[MRG] Docs updates (#298)

* bregman docs

* sliced docs

* docs partial

* unbalanced docs

* stochastic docs

* plot docs

* datasets docs

* utils docs

* dr docs

* dr docs corrected

* smooth docs

* docs da

* pep8

* docs gromov

* more space after min and argmin

* docs lp

* bregman docs

* bregman docs mistake corrected

* pep8

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

1 files changed, 4 insertions, 3 deletions

diff --git a/ot/sliced.py b/ot/sliced.py
index d3dc3f2..7c09111 100644
--- a/ot/sliced.py
+++ b/ot/sliced.py
@@ -17,7 +17,7 @@ from .utils import list_to_array
 
 def get_random_projections(d, n_projections, seed=None, backend=None, type_as=None):
     r"""
-    Generates n_projections samples from the uniform on the unit sphere of dimension d-1: :math:`\mathcal{U}(\mathcal{S}^{d-1})`
+    Generates n_projections samples from the uniform on the unit sphere of dimension :math:`d-1`: :math:`\mathcal{U}(\mathcal{S}^{d-1})`
 
     Parameters
     ----------
@@ -67,11 +67,12 @@ def sliced_wasserstein_distance(X_s, X_t, a=None, b=None, n_projections=50, p=2,
     Computes a Monte-Carlo approximation of the p-Sliced Wasserstein distance
 
     .. math::
-        \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}[\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)]^{\frac{1}{p}}
+        \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}\left(\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)\right)^{\frac{1}{p}}
+
 
     where :
 
-    - :math:`\theta_\# \mu` stands for the pushforwars of the projection :math:`\mathbb{R}^d \ni X \mapsto \langle \theta, X \rangle`
+    - :math:`\theta_\# \mu` stands for the pushforwards of the projection :math:`X \in \mathbb{R}^d \mapsto \langle \theta, X \rangle`
 
 
     Parameters