From ebe424beb7635b3db71d35a79cfb89bcefdbf76d Mon Sep 17 00:00:00 2001
From: Stijn de Waele <stijn.de.waele123@gmail.com>
Date: Mon, 2 Dec 2019 23:26:23 -0500
Subject: [PATCH 1/4] matrix exp(A) returns real-valued adjoint for real-valued
 A

---
 src/lib/array.jl  |  3 ++-
 test/gradcheck.jl | 13 +++++++++++++
 2 files changed, 15 insertions(+), 1 deletion(-)

diff --git a/src/lib/array.jl b/src/lib/array.jl
index 378110af2..ab8909418 100644
--- a/src/lib/array.jl
+++ b/src/lib/array.jl
@@ -485,7 +485,8 @@ end
   X = _pairdiffquotmat(exp, n, w, ew, ew, ew)
   V = E.vectors
   VF = factorize(V)
-  Ā = (V * ((VF \ F̄' * V) .* X) / VF)'
+  Āc = (V * ((VF \ F̄' * V) .* X) / VF)'
+  Ā = eltype(A) <: Real ? real(Āc) : Āc
   return (Ā,)
 end
 
diff --git a/test/gradcheck.jl b/test/gradcheck.jl
index a069ff207..0ccfb0fd0 100644
--- a/test/gradcheck.jl
+++ b/test/gradcheck.jl
@@ -566,6 +566,19 @@ end
       end
     end
   end
+
+  @testset "real-valued"
+    A = [ 0.0    1.0    0.0
+          0.0    0.0    1.0
+         -4.34 -18.31  -0.43]
+    _,B = Zygote.pullback(exp,A)
+    Ȳ = rand(MersenneTwister(347392),3,3)
+    @test isreal(B(Ȳ)[1])
+    # Works when `exp` adjoint returns a real-valued array
+    x = [1.0]
+    f(A,x) = exp(A*x[1])
+    @test gradtest(f,A,x)
+  end
 end
 
 _hermsymtype(::Type{<:Symmetric}) = Symmetric

From 9acd17910d8a7761287f047cb634e72cbd9aa9e8 Mon Sep 17 00:00:00 2001
From: sdewaele <14310676+sdewaele@users.noreply.github.com>
Date: Tue, 3 Dec 2019 13:31:05 -0500
Subject: [PATCH 2/4] Update src/lib/array.jl

Co-Authored-By: Michael Abbott <32575566+mcabbott@users.noreply.github.com>
---
 src/lib/array.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/lib/array.jl b/src/lib/array.jl
index ab8909418..a881eb091 100644
--- a/src/lib/array.jl
+++ b/src/lib/array.jl
@@ -486,7 +486,7 @@ end
   V = E.vectors
   VF = factorize(V)
   Āc = (V * ((VF \ F̄' * V) .* X) / VF)'
-  Ā = eltype(A) <: Real ? real(Āc) : Āc
+  Ā = eltype(A) <: Real && eltype(F̄) <: Real ? real(Āc) : Āc
   return (Ā,)
 end
 

From 17a36b0a1e1a9fd2934ac31a8606edef0f814ab2 Mon Sep 17 00:00:00 2001
From: Stijn de Waele <stijn.de.waele123@gmail.com>
Date: Tue, 3 Dec 2019 21:49:39 -0500
Subject: [PATCH 3/4] fixed isreal test for real-valued exp pullback

---
 test/gradcheck.jl | 15 ++++-----------
 1 file changed, 4 insertions(+), 11 deletions(-)

diff --git a/test/gradcheck.jl b/test/gradcheck.jl
index 0ccfb0fd0..4457fa83b 100644
--- a/test/gradcheck.jl
+++ b/test/gradcheck.jl
@@ -565,19 +565,12 @@ end
         end
       end
     end
-  end
-
-  @testset "real-valued"
     A = [ 0.0    1.0    0.0
           0.0    0.0    1.0
-         -4.34 -18.31  -0.43]
-    _,B = Zygote.pullback(exp,A)
-    Ȳ = rand(MersenneTwister(347392),3,3)
-    @test isreal(B(Ȳ)[1])
-    # Works when `exp` adjoint returns a real-valued array
-    x = [1.0]
-    f(A,x) = exp(A*x[1])
-    @test gradtest(f,A,x)
+          -4.34 -18.31  -0.43]
+    _,back = Zygote.pullback(exp,A)
+    Ȳ = rand(3,3)
+    @test isreal(back(Ȳ)[1])
   end
 end
 

From 2c22210a068603dd4e544f67fb92222e214ef118 Mon Sep 17 00:00:00 2001
From: Stijn de Waele <stijn.de.waele123@gmail.com>
Date: Sat, 14 Dec 2019 19:39:32 -0500
Subject: [PATCH 4/4] use isreal(M) instead of eltype(M)<: Real

---
 src/lib/array.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/lib/array.jl b/src/lib/array.jl
index a881eb091..c8cfa44f3 100644
--- a/src/lib/array.jl
+++ b/src/lib/array.jl
@@ -486,7 +486,7 @@ end
   V = E.vectors
   VF = factorize(V)
   Āc = (V * ((VF \ F̄' * V) .* X) / VF)'
-  Ā = eltype(A) <: Real && eltype(F̄) <: Real ? real(Āc) : Āc
+  Ā = isreal(A) && isreal(F̄) ? real(Āc) : Āc
   return (Ā,)
 end