Optimal Transport

In optimal transport, a quantity known as the MTW tensor plays an important role in the regularity theory. However, calculating the MTW tensor is very tedious. These are some Mathematica notebooks that can be used to compute the MTW tensor for various different cost functions. At some point I might try to host them online, but for now these links are to download the Mathematica notebooks.


  1. This notebook uses the logarithmic cost as a default. As such, it can be used to help verify the computations in the work of Jun Zhang and myself. This can be easily modified to work for any cost function.
    MTW Notebook
  2. This notebook was written to compute the curvature of the Sasaki metric, which is closely related to the MTW tensor. By default, this uses the example we found with non-negative orthogonal anti-bisectional curvature but can be modified for other potentials as well.
    Curvature of Sasaki metric