type stability of left division

[araujoms]

Closes #930

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.90%. Comparing base (52c41f7) to head (86bc9c9).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1475      +/-   ##
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- Coverage   93.90%   93.90%   -0.01%     
==========================================
  Files          34       34              
  Lines       15930    15937       +7     
==========================================
+ Hits        14959    14965       +6     
- Misses        971      972       +1     

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[ViralBShah]

I assume that the _lucopy and copy_similar will not make copies in the cases where there is no need to promote the type. It appears to be the case on a quick look - but just want to make sure.

[araujoms]

Sorry, no, they always copy. I'm just reusing the implementations of lu and qr, so I'm not making any more copies than before, though.

[jishnub]

I think the idea of this generic method is to dispatch to an optimized lu method for a custom AbstractArray, if one exists. Using the internal _lu here would bypass such dispatches. E.g.: SparseMatrixCSC has an optimized lu implementation.

We may add special cases for StridedMatrixes, if this helps with type stability.

[araujoms]

I see. What's the solution, though? lu(copy_similar(A, T))? That would create yet another copy.

[araujoms]

I can just do a hack maybecopy(A, ::Type{T}) where {T} = eltype(A) <: T ? A : copy_similar(A, T), but surely there must be a better way to do it.

[stevengj]

Can you change the UpperTriangular case instead?

[araujoms]

Why? That case is working correctly.

[araujoms]

Ok, I've used a slightly better version of the hack, I think it's fine, it doesn't affect the dispatch, and only copies when necessary.

[araujoms]

I've also fixed the specialized vector methods, because even though they were not type unstable they were returning an answer of the incorrect type. Luckily this involved less copying, not more.