Function solve_sample

ot/solvers.py:1351–1985

r"""Solve the discrete optimal transport problem using the samples in the source and target domains. The function solves the following general optimal transport problem .. math:: \min_{\mathbf{T}\geq 0} \quad \sum_{i,j} T_{i,j}M_{i,j} + \lambda_r R(\mathbf{T}) + \lambda_u U

(
    X_a,
    X_b,
    a=None,
    b=None,
    metric="sqeuclidean",
    reg=None,
    c=None,
    reg_type="KL",
    unbalanced=None,
    unbalanced_type="KL",
    lazy=False,
    batch_size=None,
    method=None,
    n_threads=1,
    max_iter=None,
    plan_init=None,
    rank=100,
    scaling=0.95,
    potentials_init=None,
    X_init=None,
    tol=None,
    verbose=False,
    grad="autodiff",
    random_state=None,
)

def solve_sample(
    X_a,
    X_b,
    a=None,
    b=None,
    metric="sqeuclidean",
    reg=None,
    c=None,
    reg_type="KL",
    unbalanced=None,
    unbalanced_type="KL",
    lazy=False,
    batch_size=None,
    method=None,
    n_threads=1,
    max_iter=None,
    plan_init=None,
    rank=100,
    scaling=0.95,
    potentials_init=None,
    X_init=None,
    tol=None,
    verbose=False,
    grad="autodiff",
    random_state=None,
):
    r"""Solve the discrete optimal transport problem using the samples in the source and target domains.

    The function solves the following general optimal transport problem

    .. math::
        \min_{\mathbf{T}\geq 0} \quad \sum_{i,j} T_{i,j}M_{i,j} + \lambda_r R(\mathbf{T}) +
        \lambda_u U(\mathbf{T}\mathbf{1},\mathbf{a}) +
        \lambda_u U(\mathbf{T}^T\mathbf{1},\mathbf{b})

    where the cost matrix :math:`\mathbf{M}` is computed from the samples in the
    source and target domains such that :math:`M_{i,j} = d(x_i,y_j)` where
    :math:`d` is a metric (by default the squared Euclidean distance).

    The regularization is selected with `reg` (:math:`\lambda_r`) and `reg_type`. By
    default ``reg=None`` and there is no regularization. The unbalanced marginal
    penalization can be selected with `unbalanced` (:math:`\lambda_u`) and
    `unbalanced_type`. By default ``unbalanced=None`` and the function
    solves the exact optimal transport problem (respecting the marginals).

    Parameters
    ----------
    X_a : array-like, shape (n_samples_a, dim)
        samples in the source domain
    X_b : array-like, shape (n_samples_b, dim)
        samples in the target domain
    a : array-like, shape (dim_a,), optional
        Samples weights in the source domain (default is uniform)
    b : array-like, shape (dim_b,), optional
        Samples weights in the source domain (default is uniform)
    reg : float, optional
        Regularization weight :math:`\lambda_r`, by default None (no reg., exact
        OT)