normal_dist.hpp

// Copyright (c) 2000-2022, Heiko Bauke
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#if !(defined TRNG_NORMAL_DIST_HPP)
 
#define TRNG_NORMAL_DIST_HPP
 
#include <trng/cuda.hpp>
#include <trng/constants.hpp>
#include <trng/limits.hpp>
#include <trng/utility.hpp>
#include <trng/math.hpp>
#include <trng/special_functions.hpp>
#include <ostream>
#include <istream>
#include <iomanip>
#include <ciso646>
 
namespace trng {
 
  // uniform random number generator class
  template<typename float_t = double>
  class normal_dist {
  public:
    using result_type = float_t;
 
    class param_type {
    private:
      result_type mu_{0}, sigma_{1};
 
    public:
      TRNG_CUDA_ENABLE
      result_type mu() const { return mu_; }
      TRNG_CUDA_ENABLE
      void mu(result_type mu_new) { mu_ = mu_new; }
      TRNG_CUDA_ENABLE
      result_type sigma() const { return sigma_; }
      TRNG_CUDA_ENABLE
      void sigma(result_type sigma_new) { sigma_ = sigma_new; }
      TRNG_CUDA_ENABLE
      param_type() = default;
      TRNG_CUDA_ENABLE
      explicit param_type(result_type mu, result_type sigma) : mu_{mu}, sigma_{sigma} {}
 
      friend class normal_dist;
 
      // EqualityComparable concept
      friend TRNG_CUDA_ENABLE inline bool operator==(const param_type &P1,
                                                     const param_type &P2) {
        return P1.mu_ == P2.mu_ and P1.sigma_ == P2.sigma_;
      }
 
      friend TRNG_CUDA_ENABLE inline bool operator!=(const param_type &P1,
                                                     const param_type &P2) {
        return not(P1 == P2);
      }
 
      // -------------------------------------------------------------------
 
      // Streamable concept
      template<typename char_t, typename traits_t>
      friend std::basic_ostream<char_t, traits_t> &operator<<(
          std::basic_ostream<char_t, traits_t> &out, const param_type &P) {
        std::ios_base::fmtflags flags(out.flags());
        out.flags(std::ios_base::dec | std::ios_base::fixed | std::ios_base::left);
        out << '(' << std::setprecision(math::numeric_limits<float_t>::digits10 + 1) << P.mu()
            << ' ' << P.sigma() << ')';
        out.flags(flags);
        return out;
      }
 
      template<typename char_t, typename traits_t>
      friend std::basic_istream<char_t, traits_t> &operator>>(
          std::basic_istream<char_t, traits_t> &in, param_type &P) {
        float_t mu, sigma;
        std::ios_base::fmtflags flags(in.flags());
        in.flags(std::ios_base::dec | std::ios_base::fixed | std::ios_base::left);
        in >> utility::delim('(') >> mu >> utility::delim(' ') >> sigma >> utility::delim(')');
        if (in)
          P = param_type(mu, sigma);
        in.flags(flags);
        return in;
      }
    };
 
  private:
    param_type P;
 
  public:
    // constructor
    TRNG_CUDA_ENABLE
    explicit normal_dist(result_type mu, result_type sigma) : P{mu, sigma} {}
    TRNG_CUDA_ENABLE
    explicit normal_dist(const param_type &P) : P{P} {}
    // reset internal state
    TRNG_CUDA_ENABLE
    void reset() {}
    // random numbers
    template<typename R>
    TRNG_CUDA_ENABLE result_type operator()(R &r) {
      return icdf(utility::uniformoo<result_type>(r));
    }
    template<typename R>
    TRNG_CUDA_ENABLE result_type operator()(R &r, const param_type &P) {
      normal_dist g(P);
      return g(r);
    }
    // property methods
    TRNG_CUDA_ENABLE
    result_type min() const { return -math::numeric_limits<result_type>::infinity(); }
    TRNG_CUDA_ENABLE
    result_type max() const { return math::numeric_limits<result_type>::infinity(); }
    TRNG_CUDA_ENABLE
    const param_type &param() const { return P; }
    TRNG_CUDA_ENABLE
    void param(const param_type &P_new) { P = P_new; }
    TRNG_CUDA_ENABLE
    result_type mu() const { return P.mu(); }
    TRNG_CUDA_ENABLE
    void mu(result_type mu_new) { P.mu(mu_new); }
    TRNG_CUDA_ENABLE
    result_type sigma() const { return P.sigma(); }
    TRNG_CUDA_ENABLE
    void sigma(result_type sigma_new) { P.sigma(sigma_new); }
    // probability density function
    TRNG_CUDA_ENABLE
    result_type pdf(result_type x) const {
      const result_type t{x - P.mu()};
      return math::constants<result_type>::one_over_sqrt_2pi / P.sigma() *
             math::exp(t * t / (-2 * P.sigma() * P.sigma()));
    }
    // cumulative density function
    TRNG_CUDA_ENABLE
    result_type cdf(result_type x) const {
      x -= P.mu();
      x /= P.sigma();
      return math::Phi(x);
    }
    // inverse cumulative density function
    TRNG_CUDA_ENABLE
    result_type icdf(result_type x) const { return math::inv_Phi(x) * P.sigma() + P.mu(); }
  };
 
  // -------------------------------------------------------------------
 
  // EqualityComparable concept
  template<typename float_t>
  TRNG_CUDA_ENABLE inline bool operator==(const normal_dist<float_t> &g1,
                                          const normal_dist<float_t> &g2) {
    return g1.param() == g2.param();
  }
 
  template<typename float_t>
  TRNG_CUDA_ENABLE inline bool operator!=(const normal_dist<float_t> &g1,
                                          const normal_dist<float_t> &g2) {
    return g1.param() != g2.param();
  }
 
  // Streamable concept
  template<typename char_t, typename traits_t, typename float_t>
  std::basic_ostream<char_t, traits_t> &operator<<(std::basic_ostream<char_t, traits_t> &out,
                                                   const normal_dist<float_t> &g) {
    std::ios_base::fmtflags flags(out.flags());
    out.flags(std::ios_base::dec | std::ios_base::fixed | std::ios_base::left);
    out << "[normal " << g.param() << ']';
    out.flags(flags);
    return out;
  }
 
  template<typename char_t, typename traits_t, typename float_t>
  std::basic_istream<char_t, traits_t> &operator>>(std::basic_istream<char_t, traits_t> &in,
                                                   normal_dist<float_t> &g) {
    typename normal_dist<float_t>::param_type p;
    std::ios_base::fmtflags flags(in.flags());
    in.flags(std::ios_base::dec | std::ios_base::fixed | std::ios_base::left);
    in >> utility::ignore_spaces() >> utility::delim("[normal ") >> p >> utility::delim(']');
    if (in)
      g.param(p);
    in.flags(flags);
    return in;
  }
 
}  // namespace trng
 
#endif