fix_likelihood.cpp¶

Random Likelihood: Example and Test¶

# 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::a1_double;
    using CppAD::mixed::d_vector;
    using CppAD::mixed::a1_vector;
    //
    class mixed_derived : public cppad_mixed {
    private:
        const d_vector&       z_;
    public:
        // constructor
        mixed_derived(
            size_t                 n_fixed       ,
            size_t                 n_random      ,
            bool                   quasi_fixed   ,
            bool                   bool_sparsity ,
            const d_vector&        z             ) :
            cppad_mixed(n_fixed, n_random, quasi_fixed, bool_sparsity) ,
            z_(z)
        { }
        // implementation of fix_likelihood
        a1_vector fix_likelihood(
            const a1_vector&         theta  )
        {
            a1_vector vec(1);

            // compute this factor once
            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 < z_.size(); i++)
            {   a1_double mu     = theta[i];
                a1_double res    = (z_[i] - mu) / 1.0;

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

bool fix_likelihood_xam(void)
{
    bool   ok  = true;
    double pi  = 4.0 * std::atan(1.0);
    double eps = 100. * std::numeric_limits<double>::epsilon();
    //
    // typedef cppad_mixed::a1_double a1_double
    size_t n_data   = 10;
    size_t n_fixed  = n_data;
    size_t n_random = 0;
    d_vector    data(n_data);
    d_vector    fixed_vec(n_fixed), random_vec(n_random);
    a1_vector a1_fixed(n_fixed);

    for(size_t i = 0; i < n_data; i++)
    {   data[i]       = double(i + 1);
        //
        fixed_vec[i]  = 1.5;
        a1_fixed[i]   = a1_double( fixed_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 fix_likelihood
    a1_vector a1_vec(1);
    a1_vec = mixed_object.fix_likelihood(a1_fixed);

    // check the random likelihood
    double sum = 0.0;
    for(size_t i = 0; i < n_data; i++)
    {   double mu     = fixed_vec[i];
        double res    = (data[i] - mu);
        sum          += (std::log(2 * pi) + res * res) / 2.0;
    }
    ok &= fabs( a1_vec[0] / a1_double(sum) - a1_double(1.0) ) < eps;

    return ok;
}