* [xdoctest] reformat example code with google style in `paddle/tensor/math`

* preview, test=docs_preview

* scale, test=docs_preview

* stanh, test=docs_preview

* multiplex, test=docs_preview

* pow, test=docs_preview

* max, test=docs_preview

* others..., test=docs_preview

* update trunc example code, test=docs_preview

* add int32/int64 for outer/matmul Kernel.

* fix by comment.

* fix by comment

【inplace api】batch add inplace api paddle.log_, paddle.i0_, paddle.nn.functional.leaky_relu_... (#55576)

* batch add inplace api

* add inplace test

* add activation inplace

* fix test

* remove atan2 ge, gt, le, lt, nq

* remove atan2 ge, gt, le, lt, nq

* fix windows ci error

* rerun ci

* fix typro

* fix bugs

---------
Co-authored-by: Nzhangrui34 <v_zhangrui34@baidu.com>

* add paddle.static.setitem

* add some help doc

* support setitem

* support machanism

* add more unittest

* remove usless code

* raise error in static setitem

* fix d2s UT

* remove static only for both-used code

* fix bool set_value in static, fix set_value_op UT

* fix unittests

* [May case some error]: remove inplace-version check

* add two test case for dy2st

* fix function in vision

* fix dy2st setitem support, refine UT case

* fix slice in static_mode

* add ParametersMap

* remove pop

* modify place

* [fix]: variable is also a tensor

* rewrite some ut & remove slicetransformer in dy2st

* solve error in static-mode

* fix ut

* return a result for set_array_write

* fix test_set_value_op_xpu

* code is different in dynamic / static mode

---------
Co-authored-by: NAurelius84 <zhangliujie@baidu.com>
Co-authored-by: NNotHaozi <zhangmenghao@baidu.com>

* batch add inpalce api

* fix inplace fn generate

* add test for  new inpalce api

* fix typro

* fix typro

* fix typro

* fix test error

* fix atan2

* remove atan2

* auto genereate inpalce api

* fix inplace generate fn error

* fix windows error

* fix test error

* fix test error

* fix windows ci error

* fix test error

* fix test_error

* fix test error

* fix eigen aliasing error in inplace

* remove elementwise_pow inplace

* fix doc error

* fix test error

* add more data type for all/any.

* remove xpu fix.

* add test unit.

* fix typename name.

* fix output data type.

* DOCS: Adding imformation about datatype in math.py

* replaced uint16 with bfloat16.

* add lerp bf16 support

* fix bug

* Update test_lerp_op.py

modify the input dtype

* modify the test_lerp_op.py

* Update test_lerp_op.py

* fix bug of import

* add user_defined_grads

* Update test_lerp_op.py

* fix bug of grad

* fix bug of grad

* fix bug of grad

* add the check for bfloat16 dtype

* add clone for inpalce

* fix name

* add inplace pow

* fix typro

* add note

* fix typro

* fix typro

* fix bug

* fix test error

* add type error test

* adjust indentation

* fix for log xxx

* add int32/int64 for cpu/gpu; add float16/bfloat16 for cpu forward

* fix docstring

* fix bug

* fix bugs

* fix bugs

* fix bugs

* fix bugs

* fix bug

* using cast

* fix test

* fix api

* fix other bugs

* fix ci bug for not using dygraph guard

* add bfloat16 test

* fix ut

* bf16

* bump ruff to 0.0.271 and update config

* exclude third_party

* bump ruff to 0.0.272

* refine config

* add ldexp api

* fix ldexp

* Update math.py

fix math.py

* rewrite the ldexp

* Simplify ldexp implementation

* fix codestyle

* Update math.py

* Update math.py

* modify the test_ldexp.py

* fix the input bug of np.ldexp

* fix the bug of np.ldexp in windows

* modify the ldexp function and add the dtype check of output

* Update test_ldexp.py

* fix the dtype

* fix codestyle

* Update python/paddle/tensor/math.py

add note for code description
Co-authored-by: Nzachary sun <70642955+sunzhongkai588@users.noreply.github.com>

---------
Co-authored-by: Nzachary sun <70642955+sunzhongkai588@users.noreply.github.com>

* feat: added polygamma init code

* feat: added polygamma unittest code

* test: added more test cases

* refactor: added forward impl

* refactor: added backward impl

* test: updated cases

* refactor: updated test cases

* refactor: added more case and fixed some bugs

* test: updated ref func

* refactor: updated code style

* refactor: move the code

* refactor: updated test

* refactor: updated test

* docs: updated en doc
Co-authored-by: Nzachary sun <70642955+sunzhongkai588@users.noreply.github.com>

* docs: updated math eq

---------
Co-authored-by: Nzachary sun <70642955+sunzhongkai588@users.noreply.github.com>

* floor div support float/double/bfloat16/float16

* add ut

* fix bug

* fix fft.ifftshift for floor_divide upgrade

* fix comment

* fix bugs

* fix bug

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* fixed cyclic reference that caused patial import

* fixed bad change

* fix bad import

* fix bad import

* fix bad import

* fix ut failed caused by change in_dynamic_mode

* fix ut failed caused by change in_dynamic_mode

* fixed usage of in_dynamic_mode() or in_dygraph_mode()

* revert python3 to python in .pre-commit-config.yaml

* fix merge conflicts

* add meshgrid,expand_as, prod and grad bf16 kernel

* fix bf16 for optest

* modify code style

* fix amp test

* Add i1 and i1e op

* resolve merge conflicts

* added base code for i0 and i0e

* added grad base code for i0 and i0e

* added i0 and i0e python code

* added ops and backward yaml config

* added i0 and i0e cpu kernel, but not test.

* added i0 and i0e code and unitest files

* added test files

* added i0/i0e gpu implementation code

* updated code style

* updated code style

* fixed unitests code

* updated i0 with eigen3

* fixed bug and added more test cases

* refactor: fixed static graph bug

* refactor: removed i0 and i0e from op_compat

* refactor: updated code style

* refactor: updated op_compat.yaml

* refactor: updated op_compat.yaml

* refactor: fixed op name mapping and optimize unittest case

* refactor: manually implement i0 / i0e

* refactor: added grad kernel for i0 / i0e,didn't finish

* Update math.py

* refactor: added equation to doc in English and added comments for computing i0 / i0e gradient

* refactor: removed eigen implementation

* refactor: finished i0 / i0e cpu and gpu op

* refactor: updated code style

* fix: find  a bug but not fix

* fix: incorrect unittest cases

* update: updated code style and remove my file

* update: updated unittest case

* fix: fixed sign error

* fix: fixed mistakes when merging

* refactor: updated code style

* refactor: remove unused code

* refactor: updated code style

* add logaddexp

* update

* Add addmm tests

* Fix code

* Fix some problems in Paddle english instruction doc files.

* fix some new questions

* fix cn doc problems, test=document_fix

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* fix doc erros, test=allcase

[Zero-Dim] support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy, test=allcase (#52850)

* [Zero-Dim] support output 0D for is_empty/as_complex/, test=allcase

* [Zero-Dim] support output 0D for is_empty/as_complex/, test=allcase

* add test case

* modify dot/metric.accuracy/static.accuracy/static.auc

* modfiy inner/tensordot bug

* test 9 api

* [Zero-Dim] support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy, test=allcase

* fix bug

* support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy

* code style

* fix bug

* fix test_dot_op bug

* fix accuracy bug

* fix bug

* fix bug

* fix bug

* fix bug

* codestyle

* fix dot bug

* fix dot bug

* fix dot bug

* code style

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* modify code

* [AMP OP&Test] Add check_dtype for some API (part 2)

* fix ci

* fix ci

* [AMP OP&Test] Add check_dtype for some API (part 1)

* fix

* Add digamma, dirichlet tests

* Fix code

* support uint16 python op in d2s

* convert uint16 -> bfloat16 in docstring

* [AMP OP&Test] Support fp16&bf16 in reduce_max