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<h3 style="text-align: center;"><strong style="font-size: 130%;">Additive Random Utility Models (ARUMs)</strong></h3>
<hr>
<p>   </p>
<h3 style="text-align: left;"><strong style="font-size: 120%;">Probit Class</strong></h3>
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<div class="col-md-4">
<div class="panel panel-default">
<div class="panel-body">
<a href="#CD">Class Definition</a> <br>
<a href="#MO">Member Objects</a> <br>
<a href="#MF">Member Functions</a> <br>
<a href="#NTS">Notes</a> <br>
<a href="#EX">Example</a> <br>
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</div>
<hr>
<h3 style="text-align: left;"><strong style="font-size: 120%;">Class Definition</strong></h3>
<p>Definition:</p>
<pre class="brush: cpp;">
class probit
{
public:
// build objects
int nbX;
int nbY;
int nbParams;
int aux_nbOptions;
bool outsideOption;
double rho;
arma::cube Covar;
// member functions
~probit(){};
probit(){};
explicit probit(int nbX_inp, int nbY_inp);
explicit probit(int nbX_inp, int nbY_inp, bool outsideOption_inp);
explicit probit(int nbX_inp, int nbY_inp, double rho_inp, bool outsideOption_inp);
void build(int nbX_inp, int nbY_inp);
void build(int nbX_inp, int nbY_inp, bool outsideOption_inp);
void build(int nbX_inp, int nbY_inp, double rho_inp, bool outsideOption_inp);
void unifCorrelCovMatrices();
void unifCorrelCovMatrices(double rho_inp);
empirical simul();
empirical simul(int* nbDraws, int* seed);
void simul(empirical& obj_out);
void simul(empirical& obj_out, int* nbDraws, int* seed);
private:
void build_prv(int nbX_inp, int nbY_inp, double* rho_inp, bool outsideOption_inp);
};</pre>
<hr>
<h3 style="text-align: left;" id="MO"><strong style="font-size: 120%;">Member Objects</strong></h3>
<hr>
<h3 style="text-align: left;" id="MF"><strong style="font-size: 120%;">Member Functions</strong></h3>
<hr>
<h3 style="text-align: left;" id="NTS"><strong style="font-size: 120%;">Notes</strong></h3>
<hr>
<h3 style="text-align: left;" id="EX"><strong style="font-size: 120%;">Examples</strong></h3>
<p>Example:</p>
<pre class="brush: cpp;">
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;
//
int nbX = U.n_rows;
int nbY = U.n_cols;
arma::vec n = arma::sum(mu,1);
trame::probit probits;
probits.build(nbX,nbY,true);
//
// correlation matrices
probits.rho = 0.5;
probits.unifCorrelCovMatrices();
//
// empirical object:
int sim_seed = 1777;
int n_draws = 1000;
trame::empirical emp_obj;
probits.simul(emp_obj, &n_draws, &sim_seed);
emp_obj.U = U;
emp_obj.mu = mu;
//
// first compute optimal assignment (mu)
double G_sim_val = emp_obj.G(n);
arma::cout << "G-sim(U): \n" << G_sim_val << arma::endl;
arma::cout << "G-sim -> mu: \n" << emp_obj.mu_sol << arma::endl;
//
// solution to dual problem U*
arma::mat U_star_sim;
double Gstar_sim_val = emp_obj.Gstar(n);
//double Gstar_sim_val = emp_obj.Gstar(n,emp_obj.mu_sol,U_star_sim);
arma::cout << "G*-sim(mu): \n" << Gstar_sim_val << arma::endl;
arma::cout << "\\nabla G-sim*(\\nabla G-sim(U)): \n" << emp_obj.U_sol << arma::endl;
//
// Gbar
arma::mat mu_bar(2,3);
mu_bar.fill(2);
arma::mat U_bar_temp, mu_bar_temp;
double val_Gbar_sim = emp_obj.Gbar(emp_obj.U_sol, mu_bar, n, U_bar_temp, mu_bar_temp);
arma::cout << "Gbar-sim val: \n" << val_Gbar_sim << arma::endl;</pre>
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