };
 
        template<typename _Scalar>
        class ChiSquaredGen : public GenBase<ChiSquaredGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "chiSquaredDist needs floating point types.");
            GammaGen<_Scalar> gamma;
        public:
            using Scalar = _Scalar;
            
            ChiSquaredGen(_Scalar n = 1)
                : gamma{ n * _Scalar(0.5), 2 }
            {
            }
 
            ChiSquaredGen(const ChiSquaredGen&) = default;
            ChiSquaredGen(ChiSquaredGen&&) = default;
 
            ChiSquaredGen& operator=(const ChiSquaredGen&) = default;
            ChiSquaredGen& operator=(ChiSquaredGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                return gamma(rng);
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                return gamma.template packetOp<Packet>(rng);
            }
        };
        
        template<typename _Scalar>
        class CauchyGen : public GenBase<CauchyGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "cauchyDist needs floating point types.");
            UniformRealGen<_Scalar> ur; 
            _Scalar a = 0, b = 1;
 
        public:
            using Scalar = _Scalar;
 
            CauchyGen(_Scalar _a = 0, _Scalar _b = 1)
                : a{ _a }, b{ _b }
            {
            }
 
            CauchyGen(const CauchyGen&) = default;
            CauchyGen(CauchyGen&&) = default;
 
            CauchyGen& operator=(const CauchyGen&) = default;
            CauchyGen& operator=(CauchyGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                return a + b * std::tan(constant::pi * (ur(std::forward<Rng>(rng)) - 0.5));
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                Packet s, c;
                psincos(pmul(pset1<Packet>(constant::pi),
                    psub(ur.template packetOp<Packet>(std::forward<Rng>(rng)), pset1<Packet>(0.5))
                ), s, c);
                return padd(pset1<Packet>(a),
                    pmul(pset1<Packet>(b), pdiv(s, c))
                );
            }
        };
 
        template<typename> class FisherFGen;
 
        template<typename _Scalar>
        class BetaGen : OptCacheStore, public GenBase<BetaGen<_Scalar>, _Scalar>
        {
            friend FisherFGen<_Scalar>;
            static_assert(std::is_floating_point<_Scalar>::value, "betaDist needs floating point types.");
            int cache_rest_cnt = 0;
            UniformRealGen<_Scalar> ur;
            _Scalar a, b;
            GammaGen<_Scalar> gd1, gd2;
 
        public:
            using Scalar = _Scalar;
 
            BetaGen(_Scalar _a = 1, _Scalar _b = 1)
                : a{ _a }, b{ _b },
                gd1{ _a }, gd2{ _b }
            {
            }
 
            BetaGen(const BetaGen&) = default;
            BetaGen(BetaGen&&) = default;
 
            BetaGen& operator=(const BetaGen&) = default;
            BetaGen& operator=(BetaGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                if (a < 1 && b < 1)
                {
                    _Scalar x, p1, p2;
                    while (1)
                    {
                        p1 = std::pow(ur(rng), 1 / a);
                        p2 = std::pow(ur(rng), 1 / b);
                        x = p1 + p2;
                        if (x <= 1) break;
                    }
                    return p1 / x;
                }
                else
                {
                    _Scalar p1 = gd1(rng), p2 = gd2(rng);
                    return p1 / (p1 + p2);
                }
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                if (a < 1 && b < 1)
                {
                    auto& cm = Rand::detail::CompressMask<sizeof(Packet)>::get_inst();
                    Packet x, p1, p2;
                    while (1)
                    {
                        p1 = pexp(pmul(plog(ur.template packetOp<Packet>(rng)), pset1<Packet>(1 / a)));
                        p2 = pexp(pmul(plog(ur.template packetOp<Packet>(rng)), pset1<Packet>(1 / b)));
                        x = padd(p1, p2);
                        Packet cands = pdiv(p1, x);
                        bool full = false;
                        cache_rest_cnt = cm.compress_append(cands, pcmple(x, pset1<Packet>(1)),
                            OptCacheStore::template get<Packet>(), cache_rest_cnt, full);
                        if (full) return cands;
                    }
                }
                else
                {
                    auto p1 = gd1.template packetOp<Packet>(rng),
                        p2 = gd2.template packetOp<Packet>(rng);
                    return pdiv(p1, padd(p1, p2));
                }
            }
        };
 
        template<typename _Scalar>
        class FisherFGen : public GenBase<FisherFGen<_Scalar>, _Scalar>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "fisherF needs floating point types.");
            BetaGen<_Scalar> beta;
        public:
            using Scalar = _Scalar;
 
            FisherFGen(_Scalar m = 1, _Scalar n = 1)
                : beta{ m * _Scalar(0.5), n * _Scalar(0.5) }
            {
            }
            
            FisherFGen(const FisherFGen&) = default;
            FisherFGen(FisherFGen&&) = default;
 
            FisherFGen& operator=(const FisherFGen&) = default;
            FisherFGen& operator=(FisherFGen&&) = default;
 
            template<typename Rng>
            EIGEN_STRONG_INLINE const _Scalar operator() (Rng&& rng)
            {
                using namespace Eigen::internal;
                auto x = beta(std::forward<Rng>(rng));
                return beta.b / beta.a * x / (1 - x);
            }
 
            template<typename Packet, typename Rng>
            EIGEN_STRONG_INLINE const Packet packetOp(Rng&& rng)
            {
                using namespace Eigen::internal;
                auto x = beta.template packetOp<Packet>(std::forward<Rng>(rng));
                return pdiv(pmul(pset1<Packet>(beta.b / beta.a), x), psub(pset1<Packet>(1), x));
            }
        };
 
 
        template<typename Derived, typename Urng>
        using BetaType = CwiseNullaryOp<internal::scalar_rng_adaptor<BetaGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const BetaType<Derived, Urng>
            beta(Index rows, Index cols, Urng&& urng, typename Derived::Scalar a = 1, typename Derived::Scalar b = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), BetaGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const BetaType<Derived, Urng>
            betaLike(Derived& o, Urng&& urng, typename Derived::Scalar a = 1, typename Derived::Scalar b = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), BetaGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        using CauchyType = CwiseNullaryOp<internal::scalar_rng_adaptor<CauchyGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const CauchyType<Derived, Urng>
            cauchy(Index rows, Index cols, Urng&& urng, typename Derived::Scalar a = 0, typename Derived::Scalar b = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), CauchyGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const CauchyType<Derived, Urng>
            cauchyLike(Derived& o, Urng&& urng, typename Derived::Scalar a = 0, typename Derived::Scalar b = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), CauchyGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        using NormalType = CwiseNullaryOp<internal::scalar_rng_adaptor<StdNormalGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const NormalType<Derived, Urng>
            normal(Index rows, Index cols, Urng&& urng)
        {
            return {
                rows, cols, { std::forward<Urng>(urng) }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const NormalType<Derived, Urng>
            normalLike(Derived& o, Urng&& urng)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng) }
            };
        }
 
        template<typename Derived, typename Urng>
        using Normal2Type = CwiseNullaryOp<internal::scalar_rng_adaptor<NormalGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const Normal2Type<Derived, Urng>
            normal(Index rows, Index cols, Urng&& urng, typename Derived::Scalar mean, typename Derived::Scalar stdev = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), NormalGen<typename Derived::Scalar>{mean, stdev} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const Normal2Type<Derived, Urng>
            normalLike(Derived& o, Urng&& urng, typename Derived::Scalar mean, typename Derived::Scalar stdev = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), NormalGen<typename Derived::Scalar>{mean, stdev} }
            };
        }
 
        template<typename Derived, typename Urng>
        using LognormalType = CwiseNullaryOp<internal::scalar_rng_adaptor<LognormalGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const LognormalType<Derived, Urng>
            lognormal(Index rows, Index cols, Urng&& urng, typename Derived::Scalar mean = 0, typename Derived::Scalar stdev = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), LognormalGen<typename Derived::Scalar>{mean, stdev} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const LognormalType<Derived, Urng>
            lognormalLike(Derived& o, Urng&& urng, typename Derived::Scalar mean = 0, typename Derived::Scalar stdev = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), LognormalGen<typename Derived::Scalar>{mean, stdev} }
            };
        }
 
        template<typename Derived, typename Urng>
        using StudentTType = CwiseNullaryOp<internal::scalar_rng_adaptor<StudentTGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const StudentTType<Derived, Urng>
            studentT(Index rows, Index cols, Urng&& urng, typename Derived::Scalar n = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), StudentTGen<typename Derived::Scalar>{n} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const StudentTType<Derived, Urng>
            studentTLike(Derived& o, Urng&& urng, typename Derived::Scalar n = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), StudentTGen<typename Derived::Scalar>{n} }
            };
        }
 
        template<typename Derived, typename Urng>
        using ExponentialType = CwiseNullaryOp<internal::scalar_rng_adaptor<ExponentialGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const ExponentialType<Derived, Urng>
            exponential(Index rows, Index cols, Urng&& urng, typename Derived::Scalar lambda = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), ExponentialGen<typename Derived::Scalar>{lambda} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const ExponentialType<Derived, Urng>
            exponentialLike(Derived& o, Urng&& urng, typename Derived::Scalar lambda = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), ExponentialGen<typename Derived::Scalar>{lambda} }
            };
        }
 
        template<typename Derived, typename Urng>
        using GammaType = CwiseNullaryOp<internal::scalar_rng_adaptor<GammaGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const GammaType<Derived, Urng>
            gamma(Index rows, Index cols, Urng&& urng, typename Derived::Scalar alpha = 1, typename Derived::Scalar beta = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), GammaGen<typename Derived::Scalar>{alpha, beta} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const GammaType<Derived, Urng>
            gammaLike(Derived& o, Urng&& urng, typename Derived::Scalar alpha = 1, typename Derived::Scalar beta = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), GammaGen<typename Derived::Scalar>{alpha, beta} }
            };
        }
 
        template<typename Derived, typename Urng>
        using WeibullType = CwiseNullaryOp<internal::scalar_rng_adaptor<WeibullGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const WeibullType<Derived, Urng>
            weibull(Index rows, Index cols, Urng&& urng, typename Derived::Scalar a = 1, typename Derived::Scalar b = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), WeibullGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const WeibullType<Derived, Urng>
            weibullLike(Derived& o, Urng&& urng, typename Derived::Scalar a = 1, typename Derived::Scalar b = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), WeibullGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        using ExtremeValueType = CwiseNullaryOp<internal::scalar_rng_adaptor<ExtremeValueGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const ExtremeValueType<Derived, Urng>
            extremeValue(Index rows, Index cols, Urng&& urng, typename Derived::Scalar a = 0, typename Derived::Scalar b = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), ExtremeValueGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const ExtremeValueType<Derived, Urng>
            extremeValueLike(Derived& o, Urng&& urng, typename Derived::Scalar a = 0, typename Derived::Scalar b = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), ExtremeValueGen<typename Derived::Scalar>{a, b} }
            };
        }
 
        template<typename Derived, typename Urng>
        using ChiSquaredType = CwiseNullaryOp<internal::scalar_rng_adaptor<ChiSquaredGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const ChiSquaredType<Derived, Urng>
            chiSquared(Index rows, Index cols, Urng&& urng, typename Derived::Scalar n = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), ChiSquaredGen<typename Derived::Scalar>{n} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const ChiSquaredType<Derived, Urng>
            chiSquaredLike(Derived& o, Urng&& urng, typename Derived::Scalar n = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), ChiSquaredGen<typename Derived::Scalar>{n} }
            };
        }
 
        template<typename Derived, typename Urng>
        using FisherFType = CwiseNullaryOp<internal::scalar_rng_adaptor<FisherFGen<typename Derived::Scalar>, typename Derived::Scalar, Urng, true>, const Derived>;
 
        template<typename Derived, typename Urng>
        inline const FisherFType<Derived, Urng>
            fisherF(Index rows, Index cols, Urng&& urng, typename Derived::Scalar m = 1, typename Derived::Scalar n = 1)
        {
            return {
                rows, cols, { std::forward<Urng>(urng), FisherFGen<typename Derived::Scalar>{m, n} }
            };
        }
 
        template<typename Derived, typename Urng>
        inline const FisherFType<Derived, Urng>
            fisherFLike(Derived& o, Urng&& urng, typename Derived::Scalar m = 1, typename Derived::Scalar n = 1)
        {
            return {
                o.rows(), o.cols(), { std::forward<Urng>(urng), FisherFGen<typename Derived::Scalar>{m, n} }
            };
        }
    }
}
 
#endif