From f13e0a45d10bb13f48d6208e9c9d5b4a52b96732 Mon Sep 17 00:00:00 2001
From: Michael Goerz <mail@michaelgoerz.net>
Date: Sun, 20 Mar 2022 18:21:22 -0400
Subject: [PATCH] Fix `rrule` for  complex-valued determinants (#601)
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* 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 <seth.axen@gmail.com>

* 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 <seth.axen@gmail.com>

Co-authored-by: Seth Axen <seth.axen@gmail.com>
---
 Project.toml                         | 2 +-
 src/rulesets/LinearAlgebra/dense.jl  | 2 +-
 test/rulesets/LinearAlgebra/dense.jl | 6 ++++++
 3 files changed, 8 insertions(+), 2 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7b80db3e1..bfcd14aef 100644
--- a/Project.toml
+++ b/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"
diff --git a/src/rulesets/LinearAlgebra/dense.jl b/src/rulesets/LinearAlgebra/dense.jl
index 13d77d302..ebd0c07ce 100644
--- a/src/rulesets/LinearAlgebra/dense.jl
+++ b/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
diff --git a/test/rulesets/LinearAlgebra/dense.jl b/test/rulesets/LinearAlgebra/dense.jl
index d8eb50eb0..ec8288a84 100644
--- a/test/rulesets/LinearAlgebra/dense.jl
+++ b/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)