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MATLAB functions for solving semi-discrete optimal transport problems.

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MATLAB-SDOT

MATLAB functions for solving semi-discrete optimal transport problems in 2D & 3D.

  • SDOT_damped_Newton.m computes the optimal transport cost between the Lebesgue measure and a discrete measure on a 3D box with respect to the quadratic cost or the periodic quadratic cost, using the damped Newton method from
    • Jun Kitagawa, Quentin Mérigot, Boris Thibert, Convergence of a Newton algorithm for semi-discrete optimal transport. J. Eur. Math. Soc. 21 (2019), no. 9, pp. 2603–2651.
  • SDOT_fminunc.m solves the same problem using the MATLAB function fminunc (slower).
  • kantorovich.m computes the Kantorovich function and its gradient and Hessian.

Getting started

To use these MATLAB functions you must first install

Examples

See the MATLAB live script Examples_MATLAB_SDOT.mlx and the corresponding PDF file Examples_MATLAB_SDOT.pdf. We have tested the code with target measures with up to 100,000 Dirac masses.

Licence

See LICENCE.md

Software limitations

  • The source measure is the Lebesgue measure on a cuboid.
  • The support of the discrete target measure must be contained in the support of the source measure.
  • The transport cost is either the quadratic cost or the periodic quadratic cost.

We plan to address some of these limitations in future updates.

Related software

Main contributors

  • Steve Roper, University of Glasgow
  • David Bourne, Heriot-Watt University and the Maxwell Institute for Mathematical Sciences
  • Mason Pearce, Heriot-Watt University and the Maxwell Institute for Mathematical Sciences

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MATLAB functions for solving semi-discrete optimal transport problems.

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