topic Re:?potrf and ?potrs: memory requirement for a coefficient matrix in Intel® oneAPI Math Kernel Library

?potrf and ?potrs: memory requirement for a coefficient matrix

Frolo — Fri, 04 Nov 2022 06:55:37 GMT

Hello Forums,

If the coefficient matrix A is a large dense but symmetric matrix, how can I handle memory efficiently when solving Ax=b?

I have used dpotrf and dpotrs for an n-by-n double precision real-valued matrix A, but I am wondering whether I should allocate n-by-n array all the time for A. This matrix is symmetric, which means only the upper (or lower) triangular part is necessary, n*(n+1)/2 entries. Does A's memory requirement have to be 8bytes*n*n or can it be lowered? Is there a way or should we reserve n-by-n array for possible fill-ins during factorization?

Any comments would be appreciated.

Best,

Yonghyun

Re: ?potrf and ?potrs: memory requirement for a coefficient matrix

kdv — Mon, 07 Nov 2022 10:32:14 GMT

Hi, Yonghyun!

For dpotrf and dpotrs the only usage is allocation of n x n memory.

Try to use routines dpptrf and dpptrs in special packed format. Dimension of input arrays n * (n - 1) / 2. But performance can be different, than dpotrf and dpotrs have.

Best regards,

Dmitry

Re: ?potrf and ?potrs: memory requirement for a coefficient matrix

Frolo — Mon, 07 Nov 2022 23:37:15 GMT

Thank you very much.

Your answer is what I am looking for. I will try those routines right now.

If possible, can you tell me more about how the performance might be differ? As soon as possible, I would like to know.

Best,

Yonghyun

Re: ?potrf and ?potrs: memory requirement for a coefficient matrix

kdv — Tue, 08 Nov 2022 04:10:16 GMT

Performance of packed routines could be lower, than dpotrf and dpotrs have since another type of data structure is used. But I don't know actual value since I am not a developer of MKL. Maybe its performance is good enough for you. The fastest way to know it is just to implement a performance test and compare results.

Best regards,

Dmitry

Re: ?potrf and ?potrs: memory requirement for a coefficient matrix

Frolo — Tue, 08 Nov 2022 04:50:21 GMT

Hello Dmitry!

Thank you for your kind reply. Your explanation helped my understanding a lot.

Best regards,

Yonghyun

Re:?potrf and ?potrs: memory requirement for a coefficient matrix

VidyalathaB_Intel — Tue, 08 Nov 2022 09:35:42 GMT

Hi Yonghyun,

Glad to know that your issue is resolved and 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.

Regards,

Vidya.