ott.solvers.linear.sinkhorn.SinkhornOutput

class ott.solvers.linear.sinkhorn.SinkhornOutput(potentials, errors=None, reg_ot_cost=None, ot_prob=None, threshold=None, converged=None, inner_iterations=None)

Holds the output of a Sinkhorn solver applied to a problem.

Objects of this class contain both solutions and problem definition of a regularized OT problem, along several methods that can be used to access its content, to, for instance, materialize an OT matrix or apply it to a vector (without having to materialize it when not needed).

Parameters:

• potentials (Tuple[Array, ...]) – list of optimal dual variables, two vector of size ot.prob.shape[0] and ot.prob.shape[1] returned by Sinkhorn

• errors (Optional[Array]) – vector or errors, along iterations. This vector is of size max_iterations // inner_iterations where those were the parameters passed on to the Sinkhorn solver. For each entry indexed at i, errors[i] can be either a real non-negative value (meaning the algorithm recorded that error at the i * inner_iterations iteration), a jnp.inf value (meaning the algorithm computed that iteration but did not compute its error, because, for instance, i < min_iterations // inner_iterations), or a -1, meaning that execution was terminated before that iteration, because the criterion was found to be smaller than threshold.

• reg_ot_cost (Optional[Array]) – the regularized optimal transport cost. By default this is the linear contribution + KL term. See ent_reg_cost, primal_cost and dual_cost for other objective values.

• ot_prob (Optional[LinearProblem]) – stores the definition of the OT problem, including geometry, marginals, unbalanced regularizers, etc.

• threshold (Optional[Array]) – convergence threshold used to control the termination of the algorithm.

• converged (Optional[bool]) – whether the output corresponds to a solution whose error is below the convergence threshold.

• inner_iterations (Optional[int]) – number of iterations that were run between two computations of errors.

Methods

apply(inputs[, axis, lse_mode])	Apply the transport to a ndarray; axis=1 for its transpose.
cost_at_geom(other_geom)	Return reg-OT cost for matrix, evaluated at other cost matrix.
count(value, /)	Return number of occurrences of value.
index(value[, start, stop])	Return first index of value.
marginal(axis)
set(**kwargs)	Return a copy of self, with potential overwrites.
set_cost(ot_prob, lse_mode, use_danskin)
to_dual_potentials([epsilon])	Compute dual potential functions.
transport_cost_at_geom(other_geom)	Return bare transport cost of current solution at any geometry.

Attributes

a
b
converged	Alias for field number 5
diag	Diagonal of the transport matrix.
dual_cost	Return dual transport cost, without considering regularizer.
ent_reg_cost	Entropy regularized cost.
entropy	Entropy of the coupling.
errors	Alias for field number 1
f	The first dual potential.
g	The second dual potential.
geom
inner_iterations	Alias for field number 6
kl_reg_cost	KL regularized OT transport cost.
matrix	Transport matrix if it can be instantiated.
n_iters	Returns the total number of iterations that were needed to terminate.
normalized_entropy	Renormalized entropy of coupling when the problem is assignment.
ot_prob	Alias for field number 3
potentials	Alias for field number 0
primal_cost	Return transport cost of current transport solution at geometry.
reg_ot_cost	Alias for field number 2
scalings
threshold	Alias for field number 4
transport_mass	Sum of transport matrix.