libSparse direct solving methods and matrix arithmetic

[luke-kiernan]

libSparse/wrappers.jl contains wrappers for the classes in libSparse, calling the Objective-C functions with @ccall as if they're C. This has its challenges--e.g. Julia doesn't recognize Objective-C's os_log_error--but so far, I've been able to work around them. I matched up the mangled and de-mangled functions via a dyld extractor and llvm-cxxfilt, as suggested on Discourse.

The AASparseMatrix{T} struct is a wrapper for Apple's SparseMatrix_{Float/Double}. I've implemented the supported matrix arithmetic operations the AASparseMatrix class: * for Apple's SparseMultiply and muladd! for Apple's SparseMultiplyAdd.

Likewise, AAFactorization{T} is a wrapper for Apple's SparseOpaqueFactorization_{Float/Double}. Unlike Julia, you need to explicitly construct the factorization object, and provide it the first argument to solve (or ldiv!). You can do things like

using SparseArrays, AppleAccelerate
N = 10
jlM = sprand(N, N, .4)
aaM = AASparseMatrix(jlM)
f = AAFactorization(aaM) 
b = rand(N)
@assert f \ b ≈ jlM \ b # this will error if jlM is singular.

Places where this could use some work:

1. My way of attaching a Julia function to each C function is very copy-paste heavy. Writing a macro is probably a better way to go, but a bit beyond my skills at this point.
2. I'm hard-coding in the mangled names. Those very well could change at some point in the future: add guardrails so that it's an informative error if things do break. Or better yet, automate the de-mangling.
3. Bring the interface of AAFactorization more in line with Julia's LinearAlgebra.
4. Expand functionality, beyond direct methods and Cholesky/QR factorizations.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 147 lines in your changes missing coverage. Please review.

Project coverage is 0.51%. Comparing base (9874fe4) to head (1e4b9f8).

Files with missing lines	Patch %	Lines
src/libSparse/wrappers.jl	0.00%	61 Missing ⚠️
src/libSparse/AASparseMatrices.jl	0.00%	50 Missing ⚠️
src/libSparse/AAFactorizations.jl	0.00%	36 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff            @@
##           master     #79      +/-   ##
=========================================
- Coverage    0.84%   0.51%   -0.33%     
=========================================
  Files           4       7       +3     
  Lines         238     385     +147     
=========================================
  Hits            2       2              
- Misses        236     383     +147     

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[ViralBShah]

Nice work. Happy to give you commit access. Please let me know.

[luke-kiernan]

Sure! Should I make this a feature branch, or close merge it into main? I see I can now the close PR. I'm relatively new to Julia and to GitHub collaboration, so I'm not sure what level of fit and finish is "good enough."

[ViralBShah]

The important thing is to have tests and make sure CI passes. You can then merge to master and eventually tag a release.

Invited you for write access: https://github.com/JuliaLinearAlgebra/AppleAccelerate.jl/invitations

[luke-kiernan]

I've accepted the invite and added libSparse as a new branch.