Implementation of LU decomposition using data flow tasks

[AZEY4]

This is the simple parallelization of LU decomposition using DataFlowTasks library. To see the DAG and performance plot run lu_test_3.

[codecov[bot]]

Codecov Report

:x: Patch coverage is 98.30508% with 1 line in your changes missing coverage. Please review. :white_check_mark: Project coverage is 76.47%. Comparing base (fbebdb2) to head (4bfb148). :warning: Report is 32 commits behind head on main.

Files with missing lines	Patch %	Lines
src/hmatrix.jl	96.42%	1 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #65      +/-   ##
==========================================
+ Coverage   75.64%   76.47%   +0.83%     
==========================================
  Files          14       14              
  Lines        1466     1522      +56     
==========================================
+ Hits         1109     1164      +55     
- Misses        357      358       +1     

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[maltezfaria]

I see that we are getting the same but with a missing key when AirSpeedVelocity tries to generate the plots. Do you think it is a bug on their side?

[AZEY4]

Here is a performance plot for this kind of implementation. As it can be seen we should try to split the computation of hmul, rdiv and ldiv. I used only two threads because it is maximum possible number of tasks which can be run at the same time.

[AZEY4]

Here is the DAG of HLU (https://github.com/IntegralEquations/HMatrices.jl/assets/72526361/ee138b14-53fa-42ad-af1f-c2798c9ffa89)

[AZEY4]

I see that we are getting the same but with a missing key when AirSpeedVelocity tries to generate the plots. Do you think it is a bug on their side?

I think it is a bug from there side because I have never seen this problem running benchmarks locally or running workflows in the Docker container. I will check it carefully again and try to find a solution.