Marginal violation of a coupling, in the sup norm

$$\max(\|T1 - a\|_\infty, \|T^\top 1 - b\|_\infty)$$ Peyre & Cuturi (2019), Sec. 4.2 – Sinkhorn's stopping criterion.

Usage

Otsinktol(T, a, b)

Arguments

T

Coupling matrix.

a, b

Target marginals; each closed here.

Value

Named list with estimate, row_error, col_error, nrow, ncol, method.

References

Peyre & Cuturi (2019), Sec. 4.2.

Examples

Otsinktol(T = c(1, 2, 3, 4, 5, 6, 7, 8), a = c(1, 2, 3, 4, 5, 6, 7, 8), b = 5L)
#> $estimate
#> [1] 35
#> 
#> $row_error
#> [1] 7.777778
#> 
#> $col_error
#> [1] 35
#> 
#> $nrow
#> [1] 8
#> 
#> $ncol
#> [1] 1
#> 
#> $method
#> [1] "Sinkhorn marginal violation -- Peyre & Cuturi (2019) Sec. 4.2"
#>