Algorithm 2 An Entropy Regularised Approach [5, 16]
Input: discrete functions f = (f1,…,fn), g = (g1, …, gn), discrete measures $\mu ={\sum }_{i=1}^n{p}_i\delta x_i,\nu ={\sum }_{j=1}^n{q}_j\delta x_j$, the parameter ε and a stopping condition.
1:	Set r = 0, $\mathcal{K}={\left(exp\left(-\frac{c\left(x_i,x_j;f,g\right)}{\varepsilon }\right)\right)}_{ij}$ and u(0) = 𝕀 ∈ ℝn.
2:	repeat
3:	Let r↦r+ 1, ${\upsilon }^{\left(r\right)}=\frac{\underset{\_}{q}}{{\mathcal{K}}^{⊺}{u}^{(r-1)}}\text{and }{u}^{(r)}=\frac{\underset{\_}{p}}{\mathcal{K}{u}^{(r)}}$ where p =(p1,…pn),q= (q1,…qn)
4:	until Stopping condition has been reached
5:	Set π = diag(u(r))𝒦diag(v (r)).
Output: An estimate π on the optimal plan for Sε where the accuracy is determined by the stopping condition.