prng_extension.hpp

#ifndef __PRNG_EXTENSION_HPP__
#define __PRNG_EXTENSION_HPP__
 
#include "Kokkos_Macros.hpp"
#include "common/maths.hpp"
#include "mc/alias.hpp"
#include <Kokkos_Core.hpp>
#include <Kokkos_MathematicalConstants.hpp>
#include <Kokkos_Random.hpp>
#include <cmath>
#include <common/traits.hpp>

namespace MC::Distributions
{
  template <typename T, typename F, class DeviceType>
  concept ProbabilityLaw =
      FloatingPointType<F> &&
      requires(const T& obj, Kokkos::Random_XorShift1024<DeviceType>& gen) {
        { obj.draw(gen) } -> std::same_as<F>;
        { obj.mean() } -> std::same_as<F>;
        { obj.var() } -> std::same_as<F>;
        { obj.skewness() } -> std::same_as<F>;
      };

  template <FloatingPointType F> KOKKOS_INLINE_FUNCTION F erfinv(F x)
  {
 
    // Use the Winitzki’s method to calculate get an approached expression of
    // erf(x) and inverse it
 
    constexpr F a = 0.147;
    constexpr F inv_a = 1. / a;
    constexpr F tmp = (2 / (M_PI * a));
    const double ln1mx2 = Kokkos::log((1. - x) * (1. + x));
    const F term1 = tmp + (0.5 * ln1mx2);
    const F term2 = inv_a * ln1mx2;
    return Kokkos::copysign(
        Kokkos::sqrt(Kokkos::sqrt(term1 * term1 - term2) - term1), x);
  }
 
  // Inverse error function approximation (Using the rational approximation)
  //  template <FloatingPointType F> KOKKOS_INLINE_FUNCTION constexpr F
  //  erf_inv(F x)
  // {
  //     constexpr F a[4] = {0.147, 0.147, 0.147, 0.147};
  //     constexpr F b[4] = {-1.0, 0.5, -0.5, 1.0};
  //     KOKKOS_ASSERT(x <= -1.0 || x >= 1.0);
 
  //     F z = (x < 0.0) ? -x : x;
 
  //     F t = 2.0 / (Kokkos::numbers::pi * 0.147) + 0.5 * Kokkos::log(1.0 - z);
  //     F result = a[0] * Kokkos::pow(t, b[0]) +
  //                a[1] * Kokkos::pow(t, b[1]) +
  //                a[2] * Kokkos::pow(t, b[2]) +
  //                a[3] * Kokkos::pow(t, b[3]);
  //     KOKKOS_ASSERT(Kokkos::isfinite(result));
  //     return result;
  // }

  template <FloatingPointType F>
  KOKKOS_INLINE_FUNCTION F norminv(F p, F mean, F stddev)
  {
    constexpr F erfinv_lb = -5;
    constexpr F erfinv_up = 5;
    auto clamped_inverse =
        Kokkos::clamp(erfinv(2 * p - 1), erfinv_lb, erfinv_up);
    KOKKOS_ASSERT(
        Kokkos::isfinite(stddev * Kokkos::numbers::sqrt2 * clamped_inverse));
    return mean + stddev * Kokkos::numbers::sqrt2 * clamped_inverse;
  }

  template <FloatingPointType F> KOKKOS_INLINE_FUNCTION F std_normal_pdf(F x)
  {
    // NOLINTBEGIN(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
    constexpr double inv_sqrt_2_pi = 0.3989422804014327; // 1/sqrt(2pi)
    return inv_sqrt_2_pi * Kokkos::exp(-0.5 * x * x);
    // NOLINTEND(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
  }

  template <FloatingPointType F> KOKKOS_INLINE_FUNCTION F std_normal_cdf(F x)
  {
    // NOLINTBEGIN(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
    return 0.5 * (1 + Kokkos::erf(x / Kokkos::numbers::sqrt2));
    // NOLINTEND(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
  }
 
  /*DISTRIBUTIONS*/
 
  template <FloatingPointType F> struct Uniform
  {
    F min; 
    F max; 

    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      return draw_from(gen, min, max);
    }

    template <class DeviceType>
    static KOKKOS_INLINE_FUNCTION F
    draw_from(Kokkos::Random_XorShift1024<DeviceType>& gen, F min, F max)
    {
      return gen.drand(min, max);
    }

    KOKKOS_INLINE_FUNCTION F mean() const
    {
      return (min + max) / F(2);
    }

    KOKKOS_INLINE_FUNCTION F var() const
    {
      return (max - min) * (max - min) / F(12);
    }

    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      return F(0);
    }
  };

  template <FloatingPointType F> struct Normal
  {
    F mu;    
    F sigma; 

    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      return draw_from(gen, mu, sigma);
    }

    template <class DeviceType>
    static KOKKOS_INLINE_FUNCTION F
    draw_from(Kokkos::Random_XorShift1024<DeviceType>& gen, F mu, F sigma)
    {
      return gen.normal(mu, sigma);
    }

    KOKKOS_INLINE_FUNCTION F mean() const
    {
      return mu;
    }

    KOKKOS_INLINE_FUNCTION F var() const
    {
      return sigma * sigma;
    }

    KOKKOS_INLINE_FUNCTION F stddev() const
    {
      return sigma;
    }

    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      return F(0);
    }
  };

  template <FloatingPointType F> struct TruncatedNormal
  {
 
    F mu;    // Mean
    F sigma; // Standard deviation
    F lower; // Standard deviation
    F upper; // Standard deviation
 
    TruncatedNormal() = default;
 
    KOKKOS_INLINE_FUNCTION constexpr TruncatedNormal(F m, F s, F l, F u)
        : mu(m), sigma(s), lower(l), upper(u)
    {
      X_ASSERT(mu > lower);
      X_ASSERT(mu < upper);
      KOKKOS_ASSERT(mu > lower && mu < upper);
    }
 
    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      return draw_from(gen, mu, sigma, lower, upper);
    }
 
    template <class DeviceType>
    static KOKKOS_INLINE_FUNCTION F
    draw_from(Kokkos::Random_XorShift1024<DeviceType>& gen,
              F mu,
              F sigma,
              F lower,
              F upper)
    {
      // NOLINTBEGIN(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
      const F rand = static_cast<F>(gen.drand());
 
      // Max bounded because if sigma <<1 z -> Inf not wanted because
      // erf/erfc/erfinv are not stable for extrem value Min bounded if
      // |mu-bound| <<1 z -> 0 which is also not wanted for error function
 
      F zl = Kokkos::clamp(
          (lower - mu) / sigma, F(-5e3), F(0)); // upper-mu is by defintion <0
      F zu = Kokkos::clamp(
          (upper - mu) / sigma, F(0), F(5e3)); // upper-mu is by defintion >0
 
      F pl = 0.5 * Kokkos::erfc(-zl / Kokkos::numbers::sqrt2);
      KOKKOS_ASSERT(
          Kokkos::isfinite(pl) &&
          "Truncated normal draw leads to Nan of Inf with given parameters");
      F pu = 0.5 * Kokkos::erfc(-zu / Kokkos::numbers::sqrt2);
      KOKKOS_ASSERT(
          Kokkos::isfinite(pu) &&
          "Truncated normal draw leads to Nan of Inf with given parameters");
      F p = rand * (pu - pl) + pl;
      F x = norminv(p, mu, sigma);
      KOKKOS_ASSERT(
          Kokkos::isfinite(x) &&
          "Truncated normal draw leads to Nan of Inf with given parameters");
      return x;
 
      // NOLINTEND(cppcoreguidelines-avoid-magic-numbers,readability-magic-numbers)
    }
 
    KOKKOS_INLINE_FUNCTION F mean() const
    {
      const F alpha = (lower - mu) / sigma;
      const F beta = (upper - mu) / sigma;
      F Z = std_normal_cdf(beta) - std_normal_cdf(alpha);
      return mu + sigma * (std_normal_pdf(alpha) - std_normal_pdf(beta)) / Z;
    }
 
    KOKKOS_INLINE_FUNCTION F var() const
    {
      const F alpha = (lower - mu) / sigma;
      const F beta = (upper - mu) / sigma;
      F Z = std_normal_cdf(beta) - std_normal_cdf(alpha);
      const auto phi_b = std_normal_pdf(beta);
      const auto phi_a = std_normal_pdf(alpha);
      const auto tmp = (phi_a - phi_b) / Z;
      const auto tmp2 = (alpha * phi_a - beta * phi_b) / Z;
      return sigma * sigma * (1 - tmp2 - tmp * tmp);
    }
    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      return 0.;
    }
  };

  template <FloatingPointType F> struct ScaledTruncatedNormal
  {
 
    F scale_factor;
    F inverse_factor;
    TruncatedNormal<F> dist;
 
    constexpr ScaledTruncatedNormal(F factor, F m, F s, F l, F u)
        : scale_factor(factor), inverse_factor(1. / scale_factor),
          dist(scale_factor * m,
               s * scale_factor,
               scale_factor * l,
               scale_factor * u)
    {
    }
 
    template <class DeviceType>
    static KOKKOS_INLINE_FUNCTION F
    draw_from(Kokkos::Random_XorShift1024<DeviceType>& gen,
              F factor,
              F mu,
              F sigma,
              F lower,
              F upper)
    {
      return 1. / factor *
             TruncatedNormal<F>::draw_from(gen,
                                           factor * mu,
                                           factor * sigma,
                                           factor * lower,
                                           factor * upper);
    }
 
    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      return inverse_factor * dist.draw(gen);
    }
 
    KOKKOS_INLINE_FUNCTION F mean() const
    {
 
      return inverse_factor * dist.mean();
    }
 
    KOKKOS_INLINE_FUNCTION F var() const
    {
      return (inverse_factor * inverse_factor) * dist.var();
    }
    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      return 0.;
    }
  };

  template <FloatingPointType F> struct LogNormal
  {
    F mu;    // Mean
    F sigma; // Standard deviation
 
    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      return Kokkos::exp(gen.normal(mu, sigma));
    }
 
    KOKKOS_INLINE_FUNCTION F mean() const
    {
      return Kokkos::exp(mu + sigma * sigma / 2);
    }
    KOKKOS_INLINE_FUNCTION F var() const
    {
      const auto sigma2 = sigma * sigma;
      return (Kokkos::exp(sigma2) - 1) * Kokkos::exp(2 * mu + sigma2);
    }
    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      const auto sigma2 = sigma * sigma;
      return (Kokkos::exp(sigma2) + 2) * Kokkos::sqrt(Kokkos::exp(sigma2) - 1);
    }
  };

  template <FloatingPointType F> struct SkewNormal
  {
    F xi;    // Mean
    F omega; // Standard deviation
    F alpha;
 
    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
 
      const double Z0 = gen.normal();
      const double Z1 = gen.normal();
      const double delta = alpha / Kokkos::sqrt(1. + alpha * alpha);
      const double scale_factor = Kokkos::sqrt(1. + delta * delta);
      const double X = (Z0 + delta * Kokkos::abs(Z1)) / scale_factor;
      return xi + omega * X;
    }
    KOKKOS_INLINE_FUNCTION F mean() const
    {
      return xi + omega * (alpha / (Kokkos::sqrt(1 + alpha * alpha))) *
                      Kokkos::sqrt(2 / M_PI);
    }
    KOKKOS_INLINE_FUNCTION F var() const
    {
      const auto delta = alpha / (Kokkos::sqrt(1 + alpha * alpha));
      return omega * omega * (1 - 2 * delta * delta / M_PI);
    }
    KOKKOS_INLINE_FUNCTION F skewness() const
    {
      const auto delta = alpha / (Kokkos::sqrt(1 + alpha * alpha));
      return ((4 - M_PI) * Kokkos::pow(delta * std::sqrt(2 / M_PI), 3)) /
             Kokkos::pow(1 - 2 * delta * delta / M_PI, 1.5);
    }
  };
 
  static_assert(ProbabilityLaw<SkewNormal<float>, float, ComputeSpace>);

  template <FloatingPointType F> struct Exponential
  {
    F lambda;
 
    static constexpr bool use_kokkos_log = true;
 
    template <class DeviceType>
    KOKKOS_INLINE_FUNCTION F
    draw(Kokkos::Random_XorShift1024<DeviceType>& gen) const
    {
      const float rnd = gen.frand();
      return F(-1) * CommonMaths::_ln<use_kokkos_log>(rnd) / lambda;
    }
 
    [[nodiscard]] KOKKOS_INLINE_FUNCTION F mean() const
    {
      return F(1) / lambda;
    }
    [[nodiscard]] KOKKOS_INLINE_FUNCTION F var() const
    {
 
      return F(1) / (lambda * lambda);
    }
    [[nodiscard]] KOKKOS_INLINE_FUNCTION F skewness() const
    {
      return 2;
    }
  };
 
  static_assert(ProbabilityLaw<Exponential<float>, float, ComputeSpace>);
 
} // namespace MC::Distributions
 
#endif