# include <cppad/cppad.hpp>
# include <cppad/mixed/cppad_mixed.hpp>


namespace {
     using CppAD::log;
     using CppAD::AD;
     //
     using CppAD::mixed::d_sparse_rcv;
     using CppAD::mixed::d_vector;
     using CppAD::mixed::a1_vector;
     using CppAD::mixed::s_vector;
     //
     class mixed_derived : public cppad_mixed {
     private:
          const d_vector&       y_;
     public:
          // constructor
          mixed_derived(
               size_t                 n_fixed       ,
               size_t                 n_random      ,
               bool                   quasi_fixed   ,
               bool                   bool_sparsity ,
               const d_vector&       y              ) :
               cppad_mixed(n_fixed, n_random, quasi_fixed, bool_sparsity) ,
               y_(y)
          { }
          // implementation of ran_likelihood
          a1_vector ran_likelihood(
               const a1_vector&         theta  ,
               const a1_vector&         u      ) override
          {
               a1_vector vec(1);

               // compute this factor once
               a1_double sqrt_2pi =  CppAD::sqrt( 8.0 * CppAD::atan(1.0) );

               // initialize summation
               vec[0] = 0.0;

               // for each data and random effect
               for(size_t i = 0; i < y_.size(); i++)
               {    a1_double mu     = u[i];
                    a1_double sigma  = theta[i] + double(i) / double( y_.size() );
                    a1_double res    = (y_[i] - mu) / sigma;

                    // This is a Gaussian term, so entire density is smooth
                    vec[0]  += log(sqrt_2pi * sigma) + res * res / 2.0;
               }
               return vec;
          }
     };
}

bool hes_random_obj_xam(void)
{
     bool   ok  = true;
     double eps = 100. * std::numeric_limits<double>::epsilon();
     //
     size_t n_data   = 10;
     size_t n_fixed  = n_data;
     size_t n_random = n_data;
     d_vector  data(n_data);
     d_vector  fixed_vec(n_fixed), random_vec(n_random);
     a1_vector a1_fixed(n_fixed), a1_random(n_random);

     for(size_t i = 0; i < n_data; i++)
     {    data[i]       = double(i + 1);
          //
          fixed_vec[i]  = 1.5;
          a1_fixed[i]   = fixed_vec[i];
          //
          random_vec[i] = 0.0;
          a1_random[i]  = random_vec[i];
     }

     // object that is derived from cppad_mixed
     bool quasi_fixed  = true;
     bool bool_sparsity = true;
     mixed_derived mixed_object(
          n_fixed, n_random, quasi_fixed, bool_sparsity, data
     );
     mixed_object.initialize(fixed_vec, random_vec);

     // Evaluate Hessian of random likelihood w.r.t random effects
     d_sparse_rcv hes_random_obj_rcv =
          mixed_object.hes_random_obj(fixed_vec, random_vec);

     // check the Hessian
     ok &= hes_random_obj_rcv.nnz() == n_data;

     for(size_t k = 0; k < n_data; ++k)
     {    size_t r     = hes_random_obj_rcv.row()[k];
          size_t c     = hes_random_obj_rcv.col()[k];
          double v     = hes_random_obj_rcv.val()[k];
          ok          &= r == c;
          double sigma = fixed_vec[r] + double(r) / double(n_data);
          double check = 1.0 / (sigma * sigma);
          ok          &= fabs( check / v - 1.0 ) < eps;
     }
     return ok;
}