Julia is a new and promising language and I plan to cover some algorithms in Optimal Transport with implementation of Julia. To the best of my knowledge, there does not exist such package in Julia communities.
Given Julia's performance, it should run faster than other high-level languages (for example Python). Whereas OT problems often suffers from its computational complexity in high-dimensional space. Therefore I consider Julia to be a good choice of solving OT problems.
The first algorithm is Sinkhorn-Knopp (SK) matrix-scaling algorithm. It will be translated from POT (Python Optimal Transport) library, and I will compare running time given two different languages. SK algorithm in POT is written using numpy library, but Julia are supposed to be even faster.
TO DO:
Recent paper for benchmark test of OT algorithms.
Schrieber, J., Schuhmacher, D., & Gottschlich, C. (2017). DOTmark -
A Benchmark for Discrete Optimal Transport. IEEE Access, 5, 271–282.
https://doi.org/10.1109/ACCESS.2016.2639065