text: # Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  from paddle.fluid import core
  from paddle.fluid import framework
  from paddle.fluid.backward import gradients_with_optimizer
  import paddle
  
  __all__ = []
  
  
  @framework.dygraph_only
  def backward(tensors, grad_tensors=None, retain_graph=False):
      """
      Compute the backward gradients of given tensors.
      
      Args:
          tensors(list of Tensors): the tensors which the gradient to be computed. The tensors can not contain the same tensor.
  
          grad_tensors(list of Tensors of None, optional): the init gradients of the `tensors`` .If not None, it must have the same length with ``tensors`` ,
              and if any of the elements is None, then the init gradient is the default value which is filled with 1.0. 
              If None, all the gradients of the ``tensors`` is the default value which is filled with 1.0.
              Defaults to None.
  
          retain_graph(bool, optional): If False, the graph used to compute grads will be freed. If you would
              like to add more ops to the built graph after calling this method( :code:`backward` ), set the parameter
              :code:`retain_graph` to True, then the grads will be retained. Thus, seting it to False is much more memory-efficient.
              Defaults to False.
      
      Returns:
          NoneType: None
  
  
      Examples:
          .. code-block:: python
  
              import paddle
              x = paddle.to_tensor([[1, 2], [3, 4]], dtype='float32', stop_gradient=False)
              y = paddle.to_tensor([[3, 2], [3, 4]], dtype='float32')
  
              grad_tensor1 = paddle.to_tensor([[1,2], [2, 3]], dtype='float32')
              grad_tensor2 = paddle.to_tensor([[1,1], [1, 1]], dtype='float32')
  
              z1 = paddle.matmul(x, y)
              z2 = paddle.matmul(x, y)
  
              paddle.autograd.backward([z1, z2], [grad_tensor1, grad_tensor2], True)
              print(x.grad)
              #[[12. 18.]
              # [17. 25.]]
  
              x.clear_grad()
  
              paddle.autograd.backward([z1, z2], [grad_tensor1, None], True)
              print(x.grad)
              #[[12. 18.]
              # [17. 25.]]
  
              x.clear_grad()
  
              paddle.autograd.backward([z1, z2])
              print(x.grad)
              #[[10. 14.]
              # [10. 14.]]
  
      """
  
      def check_tensors(in_out_list, name):
          assert in_out_list is not None, "{} should not be None".format(name)
  
          if isinstance(in_out_list, (list, tuple)):
              assert len(in_out_list) > 0, "{} connot be empyt".format(name)
              for each_var in in_out_list:
                  assert isinstance(
                      each_var,
                      (paddle.Tensor, core.eager.Tensor
                       )), "Elements of {} must be paddle.Tensor".format(name)
              return in_out_list
          else:
              assert isinstance(
                  in_out_list,
                  (paddle.Tensor, core.eager.Tensor
                   )), "{} must be Tensor or list of Tensor".format(name)
              return [in_out_list]
  
      tensors = check_tensors(tensors, "tensors")
  
      assert len(tensors) == len(
          set(tensors)
      ), "The argument 'tensors' of paddle.autograd.backward contains duplicate paddle.Tensor object."
  
      if grad_tensors is not None:
          if not isinstance(grad_tensors, (list, tuple)):
              grad_tensors = [grad_tensors]
  
          for each_tensor in grad_tensors:
              if each_tensor is not None:
                  assert isinstance(
                      each_tensor, (paddle.Tensor, core.eager.Tensor)
                  ), "The argument 'grad_tensors' of paddle.autograd.backward is invalid, it can be 'None', 'paddle.Tensor' or 'list[None/paddle.Tensor]'."
      else:
          if framework._in_eager_mode_:
              grad_tensors = []
          else:
              grad_tensors = [None] * len(tensors)
  
      if len(grad_tensors) > 0:
          assert len(tensors) == len(
              grad_tensors), "The length of grad_tensors must be equal to tensors"
  
      assert isinstance(retain_graph, bool), "retain_graph must be True or False"
  
      if framework._in_eager_mode_:
          core.eager.run_backward(tensors, grad_tensors, retain_graph)
      else:
          core.dygraph_run_backward(tensors, grad_tensors, retain_graph,
                                    framework._dygraph_tracer())
  