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<h3 style="text-align: center;"><strong style="font-size: 130%;">Transfers</strong></h3>
<hr>
<p>   </p>
<h3 style="text-align: left;"><strong style="font-size: 120%;">Linearly Transferable Utility (ETU) Class</strong></h3>
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<div class="col-md-4">
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<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>
</div>
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<hr>
<h3 style="text-align: left;"><strong style="font-size: 120%;">Class Definition</strong></h3>
<p>Definition:</p>
<pre class="brush: cpp;">
class ltu
{
public:
// build objects
bool need_norm;
int transfers_type = 1;
int nbX;
int nbY;
int nbParams;
arma::mat lambda;
arma::mat phi;
arma::mat aux_zeta; // could be 1 - lambda_LTU;
arma::mat aux_phi_exp; // aux_phi_exp = exp(phi); will probably end up as exp(phi / sigma) when using MFE, K_LTU
// member functions
void build(const arma::mat& lambda_LTU, const arma::mat& phi_LTU, bool need_norm_LTU);
void trans();
//
// DSE-related functions
arma::mat Psi(const arma::mat& U, const arma::mat& V) const;
arma::mat Psi(const arma::mat& U, const arma::mat& V, arma::uvec* xs, arma::uvec* ys) const;
arma::mat Psi(const double& U, const arma::mat& V, arma::uvec* xs, arma::uvec* ys) const;
arma::mat Psi(const arma::mat& U, const double& V, arma::uvec* xs, arma::uvec* ys) const;
double Psi(const double& U, const double& V, int x_ind, int y_ind) const;
arma::mat du_Psi(const arma::mat& U, const arma::mat& V) const;
arma::mat du_Psi(const arma::mat& U, const arma::mat& V, arma::uvec* xs, arma::uvec* ys) const;
arma::mat du_Psi(const double& U, const arma::mat& V, arma::uvec* xs, arma::uvec* ys) const;
arma::mat du_Psi(const arma::mat& U, const double& V, arma::uvec* xs, arma::uvec* ys) const;
arma::mat dtheta_Psi(const arma::mat& U, const arma::mat& V, const arma::mat& dtheta);
arma::mat dtheta_Psi(const arma::mat& U, const arma::mat& V, const arma::mat* dtheta);
arma::mat Ucal(const arma::mat& vs) const;
arma::mat Ucal(const arma::mat& vs, arma::uvec* xs, arma::uvec* ys) const;
double Ucal(const double& vs, int xs, int ys) const;
arma::mat Vcal(const arma::mat& us) const;
arma::mat Vcal(const arma::mat& us, arma::uvec* xs, arma::uvec* ys) const;
double Vcal(const double& us, int xs, int ys) const;
arma::mat UW(const arma::mat& Ws) const;
arma::mat UW(const arma::mat& Ws, arma::uvec* xs, arma::uvec* ys) const;
double UW(const double& Ws, int x_ind, int y_ind) const;
arma::mat VW(const arma::mat& Ws) const;
arma::mat VW(const arma::mat& Ws, arma::uvec* xs, arma::uvec* ys) const;
double VW(const double& Ws, int x_ind, int y_ind) const;
arma::mat dw_UW(const arma::mat& Ws) const;
arma::mat dw_UW(const arma::mat& Ws, arma::uvec* xs, arma::uvec* ys) const;
arma::mat dw_VW(const arma::mat& Ws) const;
arma::mat dw_VW(const arma::mat& Ws, arma::uvec* xs, arma::uvec* ys) const;
arma::mat WU(const arma::mat& Us);
arma::mat WU(const arma::mat& Us, arma::uvec* xs, arma::uvec* ys);
arma::mat WV(const arma::mat& Vs);
arma::mat WV(const arma::mat& Vs, arma::uvec* xs, arma::uvec* ys);
};</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>
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