Additive Random Utility Models (ARUMs)

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Logit Class

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Class Definition

Definition:

 
class logit
{
    public:
        // build objects
        int nbX;
        int nbY;
        int nbParams;
        double sigma = 1.0; // this obviates issues with general market construction (DSE)
        bool outsideOption = true;
        
        // input objects
        arma::mat U;
        arma::mat mu;
        
        // equilibrium objects
        arma::mat U_sol;
        arma::mat mu_sol;
        
        // member functions
        ~logit(){};
         logit(){};
        explicit logit(int nbX_inp, int nbY_inp);
        explicit logit(int nbX_inp, int nbY_inp, double sigma_inp, bool outsideOption_inp);

        void build(int nbX_inp, int nbY_inp);
        void build(int nbX_inp, int nbY_inp, double sigma_inp, bool outsideOption_inp);
        
        double G(const arma::vec& n);
        double G(const arma::vec& n, const arma::mat& U_inp, arma::mat& mu_out);
        //double Gx(const arma::mat& U_x_inp, arma::mat& mu_x_out, int x);
        
        double Gstar(const arma::vec& n);
        double Gstar(const arma::vec& n, const arma::mat& mu_inp, arma::mat& U_out);
        double Gstarx(const arma::mat& mu_x_inp, arma::mat &U_x_out);
        double Gstarx(const arma::mat& mu_x_inp, arma::mat &U_x_out, int x);
        
        double Gbar(const arma::mat& Ubar, const arma::mat& mubar, const arma::vec& n, arma::mat& U_out, arma::mat& mu_out);
        double Gbarx(const arma::vec& Ubar_x, const arma::vec& mubar_x, arma::mat& U_x_out, arma::mat& mu_x_out);
        double Gbarx(const arma::vec& Ubar_x, const arma::vec& mubar_x, arma::mat& U_x_out, arma::mat& mu_x_out, int x);
        
        arma::mat D2G(const arma::vec& n, bool xFirst);
        void D2G(arma::mat &H, const arma::vec& n, bool xFirst);
        void D2G(arma::mat &H, const arma::vec& n, const arma::mat& U_inp, bool xFirst);

        arma::mat D2Gstar(const arma::vec& n, bool xFirst);
        arma::mat D2Gstar(const arma::vec& n, const arma::mat& mu_inp, bool xFirst);
        void D2Gstar(arma::mat &H, const arma::vec& n, bool xFirst);
        void D2Gstar(arma::mat &H, const arma::vec& n, const arma::mat& mu_inp, bool xFirst);

        arma::mat dtheta_NablaGstar(const arma::vec& n, arma::mat* dtheta_inp, bool xFirst);
        void dtheta_NablaGstar(arma::mat &ret, const arma::vec& n, arma::mat* dtheta_inp, bool xFirst);
        
        empirical simul();
        empirical simul(int* nbDraws, int* seed);
        void simul(empirical& obj_out);
        void simul(empirical& obj_out, int* nbDraws, int* seed);

    private:
        static double differMargX(double z, void* opt_data);
};

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Member Objects

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Member Functions

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Notes

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Examples

 
    arma::mat U(2,3);
    U  << 1.6 << 3.2 << 1.1 << arma::endr
       << 2.9 << 1.0 << 3.1 << arma::endr;
    
    arma::mat mu(2,3);
    mu << 1.0 << 3.0 << 1.0 << arma::endr
       << 2.0 << 1.0 << 3.0 << arma::endr;
    //
    // setup logit class object
    int nbX = U.n_rows;
    int nbY = U.n_cols;
    
    arma::vec n = arma::sum(mu,1);

    trame::logit logits(nbX,nbY);
    //
    // empirical object:
    int sim_seed = 1777;
    int n_draws = 1000;

    trame::empirical logit_sim;
    logits.simul(logit_sim, &n_draws, &sim_seed);
    //
    // first compute optimal assignment (mu)
    arma::mat mu_sol, mu_sol_sim;

    double G_val = logits.G(n,U,mu_sol);
    double G_sim_val = logit_sim.G(n,U,mu_sol_sim);
    
    std::cout << "G(U) and G-sim(U): \n" << G_val << " and " << G_sim_val << std::endl;
    
    arma::cout << "\nG -> mu: \n" << mu_sol << arma::endl;
    arma::cout << "G-sim -> mu: \n" << mu_sol_sim << arma::endl;
    //
    // solution to dual problem U*
    arma::mat U_star;
    arma::mat U_star_sim;
    
    double Gstar_val = logits.Gstar(n,mu_sol,U_star);
    double Gstar_sim_val = logit_sim.Gstar(n,mu_sol,U_star_sim);
    
    std::cout << "G*(mu) and G*-sim(mu): \n" << Gstar_val << " and " << Gstar_sim_val << std::endl;
    
    arma::cout << "\n\\nabla G*(\\nabla G(U)): \n" << U_star << arma::endl;
    arma::cout << "\\nabla G-sim*(\\nabla G-sim(U)): \n" << U_star_sim << arma::endl;
    //
    // Gbar
    arma::mat mu_bar(2,3);
    mu_bar.fill(2);
    
    arma::mat U_bar_temp, mu_bar_temp;
    arma::mat U_bar_sim_temp, mu_bar_sim_temp;
    
    double val_Gbar     = logits.Gbar(U,mu_bar,n,U_bar_temp,mu_bar_temp);
    double val_Gbar_sim = logit_sim.Gbar(U,mu_bar,n,U_bar_sim_temp,mu_bar_sim_temp);
    
    std::cout << "Gbar val: \n" << val_Gbar << std::endl;
    std::cout << "Gbar-sim val: \n" << val_Gbar_sim << std::endl;

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