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hoemin's avatar
hoemin
Icon for New Contributor rankNew Contributor
3 years ago

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

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 geophys...
aikeu's avatar
aikeu
Icon for Regular Contributor rankRegular Contributor
3 years ago

Hi hoemin,


Any update from the previous comment?


Thanks.

Regards,

Aik Eu


  • hoemin's avatar
    hoemin
    Icon for New Contributor rankNew Contributor
    3 years ago

    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's avatar
      hoemin
      Icon for New Contributor rankNew Contributor
      3 years ago

      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