BUG: Fixes optimal einsum path for multi-contraction intermediates

numpy/core/einsumfunc.py

@@ -166,8 +166,14 @@ def _optimal_path(input_sets, output_set, idx_dict, memory_limit):
                 new_pos = positions + [con]
                 iter_results.append((new_cost, new_pos, new_input_sets))
 
-        # Update list to iterate over
-        full_results = iter_results
+        # Update combinatorial list, if we did not find anything return best
+        # path + remaining contractions
+        if iter_results:
+            full_results = iter_results
+        else:
+            path = min(full_results, key=lambda x: x[0])[1]
+            path += [tuple(range(len(input_sets) - iteration))]
+            return path
 
     # If we have not found anything return single einsum contraction
     if len(full_results) == 0:

numpy/core/tests/test_einsum.py

@@ -767,13 +767,13 @@ def test_random_cases(self):
 
 
 class TestEinSumPath(object):
-    def build_operands(self, string):
+    def build_operands(self, string, size_dict=global_size_dict):
 
         # Builds views based off initial operands
         operands = [string]
         terms = string.split('->')[0].split(',')
         for term in terms:
-            dims = [global_size_dict[x] for x in term]
+            dims = [size_dict[x] for x in term]
             operands.append(np.random.rand(*dims))
 
         return operands
@@ -863,6 +863,16 @@ def test_edge_paths(self):
         path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
         self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
 
+        # Edge test5
+        edge_test4 = self.build_operands('a,ac,ab,ad,cd,bd,bc->',
+                                         size_dict={"a": 20, "b": 20, "c": 20, "d": 20})
+        path, path_str = np.einsum_path(*edge_test4, optimize='greedy')
+        self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
+
+        path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
+        self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
+
+
     def test_path_type_input(self):
         # Test explicit path handeling
         path_test = self.build_operands('dcc,fce,ea,dbf->ab')