This toolbox reproduces the numerical illustrations of the paper:
Gabriel Peyré. Entropic Approximation of Wasserstein Gradient Flows. SIAM Journal on Imaging Sciences, 8(4), pp. 2323–2351, 2015
The main scripts are:
- test_image.m: reproduces the figures of 2-D flows on a rectangular grid.
- test_mesh.m: reproduces the figures of flows on a triangulated mesh.
- test_prox_porous.m: display the proximal map of generalized entropies.
- test_barycenters.m: computation of Wasserstein barycenters (this is a simple example of use of perform_dikstra_scaling).
- test_pairwise_attraction: evolution of two densities connected by a Wasserstein distance
- test_pairwise_sum: evolution of two densities with a coupling on the sum
- test_wasserstein_attraction: minimization of a Wasserstein distance by Wasserstein flow.
The main functions are:
- perform_jko_stepping.m: perform the actual computation of a JKO step. It needs a callback to the Gibbs kernel.
- perform_dikstra_scaling.m: a generic solver for KL optimization problems.
Helpers functions:
- compute_geodesic_heat.m: compute approximate geodesic distances by the "geodesic in heat method".
- deconv_richlucy.m: linear deconvolution by Richardson-Lucy algorithm.
- load_porous_prox.m: implements the proximal operator of generalized entropies, computed using a look-up table.
- porous_prox_newton: same but implemented using a Newton scheme, useful to deal with spacially varying densities.
- load_setup.m: load various setup for the numerical experiments (i.e. metric, potential, initial densities, etc)
- load_kernel: load a Gibbs kernel.
Copyright (c) 2015 Gabriel Peyré
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