add new linearizatino method

Author: bartvanerp

src/approximations/linearization.jl

@@ -77,6 +77,13 @@ function local_linearization(r::Real, splitg::S, x_hat::H) where {S, H}
     return local_linearization_split(r, fA, x_hat)
 end
 
+# In case if `g(x_hat)` returns a vector, but input is a number
+function local_linearization(result::AbstractVector, g::G, x_hat::Tuple{T}) where {G, T <: Real}
+    A = ForwardDiff.derivative(g, first(x_hat))
+    b = result - A * first(x_hat)
+    return (A, b)
+end
+
 # In case if `g(x_hat)` returns a vector, but inputs are numbers
 function local_linearization(r::AbstractVector, splitg::S, x_hat::H) where {S, H}
     # `r` is a vector, so we need to use `jacobian` instead of `gradient`

test/approximations/linearization_tests.jl

@@ -11,5 +11,6 @@
         @test @inferred(approximate(Linearization(), (x, y) -> x - y, (1, 2))) == ([1 -1], 0)
         @test @inferred(approximate(Linearization(), (x, y) -> x .- y, ([1.0, 2.0], 1.0))) == ([1.0 0.0 -1.0; 0.0 1.0 -1.0], [0.0, 0.0])
         @test @inferred(approximate(Linearization(), (x, y) -> x .- y, ([1.0, 2.0], [1.0, 1.0]))) == ([1.0 0.0 -1.0 0.0; 0.0 1.0 0.0 -1.0], [0.0, 0.0])
+        @test @inferred(approximate(Linearization(), (x) -> x .- [1, 1], (1.0,))) == ([1.0, 1.0], [-1.0, -1.0])
     end
 end