ott.geometry.semidiscrete_pointcloud.SemidiscretePointCloud

class ott.geometry.semidiscrete_pointcloud.SemidiscretePointCloud(sampler, y, cost_fn=None, epsilon=None, relative_epsilon=None, scale_cost=1.0, relative_epsilon_seed=0, relative_epsilon_num_samples=1024)

Semidiscrete point cloud geometry.

Instances of this geometry can be sampled using the sample() method.

Parameters:

• sampler (Callable[[Array, Tuple[int, ...], Optional[dtype]], Array]) – Function with a signature (rng, shape, dtype) -> array corresponding to the source distribution.

• y (Array) – Array of shape [m, ...] corresponding to the target distribution.

• cost_fn (Optional[CostFn]) – Cost function. If None, use SqEuclidean.

• epsilon (Union[float, Array, None]) – Regularization parameter. Can be set to \(0\) to solve the unregularized semidiscrete problem.

• relative_epsilon (Optional[Literal['mean', 'std']]) – Whether epsilon refers to a fraction of the mean_cost_matrix or std_cost_matrix.

• scale_cost (Union[float, Literal['mean', 'max_norm', 'max_bound', 'max_cost', 'median']]) – Option to rescale the cost matrix.

• relative_epsilon_seed (int) – Random seed when estimating the epsilon.

• relative_epsilon_num_samples (int) – Number of samples when estimating the epsilon.

Methods

sample(rng, num_samples, *[, epsilon])

Sample a point cloud.

Attributes

dtype	The data type.
epsilon	Epsilon regularization value.
is_entropy_regularized	Whether epsilon > 0.
shape	Shape of the geometry.