Sparse G matrix for EMD1d + standard metrics computed without cdist

Author: rtavenar

ot/lp/__init__.py

@@ -10,6 +10,7 @@
 import multiprocessing
 
 import numpy as np
+from scipy.sparse import coo_matrix
 
 from .import cvx
 
@@ -19,7 +20,8 @@
 from .cvx import barycenter
 from ..utils import dist
 
-__all__=['emd', 'emd2', 'barycenter', 'free_support_barycenter', 'cvx', 'emd_1d_sorted']
+__all__=['emd', 'emd2', 'barycenter', 'free_support_barycenter', 'cvx',
+         'emd_1d', 'emd2_1d']
 
 
 def emd(a, b, M, numItermax=100000, log=False):
@@ -311,33 +313,57 @@ def free_support_barycenter(measures_locations, measures_weights, X_init, b=None
         return X
 
 
-def emd_1d(a, b, x_a, x_b, metric='sqeuclidean', log=False):
+def emd_1d(a, b, x_a, x_b, metric='sqeuclidean', dense=True, log=False):
     """Solves the Earth Movers distance problem between 1d measures and returns
     the OT matrix
 
     """
-    assert x_a.shape[1] == x_b.shape[1] == 1, "emd_1d should only be used " + \
-            "with monodimensional data"
-
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
+    x_a = np.asarray(x_a, dtype=np.float64)
+    x_b = np.asarray(x_b, dtype=np.float64)
+
+    assert (x_a.ndim == 1 or x_a.ndim == 2 and x_a.shape[1] == 1), \
+        "emd_1d should only be used with monodimensional data"
+    assert (x_b.ndim == 1 or x_b.ndim == 2 and x_b.shape[1] == 1), \
+        "emd_1d should only be used with monodimensional data"
 
     # if empty array given then use uniform distributions
     if len(a) == 0:
         a = np.ones((x_a.shape[0],), dtype=np.float64) / x_a.shape[0]
     if len(b) == 0:
         b = np.ones((x_b.shape[0],), dtype=np.float64) / x_b.shape[0]
 
-    perm_a = np.argsort(x_a.reshape((-1, )))
-    perm_b = np.argsort(x_b.reshape((-1, )))
-    inv_perm_a = np.argsort(perm_a)
-    inv_perm_b = np.argsort(perm_b)
-
-    G_sorted, cost = emd_1d_sorted(a, b, x_a[perm_a], x_b[perm_b],
-                                   metric=metric)
-    G = G_sorted[inv_perm_a, :][:, inv_perm_b]
+    x_a_1d = x_a.reshape((-1, ))
+    x_b_1d = x_b.reshape((-1, ))
+    perm_a = np.argsort(x_a_1d)
+    perm_b = np.argsort(x_b_1d)
+
+    G_sorted, indices, cost = emd_1d_sorted(a, b,
+                                            x_a_1d[perm_a], x_b_1d[perm_b],
+                                            metric=metric)
+    G = coo_matrix((G_sorted, (perm_a[indices[:, 0]], perm_b[indices[:, 1]])),
+                   shape=(a.shape[0], b.shape[0]))
+    if dense:
+        G = G.todense()
     if log:
         log = {}
         log['cost'] = cost
         return G, log
-    return G
+    return G
+
+
+def emd2_1d(a, b, x_a, x_b, metric='sqeuclidean', dense=True, log=False):
+    """Solves the Earth Movers distance problem between 1d measures and returns
+    the loss
+
+    """
+    # If we do not return G (log==False), then we should not to cast it to dense
+    # (useless overhead)
+    G, log_emd = emd_1d(a=a, b=b, x_a=x_a, x_b=x_b, metric=metric,
+                        dense=dense and log, log=True)
+    cost = log_emd['cost']
+    if log:
+        log_emd = {'G': G}
+        return cost, log_emd
+    return cost