tangent_arithmetic: add norm for NoTangent and ZeroTangent

Author: lukas-weber

src/tangent_types/abstract_zero.jl

@@ -23,6 +23,8 @@ Base.last(x::AbstractZero) = x
 Base.Broadcast.broadcastable(x::AbstractZero) = Ref(x)
 Base.Broadcast.broadcasted(::Type{T}) where {T<:AbstractZero} = T()
 
+LinearAlgebra.norm(::AbstractZero) = 0
+
 # Linear operators
 Base.adjoint(z::AbstractZero) = z
 Base.transpose(z::AbstractZero) = z

test/tangent_types/abstract_zero.jl

@@ -120,6 +120,9 @@
         @test dot(ZeroTangent(), dne) == ZeroTangent()
         @test dot(dne, ZeroTangent()) == ZeroTangent()
 
+        @test norm(ZeroTangent()) == 0
+        @test norm(ZeroTangent(), 0.4) == 0
+
         for x in dne
             @test x === dne
         end

test/tangent_types/tangent.jl

@@ -329,11 +329,15 @@ end
         @test c * NoTangent() == NoTangent()
         @test dot(NoTangent(), c) == NoTangent()
         @test dot(c, NoTangent()) == NoTangent()
+        @test norm(Tangent{Foo}(; y=c.y, x=NoTangent())) == c.y
+        @test norm(NoTangent(), Inf) == 0
 
         @test ZeroTangent() * c == ZeroTangent()
         @test c * ZeroTangent() == ZeroTangent()
         @test dot(ZeroTangent(), c) == ZeroTangent()
         @test dot(c, ZeroTangent()) == ZeroTangent()
+        @test norm(ZeroTangent()) == 0
+        @test norm(ZeroTangent(), 0.4) == 0
 
         @test true * c === c
         @test c * true === c