implement paralell sinkhorn

Author: rflamary

examples/plot_OT_1D.py

@@ -50,7 +50,7 @@
 #%% Sinkhorn
 
 lambd=1e-3
-Gs=ot.sinkhorn(a,b,M,lambd)
+Gs=ot.sinkhorn(a,b,M,lambd,verbose=True)
 
 pl.figure(4)
 ot.plot.plot1D_mat(a,b,Gs,'OT matrix Sinkhorn')

examples/plot_compute_emd.py

@@ -32,10 +32,11 @@
 for i,m in enumerate(lst_m):
     B[:,i]=gauss(n,m=m,s=5)
 
-# loss matrix
+# loss matrix and normalization
 M=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'euclidean')
+M/=M.max()
 M2=ot.dist(x.reshape((n,1)),x.reshape((n,1)),'sqeuclidean')
-
+M2/=M2.max()
 #%% plot the distributions
 
 pl.figure(1)
@@ -46,12 +47,28 @@
 pl.plot(x,B,label='Target distributions')
 pl.title('Target distributions')
 
-#%% plot distributions and loss matrix
+#%% Compute and plot distributions and loss matrix
+
+d_emd=ot.emd2(a,B,M) # direct computation of EMD
+d_emd2=ot.emd2(a,B,M2)  # direct computation of EMD with loss M3
+
 
-emd=ot.emd2(a,B,M)
-emd2=ot.emd2(a,B,M2)
 pl.figure(2)
-pl.plot(emd,label='Euclidean loss')
-pl.plot(emd,label='Squared Euclidean loss')
+pl.plot(d_emd,label='Euclidean EMD')
+pl.plot(d_emd2,label='Squared Euclidean EMD')
+pl.title('EMD distances')
 pl.legend()
 
+#%%
+reg=1e-2
+d_sinkhorn=ot.sinkhorn(a,B,M,reg)
+d_sinkhorn2=ot.sinkhorn(a,B,M2,reg)
+
+pl.figure(2)
+pl.clf()
+pl.plot(d_emd,label='Euclidean EMD')
+pl.plot(d_emd2,label='Squared Euclidean EMD')
+pl.plot(d_sinkhorn,label='Euclidean Sinkhorn')
+pl.plot(d_emd2,label='Squared Euclidean Sinkhorn')
+pl.title('EMD distances')
+pl.legend()

ot/bregman.py

@@ -7,7 +7,7 @@
 
 def sinkhorn(a,b, M, reg,method='sinkhorn', numItermax = 1000, stopThr=1e-9, verbose=False, log=False,**kwargs):
     u"""
-    Solve the entropic regularization optimal transport problem
+    Solve the entropic regularization optimal transport problem and return the OT matrix
 
     The function solves the following optimization problem:
 
@@ -107,12 +107,9 @@ def sinkhorn(a,b, M, reg,method='sinkhorn', numItermax = 1000, stopThr=1e-9, ver
     return sink()
 
 
-
-
-
 def sinkhorn_knopp(a,b, M, reg, numItermax = 1000, stopThr=1e-9, verbose=False, log=False,**kwargs):
     """
-    Solve the entropic regularization optimal transport problem
+    Solve the entropic regularization optimal transport problem and return the OT matrix
 
     The function solves the following optimization problem:
 
@@ -188,22 +185,35 @@ def sinkhorn_knopp(a,b, M, reg, numItermax = 1000, stopThr=1e-9, verbose=False,
     a=np.asarray(a,dtype=np.float64)
     b=np.asarray(b,dtype=np.float64)
     M=np.asarray(M,dtype=np.float64)
+    
 
     if len(a)==0:
         a=np.ones((M.shape[0],),dtype=np.float64)/M.shape[0]
     if len(b)==0:
         b=np.ones((M.shape[1],),dtype=np.float64)/M.shape[1]
+        
 
     # init data
     Nini = len(a)
     Nfin = len(b)
+    
+    if len(b.shape)>1:
+        nbb=b.shape[1]
+    else:
+        nbb=0
+    
 
     if log:
         log={'err':[]}
 
     # we assume that no distances are null except those of the diagonal of distances
-    u = np.ones(Nini)/Nini
-    v = np.ones(Nfin)/Nfin
+    if nbb:
+        u = np.ones((Nini,nbb))/Nini
+        v = np.ones((Nfin,nbb))/Nfin
+    else:
+        u = np.ones(Nini)/Nini
+        v = np.ones(Nfin)/Nfin
+    
 
     #print(reg)
 
@@ -231,8 +241,11 @@ def sinkhorn_knopp(a,b, M, reg, numItermax = 1000, stopThr=1e-9, verbose=False,
             break
         if cpt%10==0:
             # we can speed up the process by checking for the error only all the 10th iterations
-            transp = u.reshape(-1, 1) * (K * v)
-            err = np.linalg.norm((np.sum(transp,axis=0)-b))**2
+            if nbb:
+                err = np.sum((u-uprev)**2)/np.sum((u)**2)+np.sum((v-vprev)**2)/np.sum((v)**2)
+            else:
+                transp = u.reshape(-1, 1) * (K * v)
+                err = np.linalg.norm((np.sum(transp,axis=0)-b))**2
             if log:
                 log['err'].append(err)
 
@@ -244,12 +257,23 @@ def sinkhorn_knopp(a,b, M, reg, numItermax = 1000, stopThr=1e-9, verbose=False,
     if log:
         log['u']=u
         log['v']=v
-
-    #print('err=',err,' cpt=',cpt)
-    if log:
-        return u.reshape((-1,1))*K*v.reshape((1,-1)),log
-    else:
-        return u.reshape((-1,1))*K*v.reshape((1,-1))
+        
+    if nbb: #return only loss 
+        res=np.zeros((nbb))
+        for i in range(nbb):
+            res[i]=np.sum(u[:,i].reshape((-1,1))*K*v[:,i].reshape((1,-1))*M)
+        if log:
+            return res,log
+        else:
+            return res        
+        
+    else: # return OT matrix
+        
+        if log:
+            return u.reshape((-1,1))*K*v.reshape((1,-1)),log
+        else:
+            return u.reshape((-1,1))*K*v.reshape((1,-1))
+     
 
 def sinkhorn_stabilized(a,b, M, reg, numItermax = 1000,tau=1e3, stopThr=1e-9,warmstart=None, verbose=False,print_period=20, log=False,**kwargs):
     """