* add regularation and Nesterov for mergerd_momentum

* refine unittest for use_nesterov attr

* refine op check

* refine code

* fix bug

* refine code of regularization_flag

* delete useless code

* [Auto Parallel] elastic support auto parallel re-launch

* [Auto Parallel] elastic support auto parallel re-launch

* fix ci issue

* fix ci issue

* fix rank mapping unittest

* fix rank mapping unittest

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* fix ci issue

* Refactored eager legacy namespace

* Fixed namespace issues

* Enabled performance benchmark tests for Eager Dygraph

* Protected CUDA tests with macro

* Fixed dependency issues for windows-ci

* add diff op, test=develop

* rm some notes, test=develop

* update diff doc

* update sample code

* fix diff api params and example code, test=develop

* modify for wincheck-inference case

* modify according to zhouwei's comment

* open with_trt and block failed unittests in windows

* test

* support data_format='NHWC' for prelu channel mode

* [Auto Parallel]  Add the unified cluster representation

* [Auto Parallel] Add the graph class for physical mapping

* [Auto Parallel] Add the simple physical mapper

* Set the timeout of the mapper

* Merge the upstream develop unittests cmake files

* Fix a bug of the process group

* Remove mapper unittest from platforms which is not GPU

* Move the instantiation of process group after resharding

* Add the local id for devices

* Update the rank mapping format

* Add some comments

* Remove the related files about mapping

* Update the unittest for auto mapping

* Remove unused rank_mapping unittest

* Improve the unittest coverage

* Improve the unittest coverage

* add scope_guard

* 1. fix control flow cases 2. fix calc_gradient

* add pten reduce kernel

* add reduce_sum kernel

* update attribute args and order

* make out dtype undefined

* fix empty input error

* merge develop branch

* rename sum as reduce function

* rename sum as reduce function

* fix reducekernelImpl args error

* add reduce cuda kernel

* modify dims type to const &

* remove unsed log

* fix reduce_all out eigen function error

* remove unused codes

* add the missing sum api define and testcase

* merge develop branch

* fix sum test axis value error

* replace pten mean kernel with reduce_mean

* revcover meam cuda to original implement

* add expand_v2/expand_as_v2 for kunlun

* update expand_as_v2

* update expand_as_v2

* support float16/bool

* update xpu.cmake

* add cuda implement of cast kernel

* remove bfloat16 when defined paddle_with_hip

* amp.decorate optimizers set to None is ok

* refine unittest

* add unittest and refine example code

* refine unittest

* suport fetch lodtensor array, test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop

* auc temp

* cuballocator

* code format

* code format

* 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>

Co-authored-by: NChen Long <1300851984@qq.com>