Update ForwardDiff approach (#37)

`ForwardDiff` [recently added](JuliaDiff/ForwardDiff.jl#583) support for complex-valued functions of real arguments, which demonstrates the (presumably) right way to support geometric-algebra-valued functions, including quaternion-valued functions. I was on roughly the right track, but the default method should return 0, and the specific methods of quaternions over `Dual`s should have extracted the `partials` field of each components. This implements that approach.
moble · May 19, 2022 · 968190e · 968190e
1 parent 65a1e0c
commit 968190e
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Showing 3 changed files with 19 additions and 11 deletions.
diff --git a/Project.toml b/Project.toml
@@ -19,9 +19,3 @@ Requires = "1"
 StaticArrays = "1"
 Symbolics = "0.1, 1, 2, 3, 4"
 julia = "1.6"
-
-[extras]
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-
-[targets]
-test = ["Test"]
diff --git a/src/Quaternionic.jl b/src/Quaternionic.jl
@@ -40,8 +40,25 @@ include("examples.jl")
 function __init__()
     @require ForwardDiff="f6369f11-7733-5829-9624-2563aa707210" begin
         # Let ForwardDiff act naturally on quaternions.
-        @inline function ForwardDiff.extract_derivative(::Type{T}, y::AbstractQuaternion) where {T}
-            Quaternion(ForwardDiff.extract_derivative(T, y.components))
+        # This is cribbed from similar expressions enabling differentiation of complex-valued functions in
+        # https://github.com/JuliaDiff/ForwardDiff.jl/blob/78c73afd9a21593daf54f61c7d0db67130cf29e1/src/derivative.jl#L83-L88
+        @inline ForwardDiff.extract_derivative(::Type{T}, y::AbstractQuaternion) where {T} = zero(y)
+        # Both Quaternion and Rotor, when differentiated, result in a Quaternion
+        @inline function ForwardDiff.extract_derivative(::Type{T}, y::AbstractQuaternion{TD}) where {T, TD <: ForwardDiff.Dual}
+            Quaternion(
+                ForwardDiff.partials(T, y.w, 1),
+                ForwardDiff.partials(T, y.x, 1),
+                ForwardDiff.partials(T, y.y, 1),
+                ForwardDiff.partials(T, y.z, 1)
+            )
+        end
+        # But QuatVec results in a QuatVec
+        @inline function ForwardDiff.extract_derivative(::Type{T}, y::QuatVec{TD}) where {T, TD <: ForwardDiff.Dual}
+            QuatVec(
+                ForwardDiff.partials(T, y.x, 1),
+                ForwardDiff.partials(T, y.y, 1),
+                ForwardDiff.partials(T, y.z, 1)
+            )
         end
     end
 

diff --git a/test/Project.toml b/test/Project.toml
@@ -2,9 +2,6 @@
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 EllipsisNotation = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
-Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
-Quaternionic = "0756cd96-85bf-4b6f-a009-b5012ea7a443"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"