Added more docstrings (Cython) + fixed link to ot.dist doc

Author: rtavenar

ot/lp/__init__.py

@@ -343,7 +343,7 @@ def emd_1d(x_a, x_b, a, b, metric='sqeuclidean', dense=True, log=False):
     b : (nt,) ndarray, float64
         Target histogram (uniform weight if empty list)
     metric: str, optional (default='sqeuclidean')
-        Metric to be used. Only strings listed in ... are accepted.
+        Metric to be used. Only strings listed in :func:`ot.dist` are accepted.
         Due to implementation details, this function runs faster when
         `'sqeuclidean'`, `'cityblock'`,  or `'euclidean'` metrics are used.
     dense: boolean, optional (default=True)
@@ -454,7 +454,7 @@ def emd2_1d(x_a, x_b, a, b, metric='sqeuclidean', dense=True, log=False):
     b : (nt,) ndarray, float64
         Target histogram (uniform weight if empty list)
     metric: str, optional (default='sqeuclidean')
-        Metric to be used. Only strings listed in ... are accepted.
+        Metric to be used. Only strings listed in :func:`ot.dist` are accepted.
         Due to implementation details, this function runs faster when
         `'sqeuclidean'`, `'cityblock'`,  or `'euclidean'` metrics are used.
     dense: boolean, optional (default=True)

ot/lp/emd_wrap.pyx

@@ -105,7 +105,33 @@ def emd_1d_sorted(np.ndarray[double, ndim=1, mode="c"] u_weights,
                   np.ndarray[double, ndim=1, mode="c"] v,
                   str metric='sqeuclidean'):
     r"""
-    Roro's stuff
+    Solves the Earth Movers distance problem between sorted 1d measures and
+    returns the OT matrix and the associated cost
+
+    Parameters
+    ----------
+    u_weights : (ns,) ndarray, float64
+        Source histogram
+    v_weights : (nt,) ndarray, float64
+        Target histogram
+    u : (ns,) ndarray, float64
+        Source dirac locations (on the real line)
+    v : (nt,) ndarray, float64
+        Target dirac locations (on the real line)
+    metric: str, optional (default='sqeuclidean')
+        Metric to be used. Only strings listed in :func:`ot.dist` are accepted.
+        Due to implementation details, this function runs faster when
+        `'sqeuclidean'`, `'cityblock'`,  or `'euclidean'` metrics are used.
+
+    Returns
+    -------
+    gamma: (n, ) ndarray, float64
+        Values in the Optimal transportation matrix
+    indices: (n, 2) ndarray, int64
+        Indices of the values stored in gamma for the Optimal transportation
+        matrix
+    cost
+        cost associated to the optimal transportation
     """
     cdef double cost = 0.
     cdef int n = u_weights.shape[0]