Make parentof_applytri fully type-stable

[jishnub]

This should make each branch in applytri return the same type, as the UpperTriangular or LowerTriangular wrapper will be removed.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.99%. Comparing base (e53b50c) to head (85dbca3).
Report is 4 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1243      +/-   ##
==========================================
- Coverage   92.03%   91.99%   -0.04%     
==========================================
  Files          34       34              
  Lines       15459    15459              
==========================================
- Hits        14227    14222       -5     
- Misses       1232     1237       +5     

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[ViralBShah]

@dkarrasch Bumping for a quick look.

[dkarrasch]

Honestly, I can't wrap my head around this. I could use some hints as to why this is currently type-unstable and why this makes it stable.

[jishnub]

In

LinearAlgebra.jl/src/symmetric.jl

Lines 302 to 308 in c64c328

	function applytri(f, A::HermOrSym)
	if A.uplo == 'U'
	f(uppertriangular(A.data))
	else
	f(lowertriangular(A.data))
	end
	end

, the first branch usually returns an UpperTriangular, and the second returns a LowerTriangular. The result therefore is inferred as a Union{UpperTriangular, LowerTriangular}.

We sometimes call parent(applytri(f, A::Symmetric)) to strip the triangular layer:

LinearAlgebra.jl/src/symmetric.jl

Lines 321 to 323 in c64c328

	_parent_tri(U::UpperOrLowerTriangular) = parent(U)
	_parent_tri(U) = U
	parentof_applytri(f, args...) = _parent_tri(applytri(f, args...))

When we pass the result of applytri to parent, type-inference has to carry out a union-splitting. If all we want is the parent, though, then we can directly return the parent from each branch by removing the triangular wrapper. This way, both the branches end up returning the same type. In a way, this is inlining parent within the branches of applytri, instead of having a separate call to parent with the result.