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https://github.com/JuliaOptimalTransport/OptimalTransport.jl

Optimal transport algorithms for Julia
https://github.com/JuliaOptimalTransport/OptimalTransport.jl

julia optimal-transport optimal-transport-algorithms optimization scaling-algorithms sinkhorn-algorithm wasserstein wasserstein-distance

Last synced: 3 months ago
JSON representation

Optimal transport algorithms for Julia

Host: GitHub
URL: https://github.com/JuliaOptimalTransport/OptimalTransport.jl
Owner: JuliaOptimalTransport
License: mit
Created: 2020-04-05T21:12:48.000Z (over 4 years ago)
Default Branch: master
Last Pushed: 2024-07-06T23:46:02.000Z (4 months ago)
Last Synced: 2024-07-07T00:25:21.557Z (4 months ago)
Topics: julia, optimal-transport, optimal-transport-algorithms, optimization, scaling-algorithms, sinkhorn-algorithm, wasserstein, wasserstein-distance
Language: Julia
Homepage: https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev
Size: 24.8 MB
Stars: 93
Watchers: 6
Forks: 8
Open Issues: 24
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE

Awesome Lists containing this project

awesome-sciml - JuliaOptimalTransport/OptimalTransport.jl: Optimal transport algorithms for Julia

README

        # OptimalTransport.jl 

[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaOptimalTransport.github.io/OptimalTransport.jl/stable)

[![](https://img.shields.io/badge/docs-dev-blue.svg)](https://JuliaOptimalTransport.github.io/OptimalTransport.jl/dev)

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This package provides some [Julia](https://julialang.org/) implementations of algorithms for computational [optimal transport](https://optimaltransport.github.io/), including the Earth-Mover's (Wasserstein) distance, Sinkhorn algorithm for entropically regularized optimal transport as well as some variants or extensions.

Notably, OptimalTransport.jl provides GPU acceleration through [CUDA.jl](https://github.com/JuliaGPU/CUDA.jl/) and [NNlibCUDA.jl](https://github.com/FluxML/NNlibCUDA.jl).

This package is inspired by the [Python Optimal Transport](https://optimaltransport.github.io/)

package.

## Example

```julia

using OptimalTransport

using Distances

# uniform histograms

μ = fill(1/250, 250)

ν = fill(1/200, 200)

# random cost matrix

C = pairwise(SqEuclidean(), rand(1, 250), rand(1, 200); dims=2)

# regularization parameter

ε = 0.01

# solve entropically regularized optimal transport problem

sinkhorn(μ, ν, C, ε)

```

Please see the documentation pages for further information.

## Related packages

- [ExactOptimalTransport.jl](https://github.com/JuliaOptimalTransport/ExactOptimalTransport.jl): Julia implementation of algorithms for exact unregularized (Kantorovich) optimal transport problems.

- [PythonOT.jl](https://github.com/JuliaOptimalTransport/PythonOT.jl): Julia interface for the [Python Optimal Transport (POT) package](https://pythonot.github.io/).

- [StochasticOptimalTransport.jl](https://github.com/JuliaOptimalTransport/StochasticOptimalTransport.jl): Julia implementation of stochastic optimization algorithms for large-scale optimal transport.

## Contributing

Contributions are more than welcome! Please feel free to submit an issue or pull request in this repository.

## Acknowledgements

Contributors include:

- Tim Matsumoto (UBC)

- David Widmann (Uppsala)

- Davi Barreira (FGV)

- Stephen Zhang (UBC)

## References

- Peyré, G. and Cuturi, M., 2019. Computational optimal transport. Foundations and Trends® in Machine Learning, 11(5-6), pp.355-607.

- Lorenz, D.A., Manns, P. and Meyer, C., 2019. Quadratically regularized optimal transport. Applied Mathematics & Optimization, pp.1-31.

- Rémi Flamary and Nicolas Courty, POT Python Optimal Transport library, https://pythonot.github.io/, 2017

- Chizat, L., Peyré, G., Schmitzer, B. and Vialard, F.X., 2016. Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.

- Schmitzer, B., 2019. Stabilized sparse scaling algorithms for entropy regularized transport problems. SIAM Journal on Scientific Computing, 41(3), pp.A1443-A1481.