QRD and QRI to solve LLS problem with oneMKL LAPACK gels or gelsy?

[hoemin]

Dear Sir/Madam,

I am an Intel DevCloud user base on oneAPI and DPC++FPGA.

The task is to take the Ground-Base TEM (Transient ElectroMagnetic) data in Universal Sounding Format (USF) for geophysical groundwater investigations to convert to matrices (if required) and process with qrd and qri from oneapi-src/oneAPI-samples/ DirectProgramming/ DPC++FPGA/ ReferenceDesigns to solve the Linear Least Square (LLS) problem.

Since unable to find any reference design for LLS for DPC++FPGA, would presume to take the above outputs to solve with LLS  LAPACK Driver Routines, but not sue to use gels or gelsy?

Any help that you could provide will be most appreciated.

Thanks. Best Regards

Min HOE

[aikeu]

Hi hoemin,

I will get back to your when I have relevant info to your question.

Thanks.

Regards,

Aik Eu

[hoemin]

Thanks, Aik Eu. Look forward to hear from you soon.

Best Regards
Hoe Min 

[aikeu]

Hi hoemin,

I have sent you an email regarding the info I get from my team.

Thanks.

Regards,

Aik Eu

[aikeu]

Hi hoemin,

I will close this thread if no further question.

Thanks.

Regards,

Aik Eu

[hoemin]

Dear Aik Eu, 

I will work on it on this weekend and get back to you for any issue. 

Thanks for your help.

Best Regards

Hoe Min 

[aikeu]

Hi hoemin,

Any update from the previous comment?

Thanks.

Regards,

Aik Eu

[hoemin]

Dear Aik Eu, 

I had already replied you on 16th May, 2022, see copy below. Thanks and Best Regards Hoe Min

From: hm3_KL <hm3_KL@student.wou.edu.my>
Sent: 16 May 2022 16:40
To: Intel Customer Support <supportreplies@intel.com>
Subject: Re: QRD and QRI to solve LLS problem with oneMKL LAPACK gels or gelsy?

Dear Aik Eu, 

I fully agree with one of your respective team member recommendation to use the existing QRD from FPGA code samples especially this project continues to make use of Direct Programming DPC++FPGA and that is my main objective.

As I am just a beginner in using FPGA, there are many areas not well understood and much to learn.  Appreciate your team member(s) to enlighten me on the followings:

1) The TEM data in USF format are attached.  The attached zip file consists of 3 sets of data (K004 to K006) both in raw.usf and stcked.usf formats were taken from TEM Instrument and already converted to raw and stack data in USF formats. 

2) Presume these USF data can be converted/read/imported directly into QRD of the FPGA code sample?  Please provide example or sample code for me to convert/read/import in to QRD. By doing so am I able to get the 

-matrix and 

-vector in order for me to implement 1. perform QRD on 

-matrix to generate 

 using the library in code samples, kindly advise the name of the code sample in the library. 

3) After successfully implemented above steps, I then continue to implement 2.Calculate  

 using matrix-vector product (this is very trivial) and 3. Back-substitute to solve 

(this is also very trivial).

Thank you very much for your help. 

Best Regards
Hoe Min

---

From: Intel Customer Support <supportreplies@intel.com>
Sent: 10 May 2022 09:32
To: hm3_KL <hm3_KL@student.wou.edu.my>
Subject: QRD and QRI to solve LLS problem with oneMKL LAPACK gels or gelsy?

Hi hoemin,

I obtained the following info as below:
"
According to one of the repective team member, It is much better performance by using the existing QRD from the FPGA code samples than by trying to use the MKL libraries which are not optimized for FPGA.
 
Linear Least Squares is used to solve coefficients  ,  ,  , …  for a system of linear equations when you know  ,  ,  …  and have measured ordered pairs  ,  ,  …  .
 





 
You can model this as a matrix equation like this:

Where  is a matrix  ,  is a vector  ,  ,  , …  and  is a vector  .
 
 

If you factor  with QRD, you get  , and can find  . Since  is rectangular ( ), the resulting  - matrix will be made of an  upper-triangular matrix  , and a  matrix of 0s. then we can split the vector  into an n-element vector  and an  element vector  :

 
We can find a solution for  by solving  ; we can solve for  using back-substitution since  is upper-triangular.
 

Therefore, to implement a LLS given an existing QRD when the  -matrix and  -vector are known, I think you will need to

1. Perform QRD on  -matrix to generate  using the library in code samples
2. Calculate    using matrix-vector product (this is very trivial)
3. Back-substitute to solve  (this is also very trivial)

"

Thanks.
Regards,
Aik Eu

ref:_00DU0YT3c._5004UxX9Ie:ref

[hoemin]

Dear Aik Eu, 

I am not sure you have received my reply on May 16, 2022 as I received undeliverable message on May 19, therefore attached here again the pdf version of the followings:

1) Email - hm3_KL - Outlook (Reply sent on 16 May 2022) with USF Format zipped file

2) Email - hm3_KL - Outlook (Undeliverable message received on 19 May 22).

Please confirm receipt.

Look forward to your early reply.

Thanks.

Best Regards
Hoe Min

[aikeu]

Hi hoemin,

I get your reply. I was trying to ask about the info to your question.

I am not able to be certain that there will be answer to your latest questions.

Thanks.

Regards,

Aik Eu

[aikeu]

Hi hoemin,

I get the below respond from the team:

The QRD Code sample is here: https://github.com/oneapi-src/oneAPI-samples/tree/master/DirectProgramming/DPC%2B%2BFPGA/ReferenceDesigns/qrd

Unfortunately, we do not have a code sample for reading from USF. Those USF files are simply comma-separated text files, so user can either find a library or make one themselves.

Thanks.

Regards,

Aik Eu

[aikeu]

Hi hoemin,,

I will close this thread if no further question.

Thanks.

Regards,

Aik Eu