Add issymmetrictype and ishermitiantype

[jishnub]

Add functions that determine if all instances of a type T satisfy issymmetric/ishermitian without having to check the values. In other words, the symmetry is known at compile time from the type.

The main use case for this would be if we wish to have Symmetric/Hermitian broadcasting in the future, where we would want to generate the destination by checking if the arguments are all symmetric.

[codecov]

Codecov Report

❌ Patch coverage is 27.27273% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 93.85%. Comparing base (98723df) to head (a5975d8).
⚠️ Report is 54 commits behind head on master.

Files with missing lines	Patch %	Lines
src/symmetric.jl	11.11%	8 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1436      +/-   ##
==========================================
- Coverage   93.89%   93.85%   -0.04%     
==========================================
  Files          34       34              
  Lines       15920    15927       +7     
==========================================
+ Hits        14948    14949       +1     
- Misses        972      978       +6     

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[stevengj]

Shouldn't it be

issymmetrictype(::Type{<:Number}) = true

?

[jishnub]

The exception is NaN, which isn't equal to itself. I didn't want to make this more generic in case the number types contain NaN as a field.

[stevengj]

I don't understand this AbstractFloat rule?

[jishnub]

This is to stay consistent with the current behavior

julia> issymmetric(NaN)
false

[stevengj]

That seems highly questionable to me, as opposed to issymmetric(::Number) = true and ishermitian(x::Number) = isreal(x).

e.g. we have have a type-based issymmetric test for floating-point Symmetric matrices, even though they can also have NaN values.

julia> A = Symmetric(fill(NaN, 3,3))
3×3 Symmetric{Float64, Matrix{Float64}}:
 NaN  NaN  NaN
 NaN  NaN  NaN
 NaN  NaN  NaN

julia> A == A'
false

julia> issymmetric(A)
true