class ott.geometry.pointcloud.PointCloud(x, y=None, cost_fn=None, batch_size=None, scale_cost=1.0, **kwargs)[source]#

Defines geometry for 2 point clouds (possibly 1 vs itself).

Creates a geometry, specifying a cost function passed as CostFn type object. When the number of points is large, setting the batch_size flag implies that cost and kernel matrices used to update potentials or scalings will be recomputed on the fly, rather than stored in memory. More precisely, when setting batch_size, the cost function will be partially cached by storing norm values for each point in both point clouds, but the pairwise cost function evaluations won’t be.

  • x (Array) – n x d array of n d-dimensional vectors

  • y (Optional[Array]) – m x d array of m d-dimensional vectors. If None, use x.

  • cost_fn (Optional[CostFn]) – a CostFn function between two points in dimension d.

  • batch_size (Optional[int]) – When None, the cost matrix corresponding to that point cloud is computed, stored and later re-used at each application of apply_lse_kernel(). When batch_size is a positive integer, computations are done in an online fashion, namely the cost matrix is recomputed at each call of the apply_lse_kernel() step, batch_size lines at a time, used on a vector and discarded. The online computation is particularly useful for big point clouds whose cost matrix does not fit in memory.

  • scale_cost (Union[bool, int, float, Literal['mean', 'max_norm', 'max_bound', 'max_cost', 'median']]) – option to rescale the cost matrix. Implemented scalings are ‘median’, ‘mean’, ‘max_cost’, ‘max_norm’ and ‘max_bound’. Alternatively, a float factor can be given to rescale the cost such that cost_matrix /= scale_cost. If True, use ‘mean’.

  • kwargs (Any) – keyword arguments for Geometry.


apply_cost(arr[, axis, fn, is_linear])

Apply cost matrix to array (vector or matrix).

apply_kernel(scaling[, eps, axis])

Apply kernel_matrix on positive scaling vector.

apply_lse_kernel(f, g, eps[, vec, axis])

Apply kernel_matrix in log domain.

apply_square_cost(arr[, axis])

Apply elementwise-square of cost matrix to array (vector or matrix).

apply_transport_from_potentials(f, g, vec[, ...])

Apply transport matrix computed from potentials to a (batched) vec.

apply_transport_from_scalings(u, v, vec[, axis])

Apply transport matrix computed from scalings to a (batched) vec.


Compute barycenter of points in self.x using weights.


Copy the epsilon parameters from another geometry.

marginal_from_potentials(f, g[, axis])

Output marginal of transportation matrix from potentials.

marginal_from_scalings(u, v[, axis])

Output marginal of transportation matrix from scalings.

mask(src_mask, tgt_mask[, mask_value])

Mask rows or columns of a geometry.


Compute dual potential vector from scaling vector.

prepare_divergences(x, y[, static_b, ...])

Instantiate the geometries used for a divergence computation.


Compute scaling vector from dual potential.


Modify how to rescale of the cost_matrix.

subset(src_ixs, tgt_ixs, **kwargs)

Subset rows or columns of a geometry.


Convert point cloud to low-rank geometry.

transport_from_potentials(f, g)

Output transport matrix from potentials.

transport_from_scalings(u, v)

Output transport matrix from pair of scalings.

update_potential(f, g, log_marginal[, ...])

Carry out one Sinkhorn update for potentials, i.e. in log space.

update_scaling(scaling, marginal[, ...])

Carry out one Sinkhorn update for scalings, using kernel directly.

vec_apply_cost(arr[, axis, fn])

Apply the geometry's cost matrix in a vectorized way.



Batch size for online mode.


Check quickly if casting geometry as LRC makes sense.


Cost matrix, recomputed from kernel if only kernel was specified.


Output rank of cost matrix, if any was provided.


The data type.


Epsilon regularization value.


Compute and return inverse of scaling factor for cost matrix.


Whether the cost/kernel is computed on-the-fly.


Whether cost is computed by taking squared Euclidean distance.


Whether geometry cost/kernel is a symmetric matrix.


Kernel matrix.


Mean of the cost_matrix.


Median of the cost_matrix.


Shape of the geometry.


Mask of shape [num_a,] to compute cost_matrix statistics.


Mask of shape [num_b,] to compute cost_matrix statistics.