Speed-up Sinkhorn

Speed-up in 3 places:
 - the computation of pairwise distance is faster with sklearn.metrics.pairwise.euclidean_distances
 - faster computation of K = np.exp(-M / reg)
 - faster computation of the error every 10 iterations

Example with this little script:

import time
import numpy as np
import ot
rng = np.random.RandomState(0)
transport = ot.da.SinkhornTransport()
time1 = time.time()
Xs, ys, Xt = rng.randn(10000, 100), rng.randint(0, 2, size=10000), rng.randn(10000, 100)
transport.fit(Xs=Xs, Xt=Xt)
time2 = time.time()
print("OT Computation Time {:6.2f} sec".format(time2-time1))
transport = ot.da.SinkhornLpl1Transport()
transport.fit(Xs=Xs, ys=ys, Xt=Xt)
time3 = time.time()
print("OT LpL1 Computation Time {:6.2f} sec".format(time3-time2))

Before
OT Computation Time  19.93 sec
OT LpL1 Computation Time 133.43 sec

After
OT Computation Time   7.55 sec
OT LpL1 Computation Time  82.25 sec

Author: toto6

ot/bregman.py

@@ -344,8 +344,13 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000,
 
     # print(reg)
 
-    K = np.exp(-M / reg)
+    K = np.empty(M.shape, dtype=M.dtype)
+    np.divide(M, -reg, out=K)
+    np.exp(K, out=K)
+
     # print(np.min(K))
+    tmp = np.empty(K.shape, dtype=M.dtype)
+    tmp2 = np.empty(b.shape, dtype=M.dtype)
 
     Kp = (1 / a).reshape(-1, 1) * K
     cpt = 0
@@ -373,8 +378,11 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000,
                 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
+                np.multiply(u.reshape(-1, 1), K, out=tmp)
+                np.multiply(tmp, v.reshape(1, -1), out=tmp)
+                np.sum(tmp, axis=0, out=tmp2)
+                tmp2 -= b
+                err = np.linalg.norm(tmp2)**2
             if log:
                 log['err'].append(err)
 

ot/utils.py

@@ -13,6 +13,7 @@
 
 import numpy as np
 from scipy.spatial.distance import cdist
+from sklearn.metrics.pairwise import euclidean_distances
 import sys
 import warnings
 try:
@@ -104,7 +105,8 @@ def dist(x1, x2=None, metric='sqeuclidean'):
     """
     if x2 is None:
         x2 = x1
-
+    if metric == "sqeuclidean":
+        return euclidean_distances(x1, x2, squared=True)
     return cdist(x1, x2, metric=metric)