Structured broadcasting for UpperHessenberg

[jishnub]

This adds a custom structured broadcasting style for an UpperHessenberg, which now retains structure on some broadcasting operations.

julia> UH = UpperHessenberg(ones(4,4))
4×4 UpperHessenberg{Float64, Matrix{Float64}}:
 1.0  1.0  1.0  1.0
 1.0  1.0  1.0  1.0
  ⋅   1.0  1.0  1.0
  ⋅    ⋅   1.0  1.0

julia> UH .+ UH
4×4 UpperHessenberg{Float64, Matrix{Float64}}:
 2.0  2.0  2.0  2.0
 2.0  2.0  2.0  2.0
  ⋅   2.0  2.0  2.0
  ⋅    ⋅   2.0  2.0

julia> B = Bidiagonal(1:4, 1:3, :L);

julia> UH .+ B
4×4 UpperHessenberg{Float64, Matrix{Float64}}:
 2.0  1.0  1.0  1.0
 2.0  3.0  1.0  1.0
  ⋅   3.0  4.0  1.0
  ⋅    ⋅   4.0  5.0

Unlike an UpperTriangular, an UpperHessenberg can retain its structure in broadcasting operations involving other banded matrices such an Tridiagonal. We may also, in the future, make ::UpperTriangular .+ ::Bidiagonal produce an UpperHessenberg.

[codecov]

Codecov Report

❌ Patch coverage is 95.65217% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 93.81%. Comparing base (c64c328) to head (428d9d8).
⚠️ Report is 45 commits behind head on master.

Files with missing lines	Patch %	Lines
src/structuredbroadcast.jl	95.23%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1325   +/-   ##
=======================================
  Coverage   93.81%   93.81%           
=======================================
  Files          34       34           
  Lines       15717    15738   +21     
=======================================
+ Hits        14745    14765   +20     
- Misses        972      973    +1     

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[dkarrasch]

Awesome how "little" work needs to be done to make it work.

[dkarrasch]

Would that even work with

Suggested change

	UH2 = UH .+ UH .- UH
	UH2 = UH + UH - UH

?

[jishnub]

Yes, it would. Should I add a test to compare these?

[ViralBShah]

Ready to merge?

[jishnub]

Perhaps we may merge for now and iteratively improve this.