[autograd.functional] Fix a bug on handling v=None in vjp and jvp (#36445)

* autograd.functional passed pylint checker.

* autograd.functional: fix import errors.

* autograd.functional: fixed unit tests.

* autograd.functional minor format change

* [autograd.functional] Fixed vjp and jvp's v=None bug.

python/paddle/autograd/functional.py

@@ -23,9 +23,10 @@ from .utils import _tensors, _stack_tensor_or_return_none, _replace_none_with_ze
 
 @contextlib.contextmanager
 def gradient_scope(*var_lists, create_graph=False, allow_unused=False):
-    def grad_fn(ys, xs, v, create_graph=create_graph):
+    def grad_fn(ys, xs, v=None, create_graph=create_graph):
+        if v is not None:
             assert len(ys) == len(v), (
-            f'`v` is expected to be of the same size as the output. '
+                f'The argument {v} is expected to be of the same size as the output. '
                 f'Here the output is {ys}, and `v` is {v}.')
         if allow_unused:
             ys = [
@@ -49,6 +50,8 @@ def gradient_scope(*var_lists, create_graph=False, allow_unused=False):
             return out
 
     def process(vl):
+        if vl is None:
+            return None
         out = []
         # If v is treated as constant in the outer scope, its gradient is guaranteed
         # not to be taken beyond this scope. Within this scope, however, v's gradient
@@ -151,7 +154,9 @@ def vjp(func, inputs, v=None, create_graph=False, allow_unused=False):
         #        [[2., 1.],
         #         [1., 0.]]), None]
     """
-    xs, v = _tensors(inputs, "inputs"), _tensors(v, "v")
+    xs = _tensors(inputs, "inputs")
+    if v is not None:
+        v = _tensors(v, "v")
 
     with gradient_scope(
             xs, v, create_graph=create_graph,
@@ -221,7 +226,9 @@ def jvp(func, inputs, v=None, create_graph=False, allow_unused=False):
         #         [0., 0.]])]
 
     """
-    xs, v = _tensors(inputs, "inputs"), _tensors(v, "v")
+    xs = _tensors(inputs, "inputs")
+    if v is not None:
+        v = _tensors(v, "v")
 
     with gradient_scope(
             xs, v, create_graph=create_graph,

python/paddle/fluid/tests/unittests/autograd/test_vjp_jvp.py

@@ -205,6 +205,16 @@ class TestVJP(TestAutogradFunctional):
             vjp_result, grad_result = vjp(), grad()
             self.check_results(grad_result, vjp_result)
 
+    def test_vjp_i2o2_omitting_v_no_create_graph(self):
+        test_cases = [
+            [o2, ['A', 'A']],  #noqa
+        ]  #noqa
+        for f, inputs in test_cases:
+            inputs = self.gen_inputs(inputs)
+            vjp, grad = self.gen_test_pairs(f, inputs)
+            vjp_result, grad_result = vjp(), grad()
+            self.check_results(grad_result, vjp_result)
+
     def test_vjp_nested_no_create_graph(self):
         x = self.gen_input('a')
         test_cases = [
@@ -289,6 +299,17 @@ class TestJVP(TestAutogradFunctional):
             reverse_jac = jac(vjp, f, inputs)
             self.check_results(forward_jac, reverse_jac)
 
+    def test_jvp_i2o2_omitting_v_no_create_graph(self):
+        test_cases = [  #noqa
+            [o2, ['A', 'A']],  #noqa
+        ]  #noqa
+        for f, inputs in test_cases:
+            inputs = self.gen_inputs(inputs)
+            results_omitting_v = jvp(f, inputs)
+            v = [ones_like(x) for x in inputs]
+            results_with_v = jvp(f, inputs, v)
+            self.check_results(results_omitting_v, results_with_v)
+
 
 if __name__ == "__main__":
     unittest.main()