Reroute algebraic functions for Symmetric/Hermitian through triangular

[jishnub]

This ensures that only the triangular indices are accessed for strided parent matrices. Fix #52895

julia> M = Matrix{Complex{BigFloat}}(undef, 2, 2);

julia> M[1,1] = M[2,2] = M[1,2] = 2;

julia> H = Hermitian(M)
2×2 Hermitian{Complex{BigFloat}, Matrix{Complex{BigFloat}}}:
 2.0+0.0im  2.0+0.0im
 2.0-0.0im  2.0+0.0im

julia> H + H # works after this
2×2 Hermitian{Complex{BigFloat}, Matrix{Complex{BigFloat}}}:
 4.0+0.0im  4.0+0.0im
 4.0-0.0im  4.0+0.0im

This also provides a speed-up in several common cases (allocations mentioned only when they differ):

julia> H = Hermitian(rand(ComplexF64,1000,1000));

julia> H2 = Hermitian(rand(ComplexF64,1000,1000),:L);

Operation	master	PR
-H	2.247 ms	1.384 ms
real(H)	1.544 ms	1.175 ms
H + H	2.288 ms	1.978 ms
H + H2	5.139 ms	3.287 ms
isdiag(H)	23.042 ns (1 allocation: 16 bytes)	16.778 ns (0 allocations: 0 bytes)

I'm not entirely certain why isdiag(H) allocates on master, as union splitting should handle this automatically, but manually splitting the union appears to help.

[araujoms]

This PR exceeds my most optimistic expectations. Note that it doesn't work for mismatched uplo, though, because that will be wrapped by Adjoint, and that falls back to the non-symmetric +. Example:

function matrix_sum(T)
   d = 2
   a = Hermitian(Matrix{T}(undef,d,d),:U)
   b = Hermitian(Matrix{T}(undef,d,d),:L)
   for i=1:d
       for j=i:d
           a.data[i,j] = T(1)
           b.data[j,i] = T(1)
       end
   end
   a+b
end    

[jishnub]

Yes, fixing the mismatched uplo case would require #52530

[jishnub]

The addition/subtraction with mismatched uplo is fixed now:

julia> matrix_sum(BigFloat)
2×2 Hermitian{BigFloat, Matrix{BigFloat}}:
 2.0  2.0
 2.0  2.0

[jishnub]

This should be good to go

[jishnub]

Gentle bump

[oscardssmith]

This looks reasonable to me (although i do kind of hate that we are doing all of this with the uplo flag. Using characters is ugly. None of that is the fault of this PR though.)

[dkarrasch]

Nice work!