This PR supports linalg.solve calculation for linear algorithm module of Paddle. One may call paddle.linalg.solve to use it.

This PR implements the kernel of "eigvals" OP with the Lapack library, which has a better performance than the previous Eigen library.

cherry-pick #35812，修复Eigh OP

* Pass compat of conv_transpose_bias_mkldnn_fuse_pass

* Fix a bug of strided_slice op, about the axes parameter access memory out of bounds

* Fix a bug of transpose op, about accessing memory out of bounds of the perm param

* op:transpose_op supports bool type

ATT, cherry-pick #35690

* 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 beam_search npu op

* fix CMakeList and add unittest

* fix bug of beam search npu op

* fix unittest

* let input ids become int64

* set output ids to int64_t

* delete check_dygraph

* fix beam_width=1

* 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

* 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

* merge CMakeList.txt manual

* add platform for changethreadnum

* repair some bugs according to make error

* do nothing just flush CI

* forget change thread num

* add inplace_atol param for check_output_with_place

* Windows

* std:min and std::max should be change because of windows

* stablize depthwise conv

* clean commend

* add maxunppol2d op, test=develop

* fix typo, test=develop

* fix unpool unitest, test=develop

* fix unpool code-example, test=develop

* fix for unpool_op_unittest,test=develop

* fix example code, test=develop

* add noqa:F401, test=develop

* fix converage, test=develop

* fix unitest for unpool, test=develop

* rename unpool2d to unpool, test=develop

* rename unpool2d to unpool, test=develop

* dygraph support more ctc grad scale

* scale for 1.x

* fix unitest

* fix unitest

* format code

* fix unittest

* fix log info

* unittest cov

* fix format;notest,test=cpu,coverage

* skip ctc_loss egs;test=cpu

* warpctc grad cov;test=coverage

* add dygraph test;test=coverage

* format;test=cpu,coverage

* format;test=cpu

* add api compat;test=cpu

* add cpu test

* rename

* rename

* fix

* fix test

* format

* eigen cpu

* eigen gpu grad pass

* cuda gpu pass

* format

* fix ci

* Fix safety-bug of functional.linear

* Fix safety-bug of functional.linear

* Fix safety-bug of functional.linear

* Fix safety-bug of functional.linear

* add int16 kernel for lookup_talbe and dequantize_abs_max op

* Use CBLAS for SelectedRows elementwise add operation. It's faster.

* template compilation fix

* reverted template compilation fix

* slimmed template compilation fix
Co-authored-by: NAdam Osewski <adam.osewski@intel.com>

* Add oneDNN AXPY handler.

* Add fallback for small tensors.

* Fix ifdefs

* Remove unnecessary namespace prefixes and add missing headers.

* Guard handler_axpy with proper ifdefs.

* Compilation of this function is possible only when Paddle is not build
with CUDA nor HIP.

* Move AXPY handler code to separate files.

* Use oneDNN AXPY handler in SGD op.

* Use axpy handler only when Paddle is built with oneDNN.

* Add test for SUM BF16 with big rows.

* Fix SFINAE rules for elementwise_add_to.

* Add test case for SGD with big rows.

* update

* update
Co-authored-by: NAdam Osewski <adam.osewski@intel.com>

* replace and remove complex64/128 types in custom OP and other files

* fix custom_tensor_test fail bug

* fix custom_conj_test fail bug

* fix dispatch_test_op build fail bug

* modify matmul Op to complex template types

* remove complex64/128 head file

* optimize OP's compilation time, test=develop

* add more op and run ci test, test=develop

* CUDA Kernel register in cc file, test=develop

* fix macros, test=develop

* fix undefined symbol error, test=develop

* fix compilation error and undefined symbol, test=develop

* fix compilation error on Windows, test=develop

* fix compilation error on Windows, test=develop

* modify conj, real, imag OP to complex template

* replace with complex template to dot Op

* replace with complex template to Abs Op

* add support for complex64 and complex128

* add complex template file

* add numtraits for complex template

* add complex template type register

* modify specify template of complex

* modify specify template of complex

* modify specify template of complex

* modify specify template of complex

* make TensorCheckerVisitor support complex type

* fix operator= error

* add complex template

* add complex template type

* add complex template type to pyarray transform

* add complex template type to pyarray transform

* remove complex type for dlpack register

* set dlpack supprot complex type

* set dlpack supprot complex type

* set dlpack supprot complex type

* remove explict for complex constructor

* add complex unit test file

* fix test_unpool_op

* fix test_inplace_addto_strategy

* fix test_conv2d_fusion_op

* fix test_imperative_lod_tensor_to_selected_rows, test_imperative_selected_rows_to_lod_tensor

* fix test_dot_op

* fix test_correlation_op

* fix tracer

* fix test_memcpy_op

* [OPs] Bug fix, fix the segment mean for illegal syncthreads usage.

* fix matrix_inverse_op with rocm

* fix matrix_inverse_op with rocm

* fix matrix_inverse_op with rocm

* fix matrix_inverse_op with rocm