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

* add nll_loss yaml

* fix nll loss

* fix nll loss bug

* fix bug

* fix bug

* fix infrt problem
Co-authored-by: Nxiongkun <xiongkun03@baidu.com>

* support pinned, test=develop

* support async_write, test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop

* refine,test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop

* refine, test=develop

* [ControlFlow] Fix contrib API bug in while_loop

* format code

* change vjp to paddle.grad

* use grad and gradients api

* fix preprocess for x

* fix a bug, val_and_grad should return a Tensor

* detach value and grad to avoid assign error
Co-authored-by: Nlevi131 <limaolin01@baidu.com>

* fix inplace fill_ and zero_ API

* add eager unittest

* change inplace_version checking log

* fix

* support C_ops assign

* open unittest

* fix clone

* [Eager]Enhance eager_trace_op logic to support Optimizer Op

* fix AsDispensable

* add interploate cpu kernel

* fix nullptr bug

* add interpolate gpu kernel

* fix unit test error

* remove raw kernels

* add cuda kernel impl

* add infermeta

* recover accidentally deleted kernels in interpolate op

* fix grad x_grad name error

* remove interpolate_v2_op.h

* rm unused codes

* fix xpu build error

* fix build error

* fix namespace error

* add register header for nup

* fix infermeta error

* modify by review

* add the missing args in test_trt_convert_nearest_interp_v2

* add notes for quantile UT

* Supoort quantile in static-mode and add UT

* support multi_layer of bilstm,*test=kunlun

* support multi_layer of bilstm, *test=kunlun

* support multi_layer of bilstm, *test=kunlun

* support multi_layer of bilstm, *test=kunlun

* add yaml for ele_max ele_min

* fig

* push

* xxx

* [Refactor] refactored eager_gen.py PR #2

* [DoubleGrad PR #1] Decoupled code generation logics for Dygraph ForwardFunctions and GradNodes

* Fixed minor issue

* Adjusted logics of GenerateNodeCreationCodes and GenerateForwardDefinition

* Fixed issues

* Supported higher-order grad node generation

* [DoubleGrad PR #4] Supported higher-order GradNode generation

* [DoubleGrad #4] Bug Fixes to Double Grad Node Generation

* Fixed yaml typo

* Fixed yaml typo

* fixed minor issues

* Fixed minor issue

* back fl

* delete ssl cert

* .

* make warning

* .

* unittest paral degree

* solve unittest

* heter & multi cloud commm ready

* .

* .

* correct py36 import error

* correct py36 import error

* correct py36 import error

* correct py36 import error

* add several yaml

* polish strided slice kernel & add yaml

* reorder yaml

* add several yaml

* revert yaml config change

* resolve conflict

* Update test_strided_slice_op.py

* fix error; test=develop

* update

* close some yaml

* fix backward attrite error; test=develop

* add div test

* polish code; test=develop

* update

* update

* fix bug

* update bitwise code; test=develop

* update

* update

* fix some bug

* update

* revert cmakelist

* fix optional bug;

* fix bug

* fix bug;

* add backward test

* open bn

* update

* update

* revert eager_gen

* polish code

* fix topk error

* update

* update

* fix bug;

* move label smooth, nll loss

* revert topk

* fix topk label smooth bug;

* remove batch_norm

* remove topk

* change flip infer meta

* fix flip bug

* update yaml

* close abs

* fix histogram bug

* fix histogram bug

* add abs

* fix histogram kernel

* remove expand

* rename scalar_array to int_array

* update cmake

* fix conflict

* remove useless log

* [Yaml] Migrate sqrt/square/reciprocal yaml

* clean file

* fix unittest error

* Enhance test_eigh_op

* Use eigen decomposition to validate eigen values and vectors
* Fix that TestEighBatchAPI didn't run the batched input

* Enhance test_eigvalsh_op

* Align cusolver tolerance to validate eigenvalues
* Fix that BatchAPI didn't run the batched input

* Add abs for |d_ref|

* Remove comment

* add multiclass_nms3 converter

* add flatten2,reshape2,squueze2_trt_fuse_pass  test cast

* add flatten2,reshape2,squueze2_trt_fuse_pass  test cast

* add flatten2,reshape2,squueze2_trt_fuse_pass  test cast

* [New API]: miminize_bfgs and miminize_lbfgs

* modify for python module call correctly

* add functional package, add error raise in static_graph, change assign to set_value

* unify static_graph and dygraph, fix bug when x or H0 is float64

* now only accept input is tensor, put check args in utils.py, put exception test together

* temp

* add more detailed algorithm illustration and comment, reduce test case to limit test time in 15s

* change in_dygraph_mode to in_dynamic_mode

* fix bug of sample code; reduce test case to reduce test time

* change dir to incubate

* fix load bug and add distributed strategy from pslib

* add unittest

* use cvm config

* trainer and worker config

* add unittest

* add unittest

* add test

* code style

* fix dependency of fused optimizer

* add ut

* no

* fix operator summary table

* update unit test

* add random varaiable transformations API for paddle's distribution package

* add TransformedDistribution API for paddle's probability distribution package

* add random variable transformation unitests for static graph

* replace math.prod which not support python3.7 with functools.reduce

* add Independent and TransformedDistribution distribution

* add unittests for constraint

* fix typo and AffineTransform sample code error

* add mean,variance,rsample abstract method for Distribution