Rules for cross-product (#199)

* Add cross product rules

* Add cross product tests

* Increment version number

* Relax equality check

* Increment version number

* Bump version number

* Remove chunked frule

* Remove unused method

* Add back complex frule tests

Project.toml

@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.6.4"
+version = "0.6.5"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

src/rulesets/LinearAlgebra/dense.jl

@@ -19,6 +19,23 @@ function rrule(::typeof(dot), x, y)
     return dot(x, y), dot_pullback
 end
 
+#####
+##### `cross`
+#####
+
+function frule((_, Δa, Δb), ::typeof(cross), a::AbstractVector, b::AbstractVector)
+    return cross(a, b), cross(Δa, b) .+ cross(a, Δb)
+end
+
+# TODO: support complex vectors
+function rrule(::typeof(cross), a::AbstractVector{<:Real}, b::AbstractVector{<:Real})
+    Ω = cross(a, b)
+    function cross_pullback(ΔΩ)
+        return (NO_FIELDS, @thunk(cross(b, ΔΩ)), @thunk(cross(ΔΩ, a)))
+    end
+    return Ω, cross_pullback
+end
+
 #####
 ##### `inv`
 #####

test/rulesets/LinearAlgebra/dense.jl

@@ -25,6 +25,23 @@
             rrule_test(dot, randn(), (x, x̄), (y, ȳ))
         end
     end
+    @testset "cross" begin
+        @testset "frule" begin
+            @testset "$T" for T in (Float64, ComplexF64)
+                n = 3
+                x, y = randn(T, n), randn(T, n)
+                ẋ, ẏ = randn(T, n), randn(T, n)
+                frule_test(cross, (x, ẋ), (y, ẏ))
+            end
+        end
+        @testset "rrule" begin
+            n = 3
+            x, y = randn(n), randn(n)
+            x̄, ȳ = randn(n), randn(n)
+            ΔΩ = randn(n)
+            rrule_test(cross, ΔΩ, (x, x̄), (y, ȳ))
+        end
+    end
     @testset "inv" begin
         N = 3
         B = generate_well_conditioned_matrix(N)