Computation of the Gradients

library(rwig) |> suppressPackageStartupMessages()

To set up the computation for the sinkhorn() and barycenter() algorithms, you will need to set with_grad = TRUE for sinkhorn_control and barycenter_control.

The exact formulae of gradients were given by Xie (2025), and have been checked by the Automatic Differentiation library ForwardDiff in Julia.

See Also

See also vignette("sinkhorn"), vignette("barycenter").

References

Xie, F. (2025). Deriving the Gradients of Some Popular Optimal Transport Algorithms (No. arXiv:2504.08722). arXiv. https://doi.org/10.48550/arXiv.2504.08722