Problem with eltype of a non-numeric Symmetric matrix

General Usage
1

Hi everyone,

I have defined a custom type to wrap a Python library similarly to what SymPy.jl does. So I will focus on a custom defined for SymPy but essentially the problem is the same for my custom type too.

If I define a symmetric matrix as:

using LinearAlgebra, SymPy

x = Matrix{Sym}(undef, 2, 2)
Symmetric(x)

the type of the output is 2×2 Symmetric{Any,Array{Sym,2}}, while if I defined as

Symmetric{eltype(x),typeof(x)}(x, 'L')

the return type is 2×2 Symmetric{Sym,Array{Sym,2}}.

That means that the eltype in the definition of Symmetric returns type Any. Why is this happening and how can I resolve that? Thanks!

2

You’re looking at a really old version of Julia there. You’re probably running 1.1 or somesuch — the function that’s now called is this:

https://github.com/JuliaLang/julia/blob/release-1.1/stdlib/LinearAlgebra/src/symmetric.jl#L48-L51

Symmetric is now recursive so it needs to reason about the transpose of things — and if it can’t then it just gives up and says Any. I’m not sure what all you need to do for a custom type.

1 Like
3

I haven’t noticed that I’m looking into an older version. Thanks for pointing it out!

4

I think the main problem is that transpose(::Sym) is not type-stable, so that Base.promote_op(transpose, Sym) == Any. promote_op is used here:

https://github.com/JuliaLang/julia/blob/7132c635ab8da723c0177a9d6617bf01f4e7460a/stdlib/LinearAlgebra/src/symmetric.jl#L75

and promote_op uses Core.Compiler.return_type in its implementation.

This one case is easy enough to fix with a PR, but I’m thinking this is likely a pretty pervasive problem throughout SymPy.

1 Like
5

Thanks for pointing this out. I have a PR to fix this particular issue, but how widely it needs doing remains to be seen.

1 Like