* Some changes for Adam profiling

* Adam optimization: initial Eigen optimization

* Eigen Adam: flavour of adam can be chosen

* Eigen Adam used for CPU by default. Plain Adam used for GPU

* Eigen Adam: missing call to the Eigen functor added

* Eigen Adam: revert changes in benchmarks

* Eigen Adam: typo corrected

* "Need to re-design LoD "

* "add lod design"

* "fix lod gpu ptr pointer"

* "removed commented code"

* "fix CI"

* "remove set lod in pybind"

* "fix style check"

* "fix CI"

* "fix long type template error"

* "pybind reorder to use Place"

* "fix ci"

* "fix ci"

* fix ci

* "sperate as a new file"

* "fix CI"

* "fix ci"

* small fix

* "add test"

* "fix adam op"

* "fix lstmp op"

* "fix adam op"

* "follow comments"

* "fix ci"

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`

* Support many data types of several operators

* SeqConv only support float/double

* Revert adagrad

* 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

* Implementing the Adamax optimizer step operator
* Adding unit tests for adamax_op

* Changing learning rate and time step to inputs from attributes

* Changing learning rate and time step to input(tensors)

* Making the Adamax operator conform to naming convention

* Removing Tensor<float> from comments

* Rectifying the Adamax implementation

* Changing Unit Test values and adding comments

* Changing Unit Test to test multiple steps

Fix #3902

* use operator context

* optimize code

* update net infershape

* update InferShape

* disable override InferShape(scope) in OperatorBase

* change InferShapeImpl to InferShape

* add template to OperatorContext Input/Output

* merge Input InputVar, Output OutputVar

* change Inputs to MultiInput

* fix conflict

* fix MultiInput bugs and add unit test

* rename KernelContext to ExecutionContext

* clean code

* change InferShape to protected

* fix template bug

* refine code

* use InputVar instead of Input<Variable>

* typo

* optimize code

Make implement an operator less noisy.

* a simplest SGD op

* add inputs

* add ut for multiple inputs

* fix AddToLayer

* op_desc -> op_proto

* CreateArgumentOffsetMap -> CreateInOutOffsetMap

* move CreateInOutOffsetMap from OperatorBase to op registry

* arg_idxs_ -> in_out_idxs_

* Convert `op` --> `operators`
* Remove AddType in OpProtoMaker, because type is part of registry.
* Rename CPU_OR_GPU --> DEVICE_TYPE in registry macro.