Initialise cost term that depends on the marginals of the transport.

Uses the first term in eq. 6, p. 1 of .

Let $$p$$ [num_a,] be the marginal of the transport matrix for samples from geom_xx and $$q$$ [num_b,] be the marginal of the transport matrix for samples from geom_yy. cost_xx (resp. cost_yy) is the cost matrix of geom_xx (resp. geom_yy). The cost term that depends on these marginals can be written as:

marginal_dep_term = lin1(cost_xx) $$p \mathbb{1}_{num_b}^T$$
• (lin2(cost_yy) $$q \mathbb{1}_{num_a}^T)^T$$

Parameters
• marginal_1 (ndarray) – jnp.ndarray<float>[num_a,], marginal of the transport matrix for samples from geom_xx

• marginal_2 (ndarray) – jnp.ndarray<float>[num_b,], marginal of the transport matrix for samples from geom_yy

Return type

LRCGeometry

Returns

Low-rank geometry.