topic Combining Hadamard division and matrix multiplication in one procedure in Intel® oneAPI Math Kernel Library

Combining Hadamard division and matrix multiplication in one procedure

Chris_Mayer — Wed, 10 Aug 2022 07:52:49 GMT

Hey everyone,

I am currently optimising code that performs a series of Hadamard (element-wise) divisions (1 ./ matrix) and matrix multiplications.

For example:

C = A[1 ⊘ B] 1, B ∈ R^d×d A ∈ R^d×d

Currently, I implement the calculation in two steps:

vdDiv(d*d, mOnes, B, temp_M); // mOnes is a matrix with all elements equal 1 cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, d, d, d, alpha, A, d, temp_M, d, beta, C, d);

I want to avoid doing d^2+ d^3 operations and do instead just d^3 operations.

In theory, both steps could be performed in one procedure by defining C as:

(c_ij) = a_i1 / b_1j + a_2i / b_2j + ... + a_id / b_dj

Is there a way to implement this in MKL efficiently?

Many thanks and best,

Chris

Re:Combining Hadamard division and matrix multiplication in one procedure

VidyalathaB_Intel — Thu, 11 Aug 2022 12:33:48 GMT

Hi Chris,

Thanks for reaching out to us.

Could you please refer to the below link which contains the details of some functions of MKL which i guess might help you?

https://www.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/blas-and-sparse-blas-routines/blas-like-extensions.html

https://www.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/blas-and-sparse-blas-routines/blas-like-extensions/cblas-gemm-batch.html

Regards,

Vidya.

Re:Combining Hadamard division and matrix multiplication in one procedure

VidyalathaB_Intel — Thu, 18 Aug 2022 05:29:23 GMT

Hi Chris,

As we haven't heard back from you, could you please provide us with an update regarding your issue?

Regards,

Vidya.

Re: Combining Hadamard division and matrix multiplication in one procedure

Chris_Mayer — Thu, 18 Aug 2022 08:27:51 GMT

Hi Vidya,

Thank you for your reply!

I could not find any function in the documentation that provides the operation that I am seeking. Could you point me to a specific function that might solve the problem?

Many thanks and best,

Chris

Re: Combining Hadamard division and matrix multiplication in one procedure

VidyalathaB_Intel — Thu, 18 Aug 2022 15:33:00 GMT

Hi Chris,

The links in the earlier post lists out the routines which are extensions of BLAS that are available in MKL (i guess there is no direct routine available in MKL which combines both the cases hadamard division and gemm operation and as I mentioned you can refer to the extended functionalities of BLAS)

They may not exactly match the use case of yours but might help you for further stages.

Maybe using this function cblas-gemm-batch might help you but not sure https://www.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/blas-and-sparse-blas-routines/blas-like-extensions/cblas-gemm-batch.html

Regards,

Vidya.

Re: Combining Hadamard division and matrix multiplication in one procedure

Chris_Mayer — Mon, 22 Aug 2022 08:15:49 GMT

Hi Vidya,

Thank you!

It seems that it is not possible to perform the exact operation that I envisioned. I will try to find a work around. The question is answered for me, thank you.

Best,

Chris

Re:Combining Hadamard division and matrix multiplication in one procedure

VidyalathaB_Intel — Mon, 22 Aug 2022 09:44:23 GMT

Hi Chris,

>>The question is answered for me,

Thanks for the confirmation.

Please post a new question if you need any additional assistance from Intel as this thread will no longer be monitored.

Have a Nice Day!

Regards,

Vidya.