Is 3x3 symmetric matrix Eigen computation using Intel MKL Libraries faster than Iterative methods ?

[ravi_0602]

@mkl @intelmklpriv-id_com @oneAPI-usr 

In my fortran code, I have to determine the eigen values and vectors repeatedly for a 3x3 matrix. I was wondering if using the inbuilt dsyev() function from the MKL Library will be faster or a user written function which uses the jacobi iteration be quicker for a 3x3 matrix. 

The matrix is symmetric !!

I use this as a part of my UMAT subroutine in LS Dyna. 

So lets say if I use that UMAT in a simulation where the model contains 5000 elements and each element has 5 integration points. It means that the eigen computations are done 5000*5 = 25000 times. 

Kindly provide me insights on which is the best way to go forward. 

I will be using the oneAPI/2024.2 compiler for these tasks. 

Thanks in Advance !!

[Shiquan_Su]

Usually, the dsyev() function should be faster, since it is highly optimized. For the best chance to get all the optimization, would you please run the mkl link line advisor?

https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-link-line-advisor.html

to decide your best configuration?

[ravi_0602]

Hi @Shiquan_Su , Thank you very much for your reply. 

Usually dsyev() is the fastest, yes !!

But i was wondering if it holds for smaller 3x3 matrices too ? 

Thanks in advance !!

[Ruqiu_C_Intel]

The oneMKL library is highly optimized to fully exploit the performance of the underlying hardware and provides efficient computation even for small matrices. Computing the eigenvalues ​​and eigenvectors of a 3x3 symmetric matrix by using the dsyev() function in the Intel MKL library often has advantages over iterative methods.