topic Re:LAPACK DGGRQF and ill-conditionned matrices in Intel® oneAPI Math Kernel Library

LAPACK DGGRQF and ill-conditionned matrices

rbulle — Tue, 03 Oct 2023 16:40:24 GMT

Hello,

I am solving a constrained polynomial fitting problem in the least squares sense using a generalized RQ decomposition roughly the same way as LAPACK DGGLSE does it.

The problem I'm interested in is the following:

min ||Ax - C||
under the constraint

Bx = D

where C and D are matrices of right-hand sides.

I'm using a home-made C++ DGGLSE that allows to solve the problem above for several RHS from a single RQ decomposition (while DGGLSE only solves it for vectorial C and D). It's just a translation of LAPACK DGGLSE in C++ where I replace some LAPACK subroutines but the essential parts of DGGLSE are preserved.

As expected, I get a pretty ill-conditionned Vandermonde matrix from the minimization problem and when I try to get the general RQ decomposition using LAPACK DGGRQF, I notice that DGGRQF changes the rank of the matrix A. I suspect this is due to the very bad conditionning of the matrix.

Is there a way to specify a custom machine precision to LAPACK in order to avoid such issue ?

Thank you for your help, let me know if I'm not clear enough.

Re: LAPACK DGGRQF and ill-conditionned matrices

IntelSupport — Tue, 10 Oct 2023 10:18:31 GMT

Hi,

Thanks for posting in Intel Communities.

Thanks for sharing your requirement details. We are looking into your issue . We will get back to you soon with an update.

Regards,

Jilani

Re: LAPACK DGGRQF and ill-conditionned matrices

IntelSupport — Tue, 10 Oct 2023 10:18:52 GMT

Hi,

Could you please provide us a sample reproducer , MKL version and OS details, so that we can replicate and investigate more at our end.

Regards,

Jilani

Re:LAPACK DGGRQF and ill-conditionned matrices

IntelSupport — Tue, 17 Oct 2023 05:19:32 GMT

Hi,

A gentle reminder:

Could you please provide us a sample reproducer , MKL version and OS details that you are using, so that we can replicate and investigate more at our end.

Regards,

Jilani

Re: LAPACK DGGRQF and ill-conditionned matrices

rbulle — Fri, 20 Oct 2023 15:45:44 GMT

Hi,

sorry for the late reply. We are investigating the issue on our end in order to make sure we provide a sample reproducer spotting the issue correctly.

Regards,

Raphaël

Re:LAPACK DGGRQF and ill-conditionned matrices

IntelSupport — Fri, 27 Oct 2023 09:46:58 GMT

Hi,

A gentle reminder:

Could you please provide us a sample reproducer , MKL version and OS details, so that we can replicate and investigate more at our end.

Regards,

Jilani

Re:LAPACK DGGRQF and ill-conditionned matrices

JilaniS_Intel — Fri, 03 Nov 2023 06:40:03 GMT

Hi,

We have not heard back from you. Could you please provide us with an update?

Regards,

Jilani