# 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) Output barycenter of vectors. 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. twist_operator(vec, dual_vec, variable) Twist inverse operator of the cost function.

Attributes