Merge pull request #57 from LeoGautheron/master

Speed-up Sinkhorn

Author: rflamary

ot/bregman.py

@@ -344,8 +344,14 @@ def sinkhorn_knopp(a, b, M, reg, numItermax=1000,
 
     # print(reg)
 
-    K = np.exp(-M / reg)
+    # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute
+    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 +379,11 @@ 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

@@ -77,6 +77,34 @@ def clean_zeros(a, b, M):
     return a2, b2, M2
 
 
+def euclidean_distances(X, Y, squared=False):
+    """
+    Considering the rows of X (and Y=X) as vectors, compute the
+    distance matrix between each pair of vectors.
+    Parameters
+    ----------
+    X : {array-like}, shape (n_samples_1, n_features)
+    Y : {array-like}, shape (n_samples_2, n_features)
+    squared : boolean, optional
+        Return squared Euclidean distances.
+    Returns
+    -------
+    distances : {array}, shape (n_samples_1, n_samples_2)
+    """
+    XX = np.einsum('ij,ij->i', X, X)[:, np.newaxis]
+    YY = np.einsum('ij,ij->i', Y, Y)[np.newaxis, :]
+    distances = np.dot(X, Y.T)
+    distances *= -2
+    distances += XX
+    distances += YY
+    np.maximum(distances, 0, out=distances)
+    if X is Y:
+        # Ensure that distances between vectors and themselves are set to 0.0.
+        # This may not be the case due to floating point rounding errors.
+        distances.flat[::distances.shape[0] + 1] = 0.0
+    return distances if squared else np.sqrt(distances, out=distances)
+
+
 def dist(x1, x2=None, metric='sqeuclidean'):
     """Compute distance between samples in x1 and x2 using function scipy.spatial.distance.cdist
 
@@ -104,7 +132,8 @@ 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)