small fixes

Author: vchuravy

docs/src/index.md

@@ -4,11 +4,20 @@ Newton Method using Krylov.jl (montoison-orban-2023)[@cite]
 
 ## API
 
+#### Newton-Krylov
+
 ```@docs
 newton_krylov!
 newton_krylov
 ```
 
+#### Halley-Krylov
+
+```@docs
+halley_krylov!
+halley_krylov
+```
+
 ### Parameters
 
 ```@docs

src/NewtonKrylov.jl

@@ -315,16 +315,46 @@ function newton_krylov!(
     return u, (; solved = n_res <= tol, stats, t)
 end
 
+"""
+    halley_krylov(F, u₀::AbstractArray, M::Int = length(u₀))
+
+## Arguments
+  - `F`: `F(u)` solves `res = F(u) = 0`
+  - `u`: Initial guess
+  - `M`: Length of the output of `F`. Defaults to `length(u₀)`.
+ 
+$(KWARGS_DOCS)
+"""
 function halley_krylov(F, u₀::AbstractArray, M::Int = length(u₀); kwargs...)
     F!(res, u) = (res .= F(u); nothing)
     return halley_krylov!(F!, u₀, M; kwargs...)
 end
 
+"""
+    halley_krylov!(F!, u₀::AbstractArray, M::Int = length(u₀))
+
+## Arguments
+  - `F!`: `F!(res, u)` solves `res = F(u) = 0`
+  - `u`: Initial guess
+  - `M`: Length of the output of `F!`. Defaults to `length(u₀)`.
+ 
+$(KWARGS_DOCS)
+"""
 function halley_krylov!(F!, u₀::AbstractArray, M::Int = length(u₀); kwargs...)
     res = similar(u₀, M)
     return halley_krylov!(F!, u₀, res; kwargs...)
 end
 
+"""
+    halley_krylov!(F!, u::AbstractArray, res::AbstractArray)
+
+## Arguments
+  - `F!`: `F!(res, u)` solves `res = F(u) = 0`
+  - `u`: Initial guess
+  - `res`: Temporary for residual
+ 
+$(KWARGS_DOCS)
+"""
 function halley_krylov!(
         F!, u::AbstractArray, res::AbstractArray;
         tol_rel = 1.0e-6,

test/runtests.jl

@@ -58,6 +58,8 @@ end
     @test jvp ≈ J_Enz * v
 end
 
+import NewtonKrylov: HessianOperator
+
 # Differentiate F with respect to x twice.
 function ddf(x, a)
     return autodiff(Forward, df, DuplicatedNoNeed(x, a), Const(a)) |> first