Package index • T4transport

Representations and inspection

Construct explicit probability representations, declare costs, and inspect available numerical diagnostics.

ot_measure() as_ot_measure() ot_collection(): Finite probability measures and collections
ot_image() ot_density(): Explicit image and density conversions
ot_gaussian(): Parametric Gaussian probability measures
ot_cost(): Declare supplied transport costs or ground distances
ot_inspect(): Inspect a transport computation without recomputing it

Finite and regularized transport

Compare finite measures with exact transport, entropy regularization, or an inexact proximal iteration.

ot_distance(): Compare finite probability measures
wasserstein() wassersteinD(): Wasserstein Distance via Linear Programming
sinkhorn() sinkhornD(): Wasserstein Distance via Entropic Regularization and Sinkhorn Algorithm
ipot() ipotD(): Wasserstein Distance via Inexact Proximal Point Method

Sliced comparisons and orthogonal alignment

swdist(): Sliced Wasserstein Distance
pwdist(): Procrustes-Wasserstein Distance
pwbary(): Procrustes-Wasserstein Barycenter

Gaussian calculations

ot_gaussian_distance(): Exact Wasserstein-2 distance between Gaussian parameter objects
ot_gaussian_summary(): Summaries of Gaussian parameter objects
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 \(\mathbb{R}^p\)

Gromov–Wasserstein geometry

Compare supplied dissimilarities or estimate a dissimilarity barycenter.

gwdist(): Gromov-Wasserstein Distance
gwbary(): Gromov-Wasserstein Barycenter

Finite-measure barycenters and medians

Declare the candidate support and mass constraints before choosing an optimization method. Historical entry-point names retain their documented compatibility behavior.

ot_summary(): Barycenters and medians of finite probability measures
rbaryGD(): Free-Support Wasserstein Barycenter by Barycentric-Projection Updates
rbary23L(): Free-Support Barycenter by von Lindheim (2023)
rmedIRLS(): Free-Support Median by IRLS
rmedWB(): Free-Support Median by Weiszfeld Update with Barycentric Projection
fbary14C() fbary14Cdist(): Fixed-Support Barycenter by Cuturi & Doucet (2014)
fbary15B() fbary15Bdist(): Fixed-Support Barycenter by Benamou et al. (2015)

Interpolation

Inspect the transported probability measure separately from its histogram or image-grid display.

histinterp(): Interpolation between Histograms
imageinterp(): Interpolation between Images

CDF, histogram, and image interfaces

Cumulative distribution functions

ecdfbary(): Barycenter of Empirical CDFs
ecdfmed(): Wasserstein Median of Empirical CDFs
quantile(<t4transport_cdf>): Generalized inverse of a T4transport weighted CDF

Histograms

histdist(): Distance between Histograms
histbary(): Barycenter of Histograms
histmed(): Wasserstein Median of Histograms
histbary14C(): Barycenter of Histograms by Cuturi and Doucet (2014)
histbary15B(): Barycenter of Histograms by Benamou et al. (2015)

Images

imagedist(): Wasserstein Distance between Two Images
imagebary(): Barycenter of Images
imagemed(): Median on a Prescribed Image Grid
imagebary14C(): Barycenter of Images according to Cuturi & Doucet (2014)
imagebary15B(): Barycenter of Images according to Benamou et al. (2015)

Utilities and descriptive resampling

img2measure(): Extract a discrete measure from a gray-scale image matrix
gaussvis2d(): Draw a Bivariate Gaussian Covariance Ellipse
fiedler(): Compute the fiedler vector of a point cloud
wassboot(): Wasserstein Distance Estimation with Boostrapping

Data sets

digit3: MNIST Images of Digit 3
digits: MNIST Images of All Digits