* Support pure fp16 training for AMP API. (#29544)

* add cast ops before and after unsupported fp16 ops.

* Keep partial net in FP32 pattern.

* Support check_finite_and_unscale and update_loss_scaling for FP16 calculation mode.

* Add fp16 support for adam op.

* add multi precision attr for adam.

* Fix the bug of test_multi_precision_fp16_train UT.

* Code format for CI.

* Fix the redefine error about MPTypeTrait on windows.

* fix bugs of the _create_accumulators func in Momentum.

* fix bug when inserting post cast op.

* Add the update_loss_scaling op in allow_set of UnusedVarCheck.

* Update for ci coverage.

* Add some doc for OptimizerWithMixedPrecision.

* Fix the code style.

* Imporve the doc of `amp_init`.

* Change for fp16 testing if users have the infer program defined in separate way.

* Remove tensor copy in the update_loss_scaling op. (#29426)

* remove tensor copy in the update_loss_scaling op

* not use thrust.

* fix some cuda memory access error.

* add support for value tensor support of fill_constant Op

* Refine adam op, test=develop

* Fuse kernels together to reduce cpu time.

* Refine paddle enforce, test=develop

* Remove some comments, test=develop

* Refine code,test=develop

* Refine cuda kernel, test=develop

* Refine code according to comments, test=develop

* optimize adam speed by removing _finish_update test=develop

* fix SparseAdamFunctor param list test=develop

* Remove scale_op in expect_list of adam_op test=develop

* fix test optimizer loss assert error test=develop

* fix test optimizer loss assert error test=develop

* modify PADDLE_ENFORCE usage test=develop

* fix op_type in lamb_op.cc test=develop

* fix errors ostream format bug test=develop

* add betaPowOut in ngraph op test=develop

* fix ngraph::op api for gcc8 test=develop

* clean code test=develop

* modify struct into class test=develop

* remove code of beta1Tensor in lamb_op test=develop

* add Adam beta1/beta2 support Variable. test=develop

* replace part of the old implementation, test=develop

* restore concat op, test=develop

* update all ops implemention & delete GetDataTypeOfVar func, test=develop

Add user-friendly error message in optimizer ops to give a hint about the position sensitive problem of run(startup_program) (#19605)

* add extra error message hint in optimizer ops

* polish format & delete useless change, test=develop

* extract init judue from shape compare, test=develop

* Add LAMB optimizer

* Expose LAMB Optimizer's APIs

test=develop, test=document_preview

* Cleanup code & doc

test=develop, test=document_preview

* Update lamb optimizer's formula

test=develop

test=develop

test=develop

* wip simplify operator framework

* wip

* wip

* done test=develop

* clean test=develop

* fix test=develop

* fix deps test=develop

* fix cpu build test=develop

* fix tensorrt build test=develop

* fix tests test=develop

* fix test=develop

* fix cpu build test=develop

test=develop

* "add inplace attribute"

* "register inplace attribute"

* "change se-next model for memory-reuse"

* "fix typo"

* repick

* fix merge conflict

* "fix stupid error"

Do not use ctor

* Reduce line of codes.
* We can use virtual function for Maker now.
* The implementation does not care what maker holds, it is easier to
refactor later.

* "optimizer op support float64"

* "fix ci"

* "fix ftrl op"

* Move framework.proto to proto namespace

* Fix compile

* Fix compile

* Fix Compile

There are mainly following fixes:

- take `DeviceContext` as the template parameter of math functors and OpKernel instead of `Place`
- remove `eigen_device` interface in base class  `DeviceContext`
- remove `GetEigenDevice` interface in `ExecutionContext` and base class `DeviceContext`
- remove unused `platform::EigenDeviceConverter`
- rename `REGISTER_OP_GPU_KERNEL` to `REGISTER_OP_CUDA_KERNEL`
- rename `USE_GPU_ONLY_OP` to `USE_CUDA_ONLY_OP`

* Updating the Latex equation for Adagrad

* Fixing Latex euqations for adadelta, adam and adamax

* Support many data types of several operators

* SeqConv only support float/double

* Revert adagrad

* Adding the doc format for AdaDelta

* Updating the documentation for Adagrad, Adam and Adamax

* Updating the auc op

* Fix review comments

* Updating doc for Batch Norm

* Updating the cast op

* Updating the clip op

* Fixing review comment

* Fixing review comment:

* Small change to restart PR_CI

They are public now

* add adam op

moment1_out = beta1 * moment1 + (1 − beta1) * grad
moment2_out = beta2 * moment2 + (1 − beta2) * grad * grad
moment1_hat =  moment1_out / (1 - beta1^t)
moment2_hat =  moment2_out / (1 - beta2^t)
param_out = param - learning_rate * moment1_hat / (sqrt(moment2_hat) +
epsilon)

* fix moment 2

* Adding the Adam optimization operator

* Adding more tests for Adam op