Error in the definition of the Wasserstein distance from the user guide #779

Describe the bug

I have found a typo in the user guide which can be quite misleading.

The Wasserstein distance should be defined for a specific metric $$d$$ on the real numbers, e.g., the Euclidean norm, and a specific order $$p$$.

The definition given in the documentation is as follows:

$$ W_p(a,b)=(\min_{\gamma \in \mathbb{R}_+^{m\times n}} \sum_{i,j}\gamma_{i,j} |x_i-y_j |_p)^\frac{1}{p}$$

$$ s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 $$

The order- $$p$$ should be a power of the metric $$d$$.

See link to documentation.

To be exact, we would need a definition such as :

$$ W_p(a,b)=(\min_{\gamma \in \mathbb{R}_+^{m\times n}} \sum_{i,j}\gamma_{i,j}d(x_i,y_j)^p)^\frac{1}{p}$$

$$ s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 $$

Or if $$d$$ is specifically defined as any arbitrary norm $$|\cdot|$$ on the real numbers:

$$ W_p(a,b)=(\min_{\gamma \in \mathbb{R}_+^{m\times n}} \sum_{i,j}\gamma_{i,j}|x_i-y_j|^p)^\frac{1}{p}$$

$$ s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 $$

Thanks for your time.