ott.solvers.linear.sinkhorn.SinkhornOutput.ent_reg_cost

property SinkhornOutput.ent_reg_cost: float

Entropy regularized cost.

This outputs

\[\langle P^{\star},C\rangle - \varepsilon H(P^{\star}) + \rho_a\text{KL}(P^{\star} 1|a) + \rho_b\text{KL}(1^T P^{\star}|b),\]

where \(P^{\star}, a, b\) is the coupling returned by the Sinkhorn and the two marginal weight vectors; \(\rho_a=\varepsilon \tau_a / (1-\tau_a)\) and \(\rho_b=\varepsilon \tau_b / (1-\tau_b)\) are obtained when the problem is unbalanced from parameters tau_a and tau_b. Note that the last two terms vanish in the balanced case, when tau_a==tau_b==1.