Replace built-in linear system solver with LAPACK

[mpaiao]

Update linear system solvers with lapack libraries for improved efficiency.

Description

ED2 used to have a fairly robust linear system solver, however, it used Gaussian elimination for every case, which is not efficient. This pull requests replaces the built-in solver with the Linear Algebra Package (LAPACK) subroutines. LAPACK is a well-known and widely available library, so this change should have minimal impact on the ability to build ED2 in most local and high-performance computing systems.

This change will require new variables LAPACK_INCS and LAPACK_LIBS to be set in include.mk.[machine] files. If Lapack is installed in regular paths (e.g., /usr/local), the only addition needed is the list of libraries:

LAPACK_INCS=
LAPACK_LIBS=-llapack -lblas

Otherwise, the full path may be needed. For example, in MacOS systems using HomeBrew:

LAPACK_PATH=/usr/local/opt/lapack
LAPACK_INCS=-I$(LAPACK_PATH)/include
LAPACK_LIBS=-L$(LAPACK_PATH)/lib -llapack -lblas

I added templates in all tracked include.mk, but they may need to be adjusted.

Collaborators

@femeunier and @rgknox suggested this a while back. @robkooper because I may need to coordinate these edits to keep Docker functional.

Motivation and Context

This change removes the need for computational burdensome matrix inversion algorithms for simpler matrices, and allows leveraging efficient and well tested libraries for solving linear systems in ED2. This is called rather frequently (radiation time step), so using lapack should reduce the runtime.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Other (fix or feature that would cause existing functionality to change)

Checklist:

• My change requires a change to the documentation.
• I have updated the documentation accordingly.
• I have added tests to cover my changes.

I will update the documentation if this pull request is merged.

Testing :

• All new and existing tests passed.

[mpaiao]

@femeunier would you mind revising this one too as you had originally talked about using lapack (a while ago...)?
I tried to list you but somehow it didn't let me add you there. Thanks for considering!