ott.problems.quadratic.quadratic_problem.QuadraticProblem.update_linearization#

QuadraticProblem.update_linearization(transport, epsilon=None, old_transport_mass=1.0, relative_epsilon=None)[source]#

Update linearization of GW problem by updating cost matrix.

If the problem is balanced (tau_a = 1.0 and tau_b = 1.0), the equation follows eq. 6, p. 1 of [Peyré et al., 2016].

If the problem is unbalanced (tau_a < 1.0 or tau_b < 1.0), two cases are possible, as explained in init_linearization() above. Finally, it is also possible to consider a Fused Gromov-Wasserstein problem. Details about the resulting cost matrix are also given in init_linearization().

Parameters:

  • transport (Transport) – Solution of the linearization of the quadratic problem.

  • epsilon (Union[float, Epsilon, None]) – An epsilon scheduler or a float passed on to the linearization.

  • old_transport_mass (float) – Sum of the elements of the transport matrix at the previous iteration.

  • relative_epsilon (Optional[bool]) – Whether to use relative epsilon in the linearized geometry.

Return type:

LinearProblem

Returns:

Updated linear OT problem, a new local linearization of GW problem.