random.hpp

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/*
 * Copyright (C) 2010-2022 The ESPResSo project
 *
 * Copyright (C) 2002,2003,2004,2005,2006,2007,2008,2009,2010
 *   Max-Planck-Institute for Polymer Research, Theory Group
 *
 * This file is part of ESPResSo.
 *
 * ESPResSo is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * ESPResSo is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
#ifndef RANDOM_H
#define RANDOM_H
 
/** \file
 *  Random number generation using Philox.
 */
 
#include <utils/Vector.hpp>
#include <utils/constants.hpp>
#include <utils/u32_to_u64.hpp>
#include <utils/uniform.hpp>
 
#include <Random123/philox.h>
 
#include <cstddef>
#include <random>
#include <vector>
 
/*
 * @brief Salt for the RNGs
 *
 * This is to avoid correlations between the
 * noise on the particle coupling and the fluid
 * thermalization.
 */
enum class RNGSalt : uint32_t {
  FLUID = 0,
  PARTICLES,
  LANGEVIN,
  LANGEVIN_ROT,
  BROWNIAN_WALK,
  BROWNIAN_INC,
  BROWNIAN_ROT_INC,
  BROWNIAN_ROT_WALK,
  NPTISO0_HALF_STEP1,
  NPTISO0_HALF_STEP2,
  NPTISOV,
  SALT_DPD,
  THERMALIZED_BOND
};
 
namespace Random {
/**
 * @brief get 4 random uint 64 from the Philox RNG
 *
 * This uses the Philox PRNG, the state is controlled
 * by the counter, the salt and two keys.
 * If any of the keys and salt differ, the noise is
 * not correlated between two calls along the same counter
 * sequence.
 *
 */
template <RNGSalt salt>
auto philox_4_uint64s(uint64_t counter, uint32_t seed, int key1, int key2 = 0) {
 
  using rng_type = r123::Philox4x64;
  using ctr_type = rng_type::ctr_type;
  using key_type = rng_type::key_type;
 
  const ctr_type c{{counter, 0u, 0u, 0u}};
 
  auto const id1 = static_cast<uint32_t>(key1);
  auto const id2 = static_cast<uint32_t>(key2);
  const key_type k{{Utils::u32_to_u64(id1, id2),
                    Utils::u32_to_u64(static_cast<uint32_t>(salt), seed)}};
 
  return rng_type{}(c, k);
}
 
/**
 * @brief Generator for random uniform noise.
 *
 * Mean = 0, variance = 1 / 12.
 * This uses the Philox PRNG, the state is controlled
 * by the counter, the salt and two keys.
 * If any of the keys and salt differ, the noise is
 * not correlated between two calls along the same counter
 * sequence.
 *
 * @tparam salt RNG salt
 * @tparam N    Size of the noise vector
 * @param counter counter for random number generation
 * @param seed seed for random number generation
 * @param key1 key for random number generation
 * @param key2 key for random number generation
 *
 * @return Vector of uniform random numbers.
 */
template <RNGSalt salt, std::size_t N = 3,
          std::enable_if_t<(N > 1) and (N <= 4), int> = 0>
auto noise_uniform(uint64_t counter, uint32_t seed, int key1, int key2 = 0) {
 
  auto const integers = philox_4_uint64s<salt>(counter, seed, key1, key2);
  Utils::VectorXd<N> noise{};
  std::transform(integers.begin(), integers.begin() + N, noise.begin(),
                 [](std::size_t value) { return Utils::uniform(value) - 0.5; });
  return noise;
}
 
template <RNGSalt salt, std::size_t N, std::enable_if_t<N == 1, int> = 0>
auto noise_uniform(uint64_t counter, uint32_t seed, int key1, int key2 = 0) {
 
  auto const integers = philox_4_uint64s<salt>(counter, seed, key1, key2);
  return Utils::uniform(integers[0]) - 0.5;
}
 
/** @brief Generator for Gaussian noise.
 *
 * Mean = 0, standard deviation = 1.0.
 * Based on the Philox RNG using 4x64 bits.
 * The Box-Muller transform is used to convert from uniform to normal
 * distribution. The transform is only valid, if the uniformly distributed
 * random numbers are not zero (approx one in 2^64). To avoid this case,
 * such numbers are replaced by std::numeric_limits<double>::min()
 * This breaks statistics in rare cases but allows for consistent RNG
 * counters across MPI ranks.
 *
 * @tparam salt decorrelates different thermostat types
 * @param counter counter for random number generation
 * @param seed seed for random number generation
 * @param key1 key for random number generation
 * @param key2 key for random number generation
 *
 * @return Vector of Gaussian random numbers.
 *
 */
template <RNGSalt salt, std::size_t N = 3,
          class = std::enable_if_t<(N >= 1) and (N <= 4)>>
auto noise_gaussian(uint64_t counter, uint32_t seed, int key1, int key2 = 0) {
 
  auto const integers = philox_4_uint64s<salt>(counter, seed, key1, key2);
  static const double epsilon = std::numeric_limits<double>::min();
 
  constexpr std::size_t M = (N <= 2) ? 2 : 4;
  Utils::VectorXd<M> u{};
  std::transform(integers.begin(), integers.begin() + M, u.begin(),
                 [](std::size_t value) {
                   auto u = Utils::uniform(value);
                   return (u < epsilon) ? epsilon : u;
                 });
 
  // Box-Muller transform code adapted from
  // https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
  // optimizations: the modulo is cached (logarithms are expensive), the
  // sin/cos are evaluated simultaneously by gcc or separately by Clang
  Utils::VectorXd<N> noise{};
  constexpr double two_pi = 2.0 * Utils::pi();
  {
    auto const modulo = sqrt(-2.0 * log(u[0]));
    auto const angle = two_pi * u[1];
    noise[0] = modulo * cos(angle);
    if (N > 1) {
      noise[1] = modulo * sin(angle);
    }
  }
  if (N > 2) {
    auto const modulo = sqrt(-2.0 * log(u[2]));
    auto const angle = two_pi * u[3];
    noise[2] = modulo * cos(angle);
    if (N > 3) {
      noise[3] = modulo * sin(angle);
    }
  }
  return noise;
}
 
/** Mersenne Twister with warmup.
 *  The first 100'000 values of Mersenne Twister generators are often heavily
 *  correlated @cite panneton06a. This utility function discards the first
 *  1'000'000 values.
 *
 *  @param seed RNG seed
 */
template <typename T> std::mt19937 mt19937(T &&seed) {
  std::mt19937 generator(seed);
  generator.discard(1'000'000);
  return generator;
}
 
} // namespace Random
 
#endif