$$T = \mathrm{diag}(u) K \mathrm{diag}(v),\ K = e^{-C/\varepsilon}$$
Cuturi (2013), eq. (2) and Sec. 4.1; Peyre & Cuturi (2019), eq. (4.2).
The loop runs exactly max_iter scalings – no tolerance, no early
exit – so the result is deterministic.
Usage
Otsinkh(a, b, C, epsilon, max_iter = 200L)
Arguments
- a, b
Non-negative marginals; each closed to unit mass here.
- C
Cost matrix, length(a) by length(b).
- epsilon
Positive regularisation strength.
- max_iter
Fixed number of scalings (default 200).
Value
Named list with estimate (the cost <T,C>), T, u, v,
iters, marginal_error, method.
References
Cuturi (2013), eq. (2).
Examples
Otsinkh(c(0.5, 0.5), c(0.2, 0.5, 0.3),
matrix(c(0, 1, 1, 0, 4, 1), 2, 3), 0.5)$estimate
#> [1] 0.6204204
