# Copyright OTT-JAX
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Any, Optional, Union
import jax
import jax.numpy as jnp
from ott import utils
from ott.geometry import geometry, pointcloud
from ott.geometry import semidiscrete_pointcloud as sdpc
from ott.problems.linear import linear_problem
from ott.problems.linear import semidiscrete_linear_problem as sdlp
from ott.solvers.linear import semidiscrete, sinkhorn, sinkhorn_lr, univariate
__all__ = ["solve", "solve_univariate", "solve_semidiscrete"]
[docs]
def solve(
geom: geometry.Geometry,
a: Optional[jnp.ndarray] = None,
b: Optional[jnp.ndarray] = None,
tau_a: float = 1.0,
tau_b: float = 1.0,
rank: int = -1,
**kwargs: Any
) -> Union[sinkhorn.SinkhornOutput, sinkhorn_lr.LRSinkhornOutput]:
"""Solve linear regularized OT problem using Sinkhorn iterations.
Args:
geom: The ground geometry of the linear problem.
a: The first marginal. If :obj:`None`, it will be uniform.
b: The second marginal. If :obj:`None`, it will be uniform.
tau_a: If :math:`< 1`, defines how much unbalanced the problem is
on the first marginal.
tau_b: If :math:`< 1`, defines how much unbalanced the problem is
on the second marginal.
rank:
Rank constraint on the coupling to minimize the linear OT problem
:cite:`scetbon:21`. If :math:`-1`, no rank constraint is used.
kwargs: Keyword arguments for
:class:`~ott.solvers.linear.sinkhorn.Sinkhorn` or
:class:`~ott.solvers.linear.sinkhorn_lr.LRSinkhorn`,
depending on the ``rank``.
Returns:
The Sinkhorn output.
"""
prob = linear_problem.LinearProblem(geom, a=a, b=b, tau_a=tau_a, tau_b=tau_b)
if rank > 0:
solver = sinkhorn_lr.LRSinkhorn(rank=rank, **kwargs)
else:
solver = sinkhorn.Sinkhorn(**kwargs)
return solver(prob)
[docs]
def solve_univariate(
geom: pointcloud.PointCloud,
a: Optional[jnp.ndarray] = None,
b: Optional[jnp.ndarray] = None,
*,
return_transport: bool = False,
return_dual_variables: bool = False,
) -> univariate.UnivariateOutput:
"""Solve 1D OT problems between two :math:`d`-dimensional point clouds.
This function selects the underlying solver based on the following criteria:
- :func:`~ott.solvers.linear.univariate.north_west_solver` - if
``return_dual_variables = True``.
- :func:`~ott.solvers.linear.univariate.uniform_solver` - if ``a`` and
``b`` are both uniform and have the same size.
- :func:`~ott.solvers.linear.univariate.quantile_solver` - otherwise.
Args:
geom: Geometry containing two :math:`d`-dimensional point clouds and
a ground :class:`translation-invariant cost <ott.geometry.costs.TICost>`.
a: The first marginal. If :obj:`None`, it will be uniform.
b: The second marginal. If :obj:`None`, it will be uniform.
return_transport: Whether to also return the mapped pairs used to compute
the :attr:`~ott.solvers.linear.univariate.UnivariateOutput.transport_matrices`.
return_dual_variables: Whether to also return the dual variables.
Returns:
The univariate output.
""" # noqa: E501
prob = linear_problem.LinearProblem(geom, a=a, b=b)
if return_dual_variables:
return univariate.north_west_solver(prob)
if prob.is_uniform and prob.is_equal_size:
return univariate.uniform_solver(prob, return_transport=return_transport)
return univariate.quantile_solver(prob, return_transport=return_transport)
[docs]
def solve_semidiscrete(
geom: sdpc.SemidiscretePointCloud,
b: Optional[jnp.ndarray] = None,
rng: Optional[jax.Array] = None,
**kwargs: Any,
) -> semidiscrete.SemidiscreteOutput:
"""Solve a (regularized) semidiscrete OT problem.
Args:
geom: Semidiscrete geometry.
b: The second marginal. If :obj:`None`, it will be uniform.
rng: Random key used for seeding.
kwargs: Keyword arguments for
:class:`~ott.solvers.linear.semidiscrete.SemidiscreteSolver`.
Returns:
The semidiscrete output.
"""
rng = utils.default_prng_key(rng)
prob = sdlp.SemidiscreteLinearProblem(geom, b=b)
solver = semidiscrete.SemidiscreteSolver(**kwargs)
return solver(rng, prob)
