Entropic regularisation term of a coupling

$$\varepsilon H(T)$$ Peyre & Cuturi (2019), eq. (4.1)-(4.2); Cuturi (2013), eq. (2). The regularised problem is min <P,C> - eps H(P), so this is the term that gets subtracted.

Usage

Otentreg(T, epsilon)

Arguments

T

Non-negative coupling matrix.

epsilon

Positive regularisation strength.

Value

Named list with estimate, entropy, epsilon, n, method.

References

Peyre & Cuturi (2019), eq. (4.2).

Examples

Otentreg(T = c(1, 2, 3, 4, 5, 6, 7, 8), epsilon = 5L)
#> $estimate
#> [1] -116.4098
#> 
#> $entropy
#> [1] -23.28196
#> 
#> $epsilon
#> [1] 5
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Entropic regulariser eps*H(T) -- Peyre & Cuturi (2019) eq. (4.2)"
#>