# ott.problems.linear.potentials.EntropicPotentials.transport#

EntropicPotentials.transport(vec, forward=True)#

Transport vec according to Brenier formula .

Uses Theorem 1.17 from to compute an OT map when given the Legendre transform of the dual potentials.

That OT map can be recovered as $$x- (\nabla h)^{-1}\circ \nabla f(x)$$ For the case $$h(\cdot) = \|\cdot\|^2, \nabla h(\cdot) = 2 \cdot\,$$, and as a consequence $$h^*(\cdot) = \|.\|^2 / 4$$, while one has that $$\nabla h^*(\cdot) = (\nabla h)^{-1}(\cdot) = 0.5 \cdot\,$$.

When the dual potentials are solved in correlation form (only in the Sq. Euclidean distance case), the maps are $$\nabla g$$ for forward, $$\nabla f$$ for backward.

Parameters
• vec (Array) – Points to transport, array of shape [n, d].

• forward (bool) – Whether to transport the points from source to the target distribution or vice-versa.

Return type

Array

Returns

The transported points.