From 3cc99e6590fa87ae8705fc93315590b27bf84efc Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Fri, 7 Apr 2017 14:12:37 +0200
Subject: better dicumentation

---
 ot/dr.py | 59 +++++++++++++++++++++++++++++++++++++++++++++++++++++------
 1 file changed, 53 insertions(+), 6 deletions(-)

(limited to 'ot/dr.py')

diff --git a/ot/dr.py b/ot/dr.py
index 3732d81..3965149 100644
--- a/ot/dr.py
+++ b/ot/dr.py
@@ -1,16 +1,15 @@
 # -*- coding: utf-8 -*-
 """
-Domain adaptation with optimal transport
+Dimension reduction with optimal transport
 """
 
-
 import autograd.numpy as np
 from pymanopt.manifolds import Stiefel
 from pymanopt import Problem
 from pymanopt.solvers import SteepestDescent, TrustRegions
 
 def dist(x1,x2):
-    """ Compute squared euclidena distance between samples
+    """ Compute squared euclidean distance between samples
     """
     x1p2=np.sum(np.square(x1),1)    
     x2p2=np.sum(np.square(x2),1)
@@ -40,18 +39,66 @@ def split_classes(X,y):
 
 def wda(X,y,p=2,reg=1,k=10,solver = None,maxiter=100,verbose=0):
     """ 
-    Wasserstein Discriminant Analysis    
+    Wasserstein Discriminant Analysis [11]_
     
     The function solves the following optimization problem:
 
     .. math::
-        P = arg\min_P \frac{\sum_i W(PX^i,PX^i)}{\sum_{i,j\neq i} W(PX^i,PX^j)}
+        P = \\text{arg}\min_P \\frac{\\sum_i W(PX^i,PX^i)}{\\sum_{i,j\\neq i} W(PX^i,PX^j)}
 
     where :
-
+        
+    - :math:`P` is a linear projection operator in the Stiefel(p,d) manifold
     - :math:`W` is entropic regularized Wasserstein distances
     - :math:`X^i` are samples in the dataset corresponding to class i    
     
+    Parameters
+    ----------
+    a : np.ndarray (ns,)
+        samples weights in the source domain
+    b : np.ndarray (nt,)
+        samples in the target domain
+    M : np.ndarray (ns,nt)
+        loss matrix
+    reg : float
+        Regularization term >0
+    numItermax : int, optional
+        Max number of iterations
+    stopThr : float, optional
+        Stop threshol on error (>0)
+    verbose : bool, optional
+        Print information along iterations
+    log : bool, optional
+        record log if True
+
+
+    Returns
+    -------
+    gamma : (ns x nt) ndarray
+        Optimal transportation matrix for the given parameters
+    log : dict
+        log dictionary return only if log==True in parameters
+
+    Examples
+    --------
+
+    >>> import ot
+    >>> a=[.5,.5]
+    >>> b=[.5,.5]
+    >>> M=[[0.,1.],[1.,0.]]
+    >>> ot.sinkhorn(a,b,M,1)
+    array([[ 0.36552929,  0.13447071],
+           [ 0.13447071,  0.36552929]])
+
+
+    References
+    ----------
+
+    .. [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). Wasserstein Discriminant Analysis. arXiv preprint arXiv:1608.08063.
+
+    
+    
+    
     """
     
     mx=np.mean(X)
-- 
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