# Tools for Computational Optimal Transport

## Documentation for package ‘T4transport’ version 0.1.8

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

digit3 | MNIST Images of Digit 3
digits | MNIST Images of All Digits
ecdfbary | Barycenter of Empirical CDFs
ecdfmed | Wasserstein Median of Empirical CDFs
fbary14C | Fixed-Support Barycenter by Cuturi & Doucet (2014)
fbary14Cdist | Fixed-Support Barycenter by Cuturi & Doucet (2014)
fbary15B | Fixed-Support Barycenter by Benamou et al. (2015)
fbary15Bdist | Fixed-Support Barycenter by Benamou et al. (2015)
fiedler | Compute the fiedler vector of a point cloud
gaussbary1d | Barycenter of Gaussian Distributions in \mathbb{R}
gaussbarypd | Barycenter of Gaussian Distributions in \mathbb{R}^p
gaussmed1d | Wasserstein Median of Gaussian Distributions in \mathbb{R}
gaussmedpd | Wasserstein Median of Gaussian Distributions in \mathbb{R}^p
gaussvis2d | Sampling from a Bivariate Gaussian Distribution for Visualization
gwbary | Gromov-Wasserstein Barycenter
gwdist | Gromov-Wasserstein Distance
histbary | Barycenter of Histograms
histbary14C | Barycenter of Histograms by Cuturi and Doucet (2014)
histbary15B | Barycenter of Histograms by Benamou et al. (2015)
histdist | Distance between Histograms
histinterp | Interpolation between Histograms
histmed | Wasserstein Median of Histograms
imagebary | Barycenter of Images
imagebary14C | Barycenter of Images according to Cuturi & Doucet (2014)
imagebary15B | Barycenter of Images according to Benamou et al. (2015)
imagedist | Wasserstein Distance between Two Images
imageinterp | Interpolation between Images
imagemed | Wasserstein Median of Images
img2measure | Extract a discrete measure from a gray-scale image matrix
ipot | Wasserstein Distance via Inexact Proximal Point Method
ipotD | Wasserstein Distance via Inexact Proximal Point Method
pwbary | Procrustes-Wasserstein Barycenter
pwdist | Procrustes-Wasserstein Distance
rbary23L | Free-Support Barycenter by von Lindheim (2023)
rbaryGD | Free-Support Barycenter by Riemannian Gradient Descent
rmedIRLS | Free-Support Median by IRLS
rmedWB | Free-Support Median by Weiszfeld Update with Barycentric Projection
sinkhorn | Wasserstein Distance via Entropic Regularization and Sinkhorn Algorithm
sinkhornD | Wasserstein Distance via Entropic Regularization and Sinkhorn Algorithm
swdist | Sliced Wasserstein Distance
wassboot | Wasserstein Distance Estimation with Boostrapping
wasserstein | Wasserstein Distance via Linear Programming
wassersteinD | Wasserstein Distance via Linear Programming