multi_normal.hpp

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#ifndef STAN__PROB__DISTRIBUTIONS__MULTIVARIATE__CONTINUOUS__MULTI_NORMAL_HPP
#define STAN__PROB__DISTRIBUTIONS__MULTIVARIATE__CONTINUOUS__MULTI_NORMAL_HPP

#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>

#include <stan/agrad/rev.hpp>
#include <stan/agrad/rev/matrix.hpp>
#include <stan/math/error_handling.hpp>
#include <stan/math/matrix/trace_inv_quad_form_ldlt.hpp>
#include <stan/math/matrix/log_determinant_ldlt.hpp>
#include <stan/meta/traits.hpp>
#include <stan/prob/constants.hpp>
#include <stan/prob/traits.hpp>
#include <stan/math/error_handling/matrix/check_ldlt_factor.hpp>
#include <stan/math/error_handling/matrix/check_size_match.hpp>
#include <stan/math/error_handling/check_finite.hpp>
#include <stan/math/error_handling/matrix/check_symmetric.hpp>

namespace stan {

  namespace prob {

   template <bool propto,
             typename T_y, typename T_loc, typename T_covar>
    typename boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type
    multi_normal_log(const T_y& y,
                     const T_loc& mu,
                     const Eigen::Matrix<T_covar,Eigen::Dynamic,Eigen::Dynamic>& Sigma) {
      static const char* function = "stan::prob::multi_normal_log(%1%)";
      typedef typename boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type lp_type;
      lp_type lp(0.0);
      
      using stan::math::check_size_match;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_positive;
      using stan::math::check_symmetric;
      using stan::math::check_ldlt_factor;

      check_size_match(function,
                            Sigma.rows(), "Rows of covariance parameter",
                            Sigma.cols(), "columns of covariance parameter",
                            &lp);
      check_positive(function, Sigma.rows(), "Covariance matrix rows", &lp);
      check_symmetric(function, Sigma, "Covariance matrix", &lp);
      
      stan::math::LDLT_factor<T_covar,Eigen::Dynamic,Eigen::Dynamic> ldlt_Sigma(Sigma);
      check_ldlt_factor(function,ldlt_Sigma,"LDLT_Factor of covariance parameter",&lp);

      VectorViewMvt<const T_y> y_vec(y);
      VectorViewMvt<const T_loc> mu_vec(mu);
      //size of std::vector of Eigen vectors
      size_t size_vec = max_size_mvt(y, mu);

      //Check if every vector of the array has the same size
      int size_y = y_vec[0].size();
      int size_mu = mu_vec[0].size();
      if (size_vec > 1) {
        int size_y_old = size_y;
        int size_y_new;
        for (size_t i = 1, size_ = length_mvt(y); i < size_; i++) {
          int size_y_new = y_vec[i].size();
          check_size_match(function, 
                                size_y_new, "Size of one of the vectors of the random variable",
                                size_y_old, "Size of another vector of the random variable",
                                &lp);
          size_y_old = size_y_new;
        }
        int size_mu_old = size_mu;
        int size_mu_new;
        for (size_t i = 1, size_ = length_mvt(mu); i < size_; i++) {
          int size_mu_new = mu_vec[i].size();
          check_size_match(function, 
                                size_mu_new, "Size of one of the vectors of the location variable",
                                size_mu_old, "Size of another vector of the location variable",
                                &lp);
          size_mu_old = size_mu_new;
        }
        (void) size_y_old;
        (void) size_y_new;
        (void) size_mu_old;
        (void) size_mu_new;
      }
    
      check_size_match(function, 
                            size_y, "Size of random variable",
                            size_mu, "size of location parameter",
                            &lp);
      check_size_match(function, 
                            size_y, "Size of random variable",
                            Sigma.rows(), "rows of covariance parameter",
                            &lp);
      check_size_match(function, 
                            size_y, "Size of random variable",
                            Sigma.cols(), "columns of covariance parameter",
                            &lp);
  
      for (size_t i = 0; i < size_vec; i++) {
        check_finite(function, mu_vec[i], "Location parameter", &lp);
        check_not_nan(function, y_vec[i], "Random variable", &lp);
      }
      
      if (size_y == 0) //y_vec[0].size() == 0
        return lp;

      if (include_summand<propto>::value) 
        lp += NEG_LOG_SQRT_TWO_PI * size_y * size_vec;

      if (include_summand<propto, T_covar>::value)
        lp -= 0.5 * log_determinant_ldlt(ldlt_Sigma) * size_vec;

      if (include_summand<propto,T_y,T_loc,T_covar>::value) {
        lp_type sum_lp_vec(0.0);
        for (size_t i = 0; i < size_vec; i++) {
          Eigen::Matrix<typename 
              boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type>::type,
              Eigen::Dynamic, 1> y_minus_mu(size_y);
          for (int j = 0; j < size_y; j++)
            y_minus_mu(j) = y_vec[i](j)-mu_vec[i](j);
          sum_lp_vec += trace_inv_quad_form_ldlt(ldlt_Sigma,y_minus_mu);
        }
        lp -= 0.5*sum_lp_vec;
      }
      return lp;
    }

    template <typename T_y, typename T_loc, typename T_covar>
    inline
    typename boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type
    multi_normal_log(const T_y& y,
                     const T_loc& mu,
                     const Eigen::Matrix<T_covar,Eigen::Dynamic,Eigen::Dynamic>& Sigma) {
      return multi_normal_log<false>(y,mu,Sigma);
    }

    template <class RNG>
    inline Eigen::VectorXd
    multi_normal_rng(const Eigen::Matrix<double,Eigen::Dynamic,1>& mu,
                     const Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic>& S,
                     RNG& rng) {
      using boost::variate_generator;
      using boost::normal_distribution;

      static const char* function = "stan::prob::multi_normal_rng(%1%)";

      using stan::math::check_finite;
      using stan::math::check_positive;
      using stan::math::check_symmetric;
 
      check_positive(function, S.rows(), "Covariance matrix rows", (double*)0);
      check_symmetric(function, S, "Covariance matrix", (double*)0);
      check_finite(function, mu, "Location parameter", (double*)0);

      variate_generator<RNG&, normal_distribution<> >
        std_normal_rng(rng, normal_distribution<>(0,1));

      Eigen::VectorXd z(S.cols());
      for(int i = 0; i < S.cols(); i++)
        z(i) = std_normal_rng();

      return mu + S.llt().matrixL() * z;
    }
  }
}

#endif