# ott.geometry.costs.ElasticSTVS#

class ott.geometry.costs.ElasticSTVS(scaling_reg=1.0, matrix=None, orthogonal=False)[source]#

Cost with soft thresholding operator with vanishing shrinkage (STVS) regularization.

$\frac{1}{2} \|\cdot\|_2^2 + \text{scaling_reg}^2\mathbf{1}_d^T\left(\sigma(\cdot) - \frac{1}{2} \exp\left(-2\sigma(\cdot)\right) + \frac{1}{2}\right)$

where $$\sigma(\cdot) := \text{asinh}\left(\frac{\cdot} {2\text{scaling_reg}}\right)$$

Parameters:

Methods

 all_pairs(x, y) Compute matrix of all pairwise costs, including the norms. Compute matrix of all pairwise costs, excluding the norms. barycenter(weights, xs) Barycentric operator. h(z) TI function acting on difference of $$x-y$$ to output cost. Legendre transform of h() when it is convex. h_transform(f, **kwargs) Compute the h-transform of a concave function. pairwise(x, y) Compute cost as evaluation of h() on $$x-y$$. prox_legendre_reg(z[, tau]) Proximal operator of the Legendre transform of reg(). prox_reg(z[, tau]) Proximal operator of reg(). Regularization function.

Attributes