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.
