* 1. add interface for fft;
2. add data type predicate;
3. fix paddle.roll.

* add fft c2c cufft kernel

* implement argument checking & op calling parts for fft_c2c and fftn_c2c

* add operator and opmaker definitions

* only register float and double for cpu.

* add common code for implementing FFT, add pocketfft as a dependency

* add fft c2c cufft kernel function

* fix bugs in python interface

* add support for c2r, r2c operators, op makers, kernels and kernel functors.

* test and fix bugs

* 1. fft_c2c function: add support for onesided=False;
2. add complex<float>, complex<double> support for concat and flip.

* 1. fft: fix python api bugs;
2. shape_op: add support for complex data types.

* fft c2c cufft kernel done with complie and link

* fix shape_op, add mkl placeholder

* remove mkl

* complete fft c2c in gpu

* 1. implement mkl-based fft, FFTC2CFunctor and common function exec_fft;
2. change the design, add input and output typename as template parameter for all FFTFunctors, update pocketfft-based implementation.

* complete fft c2c on gpu in ND

* complete fft c2c on gpu in ND

* complete fft c2c backward in ND

* fix MKL-based implementation

* Add frame op and CPU/GPU kernels.

* Add frame op forward unittest.

* Add frame op forward unittest.

* Remove axis parameter in FrameFunctor.

* Add frame op grad CPU/GPU kernels and unittest.

* Add frame op grad CPU/GPU kernels and unittest.

* Update doc string.

* Update after review and remove librosa requirement in unittest.

* Update grad kernel.

* add fft_c2r op

* Remove data allocation in TransCompute function.

* add fft r2c onesided with cpu(pocketfft/mkl) and gpu

* last fft c2r functor

* fix C2R and R2C for cufft, becase the direction is not an option in these cases.

* add fft r2c onesided with cpu(pocketfft/mkl) and gpu

* fix bugs in python APIs

* fix fft_c2r grad kernal

* fix bugs in python APIs

* add cuda fft c2r grad kernal functor

* clean code

* fix fft_c2r python API

* fill fft r2c result with conjugate symmetry (#19)

fill fft r2c result with conjugate symmetry

* add placeholder for unittests (#24)

* simple parameterize test function by auto generate test case from parm list (#25)

* miscellaneous fixes for python APIs (#26)

* add placeholder for unittests

* resize fft inputs before computation is n or s is provided.

* add complex kernels for pad and pad_grad

* simplify argument checking.

* add type promotion

* add int to float or complex promotion

* fix output data type for static mode

* fix fft's input dtype dispatch, import fft to paddle

* fix typos in axes checking (#27)

* fix typos in axes checking

* fix argument checking (#28)

* fix argument checking

* Add C2R Python layer normal and abnormal use cases (#29)

* documents and single case

* test c2r case

* New C2R Python layer normal and exception use cases

* complete rfft,rfft2,rfftn,ihfft,ihfft2,ihfftn unittest and doc string (#30)

* Documentation of the common interfaces of c2r and c2c (#31)

* Documentation of the common interfaces of c2r and c2c

* clean c++ code  (#32)

* clean code

* Add numpy-based implementation of spectral ops (#33)

* add numpy reference implementation of spectral ops

* Add fft_c2r numpy based implementation for unittest. (#34)

* add fft_c2r numpy implementation

* Add deframe op and stft/istft api. (#23)

* Add frame api

* Add deframe op and kernels.

* Add stft and istft apis.

* Add deframe api. Update stft and istft apis.

* Fix bug in frame_from_librosa function when input dims >= 3

* Rename deframe to overlap_add.

* Update istft.

* Update after code review.

* Add overlap_add op and stft/istft api unittest (#35)

* Add overlap_add op unittest.

* Register complex kernels of squeeze/unsquuze op.

* Add stft/istft api unittest.

* Add unittest for fft helper functions (#36)

* add unittests for fft helper functions. add complex kernel for roll op.

* complete static graph unittest for all public api (#37)

* Unittest of op with FFT C2C, C2R and r2c added (#38)

* documents and single case

* test c2r case

* New C2R Python layer normal and exception use cases

* Documentation of the common interfaces of c2r and c2c

* Unittest of op with FFT C2C, C2R and r2c added
Co-authored-by: lijiaqi <lijiaqi0612@163.com>

* add fft related options to CMakeLists.txt

* fix typos and clean code (#39)

* fix invisible character in mkl branch and fix error in error message

* clean code: remove docstring from unittest for signal.py.

* always convert numpy array to paddle.Tensor to avoid comparing numpy dtype with paddle dtype. (#40)

* always convert numpy array to paddle.Tensor to avoid comparing numpy dtype with paddle dtype.

* fix CI Errors: numpy dtype comparison, thrust when cuda is not available (#41)

1. always convert numpy array to paddle.Tensor to avoid comparing numpy dtype with paddle dtype.
2. promote floating point tensor to complex tensor ior fft_c2c and fft_c2r;
3. fix unittest to catch UnImplementedError and RuntimeError;
4. fix compile error by avoid using thrust when cuda is not available.
5.  fix sample code, use paddle.fft instead of paddle.tensor.fft

* remove inclusion of thrust, add __all__ list for fft (#42)

* Add api doc and update unittest. (#43)

* Add doc strings.
* Update overlap_add op unittest

* fix MKL-based FFT implementation (#44)

* fix MKL-based FFT implementation, MKL CDFT's FORWARD DOMAIN is always REAL for R2C and C2R

* remove code for debug (#45)

* use dynload for cufft (#46)

* use std::ptrdiff_t as datatype of stride (instead of int64_t) to avoid argument mismatch on some platforms.

* add complex support for fill_zeros_like

* use dynload for cufft

* Update doc and unittest. (#47)

* Add doc of frame op and overlap_add op.

* Update unittest.

* use dynload for cufft (#48)

1. use dynload for cufft
2. fix unittest;
3. temporarily disable Rocm.

* fix conflicts and merge upstream (#49)

fix conflicts and merge upstream

* fix compile error: only link dyload_cuda when cuda is available (#50)

* fix compile error: only link dyload_cuda when cuda is available

* fix dynload for cufft on windows (#51)

1. fix dynload for cufft on windows;
2. fix unittests.

* add NOMINMAX to compile on windows (#52)

 add NOMINMAX to compile on windows

* explicitly specify capture mode for lambdas (#55)

 explicitly specify capture mode for lambdas

* fix fft sample (#53)

* fix fft sample

* update scipy and numpy version for unittests of fft (#56)

update scipy and numpy version for unittests of fft

* Add static graph unittests of frame and overlap_add api. (#57)

* Remove cache of cuFFT & Disable ONEMKL (#59)

1. replace numpy.fft with scipy.fft as numpy<1.20 not support ortho norm
2. remove cache of cufft plans;
3. enhance error checking.
4. default WITH_ONEMKL to OFF
Co-authored-by: Njeff41404 <jeff41404@gmail.com>
Co-authored-by: Nroot <root@bjyz-sys-gpu-kongming9.bjyz.baidu.com>
Co-authored-by: NKP <109694228@qq.com>
Co-authored-by: lijiaqi <lijiaqi0612@163.com>
Co-authored-by: NXiaoxu Chen <chenxx_id@163.com>
Co-authored-by: Nlijiaqi0612 <33169170+lijiaqi0612@users.noreply.github.com>

* Add linalg.eigvals API

* pre-commit check

* Adjust code style

* Fix conflict

* Improve code style

* Modify the test code to ignore testing CUDA kernel

* Sort ouput data before checking in test code

* Set timeout value for UT

* Improve API example code to pass CI

* Fix bug for None fetch_list in Windows

* Delete grad Op

* add pinv api, test=develop
* add linalg pinv api, test=develop
* update example code, test=develop

* update equal op, input Y can be float,int,bool or tensor

* update test

* update code style

* update code style

* update doc

* update str check

* remote str

* add type check

* Support new API linalg.cond in paddle

* check code style

* check code style

* modify codes

* add docs_eng of linalg.cond

* add svd_norm for linalg.cond

* modify docs_en of cond

* add support for empty input in dynamic mode

* modify set_time of unittest

* update

* modify unittest of cond

* update

* remove cond in paddle.__all__

* pull latest codes

* merge latest codes

* update

add fill_ backward

* fix cumprod docs

* fix cumprod op docs; test=document_fix

* fix github name

* fix CI error

* fix review and CI error

* fix inf,nan error and modify unittest samples

* add unittest samples

* add unittest samples

* fix unittest error

* test=document_fix

* test=document_fix

* modify doc and add unittest samples

* fix error newline in constant

* modify doc after mentor review

* modify __all__ and doc

* modify doc

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* fix warning error , test=document_fix

* add test_cumprod_op

* Revert "add test_cumprod_op"

This reverts commit c96cf6dff5d09ae7d8cc72c1e8ae4369a153aa19.

* recommit

* add error message

* test input(x) initialize

* test use cpu

* update test code

* add test type

* add test case

* solve ci problem

* add complex case test

* add complex case test

* fix review problem

* fix conflict

* fix some docs

* change test case

* change test case

* fix review problems again

* fix docs

* fix inclusivescan bug

* init matrix_rank op, add matrix_rank CPU code and test

* add GPU kernel, remove svd_eigen.h

* add CPU kernel when tol is tensor

* add cpu and gpu code when tol is tensor

* fix CI-ROCM error

* add matrix_rank API describe, fix PR-CI-Py3 error

* fix PR-CI-Windows error, add matrix_rank API test

* delete useless comments

* fix review

* add my code in svd_helper.h

* update doc commets

* remove spaces

multiply supports bool  

* fix scatter_nd_add doc, test=document_fix

* update
test=document_fix

Co-authored-by: Nroot <root@bjyz-sys-gpu-kongming9.bjyz.baidu.com>

* where op add broadcast, when x_shape == y_shape, and x_shape != cond_shape

* add static api tests, and delete debug codes

* Add SVD Op and it's GPU and CPU kernel

* Remove CUDAPlace in test_svd_op, make the test available in CPU package

* modfity the file

* fix windows bug/ fix ROCM / fix test timeout

* for pass the CIs

* improve error report

* for code review

* some modification to test_svd_op

* change python code style

* expose the svd interface for document

* support setting linewith when printing tensor

* fix ut

* refine code

* update comments

* use small precision since windows/linux has different ramdom value

* fix typo

* adjust parameter order for consistency

* Support append method and initialized value for List in ControlFlow

* polish error msg and en doc

* fix code style

* Enable BF16 for creating global tensor and reduce_mean.

* Functional test with small model.

* Fix typos in english docs for diag and diagflat.

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* add unique_consecutive_op

* remove unity build

* add unique_consecutive op

* add unique_consecutive op

* add enable static

* add noqa

* add space line

* add default case.

* add comma

* add space line

* modify unique_consecutive unittest

* optimize ut coverage

* rebase develop

* improve coverage

* update en docs

* update en docs

* update en docs

* update en docs

* update en docs

* update en doc

* OP dot: refactor CPU kernels and get better loop performance.

* Minor fix on code format.

* Fixed minor errors.

* Add new API: einsum

* Update the Einsum unit test.

One case failed with matmul_v2, where the dtype is int64:

a = np.arange(2 * 3 * 1).reshape(2, 3, 1)
b = np.arange(1)
paddle.einsum("...i, ...i", a, b)

* Test cases in test_einsum test floating point dtypes only.

As of now Paddle only supports float/double dtypes in matmul, which is
one of building blocks of this Einsum implementation. We decide not to
test einsum against other dtypes.

* Polish format.

* More formatting.

* Format...

* Einsum: improve test coverage.

* Einsum: bug fixes and more testcases for testing error messages

* Einsum: fix format..

* Einsum: fixed typo and format.

* Einsum: format again...

* Einsum: applied suggested changes.

* Einsum API: improve API documentation.

* Einsum API: apply suggested changes.

* Einsum API: Add dygraph only note.

* Einsum API: Add dygraph only note.

* Einsum API: fixed unittest.

* support bool dtype for paddle.sum

* cache core.ops, test=develop

* refine, test=develop

* opt dygraph python code, test=develop

* refine, test=develop

* opt dygraph python API, test=develop

* Fix unbind bug in manipulation.py