* delete legacy dygraph code in python/paddle/distributed

* refine

* isort all files

* revert conflicting files

* revert conflicting files

* revert conflicting files

* [CodeStyle][py2][U004] unecessary explicit `object` inheritance in class definition

* fix an increment

* [CodeStyle][py2][U008] remove unnecessary args in `super()`

* remove remained args

* revert changes in test_pylayer_op

* Revert "revert changes in test_pylayer_op"

This reverts commit ff185a9ae738afac3b0264f61bde6c6b7f72e7c4.

* revert some changes in example code

* update config

* re-blacken python code

* temporarily disable date and diff_py_file

* skip a format

[CodeStyle][F401] remove unused imports in python_paddle/nn_tensor_reader_tests_distributed_distribution_dataset_utils. (#46721)

* [CodeStyle] remove all future import

* revert test_error.py

* restore future import in example code

* 1. Delete some expression like 'This Op'
2. remove import numpy as np

* test=document_fix

* fix eg; test=document_fix

* fix 'import numpy' cases; test=document_fix

* fix 'import numpy' cases; test=document_fix

* fix some docs; test=document_fix

* delete raise; test=document_fix

* add some introduction; test=document_fix

* add some introduction; test=document_fix

* test=document_fix

* Fix ’note‘ format; test=document_fix

* Fix Returns of cholesky; test=document_fix

* Fix Example format; test=document_fix

* Fix det; test=document_fix

* Fix eig; test=document_fix

* Fix eigh; test=document_fix

* Fix eigh; test=document_fix

* Apply suggestions from code review;test = document_fix
Co-authored-by: NNyakku Shigure <sigure.qaq@gmail.com>

* Apply suggestions from code review;test = document_fix
Co-authored-by: NNyakku Shigure <sigure.qaq@gmail.com>

* Apply suggestions from code review;test = document_fix
Co-authored-by: NNyakku Shigure <sigure.qaq@gmail.com>

* test=document_fix

* test=document_fix

* KLDiv;test=document_fix

* norm example code; test=document_fix

* revert python/paddle/fluid/**/*

* revert python/paddle/distributed/spawn.py

* revert python/paddle/fluid/*

* fix a `Note` format

* Fix inv; test=document_fix

* Fix lu; test=document_fix

* Fix lu_unpack; test=document_fix

* Fix matrix_power; test=document_fix

* Fix multi_dot; test=document_fix

* Fix solve; test=document_fix
Co-authored-by: NNyakku Shigure <sigure.qaq@gmail.com>

* trim trailing whitespace

* fix `.cmake-format.py`

* revert npu ut changes, avoid npu ci error

* [Eager] Cast,uniform_random,assign_value use final state

* fix mistake

* fix mistake

* fix CI errors

* add dygraph test for unform

* add fp16 test case for bilinear_initializer

* use yapf to format all python file

* yapf exclude two unittests file for they rely on writing and reading file, and format will break them

* disable diff_py_file because too many diff files cause command following failed

* 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

* refactor eager flags

* fix flags error when we switch from eager to dygraph

* fix ci problem

* fix ci

* fix ci

* merge develop and fix code style

* merge develop and fix code style

* fix op test error

* fix op test error

* fix op test error

* fix op test error

* fix op test error

* merge develop

* add multinomial probability distribution
* fix categorical sample bug when logits less than zero
* fix categorical sample can't pass hypothesis test and entropy shape error bug

* add beta distribution
* add kl_divergence and register_kl api

* extend Distribution baseclass for supporting multivariant distribution and prob method

* add ExponentialFamily base class and entropy using Bregman divergence

* add dirichlet probability distribution

move distribution.py into distribution package and split into different file for better scalability (#38047)