Fix rrule for complex-valued determinants (#601)

* Fix rrule for det of complex matrix

* Add test of rules for complex determinant

* `ΔΩ * inv(x)'` ⇒ `inv(x)' * dot(Ω, ΔΩ)`

Co-authored-by: Seth Axen <[email protected]>

* Use a random matrix as a seed for the unitary

* Bump patch number

* Use `U = exp(B - B')` as complex `det` test matrix

Co-authored-by: Seth Axen <[email protected]>

Co-authored-by: Seth Axen <[email protected]>

Author: goerz

Project.toml

@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.28.0"
+version = "1.28.1"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

src/rulesets/LinearAlgebra/dense.jl

@@ -129,7 +129,7 @@ frule((_, Δx), ::typeof(det), x::Number) = (det(x), Δx)
 function rrule(::typeof(det), x::Union{Number, AbstractMatrix})
     Ω = det(x)
     function det_pullback(ΔΩ)
-        ∂x = x isa Number ? ΔΩ : Ω * ΔΩ * inv(x)'
+        ∂x = x isa Number ? ΔΩ : inv(x)' * dot(Ω, ΔΩ)
         return (NoTangent(), ∂x)
     end
     return Ω, det_pullback

test/rulesets/LinearAlgebra/dense.jl

@@ -119,6 +119,12 @@
                 test_rrule(f, B)
             end
         end
+        @testset "$f(complex determinant)" begin
+            B = randn(ComplexF64, 4, 4)
+            U = exp(B - B')
+            test_frule(f, U)
+            test_rrule(f, U)
+        end
     end
     @testset "logabsdet(::Matrix{$T})" for T in (Float64, ComplexF64)
         B = randn(T, 4, 4)