Add NoInverse

Co-authored-by: David Widmann <[email protected]>

Author: oschulz

docs/src/api.md

@@ -4,6 +4,7 @@
 
 ```@docs
 inverse
+NoInverse
 ```
 
 ## Test utility

src/inverse.jl

@@ -52,6 +52,27 @@ You can check your implementation with [`InverseFunctions.test_inverse`](@ref).
 inverse(f)
 export inverse
 
+
+
+"""
+    struct NoInverse{F}
+
+An instance `NoInverse(f)` signifies that that `inverse(f)` is not
+defined.
+"""
+struct NoInverse{F}
+    f::F
+end
+export NoInverse
+
+(f::NoInverse)(x) = error("inverse of ", f.f, " is not defined")
+
+inverse(f) = NoInverse(f)
+
+inverse(f::NoInverse) = f.f
+
+
+
 inverse(::typeof(inverse)) = inverse
 
 @static if VERSION >= v"1.6"

test/test_inverse.jl

@@ -20,6 +20,12 @@ InverseFunctions.inverse(f::Bar) = Bar(inv(f.A))
 
 
 @testset "inverse" begin
+    f_without_inverse(x) = x^2
+    @test inverse(f_without_inverse) isa NoInverse
+    @test_throws ErrorException inverse(f_without_inverse)(42)
+    @test inverse(inverse(f_without_inverse)) === f_without_inverse
+
+
     InverseFunctions.test_inverse(inverse, log, compare = ===)
 
     x = rand()