regularMTW

Project for new examples satisfying Ma-Trudinger-Wang condition. The code in this repository illustrates the paper Families of costs with zero and nonnegative MTW tensor in optimal transport

The folder src contains the main library for the examples.

• The file src/simple_mtw.py contains the main class.
  • baseSimpleMTW is the main base class. The metric, connection and curvature are implemented if we derive from it, providing the function s and its derivatives, and its inverse $u$.
  • class GenHyperbolicSimpleMTW(baseSimpleMTW) Derived class, for $s$ of the form $p_0e^{p_1u}+ p_2e^{p_3u}$
  • class LambertSimpleMTW(baseSimpleMTW) Derived class, for $s = (a_0+ a_1e^{a_2u}$
  • class TrigSimpleMTW(baseSimpleMTW Derived class, for $s = b_0e^{b_1u}\sin(b_2u+b_3)$
• The file src/space_form.py contains the class for a pseudosphere. The ambient symmetric bilinear form is given by the matrix $A$ in the constructor. THe two main cases are $A = I_n$ (sphere) and $A=(-1, 1,\cdots ,1)$ (hyperboloid model of hyperbolic geometry), but most functions work for an arbitrary symmetric invertible matrix.

Folder colab contains the colab example/demo workbooks.