* add recompute based checkpoints methods for large batch training
test=develop

* add append_backward_with_forward_recomputation
test=develop

* refine optimizer
test=develop

* update backward and optimizer
test=develop

* make Variable usable
test=develop

* add recompute code

* refine optimizer
test=develop

* refine addup _append_backward_ops_with_checkpoints_
1) for recompute part, just cache the grad_op_desc without appending to block
2) before appending grad_op_desc to backward part, addup_repetitive_vars, remove unused branch
test=develop

* make method private

* add recompute strategy into DistributedStrategy
test=develop

* checkpoint version3
test=develop

* remove some print information
test=develop

* remove unused sumop
test=develop

* try to fix recompute with graph building modules

* add input names to vars should be held

* add memory debug tool

* backup backward

* Fix bugs

* add backward desc for op not in any segments

* add exception info for sub_block

test=develop

* modify code style

test=develop

* modify code style

test=develop

* remove print functions

test=develop

* add API spec

test=develop
test=document_preview

* make Recompute a child class of Optimizer

test=develop
test=document_preview

* add API spec

test=develop
test=document_preview

* modify API spec

test=develop
test=document_preview

* add document for Recompute

test=develop
test=document_preview

* change API doc of Rcompute

test=develop
test=document_preview

* code cleaning

test=develop
test=document_preview

* modify API spec

* fix bugs when segments hold no element

* add testcase for Recompute Optimizer

test=develop
test=document_preview

* add test for apply_gradient, and code cleaning

test=develop
test=document_preview

* add test case for load function

* enable CI

test=develop
test=document

* add test case

test=develop
test=document_preview

* add sample code for 4 function of recompute optimizer

test=develop
test=document_preview

* update dygraph api-doc and backward api-doc, test=develop

* update dygraph api-doc and backward api-doc, update api.spec, test=develop

* update dygraph api-doc and backward api-doc, update api.spec, test=develop

* update API.spec, test=develop

* fix optimizer bug
test=develop

* prun backward ops
test=develop

* add not_been_used_vars to no_grad_set
test=develop

* Update backward.py:
     - If there is no input grad var in all outputs of previous ops, do not append this op into graph.
     - Only apply this stragety when double backward.
* Update some double backward op.
* Update sum_op to judge whether a tensor is empty by numel or IsInitialized().

Fix the following API examples:

paddle.fluid.scope_guard
paddle.fluid.backward.append_backward
paddle.fluid.cpu_places
paddle.fluid.cuda_pinned_places
paddle.fluid.cuda_places
paddle.fluid.in_dygraph_mode
paddle.fluid.CUDAPlace
paddle.fluid.CPUPlace
paddle.fluid.CUDAPinnedPlace

Support backward of backward for Relu and add a new gradient checker by comparing theoretical and numerical Jacobian. (#16862)

* Support backward of backward and a new gradient checker
* Rename decorators.py to decorator_helper.py, since Python on Windows CI has decorators package.

1. Add ReluDoubleGradMaker when register relu_grad.
2. Add a new gradient checker by comparing theoretical and numerical Jacobian.  Check double gradients by double_grad_check.

* fix some grad op desc maker
test=develop

* fix grad op desc makers
test=develop

test=develop

test=develop

* hide operator API

* update

* update api.spec

* fix merge

* fix test

* hide program APIs

* fix merge error

* update

Fix pb_protobuf2 FromString problem

Fix str and bytes problem
Fix sorted problem
Fix math problem
Fix CI problem

Revert part of a3ca4c99

* remove block api

* remove clone_variable

* hide block inner apis

* update

* fix tests

This reverts commit 4d8e8ee2, reversing
changes made to d6a9f005.