# Multi-threading Support

    library(rwig) |> suppressPackageStartupMessages()

The log methods for `sinkhorn()` and `barycenter()` both require row-by-row and column-by-column soft-minimum operations for each iteration of the algorithm, and therefore suffer from slow computation time compared to the vanilla/parallel version.

If the dimensions of \(M\) and \(N\) are large (recall that cost matrix C is of size \(M \times N\)), we can use multi-threading to process the rows and columns simultaneously.

This can be done by setting `n_threads` to an integer bigger than 0. By default it is 0, and it means that threading is disabled. Also, setting `n_threads` for “vanilla” or “parallel” methods will be ignored automatically.

But you might ask: if multi-threading is so wonderful, why don’t you set threading as the default? This is because threading comes with an overhead, and sometimes for small problems, it can even be slower than serial processing. So be sure to benchmark your code and see if threading actually helps.

## See Also

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

## References

Peyré, G., & Cuturi, M. (2019). Computational Optimal Transport: With Applications to Data Science. Foundations and Trends® in Machine Learning, 11(5–6), 355–607. https://doi.org/10.1561/2200000073

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