* modify format

* modify format

* autograd.functional passed pylint checker.

* autograd.functional: fix import errors.

* autograd.functional: fixed unit tests.

* autograd.functional minor format change

* init functional jacobian api

* finish test with dtype float32

* add float64 test case

* polish code

* use atol=1e-5 with dtype float64

* fix for ci

* set timeout for test_jacobian

* init hessian API

* save status

* polish API docstring

* modify docstring

* add utils.py

* save status

* fix dygraph double grad dtype error when calling for high differential senario

* reinvoke ci

* test_hessian.py is ok

* polish hessian API

* init vhp

* Revert "init vhp"

This reverts commit cbd4d3b66abe82b0ac10721b9eddeb7d82e0a1c8.

* add test for partial_engine.cc

* modify numerical_delta with dtype float32

* merge fix for dtype float64

* spell fix

* polish code

* rm _stop_gradient_pre_process
Co-authored-by: NJiabinYang <360788950@qq.com>

* init functional jacobian api

* finish test with dtype float32

* add float64 test case

* polish code

* use atol=1e-5 with dtype float64

* fix for ci

* set timeout for test_jacobian

* polish API docstring

* modify docstring

* remove autograd/grad api

* import grad, no_grad set_grad_enable from autograd module

* modify import no_grad_ as no_grad

* add gradients_with_optimizer api

* modify gradients_with_optimizer

* add gradients_with_optimizer api into paddle.auto.backward_mode

* add gradients_with_optimizer test case

* add doc for gradients_with_optimizer

* add doc for gradients_with_optimizer

* update 2.0 public api in all left files

* reverse device.py all list;
fix some flake8 errors

* custom python backward

* polish up the code

* polish up the code

* polish up the code.

* Fix code format and comments.

* Delete redundant files.

* add unnittest.

* edit unnittest.

* edit unnittest.

* Remove redundant header files.

* Improve coverage and remove redundant code.

* support saving for backward.

* polish code according to comments.

* Add support type for PyLayer.

* Modify the DOC.

* polish Doc.

* polish Doc.

* polish Doc.

* polish Doc.

* polish Doc.

* polish Doc.

* polish code and make the code robust.

* Modify the code format.

* add custom init grad for backward function

* add custom init grad for backward function

* handle when the grad_tensor is none

* handle when the grad_tensor is none

* fix the args type error on windows platform

* modify the args order and doc

* format code

* add grad_tensor to xpu

* modify the grad_tensor type check

* add paddle.backward api to support multi tensors gradient compute

* add paddle.backward api to support multi tensors gradient compute

* add paddle.atuograd module and backward api

* change tensor.backward func args

* modify tensor backward api

* remove create_graph intputs args

* add doc and examplex code for backward api

* when have the same tensor, throw error

* modify test Init func args

* modify the execute.Init func args in test files

* add paddle.autograd package in setup.py.in

* modify error msg, remove _run_backward method in class Tensor

* add test cases for backward api