Cannot sum partially initialized Hermitian matrices that are not an isbits type

[araujoms]

If T is an isbitstype, creating an uninitialized matrix a = Matrix{T}(undef,d,d) will initialize it with whatever is in memory, so the resulting matrix will be just a regular numerical matrix. Otherwise the matrix will be filled with #undef, and I'll get an error if I try to access them. So far so good.

I wanted to create, however, a Hermitian matrix, and initialize only the upper triangular. If I try to sum it with another Hermitian matrix, however, I get the error, even though I don't actually want to access the uninitialized elements. The code below shows what I mean, if you call it with matrix_sum(BigFloat).

Looking at the code of +, I see that it just adds the underlying parent and wraps it again with Hermitian, which by necessity accesses all elements. If one would sum instead only the upper (or lower) triangular this bug would be fixed, and presumably we would get a speedup as well.

A bit unrelated, but I noticed that GenericLinearAlgebra doesn't choke on such matrices, it can calculate the eigenvalues, for example.

using LinearAlgebra

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

[jishnub]

This should benefit from the recently incorporated changes for AbstractTriangular. We may wrap the parents in an appropriate triangular wrapper before adding them, and finally unwrap the result.