feat: Add kernel callable dense LA solvers for small systems.

[CusiniM]

No description provided.

[CusiniM]

@dkachuma this should be useful for the PVT module too.

[corbett5]

I feel like these would fit in better in LvArray. I mean it's already got the functions for solving 2x2 and 3x3 eigenvalue and inverse problems, why shouldn't the linear system solvers live there as well? Where ever they wind up there should be unit tests as well.

[rrsettgast]

These optimizations are not guaranteed to be done by the compiler.

we should have a plan for a central location for all operations of this type. It was in LvArray. If you want to move these out of LvArray we should discuss that. I would push for a kernel callable LA package separate from GEOS and LvArray, but that is just how I roll.

[castelletto1]

I feel like these would fit in better in LvArray. I mean it's already got the functions for solving 2x2 and 3x3 eigenvalue and inverse problems, why shouldn't the linear system solvers live there as well? Where ever they wind up there should be unit tests as well.

Yes, linear algebra operations, including tensor operations, should live in the same place.

we should have a plan for a central location for all operations of this type. It was in LvArray. If you want to move these out of LvArray we should discuss that. I would push for a kernel callable LA package separate from GEOS and LvArray, but that is just how I roll.

I agree with @rrsettgast . Linear algebra and tensor operations should be a package independent of LvArray and of GEOS.

[rrsettgast]

I feel like these would fit in better in LvArray. I mean it's already got the functions for solving 2x2 and 3x3 eigenvalue and inverse problems, why shouldn't the linear system solvers live there as well? Where ever they wind up there should be unit tests as well.

Yes, linear algebra operations, including tensor operations, should live in the same place.

we should have a plan for a central location for all operations of this type. It was in LvArray. If you want to move these out of LvArray we should discuss that. I would push for a kernel callable LA package separate from GEOS and LvArray, but that is just how I roll.

I agree with @rrsettgast . Linear algebra and tensor operations should be a package independent of LvArray and of GEOS.

isn't there a kernel callable set of dense linear algebra functions?

[castelletto1]

I feel like these would fit in better in LvArray. I mean it's already got the functions for solving 2x2 and 3x3 eigenvalue and inverse problems, why shouldn't the linear system solvers live there as well? Where ever they wind up there should be unit tests as well.

Yes, linear algebra operations, including tensor operations, should live in the same place.

we should have a plan for a central location for all operations of this type. It was in LvArray. If you want to move these out of LvArray we should discuss that. I would push for a kernel callable LA package separate from GEOS and LvArray, but that is just how I roll.

I agree with @rrsettgast . Linear algebra and tensor operations should be a package independent of LvArray and of GEOS.

isn't there a kernel callable set of dense linear algebra functions?

There are many libraries. However, our need is to solve very small problems in each thread. @corbett5 do you have any experience with using Eigen in a device (CUDA) kernel?

[corbett5]

Breaking out all the kernel callable tensor operations in LvArray into a new repo sounds fine to me.

@castelletto1 no I have not tried Eigen. I know that they have device compatible compile time fixed size 2x2 and 3x3 eigen decompositions, but I'm not sure for example if they have a general suite of device compatible fixed size routines. If they do I doubt they have the support for a static 2x2 and 3x3 symmetric format. Using Eigen would also lock us into the pattern of always performing operations on local variables, where as for example with LvArray::tensorOps you can pass in whatever mix of local variables and LvArray::Array objects you want.

[castelletto1]

I understand @CusiniM needs this kernel for #3280. I propose we move forward incrementally, and focus on the refactoring we all seem to agree on in a future PR.

@CusiniM please make sure to add unit tests as required by @corbett5.

[codecov]

Codecov Report

Attention: Patch coverage is 97.05882% with 4 lines in your changes missing coverage. Please review.

Project coverage is 56.45%. Comparing base (a3e4a51) to head (2460a17).
Report is 90 commits behind head on develop.

Files with missing lines	Patch %	Lines
...enseLinearAlgebra/unitTests/testDenseLASolvers.cpp	93.93%	4 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #3287      +/-   ##
===========================================
+ Coverage    56.36%   56.45%   +0.09%     
===========================================
  Files         1056     1059       +3     
  Lines        89233    89444     +211     
===========================================
+ Hits         50296    50498     +202     
- Misses       38937    38946       +9     

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[CusiniM]

Added unitTests. This should be good to go for now.