* Add pure fp16 training with master weights. (#27712)

* add the weight decay func for the momentum op

* Add the multi_precision function in Momentum Optimizer.

* Make sure that the initial value of master weights are same with the fp16 weights.

* add static loss scaling.

* add the rescale_grad function in the pure fp16 training.

* use the original momentum updating method.

* Polish some codes, such as variable names.

* add docstring for apis.

* update the var creation details of _create_master_weight.

* not modify codes about imperative momentum updating.

* Fix the error of test_dist_sparse_tensor_load_momentum UT.

* add unit test for multi precision fp16 training.

* add more unit tests for CI.

* Use lower threshold values for allclose comparing in test_multi_precision_fp16_train UT.

* refactor momentum op to combine weight_decay (scale op and sum op)

* fix sgd/momentum/dpsgd/rmsprop error message

* 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

test=develop

test=develop

* wip

* wip

* wip

* wip for test

* add fp16 tests test=develop

* fix cpu build test=develop

* fix test=develop

* fix py3 tests test=develop

* fix lr_scheduler dtype test=develop

* fix test=dvelop

* test fix ci compile test=develop

* fix build and merge test=develop

* fallback momentumop change to general test=develop

* make fp16 lr schedule simple test=develop

* fix ut test=develop

* fix tests test=develop

* remove fp16 learning rate cast test=develop

This reverts commit 3d750f9c.

* wip

* wip

* wip

* wip for test

* add fp16 tests test=develop

* fix cpu build test=develop

* fix test=develop

* fix py3 tests test=develop

* fix lr_scheduler dtype test=develop

* fix test=dvelop

* test fix ci compile test=develop

* fix build and merge test=develop

* fallback momentumop change to general 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

Fix code to support cpplint syntax check

test=develop

* fix nccl2 lars dist support

* put lars in momentum op

* add tests lars

* fix ci

* fix cpu kernel

* soft warning

* remove lars in test_recognize_digits.py

* move to another op

* add file

* update api.spec test=develop

* update test=develop

* fix api.spec test=develop

* wip

* wip, finish grad merge ops

* wip, finish graph build

* wip test running

* work on 1 gpu

* workable version

* update

* fix tests

* fuse broadcast op

* fix compile failed

* refine

* add batch merge test mnist

* fix CI test=develop

* fix build

* use independent bn params for batch merge test=develop

* update api.spec

* follow comments and for test

* wip

* refine tests test=develop

* follow comments test=develop

* remove startup bn modify test=develop

* follow comments test=develop

* fix merge test=develop

* add check for opt op

* fix opt op
test=develop

* fix test fail
test=develop

* fix optimization doc
test=develop

* test=develop

* Fix serious bug in nesterov momentum optimizer.

* Fix attribute naming for momentum_op

* Fix minor typo in comment

* Fix attribute name

* Fix names in test_optimizer

* Fix python wrapper

* Changing learning rate from attribute to input(float)
* Removing obsolete code

Fix #3902