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// *****************************************************************************
/*!
  \file      src/DiffEq/Dirichlet/MixDirichlet.hpp
  \copyright 2012-2015 J. Bakosi,
             2016-2018 Los Alamos National Security, LLC.,
             2019-2021 Triad National Security, LLC.
             All rights reserved. See the LICENSE file for details.
  \brief     Mixture Dirichlet SDE
  \details   This file implements the time integration of a system of stochastic
    differential equations (SDEs), whose invariant is the [Dirichlet
    distribution](http://en.wikipedia.org/wiki/Dirichlet_distribution), with
    various constraints to model multi-material mixing process in turbulent
    flows.

    In a nutshell, the equation integrated governs a set of scalars,
    \f$\color[HTML]{dcdcdc}0\!\le\!Y_\alpha\f$,
    \f$\color[HTML]{dcdcdc}\alpha\!=\!1,\dots,N-1\f$,
    \f$\color[HTML]{dcdcdc}\sum_{\alpha=1}^{N-1}Y_\alpha\!\le\!1\f$, as

    @m_class{m-show-m}

    \f[
       \mathrm{d}Y_\alpha(t) = \frac{b_\alpha}{2}\big[S_\alpha Y_N -
       (1-S_\alpha)Y_\alpha\big]\mathrm{d}t + \sqrt{\kappa_\alpha Y_\alpha
       Y_N}\mathrm{d}W_\alpha(t), \qquad \alpha=1,\dots,N-1
    \f]

    @m_class{m-hide-m}

    \f[
       \begin{split}
       \mathrm{d}Y_\alpha(t) = \frac{b_\alpha}{2}\big[S_\alpha Y_N -
       (1-S_\alpha)Y_\alpha\big]\mathrm{d}t + \sqrt{\kappa_\alpha Y_\alpha
       Y_N}\mathrm{d}W_\alpha(t), \\ \alpha=1,\dots,N-1
       \end{split}
    \f]

    with parameter vectors \f$\color[HTML]{dcdcdc}b_\alpha > 0\f$,
    \f$\color[HTML]{dcdcdc}\kappa_\alpha > 0\f$, and \f$\color[HTML]{dcdcdc}0 <
    S_\alpha < 1\f$, and \f$\color[HTML]{dcdcdc}Y_N =
    1-\sum_{\alpha=1}^{N-1}Y_\alpha\f$. Here
    \f$\color[HTML]{dcdcdc}\mathrm{d}W_\alpha(t)\f$ is an isotropic vector-valued
    [Wiener
    process](http://en.wikipedia.org/wiki/Wiener_process) with independent
    increments. The invariant distribution is the Dirichlet distribution,
    provided the parameters of the drift and diffusion terms satisfy
    \f[
      (1-S_1) b_1 / \kappa_1 = \dots = (1-S_{N-1}) b_{N-1} / \kappa_{N-1}.
    \f]
    To keep the invariant distribution Dirichlet, the above constraint on the
    coefficients must be satisfied. For more details on the Dirichlet SDE, see
    https://doi.org/10.1155/2013/842981.
*/
// *****************************************************************************
#ifndef MixDirichlet_h
#define MixDirichlet_h

#include <vector>
#include <cmath>
#include <cfenv>

#include "InitPolicy.hpp"
#include "MixDirichletCoeffPolicy.hpp"
#include "RNG.hpp"
#include "Particles.hpp"

namespace walker {

extern ctr::InputDeck g_inputdeck;
extern std::map< tk::ctr::RawRNGType, tk::RNG > g_rng;

//! \brief MixDirichlet SDE used polymorphically with DiffEq
//! \details The template arguments specify policies and are used to configure
//!   the behavior of the class. The policies are:
//!   - Init - initialization policy, see DiffEq/InitPolicy.h
//!   - Coefficients - coefficients policy, see DiffEq/DirCoeffPolicy.h
template< class Init, class Coefficients >
class MixDirichlet {

  private:
    using ncomp_t = tk::ctr::ncomp_t;
    using eq = tag::mixdirichlet;

  public:
    //! Number of derived variables computed by the MixDirichlet SDE
    //! \details Derived variables: Nth scalar, density, specific volume.
    static const std::size_t NUMDERIVED = 3;

    //! \brief Constructor
    //! \param[in] c Index specifying which MixDirichlet SDE to construct. There
    //!   can be multiple dirichlet ... end blocks in a control file. This index
    //!   specifies which MixDirichlet SDE to instantiate. The index corresponds
    //!   to the order in which the dirichlet ... end blocks are given the
    //!   control file.
    explicit MixDirichlet( ncomp_t c ) :
      m_c( c ),
      m_depvar( g_inputdeck.get< tag::param, eq, tag::depvar >().at(c) ),
      // subtract the number of derived variables computed, see advance()
      m_ncomp( g_inputdeck.get< tag::component >().get< eq >().at(c) -
               NUMDERIVED ),
      m_offset(
        g_inputdeck.get< tag::component >().offset< eq >(c) ),
      m_rng( g_rng.at( tk::ctr::raw(
        g_inputdeck.get< tag::param, eq, tag::rng >().at(c) ) ) ),
      m_norm( g_inputdeck.get< tag::param, eq, tag::normalization >().at(c) ),
      m_b(),
      m_S(),
      m_kprime(),
      m_k(),
      m_rho(),
      m_r(),
      coeff( m_ncomp,
             m_norm,
             g_inputdeck.get< tag::param, eq, tag::b >().at(c),
             g_inputdeck.get< tag::param, eq, tag::S >().at(c),
             g_inputdeck.get< tag::param, eq, tag::kappaprime >().at(c),
             g_inputdeck.get< tag::param, eq, tag::rho >().at(c),
             m_b, m_S, m_kprime, m_rho, m_r, m_k ) {}

    //! Initalize SDE, prepare for time integration
    //! \param[in] stream Thread (or more precisely stream) ID 
    //! \param[in,out] particles Array of particle properties 
    void initialize( int stream, tk::Particles& particles ) {

      // Ensure the size of the parameter vector holding the pure-fluid
      // densities is N = K+1 = m_ncomp+1
      Assert( m_rho.size() == m_ncomp+1, "Size mismatch" );

      //! Set initial conditions using initialization policy
      Init::template init< eq >( g_inputdeck, m_rng, stream, particles, m_c,
                                 m_ncomp, m_offset );

      fenv_t fe;
      feholdexcept( &fe );

      const auto npar = particles.nunk();
      for (auto p=decltype(npar){0}; p<npar; ++p) {
        // Violating boundedness here is a hard error as indicates a problem
        // with the initial conditions
        for (ncomp_t i=0; i<m_ncomp+1; ++i) {
          auto y = particles( p, i, m_offset );
          if (y < 0.0 || y > 1.0) Throw( "IC scalar out of bounds" );
        }
        // Initialize derived instantaneous variables
        derived( particles, p );
      }

      feclearexcept( FE_UNDERFLOW );
      feupdateenv( &fe );
    }

    //! \brief Advance particles according to the MixDirichlet SDE
    //! \param[in,out] particles Array of particle properties
    //! \param[in] stream Thread (or more precisely stream) ID
    //! \param[in] dt Time step size
    //! \param[in] moments Map of statistical moments
    void advance( tk::Particles& particles,
                  int stream,
                  tk::real dt,
                  tk::real,
                  const std::map< tk::ctr::Product, tk::real >& moments )
    {
      // Update SDE coefficients
      coeff.update( m_depvar, m_ncomp, m_norm, DENSITY_OFFSET, VOLUME_OFFSET,
                    moments, m_rho, m_r, m_kprime, m_b, m_k, m_S );

      fenv_t fe;
      feholdexcept( &fe );

      // Advance particles
      const auto npar = particles.nunk();
      for (auto p=decltype(npar){0}; p<npar; ++p) {
        // Generate Gaussian random numbers with zero mean and unit variance
        std::vector< tk::real > dW( m_ncomp );
        m_rng.gaussian( stream, m_ncomp, dW.data() );

        // Advance all m_ncomp (=N=K+1) scalars
        auto& yn = particles( p, m_ncomp, m_offset );
        for (ncomp_t i=0; i<m_ncomp; ++i) {
          auto& y = particles( p, i, m_offset );
          tk::real d = m_k[i] * y * yn * dt;
          if (d < 0.0) d = 0.0;
          d = std::sqrt( d );
          auto dy = 0.5*m_b[i]*( m_S[i]*yn - (1.0-m_S[i])*y )*dt + d*dW[i];
          y += dy;
          yn -= dy;
        }
        // Compute derived instantaneous variables
        derived( particles, p );
      }

      feclearexcept( FE_UNDERFLOW );
      feupdateenv( &fe );
    }

  private:
    //! Offset of particle density in solution array relative to YN
    static const std::size_t DENSITY_OFFSET = 1;
    //! Offset of particle specific volume in solution array relative to YN
    static const std::size_t VOLUME_OFFSET = 2;

    const ncomp_t m_c;                  //!< Equation system index
    const char m_depvar;                //!< Dependent variable
    const ncomp_t m_ncomp;              //!< Number of components, K = N-1
    const ncomp_t m_offset;             //!< Offset SDE operates from
    const tk::RNG& m_rng;               //!< Random number generator
    const ctr::NormalizationType m_norm;//!< Normalization type

    //! Coefficients
    std::vector< kw::sde_b::info::expect::type > m_b;
    std::vector< kw::sde_S::info::expect::type > m_S;
    std::vector< kw::sde_kappa::info::expect::type > m_kprime;
    std::vector< kw::sde_kappa::info::expect::type > m_k;
    std::vector< kw::sde_rho::info::expect::type > m_rho;
    std::vector< kw::sde_r::info::expect::type > m_r;

    //! Coefficients policy
    Coefficients coeff;

    //! \brief Return density for mass fractions
    //! \details This function returns the instantaneous density, rho,
    //!   based on the multiple mass fractions, Y_c.
    //! \param[in] particles Array of particle properties
    //! \param[in] p Particle index
    //! \return Instantaneous value of the density, rho
    //! \details This is computed based 1/rho = sum_{i=1}^N Y_i/R_i, where R_i
    //!   are the constant pure-fluid densities and the Y_i are the mass
    //!   fractions, of the N materials.
    tk::real rho( const tk::Particles& particles, ncomp_t p ) const {
      // start computing density
      tk::real d = 0.0;
      for (ncomp_t i=0; i<m_ncomp+1; ++i)
        d += particles( p, i, m_offset ) / m_rho[i];
      // return particle density
      return 1.0/d;
    }

    //! Compute instantaneous values derived from particle mass fractions
    //! \param[in,out] particles Particle properties array
    //! \param[in] p Particle index
    void derived( tk::Particles& particles, ncomp_t p ) const {<--- Parameter 'particles' can be declared with const
      // compute instantaneous fluid-density based on particle mass fractions
      auto density = rho( particles, p );
      //// Compute and store instantaneous density
      particles( p, m_ncomp+DENSITY_OFFSET, m_offset ) = density;
      // Store instantaneous specific volume
      particles( p, m_ncomp+VOLUME_OFFSET, m_offset ) = 1.0/density;
    }

};

} // walker::

#endif // MixDirichlet_h
Cppcheck report - [Walker]: /home/jbakosi/code/walker/src/DiffEq/Dirichlet/MixDirichlet.hpp
