Specialize lmul!/rmul! for adjoint/transpose

[jishnub]

This ensures that the scaling happens in a cache-friendly manner, which improves performance.

julia> A = adjoint(rand(100,100));
 
julia> @btime rmul!($A, 2.0);
  2.877 μs (0 allocations: 0 bytes) # nightly
  961.385 ns (0 allocations: 0 bytes) # this PR

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.82%. Comparing base (c5d7122) to head (a462e5a).
Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1388   +/-   ##
=======================================
  Coverage   93.81%   93.82%           
=======================================
  Files          34       34           
  Lines       15722    15724    +2     
=======================================
+ Hits        14750    14753    +3     
+ Misses        972      971    -1     

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[dkarrasch]

Do we have some sort of Quaternions available? We should test this on something that is not commutative, because otherwise the whole left- and right-multiplication difference doesn't become visible.

[jishnub]

Turns out that this only holds for commutative numbers, so I have restricted this to real and complex numbers. This should cover most use cases.

[dkarrasch]

For the adjoint case, this should work, because we still have (xy)' = y'x'.

[dkarrasch]

I'd suggest to split this and make it available to non-commutative types in the adjoint case.

Suggested change

	rmul!(X::AdjOrTrans{<:Union{Real,Complex}}, s::Union{Real,Complex}) = (lmul!(wrapperop(X)(s), parent(X)); X)
	lmul!(s::Union{Real,Complex}, X::AdjOrTrans{<:Union{Real,Complex}}) = (rmul!(parent(X), wrapperop(X)(s)); X)
	rmul!(X::Transpose{<:Union{Real,Complex}}, s::Union{Real,Complex}) = (lmul!(s, parent(X)); X)
	rmul!(X::Adjoint, s::Number) = (lmul!(s', parent(X)); X)
	lmul!(s::Union{Real,Complex}, X::Transpose{<:Union{Real,Complex}}) = (rmul!(parent(X), s); X)
	lmul!(s::Number, X::Adjoint) = (rmul!(parent(X), s'); X)