better pep8 but not solved

1 files changed, 123 insertions, 112 deletions

diff --git a/ot/gromov.py b/ot/gromov.py
index e4dd112..b1e9ee0 100644
--- a/ot/gromov.py
+++ b/ot/gromov.py
@@ -20,12 +20,12 @@ from .utils import dist
 from .optim import cg

 

 

-def init_matrix(C1,C2,T,p,q,loss_fun='square_loss'):

+def init_matrix(C1, C2, T, p, q, loss_fun='square_loss'):

     """ Return loss matrices and tensors for Gromov-Wasserstein fast computation

 

     Returns the value of \mathcal{L}(C1,C2) \otimes T with the selected loss

     function as the loss function of Gromow-Wasserstein discrepancy.

-    

+

     The matrices are computed as described in Proposition 1 in [12]

 

     Where :

@@ -56,18 +56,18 @@ def init_matrix(C1,C2,T,p,q,loss_fun='square_loss'):
     T :  ndarray, shape (ns, nt)

          Coupling between source and target spaces

     p : ndarray, shape (ns,)

-        

+

 

     Returns

     -------

-    

+

     constC : ndarray, shape (ns, nt)

            Constant C matrix in Eq. (6)

     hC1 : ndarray, shape (ns, ns)

-           h1(C1) matrix in Eq. (6)          

+           h1(C1) matrix in Eq. (6)

     hC2 : ndarray, shape (nt, nt)

            h2(C) matrix in Eq. (6)

-           

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

@@ -76,39 +76,45 @@ def init_matrix(C1,C2,T,p,q,loss_fun='square_loss'):
 

     """

 

-

     if loss_fun == 'square_loss':

         def f1(a):

-            return (a**2)/2

+            return (a**2) / 2

+

         def f2(b):

-            return (b**2)/2  

+            return (b**2) / 2

+

         def h1(a):

-            return a    

+            return a

+

         def h2(b):

             return b

     elif loss_fun == 'kl_loss':

         def f1(a):

-            return a * np.log(a + 1e-15) - a    

+            return a * np.log(a + 1e-15) - a

+

         def f2(b):

-            return b    

+            return b

+

         def h1(a):

-            return a    

+            return a

+

         def h2(b):

             return np.log(b + 1e-15)

 

-    constC1=np.dot(np.dot(f1(C1),p.reshape(-1,1)),

-                   np.ones(len(q)).reshape(1,-1))

-    constC2=np.dot(np.ones(len(p)).reshape(-1,1),

-                   np.dot(q.reshape(1,-1),f2(C2).T))

-    constC=constC1+constC2

+    constC1 = np.dot(np.dot(f1(C1), p.reshape(-1, 1)),

+                     np.ones(len(q)).reshape(1, -1))

+    constC2 = np.dot(np.ones(len(p)).reshape(-1, 1),

+                     np.dot(q.reshape(1, -1), f2(C2).T))

+    constC = constC1 + constC2

     hC1 = h1(C1)

     hC2 = h2(C2)

 

-    return constC,hC1,hC2

+    return constC, hC1, hC2

+

+

+def tensor_product(constC, hC1, hC2, T):

+    """ Return the tensor for Gromov-Wasserstein fast computation

 

-def tensor_product(constC,hC1,hC2,T):

-    """ Return the tensor for Gromov-Wasserstein fast computation 

-    

     The tensor is computed as described in Proposition 1 Eq. (6) in [12].

 

     Parameters

@@ -116,14 +122,14 @@ def tensor_product(constC,hC1,hC2,T):
     constC : ndarray, shape (ns, nt)

            Constant C matrix in Eq. (6)

     hC1 : ndarray, shape (ns, ns)

-           h1(C1) matrix in Eq. (6)          

+           h1(C1) matrix in Eq. (6)

     hC2 : ndarray, shape (nt, nt)

            h2(C) matrix in Eq. (6)

-        

+

 

     Returns

     -------

-    

+

     tens : ndarray, shape (ns, nt)

            \mathcal{L}(C1,C2) \otimes T tensor-matrix multiplication result

 

@@ -133,15 +139,16 @@ def tensor_product(constC,hC1,hC2,T):
     "Gromov-Wasserstein averaging of kernel and distance matrices."

     International Conference on Machine Learning (ICML). 2016.

 

-    """    

-    A=-np.dot(hC1, T).dot(hC2.T)

-    tens = constC+A

-    #tens -= tens.min()

+    """

+    A = -np.dot(hC1, T).dot(hC2.T)

+    tens = constC + A

+    # tens -= tens.min()

     return tens

 

-def gwloss(constC,hC1,hC2,T):

+

+def gwloss(constC, hC1, hC2, T):

     """ Return the Loss for Gromov-Wasserstein

-    

+

     The loss is computed as described in Proposition 1 Eq. (6) in [12].

 

     Parameters

@@ -149,15 +156,15 @@ def gwloss(constC,hC1,hC2,T):
     constC : ndarray, shape (ns, nt)

            Constant C matrix in Eq. (6)

     hC1 : ndarray, shape (ns, ns)

-           h1(C1) matrix in Eq. (6)          

+           h1(C1) matrix in Eq. (6)

     hC2 : ndarray, shape (nt, nt)

            h2(C) matrix in Eq. (6)

     T : ndarray, shape (ns, nt)

-           Current value of transport matrix T       

+           Current value of transport matrix T

 

     Returns

     -------

-    

+

     loss : float

            Gromov Wasserstein loss

 

@@ -166,16 +173,17 @@ def gwloss(constC,hC1,hC2,T):
     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

     International Conference on Machine Learning (ICML). 2016.

-    

+

     """

 

-    tens=tensor_product(constC,hC1,hC2,T) 

-              

-    return np.sum(tens*T) 

+    tens = tensor_product(constC, hC1, hC2, T)

+

+    return np.sum(tens * T)

+

+

+def gwggrad(constC, hC1, hC2, T):

+    """ Return the gradient for Gromov-Wasserstein

 

-def gwggrad(constC,hC1,hC2,T):

-    """ Return the gradient for Gromov-Wasserstein 

-    

     The gradient is computed as described in Proposition 2 in [12].

 

     Parameters

@@ -183,15 +191,15 @@ def gwggrad(constC,hC1,hC2,T):
     constC : ndarray, shape (ns, nt)

            Constant C matrix in Eq. (6)

     hC1 : ndarray, shape (ns, ns)

-           h1(C1) matrix in Eq. (6)          

+           h1(C1) matrix in Eq. (6)

     hC2 : ndarray, shape (nt, nt)

            h2(C) matrix in Eq. (6)

     T : ndarray, shape (ns, nt)

-           Current value of transport matrix T       

+           Current value of transport matrix T

 

     Returns

     -------

-    

+

     grad : ndarray, shape (ns, nt)

            Gromov Wasserstein gradient

 

@@ -200,10 +208,10 @@ def gwggrad(constC,hC1,hC2,T):
     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

     International Conference on Machine Learning (ICML). 2016.

-    

-    """          

-    return 2*tensor_product(constC,hC1,hC2,T) # [12] Prop. 2 misses a 2 factor 

 

+    """

+    return 2 * tensor_product(constC, hC1, hC2,

+                              T)  # [12] Prop. 2 misses a 2 factor

 

 

 def update_square_loss(p, lambdas, T, Cs):

@@ -261,7 +269,7 @@ def update_kl_loss(p, lambdas, T, Cs):
     return np.exp(np.divide(tmpsum, ppt))

 

 

-def gromov_wasserstein(C1,C2,p,q,loss_fun,log=False,**kwargs): 

+def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, **kwargs):

     """

     Returns the gromov-wasserstein transport between (C1,p) and (C2,q)

 

@@ -307,38 +315,40 @@ def gromov_wasserstein(C1,C2,p,q,loss_fun,log=False,**kwargs):
             \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}

     log : dict

         convergence information and loss

-        

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

         "Gromov-Wasserstein averaging of kernel and distance matrices."

-        International Conference on Machine Learning (ICML). 2016.   

-     

-    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the 

-        metric approach to object matching. Foundations of computational 

+        International Conference on Machine Learning (ICML). 2016.

+

+    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the

+        metric approach to object matching. Foundations of computational

         mathematics 11.4 (2011): 417-487.

-    

+

     """

 

     T = np.eye(len(p), len(q))

 

-    constC,hC1,hC2=init_matrix(C1,C2,T,p,q,loss_fun)

-    

-    G0=p[:,None]*q[None,:]

-    

+    constC, hC1, hC2 = init_matrix(C1, C2, T, p, q, loss_fun)

+

+    G0 = p[:, None] * q[None, :]

+

     def f(G):

-        return gwloss(constC,hC1,hC2,G)

+        return gwloss(constC, hC1, hC2, G)

+

     def df(G):

-        return gwggrad(constC,hC1,hC2,G)

-    

+        return gwggrad(constC, hC1, hC2, G)

+

     if log:

-        res,log=cg(p,q,0,1,f,df,G0,log=True,**kwargs)

-        log['gw_dist']=gwloss(constC,hC1,hC2,res)

-        return res,log

+        res, log = cg(p, q, 0, 1, f, df, G0, log=True, **kwargs)

+        log['gw_dist'] = gwloss(constC, hC1, hC2, res)

+        return res, log

     else:

-        return cg(p,q,0,1,f,df,G0,**kwargs)

+        return cg(p, q, 0, 1, f, df, G0, **kwargs)

+

 

-def gromov_wasserstein2(C1,C2,p,q,loss_fun,log=False,**kwargs): 

+def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, **kwargs):

     """

     Returns the gromov-wasserstein discrepancy between (C1,p) and (C2,q)

 

@@ -383,40 +393,41 @@ def gromov_wasserstein2(C1,C2,p,q,loss_fun,log=False,**kwargs):
         Gromov-Wasserstein distance

     log : dict

         convergence information and Coupling marix

-        

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

         "Gromov-Wasserstein averaging of kernel and distance matrices."

-        International Conference on Machine Learning (ICML). 2016.   

-     

-    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the 

-        metric approach to object matching. Foundations of computational 

+        International Conference on Machine Learning (ICML). 2016.

+

+    .. [13] Mémoli, Facundo. Gromov–Wasserstein distances and the

+        metric approach to object matching. Foundations of computational

         mathematics 11.4 (2011): 417-487.

-    

+

     """

 

     T = np.eye(len(p), len(q))

 

-    constC,hC1,hC2=init_matrix(C1,C2,T,p,q,loss_fun)

-    

-    G0=p[:,None]*q[None,:]

-    

+    constC, hC1, hC2 = init_matrix(C1, C2, T, p, q, loss_fun)

+

+    G0 = p[:, None] * q[None, :]

+

     def f(G):

-        return gwloss(constC,hC1,hC2,G)

+        return gwloss(constC, hC1, hC2, G)

+

     def df(G):

-        return gwggrad(constC,hC1,hC2,G)

-    res,log=cg(p,q,0,1,f,df,G0,log=True,**kwargs)

-    log['gw_dist']=gwloss(constC,hC1,hC2,res)

-    log['T']=res

+        return gwggrad(constC, hC1, hC2, G)

+    res, log = cg(p, q, 0, 1, f, df, G0, log=True, **kwargs)

+    log['gw_dist'] = gwloss(constC, hC1, hC2, res)

+    log['T'] = res

     if log:

-        return log['gw_dist'],log

+        return log['gw_dist'], log

     else:

         return log['gw_dist']

 

 

 def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon,

-                       max_iter=1000, tol=1e-9, verbose=False, log=False):

+                                max_iter=1000, tol=1e-9, verbose=False, log=False):

     """

     Returns the gromov-wasserstein transport between (C1,p) and (C2,q)

 

@@ -469,34 +480,34 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon,
     T : ndarray, shape (ns, nt)

         coupling between the two spaces that minimizes :

             \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))

-            

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

-    International Conference on Machine Learning (ICML). 2016.            

-            

+    International Conference on Machine Learning (ICML). 2016.

+

     """

 

     C1 = np.asarray(C1, dtype=np.float64)

     C2 = np.asarray(C2, dtype=np.float64)

 

     T = np.outer(p, q)  # Initialization

-    

-    constC,hC1,hC2=init_matrix(C1,C2,T,p,q,loss_fun)

+

+    constC, hC1, hC2 = init_matrix(C1, C2, T, p, q, loss_fun)

 

     cpt = 0

     err = 1

-    

+

     if log:

-        log={'err':[]}

+        log = {'err': []}

 

     while (err > tol and cpt < max_iter):

 

         Tprev = T

 

         # compute the gradient

-        tens=gwggrad(constC,hC1,hC2,T)

+        tens = gwggrad(constC, hC1, hC2, T)

 

         T = sinkhorn(p, q, tens, epsilon)

 

@@ -517,13 +528,14 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon,
         cpt += 1

 

     if log:

-        log['gw_dist']=gwloss(constC,hC1,hC2,T)

+        log['gw_dist'] = gwloss(constC, hC1, hC2, T)

         return T, log

     else:

         return T

 

+

 def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon,

-                        max_iter=1000, tol=1e-9, verbose=False, log=False):

+                                 max_iter=1000, tol=1e-9, verbose=False, log=False):

     """

     Returns the entropic gromov-wasserstein discrepancy between the two measured similarity matrices

 

@@ -569,20 +581,19 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon,
     -------

     gw_dist : float

         Gromov-Wasserstein distance

-        

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

-    International Conference on Machine Learning (ICML). 2016.     

-    

-    """

+    International Conference on Machine Learning (ICML). 2016.

 

+    """

 

     gw, logv = entropic_gromov_wasserstein(

-            C1, C2, p, q, loss_fun, epsilon, max_iter, tol, verbose, log=True)

-    

-    log['T']=gw

+        C1, C2, p, q, loss_fun, epsilon, max_iter, tol, verbose, log=True)

+

+    log['T'] = gw

 

     if log:

         return logv['gw_dist'], logv

@@ -591,7 +602,7 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon,
 

 

 def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon,

-                       max_iter=1000, tol=1e-9, verbose=False, log=False, init_C=None):

+                                max_iter=1000, tol=1e-9, verbose=False, log=False, init_C=None):

     """

     Returns the gromov-wasserstein barycenters of S measured similarity matrices

 

@@ -640,13 +651,13 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon,
     -------

     C : ndarray, shape (N, N)

         Similarity matrix in the barycenter space (permutated arbitrarily)

-        

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

-    International Conference on Machine Learning (ICML). 2016.        

-        

+    International Conference on Machine Learning (ICML). 2016.

+

     """

 

     S = len(Cs)

@@ -671,7 +682,7 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon,
         Cprev = C

 

         T = [entropic_gromov_wasserstein(Cs[s], C, ps[s], p, loss_fun, epsilon,

-                                max_iter, 1e-5, verbose, log) for s in range(S)]

+                                         max_iter, 1e-5, verbose, log) for s in range(S)]

         if loss_fun == 'square_loss':

             C = update_square_loss(p, lambdas, T, Cs)

 

@@ -698,14 +709,14 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon,
     return C

 

 

-def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, 

+def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,

                        max_iter=1000, tol=1e-9, verbose=False, log=False, init_C=None):

     """

     Returns the gromov-wasserstein barycenters of S measured similarity matrices

 

     (Cs)_{s=1}^{s=S}

 

-    The function solves the following optimization problem with block 

+    The function solves the following optimization problem with block

     coordinate descent:

 

     .. math::

@@ -747,13 +758,13 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,
     -------

     C : ndarray, shape (N, N)

         Similarity matrix in the barycenter space (permutated arbitrarily)

-        

+

     References

     ----------

     .. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,

     "Gromov-Wasserstein averaging of kernel and distance matrices."

-    International Conference on Machine Learning (ICML). 2016.        

-        

+    International Conference on Machine Learning (ICML). 2016.

+

     """

 

     S = len(Cs)

@@ -777,7 +788,7 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,
     while(err > tol and cpt < max_iter):

         Cprev = C

 

-        T = [gromov_wasserstein(Cs[s], C, ps[s], p, loss_fun, 

+        T = [gromov_wasserstein(Cs[s], C, ps[s], p, loss_fun,

                                 numItermax=max_iter, stopThr=1e-5, verbose=verbose, log=log) for s in range(S)]

         if loss_fun == 'square_loss':

             C = update_square_loss(p, lambdas, T, Cs)

@@ -802,4 +813,4 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,
 

         cpt += 1

 

-    return C
\ No newline at end of file
+    return C