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README.md

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* OT Network Flow solver for the linear program/ Earth Movers Distance [1].
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* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] with optional GPU implementation (requires cudamat).
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* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularization [17].
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* Non regularized Wasserstein barycenters [16] with LP solver.
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* Bregman projections for Wasserstein barycenter [3] and unmixing [4].
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* Optimal transport for domain adaptation with group lasso regularization [5]
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[15] Peyré, G., & Cuturi, M. (2018). [Computational Optimal Transport](https://arxiv.org/pdf/1803.00567.pdf) .
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[16] Agueh, M., & Carlier, G. (2011). [Barycenters in the Wasserstein space](https://hal.archives-ouvertes.fr/hal-00637399/document). SIAM Journal on Mathematical Analysis, 43(2), 904-924.
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[17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).

examples/plot_OT_1D_smooth.py

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# -*- coding: utf-8 -*-
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"""
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====================
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1D optimal transport
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====================
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===========================
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1D smooth optimal transport
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===========================
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This example illustrates the computation of EMD, Sinkhorn and smooth OT plans
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and their visualization.

ot/smooth.py

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#OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
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#THE POSSIBILITY OF SUCH DAMAGE.
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# Author: Mathieu Blondel
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# Remi Flamary <remi.flamary@unice.fr>
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Mathieu Blondel, Vivien Seguy, Antoine Rolet.
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In Proc. of AISTATS 2018.
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https://arxiv.org/abs/1710.06276
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[17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal
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Transport. Proceedings of the Twenty-First International Conference on
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Artificial Intelligence and Statistics (AISTATS).
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Original code from https://github.com/mblondel/smooth-ot/
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"""
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import numpy as np
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def smooth_ot_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9,
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numItermax=500, log=False):
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if reg_type.lower() in ['l2', 'squaredl2']:
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regul = SquaredL2(gamma=reg)

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