* refactor matmul directory in pten

* fix merge conflict

* add dot_grad kernel

* add dot_grad kernel in pten

* add matmul_grad kernel

* update the code

* delete useless code in fluid

* fix some bug of running matmul grad kernel

* fix merge conflict

* refactor some code

* refactor code

* add new API: paddle.linalg.triangular_solve

* add new API/OP: paddle.linalg.triangular_solve

* add new API/OP: paddle.linalg.triangular_solve

* fix comment

* Add linalg.solve op, test=develop

* Fix a bug caused by accidental deletion

* updated description and fix a bug: missing a comma

* Add linalg.solve op, test=develop

* updated solve op backward logic

* updated solve op backward logic again

* Add linalg.solve Op, test=develop

* Updated and modified to fit CI requirements

* Fix a bug

* 1)Add more test cases; 2)Fix a wrong usage in reduces operation; 3)Remove redundant code

* Remove redundant comments

* 1)Removed redundant code; 2)Updated to enhance code robustness

* Removed redundant code

* Updated API documents

* [ROCM] update fluid operators for rocm (part3), test=develop

* fix clang format error, test=develop

* use iwyu clean include, test=develop, test=win

* compilation error, test=develop

* fix compilation error2, test=develop

* fix compilation error3, test=develop

* fix compilation error4, test=develop

* fix compilation error5, test=develop

* fix compilation error6, test=develop

* fix compilation error7, test=develop

* fix compilation error8, test=develop

* fix compilation error8, test=develop

* fix compilation error10, test=develop

* fix compilation error11, test=develop

* add matmul_v2

* Add cholesky_op forward part. test=develop

* Complete cholesky_op forward part. test=develop

* Add cholesky_op backward part. test=develop

* Complete cholesky_op backward part. test=develop

* Refine cholesky_op error check and docs. test=develop

* Add grad_check unit test for cholesky_op. test=develop

* Fix sample code in cholesky doc. test=develop

* Refine some error messages of cholesky_op. test=develop

* Refine some error messages of cholesky_op. test=develop

* Remove unused input in cholesky_grad. test=develop

* Remove unused input in cholesky_grad. test=develop

* Fix stream for cusolverDnSetStream. test=develop

* Update PADDLE_ENFORCE_CUDA_SUCCESS from cholesky_op to adapt to latest code.
test=develop

* Add CUSOLVER ERROR in enforce.h
test=develop

* Fix the missing return value in cholesky. test=develop

Improve elementwise operators performance in same dimensions

* add support of matmul with multiple head even different width and height

Original matmul with multiple head supports only the mat_a.width == mat_b.height,
in that case, mat_b will be horizontally split. In this patch, we extend the
support when mat_a.width != mat_b.height but mat_a.width/head_number == mat_b.height,
in this case, mab_b will be vertically split.

One example is A is [3, 8], B is [2, 16], head_number is 4. In this
case, A will be split as [3, 2], B will be (vertically) split as
[2, 4]. The final result will be 4 matrix of 4 matrix of [3,4], i.e. [3, 16]

test=develop

* add support of matmul with multiple head even different width and height

Original matmul with multiple head supports only the mat_a.width == mat_b.height,
in that case, mat_b will be horizontally split. In this patch, we extend the
support when mat_a.width != mat_b.height but mat_a.width/head_number == mat_b.height,
in this case, mab_b will be vertically split.

One example is A is [3, 8], B is [2, 16], head_number is 4. In this
case, A will be split as [3, 2], B will be (vertically) split as
[2, 4]. The final result will be 4 matrix of 4 matrix of [3,4], i.e. [3, 16]

test=develop

* refactor the code of matmul with multiple head even different width and height

test=develop

* Implement the operator with sprase matrix multiply

* Update the URL of mklml library.

test=develop

* Disable MKLML implematation when using no-linux.

test=develop

* Ignore the deprecated status for windows

test=develop

* extend matmul op to support multiple head multiplication

With the support of multiple head, the multiplication of two big matrixes is
split into multiplication of several (head_number) small matrixes. e.g. if
Mat A is [3, 24] and Mat B is [24, 4], when multiple A and B with head_number
as 4, Mat A will be split as 4 matrix of [3, 6] and Mat B will be 4 matrix of
[6, 4]. The result of final matrix will be 4 matrix of [3, 4], i.e. [3, 16].

test=develop

test=develop

* Revert "Optimze Gelu with MKL Erf function (#15770)"

This reverts commit 676995c8.

* test=develop

* Optimize for gelu operator

* Set up the low accuracy mode of MKL ERF function.

test=develop

* Only enable MKLML ERF when OS is linux

* Use the speical mklml version included vmsErf function to verify gelu mkl kernel.

test=develop

* Add the CUDA macro to avoid NVCC's compile issue.

test=develop

* Add the TODO comments for mklml library modification.

test=develop

* Clean Code

test=develop

* Add the comment of marco for NVCC compiler.

test=develop

* rename and fix blas vsqr

test=develop

* update

Add an interface to set the number of threads for math function, and set the default value to 1 for inference.

Rename MatDim to MatDescriptor