---
title: "Multi-threading Support"
description: >
  Advanced setting to set up the threads for faster processing
  in Sinkhorn, Barycenter, WDL, and WIG models.
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Multi-threading Support}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
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