Implement foldl and foldr for CNTK keras-team#12168 (keras-team#1…

…2572)

* Implement functions `K.foldl` and `K.foldr` for CNTK

* Enable `test_foldl` and `test_foldr` backend tests for CNTK

keras/backend/cntk_backend.py

@@ -2792,8 +2792,102 @@ def map_fn(fn, elems, name=None, dtype=None):
 
 
 def foldl(fn, elems, initializer=None, name=None):
-    raise NotImplementedError
+    """Reduce `elems` by `fn` combined them from left to right on dimension 0.
+
+    # Arguments
+        fn: Callable that will be called upon each element in `elems`
+            (and on the optional `initializer`) passed as a second argument.
+            The first argument passed to `fn` is the accumulator which is the
+            accumulated value calculated from the preceding invocation of `fn`.
+            Example For `fn`:
+            ```python
+            lambda acc, x: acc + x
+            ```
+        elems: Tensor
+        initializer: (optional) Tensor, the initial value for the accumulator.
+            In case of None value is provided during the call
+            the first value is used (`elems[0]`) as `initializer` from `elems`
+        name: (optional) String, name for the foldl node in the graph.
+
+    # Returns
+        Same type and shape as `initializer`
+
+    # Raises:
+        TypeError: if `fn` is not callable.
+        TypeError: if `initializer` is neither a tensor nor None value.
+        TypeError: if `elems` is not a tensor.
+    """
+    if not callable(fn):
+        raise TypeError("`fn` must be callable.")
+    if initializer is not None and not is_tensor(initializer):
+        raise TypeError("`initializer` must be a tensor or None")
+    if not is_tensor(elems):
+        raise TypeError('`elems` must be a tensor')
+
+    if initializer is None and shape(elems)[0] > 1:
+        initializer = elems[0]
+        elems = elems[1:]
+    elif initializer is None:
+        initializer = elems[0]
+        elems = None
+
+    accumulator = initializer
+    if elems is not None:
+        for i in range(shape(elems)[0]):
+            accumulator = fn(accumulator, elems[i])
+
+    if name is not None:
+        accumulator.name = str(name)
+
+    return reshape(accumulator, shape(initializer)[1:])
 
 
 def foldr(fn, elems, initializer=None, name=None):
-    raise NotImplementedError
+    """Reduce `elems` by `fn` combined them from right to left on dimension 0.
+
+    # Arguments
+        fn: Callable that will be called upon each element in `elems`
+            (and on the optional `initializer`) passed as a second argument.
+            The first argument passed to `fn` is the accumulator which is the
+            accumulated value calculated from the preceding invocation of `fn`.
+            Example For `fn`:
+            ```python
+            lambda acc, x: acc + x
+            ```
+        elems: Tensor
+        initializer: (optional) Tensor, the initial value for the accumulator.
+            In case of None value is provided during the call
+            the last value is used (`elems[-1]`) as `initializer` from `elems`
+        name: (optional) String, name for the foldr node in the graph.
+
+    # Returns
+        Same type and shape as `initializer`
+
+    # Raises:
+        TypeError: if `fn` is not callable.
+        TypeError: if `initializer` is neither a tensor nor None value.
+        TypeError: if `elems` is not a tensor.
+    """
+    if not callable(fn):
+        raise TypeError("`fn` must be callable.")
+    if initializer is not None and not is_tensor(initializer):
+        raise TypeError("`initializer` must be a tensor or None")
+    if not is_tensor(elems):
+        raise TypeError('`elems` must be a tensor')
+
+    if initializer is None and shape(elems)[0] > 1:
+        initializer = elems[-1]
+        elems = elems[:-1]
+    elif initializer is None:
+        initializer = elems[0]
+        elems = None
+
+    accumulator = initializer
+    if elems is not None:
+        for i in range(shape(elems)[0]):
+            accumulator = fn(accumulator, elems[-i])
+
+    if name is not None:
+        accumulator.name = str(name)
+
+    return reshape(accumulator, shape(initializer)[1:])

tests/keras/backend/backend_test.py

@@ -1948,15 +1948,13 @@ def test_map(self):
         assert_allclose(x.sum(axis=1), kx, atol=1e-05)
         assert_allclose(kx, kx2, atol=1e-05)
 
-    @pytest.mark.skipif(K.backend() == 'cntk', reason='Not supported.')
     def test_foldl(self):
         x = np.random.rand(10, 3).astype(np.float32)
         kx = K.eval(K.foldl(lambda a, b: a + b, K.variable(x)))
 
         assert (3,) == kx.shape
         assert_allclose(x.sum(axis=0), kx, atol=1e-05)
 
-    @pytest.mark.skipif(K.backend() == 'cntk', reason='Not supported.')
     def test_foldr(self):
         # This test aims to make sure that we walk the array from right to left
         # and checks it in the following way: multiplying left to right 1e-40