Dual potentials from Sinkhorn scalings

$$(u,v) = (e^{f/\varepsilon}, e^{g/\varepsilon})$$ Peyre & Cuturi (2019), eq. (4.30)-(4.31), so f = eps log u.

Usage

Otlogpot(u, v, epsilon)

Arguments

u, v: Positive Sinkhorn scaling vectors.
epsilon: Positive regularisation strength.

Value

Named list with estimate (f), g, epsilon, shift, method. shift is mean(f): the dual pair is determined only up to a constant moving between f and g.

References

Peyre & Cuturi (2019), eq. (4.31).

Examples

Otlogpot(u = c(1, 2, 3, 4, 5, 6, 7, 8), v = c(1, 2, 3, 4, 5, 6, 7, 8), epsilon = 5L)
#> $estimate
#> [1]  0.000000  3.465736  5.493061  6.931472  8.047190  8.958797  9.729551
#> [8] 10.397208
#> 
#> $g
#> [1]  0.000000  3.465736  5.493061  6.931472  8.047190  8.958797  9.729551
#> [8] 10.397208
#> 
#> $epsilon
#> [1] 5
#> 
#> $shift
#> [1] 6.627877
#> 
#> $method
#> [1] "Dual potentials f = eps log u -- Peyre & Cuturi (2019) eq. (4.31)"
#>