[DOC] Corrected spelling errors (#467)

* Fix typos in docstrings and examples

* A few more fixes

* Fix ref for `center_ot_dual` function

* Another typo

* Fix titles formatting

* Explicit empty line after math blocks

* Typo: asymmetric

* Fix code cell formatting for 1D barycenters

* Empirical

* Fix indentation for references

* Fixed all WARNINGs about title formatting

* Fix empty lines after math blocks

* Fix whitespace line

* Update changelog

* Consistent Gromov-Wasserstein

* More Gromov-Wasserstein consistency

---------

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

1 files changed, 10 insertions, 4 deletions

diff --git a/ot/bregman.py b/ot/bregman.py
index 20bef7e..4503ffc 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -150,7 +150,7 @@ def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000, stopThr=1e-9,
     ot.bregman.sinkhorn_knopp : Classic Sinkhorn :ref:`[2] <references-sinkhorn>`
     ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn
         :ref:`[9] <references-sinkhorn>` :ref:`[10] <references-sinkhorn>`
-    ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling
+    ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epsilon scaling
         :ref:`[9] <references-sinkhorn>` :ref:`[10] <references-sinkhorn>`
 
     """
@@ -384,6 +384,7 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000, stopThr=1e-9,
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`dim_a`, `dim_b`) metric cost matrix
@@ -572,6 +573,7 @@ def sinkhorn_log(a, b, M, reg, numItermax=1000, stopThr=1e-9, verbose=False,
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`dim_a`, `dim_b`) metric cost matrix
@@ -784,6 +786,7 @@ def greenkhorn(a, b, M, reg, numItermax=10000, stopThr=1e-9, verbose=False,
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`dim_a`, `dim_b`) metric cost matrix
@@ -950,6 +953,7 @@ def sinkhorn_stabilized(a, b, M, reg, numItermax=1000, tau=1e3, stopThr=1e-9,
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`dim_a`, `dim_b`) metric cost matrix
@@ -2657,7 +2661,7 @@ def unmix(a, D, M, M0, h0, reg, reg0, alpha, numItermax=1000,
     ----------
 
     .. [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti,
-        Supervised planetary unmixing with optimal transport, Whorkshop
+        Supervised planetary unmixing with optimal transport, Workshop
         on Hyperspectral Image and Signal Processing :
         Evolution in Remote Sensing (WHISPERS), 2016.
     """
@@ -2908,6 +2912,7 @@ def empirical_sinkhorn(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean',
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`n_samples_a`, `n_samples_b`) metric cost matrix
@@ -3104,6 +3109,7 @@ def empirical_sinkhorn2(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean',
              \gamma^T \mathbf{1} &= \mathbf{b}
 
              \gamma &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` is the (`n_samples_a`, `n_samples_b`) metric cost matrix
@@ -3257,7 +3263,6 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
     sinkhorn divergence :math:`S`:
 
     .. math::
-
         W &= \min_\gamma \quad \langle \gamma, \mathbf{M} \rangle_F +
         \mathrm{reg} \cdot\Omega(\gamma)
 
@@ -3287,6 +3292,7 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
              \gamma_b^T \mathbf{1} &= \mathbf{b}
 
              \gamma_b &\geq 0
+
     where :
 
     - :math:`\mathbf{M}` (resp. :math:`\mathbf{M_a}`, :math:`\mathbf{M_b}`)
@@ -3352,7 +3358,7 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
     ----------
     .. [23] Aude Genevay, Gabriel Peyré, Marco Cuturi, Learning Generative
         Models with Sinkhorn Divergences,  Proceedings of the Twenty-First
-        International Conference on Artficial Intelligence and Statistics,
+        International Conference on Artificial Intelligence and Statistics,
         (AISTATS) 21, 2018
     '''
     X_s, X_t = list_to_array(X_s, X_t)