add dx methods (#77)

* add `dx` methods

* add tests for derivatives of `ZeroTangent`

* fix typo

Author: oscardssmith

src/interface.jl

@@ -53,6 +53,8 @@ However, users may provide additional overloads for custom representations of
 one dimensional Riemannian manifolds.
 """
 dx(x::Real) = one(x)
+dx(::NoTangent) = NoTangent()
+dx(::ZeroTangent) = ZeroTangent()
 dx(x::Complex) = error("Tried to take the gradient of a complex-valued function.")
 dx(x) = error("Cotangent space not defined for `$(typeof(x))`. Try a real-valued function.")
 

test/runtests.jl

@@ -184,6 +184,8 @@ end
 @test bwd(x->f_crit_edge(true, true, false, x))(1.0) == 2.0
 @test bwd(x->f_crit_edge(false, true, true, x))(1.0) == 12.0
 @test bwd(x->f_crit_edge(false, false, true, x))(1.0) == 4.0
+@test bwd(bwd(x->5))(1.0) == ZeroTangent()
+@test fwd(fwd(x->5))(1.0) == ZeroTangent()
 
 # Issue #27 - Mixup in lifting of getfield
 let var"'" = bwd