fix logdet(Diagonal{<:Real}) with negative entries (#39158)

Author: marius311

stdlib/LinearAlgebra/src/diagonal.jl

@@ -595,7 +595,6 @@ function diag(D::Diagonal, k::Integer=0)
 end
 tr(D::Diagonal) = sum(tr, D.diag)
 det(D::Diagonal) = prod(det, D.diag)
-logdet(D::Diagonal{<:Real}) = sum(log, D.diag)
 function logdet(D::Diagonal{<:Complex}) # make sure branch cut is correct
     z = sum(log, D.diag)
     complex(real(z), rem2pi(imag(z), RoundNearest))

stdlib/LinearAlgebra/test/diagonal.jl

@@ -361,6 +361,8 @@ Random.seed!(1)
         d2, s2 = logabsdet(lM)
         @test d1 ≈ d2
         @test s1 == s2
+        @test logdet(Diagonal(relty[-1,-2])) ≈ log(2)
+        @test_throws DomainError logdet(Diagonal(relty[-1,-2,-3]))
     end
 
     @testset "similar" begin