Fix eltype determination in det (#44582)

Co-authored-by: Andreas Noack <[email protected]>

stdlib/LinearAlgebra/src/generic.jl

@@ -1539,9 +1539,9 @@ julia> det(M)
 2.0
 ```
 """
-function det(A::AbstractMatrix{T}) where T
+function det(A::AbstractMatrix{T}) where {T}
  if istriu(A) || istril(A)
- S = typeof((one(T)*zero(T) + zero(T))/one(T))
+ S = promote_type(T, typeof((one(T)*zero(T) + zero(T))/one(T)))
  return convert(S, det(UpperTriangular(A)))
  end
  return det(lu(A; check = false))

stdlib/LinearAlgebra/test/generic.jl

@@ -76,6 +76,35 @@ n = 5 # should be odd
  @test logabsdet(x)[1] ≈ logabsdet(X)[1]
  @test logabsdet(x)[2] ≈ logabsdet(X)[2]
  end
+
+ @testset "det with nonstandard Number type" begin
+ struct MyDual{T<:Real} <: Real
+ val::T
+ eps::T
+ end
+ Base.:+(x::MyDual, y::MyDual) = MyDual(x.val + y.val, x.eps + y.eps)
+ Base.:*(x::MyDual, y::MyDual) = MyDual(x.val * y.val, x.eps * y.val + y.eps * x.val)
+ Base.:/(x::MyDual, y::MyDual) = x.val / y.val
+ Base.:(==)(x::MyDual, y::MyDual) = x.val == y.val && x.eps == y.eps
+ Base.zero(::MyDual{T}) where {T} = MyDual(zero(T), zero(T))
+ Base.zero(::Type{MyDual{T}}) where {T} = MyDual(zero(T), zero(T))
+ Base.one(::MyDual{T}) where {T} = MyDual(one(T), zero(T))
+ Base.one(::Type{MyDual{T}}) where {T} = MyDual(one(T), zero(T))
+ # the following line is required for BigFloat, IDK why it doesn't work via
+ # promote_rule like for all other types
+ Base.promote_type(::Type{MyDual{BigFloat}}, ::Type{BigFloat}) = MyDual{BigFloat}
+ Base.promote_rule(::Type{MyDual{T}}, ::Type{S}) where {T,S<:Real} =
+ MyDual{promote_type(T, S)}
+ Base.promote_rule(::Type{MyDual{T}}, ::Type{MyDual{S}}) where {T,S} =
+ MyDual{promote_type(T, S)}
+ Base.convert(::Type{MyDual{T}}, x::MyDual) where {T} =
+ MyDual(convert(T, x.val), convert(T, x.eps))
+ if elty <: Real
+ @show elty
+ @show istriu(triu(MyDual.(A, zero(A))))
+ @test det(triu(MyDual.(A, zero(A)))) isa MyDual
+ end
+ end 
 end
 
 @testset "diag" begin