Enhance vjp/jvp/Jacobian/Hessian API for supporting dynamic, static graph and batched, unbatched mode (#40692)

* modify vjp/jvp for both dynamic and static graph

* enforce jacobian class for supporting first/last batch

* add unittest for jvp, jacobian withlast batch, jacobian with first batch

* fix the incorrect shape when multi-index Jacobian

* enforce Hessian class for supporting dynamic graph

* add Hessian class unittest

* bugfix, jvp double_backward_trick zeros_like return stop_gradient=True in static graph

* add API beta warnnings

* add white_list for cuda11.x ci windows.

* optimize some code snippets and documments

* set unittest timeout to 100 seconds

* move vjp,jvp,Jacobian,Hessian to incubate

* fix vjp,vjp import path of sample code

* fix code style error of augtograd/__init__ file

* Supported Complex2Real Conversion for Eager Dygraph

* Supported Complex2Real Conversion for Eager Dygraph

* Enabled complex type promotion test for matmul_v2

* pylayer, test=develop

* Fix CI issues

* Support initializing specific grad tensors to zero for selected operators

* finish forward, test=develop

* create grad node finish, test=develop

* Merged adj_edges_ with GradSlotMeta

* Fixed monir issue

* backward finish, start dbg, test=develop

* Adjusted num runs

* Recovered Eager performance tests configurations

* Recovered Eager performance tests configurations

* finish, test=develop

* polish, test=develop

* polish, test=develop

* refine, test=develop

* eager, test=develop

* Adjusted performance tests configurations

* Fixed Minor Issues with performance tests

* [Phi] Fix macro name typo

* support set_materialize_grads, test=develop

* suppotr mark_non_differentiable, test=develop

* support once_differentiable, test=develop

* refine, test=develop

* refine, test=develop

* Moved out Edge from GradSlotMeta

* Fixed issues from merge

* Fixed typo

* Addressed review comments

* Fixed merge issues

* Fixed minor issues

* Fixed minor issue

* refine, test=develop

* refine, test=develop

* refine, test=develop

* Fixed major issues and enabled auto_prune test cases

* Fixed issues from merge

* refine, test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop
Co-authored-by: Njim19930609 <jim19930609@gmail.com>
Co-authored-by: NAurelius84 <zhangliujie@baidu.com>

* refactor eager flags

* fix flags error when we switch from eager to dygraph

* fix ci problem

* fix ci

* fix ci

* merge develop and fix code style

* merge develop and fix code style

* fix op test error

* fix op test error

* fix op test error

* fix op test error

* fix op test error

* merge develop

* eager, test=develop

* fix bug, test=develop

* eager, test=develop

* merge legacy to fluid

* eager, test=develop

* eager, test=develop

* Refactor TensorAdd func by template and remove gradient_accumulation in eager

* Remove needless target name

* eager, test=develop

* eager, test=develop

* Use overload instead of template

* Remove legacy code

* Remove legacy code

* selectedrows, test=develop

* Remove DataType test

* eager, test=develop

* eager, test=develop

* support gan, test=develop

* Using Tensor directly instead of using EagerTensor

* support gradient_accumulation

* make test_imperative_lod_tensor_to_selected_rows longer

* make test_imperative_lod_tensor_to_selected_rows longer

* refine code

* ptb, test=develop

* Rename all EagerTensor to Tensor

* Rename some EagerTensor to Tensor

* rename EagerTensor to EagerVariable

* eager, test=develop

* eager, test=develop

* eager, test=develop

* eager, test=develop

* add more test

* eager, test=develop

* Support copiable selected rows and merge develop

* save load, eager, test=develop

* save load, eager, test=develop

* refine, test=develop

* remove useless _set_value method

* refine, test=develop

* refine, test=develop

* revert static_runner, test=develop

* EagerTensor to Tensor, test=develop

* refine, test=develop

* refine, test=develop

* clear grad, test=develop

* merge, develop

* merge, develop

* merge, test=develop

* merge, test=develop

* Support quant and part of slice

* support legacy static save

* extend slim tests time

* remove imperative on inference

* remove imperative on inference

* merge develop

* fix typo

* fix typo

* split slice related code into 2 part for imperative and eager

* split slice from inference

* split slice from inference

* fix test_tensor_register_hook

* support custom op in eager mode

* fix inference deps error

* split eager utils from custom operator

* fix type match

* fix typo
Co-authored-by: NWang Huan <wanghuan29@baidu.com>
Co-authored-by: NWeilong Wu <veyron_wu@163.com>
Co-authored-by: Nwanghuancoder <wanghuancoder@163.com>

* fix pylayer problem with amp

* add ut

* refine code

* [autograd] static Jacobian pass tests.

* [autograd] apply CR suggested changes.

* [autograd] more tests.

* [autograd] add CPUPlace in tests.

* [autograd] bug fixes.

* [autograd] reformatted.

* [autograd] adding Hessian, in progress.

* [autograd] Hessian passes. A double grad bug fixed.

* [autograd] fix renaming conflict in double backward pass.

* [autograd] polish test.s

* fix a bug when using brackets

* debug for ci

* [autograd] fixing Hessian test.

* polish format.
Co-authored-by: Nlevi131 <83750468+levi131@users.noreply.github.com>
Co-authored-by: Nlevi131 <limaolin01@baidu.com>

* [autograd] static Jacobian pass tests.

* [autograd] apply CR suggested changes.

* [autograd] more tests.

* [autograd] add CPUPlace in tests.

* [autograd] bug fixes.

* [autograd] reformatted.

* add control/status API, test=develop

* fix import error, test=develop

* add is_grad_enabled unittest, test=develop

* add code comment for example code and API, test=develop

* add checking for type, test=develop

* add api description, test=develop

* fix docs index_en, test=document_fix

* fix doc of is_floating_point, test=document_fix

* native commit for triple grad of sigmod

* Updated unittests files

* init functional jacobian api

* Updated trible_test func

* Updated gradient_checker & test_script

* 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

* fix dygraph grad to support high differential

* polish API docstring

* Updated gradient checker and some related files

* fix double grad strip error for high differential

* fix double grad strip error for high differential

* Add Sigmoid triple grad tests

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

* Updated triple grad teses func

* Use np.random to initialize ddx

* Updated triple_grad_check func

* add todo for gradient checker and refine some comments

* remove additional code

* add test for warnging in backward.py

* format python code

* support multi input in triple gradient checker

* Add matmul triple grad kernel

* Updated comments of TODO

* Supported some special tests

* Change code-format to follow CI std

* Updated gradient_checker.py

* Fix conflicts

* Removed unnecessary printing log

* Change code style to follow CI std

* support batch in jacobian and hessian

* add batch jacobian and batch hessian

* Add batch_jacobian test, draft version

* [New features] Add elementwise_mul triple grad kernel (#37152)

* Add elementwise_mul triple grad kernel

* Removed InplaceInferer and polished code

* Add numerical_batch_jacobian,numerical_batch_hessian and tests

* Support batch_jacobian and batch_numerical

* Use pre-commit to check code format

* Update doc, polish code, add unit test

* Reset the TIMEOUT properties of test_jacobian to pass CI
Co-authored-by: Nlevi131 <limaolin01@baidu.com>
Co-authored-by: NJiabin Yang <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

* 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.

* init vhp

* finish vhp API logically

* add test for partial_engine.cc

* modify numerical_delta with dtype float32

* merge fix for dtype float64

* spell fix

* save status

* polish code

* rm _stop_gradient_pre_process

* save status

* add example for vhp interface

* add _compute_numerical_vjp and _compute_numerical_vhp

* test is ok

* vhp is ok

* add testVHPFloat64

* modify for comments

* modify format

* modify format

* save status

* test_vhp is ok

* finish code polish

* small modify for v is None
Co-authored-by: NJiabinYang <360788950@qq.com>

* 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.

* 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