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

namespace {
     using CppAD::vector;
     using CppAD::log;
     using CppAD::AD;
     //
     using CppAD::mixed::d_sparse_rcv;
     using CppAD::mixed::d_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);

               // initialize part of log-density that is always smooth
               vec[0] = 0.0;

               // sqrt_2pi = CppAD::sqrt( 8.0 * CppAD::atan(1.0) );

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

                    // Gaussian likelihood
                    vec[0]  += log(sigma) + res * res / 2.0;
                    // following term does not depend on fixed or random effects
                    // vec[0]  += log(sqrt_2pi);
               }
               return vec;
          }
     };
}

bool optimize_random_xam(void)
{
     bool   ok = true;

     size_t n_data = 10;
     d_vector data(n_data), fixed_vec(n_data), random_in(n_data);

     for(size_t i = 0; i < n_data; i++)
     {    data[i]      = double(i + 1);
          fixed_vec[i] = 1.0;
          random_in[i] = 0.0;
     }

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

     // lower and upper limits for random effects
     double inf = std::numeric_limits<double>::infinity();
     d_vector random_lower(n_data), random_upper(n_data);
     for(size_t i = 0; i < n_data; i++)
     {    random_lower[i] = -inf;
          random_upper[i] = +inf;
     }

     // -----------------------------------------------------------------------
     // use ipopt to determine the optimal random effects
     std::string ipopt_options;
     ipopt_options += "Integer print_level 0\n";
     ipopt_options += "String  sb          yes\n";
     ipopt_options += "String  derivative_test second-order\n";
     d_vector random_out = mixed_object.optimize_random(
          ipopt_options, fixed_vec, random_lower, random_upper, random_in
     );

     // check the result
     for(size_t i = 0; i < n_data; i++)
     {    // debugging print out
          // std::cout << random_out[i] / data[i] - 1.0 << std::endl;
          ok &= fabs(random_out[i] / data[i] - 1.0) < 1e-10;
     }

     return ok;
}