compare against NLSolve

docs/src/notebooks/Project.toml

@@ -1,7 +1,8 @@
 [deps]
+Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
-Ariadne = "0be81120-40bf-4f8b-adf0-26103efb66f1"
+NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
 PlutoLinks = "0ff47ea0-7a50-410d-8455-4348d5de0420"

docs/src/notebooks/comparison.jl

@@ -0,0 +1,141 @@
+### A Pluto.jl notebook ###
+# v0.20.24
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ eb792fe6-3cbe-11f1-2eca-0bd287486337
+begin
+    import Pkg
+    # careful: this is _not_ a reproducible environment
+    # activate the local environment
+    Pkg.activate(".")
+    Pkg.instantiate()
+    using PlutoUI, PlutoLinks
+    using CairoMakie
+end
+
+# ╔═╡ 869833fd-ee32-4469-ad9f-ef6489f68811
+@revise using Ariadne
+
+# ╔═╡ 0aa45e3b-433b-4385-aa8c-e71e8acf725a
+import NonlinearSolve as NLS
+
+# ╔═╡ fa13b4ca-a809-43c4-979d-e0864874d8f6
+md"""
+## Generalized Rosenbrock
+
+This example is taken from Fig. 1 of:
+> A. Pal et al., "NonlinearSolve.jl: High-performance and robust solvers for systems
+> of nonlinear equations in Julia," arXiv [math.NA], 24-Mar-2024.
+> https://arxiv.org/abs/2403.16341
+
+### Problem definition
+
+The generalized Rosenbrock function in $N$ dimensions:
+```math
+F(x)_1 = 1 - x_1, \quad F(x)_i = 10(x_i - x_{i-1}^2), \quad i = 2, \ldots, N
+```
+"""
+
+# ╔═╡ edf5d7a1-4f17-484a-aebf-729ea149b580
+function generalized_rosenbrock(x, _)
+    return vcat(
+        1 - x[1],
+        10 .* (x[2:end] .- x[1:(end - 1)] .* x[1:(end - 1)])
+    )
+end
+
+# ╔═╡ 078b6618-f037-44b1-9c17-4a1785170bfc
+N = 9
+
+# ╔═╡ 80cde332-fbd1-49a0-bd61-944720f885fe
+x_start = vcat(-1.2, ones(N - 1))
+
+# ╔═╡ 4bb5bf4b-a37b-4d02-97a6-00bece7dc9f8
+md"""
+## using Ariadne
+"""
+
+# ╔═╡ 772047e4-debd-4871-a659-f91d15c3ea45
+let
+    _, stats = newton_krylov(
+        generalized_rosenbrock,
+        copy(x_start);
+        algo = :gmres,
+        linesearch! = NoLineSearch(),
+        max_niter = 100_000
+    )
+    stats
+end
+
+# ╔═╡ 42a30e51-8cf7-49fa-8348-159803d4a1c3
+let
+    _, stats = newton_krylov(
+        generalized_rosenbrock,
+        copy(x_start);
+        algo = :gmres,
+        linesearch! = BacktrackingLineSearch(),
+        max_niter = 100_000
+    )
+    stats
+end
+
+# ╔═╡ 4ec97f25-7af2-4138-9203-f933d8e593d9
+md"""
+## using NonlinearSolve
+"""
+
+# ╔═╡ eafb63ff-857d-4cc3-84eb-19ad4dd5755a
+prob = NLS.NonlinearProblem(generalized_rosenbrock, x_start)
+
+# ╔═╡ 58fbc259-aa11-49a4-8252-7c9d8acd1dcc
+let
+    sol = NLS.solve(prob, reltol = 1.0e-6, abstol = 1.0e-12, verbose = false)
+    sol.stats
+end
+
+# ╔═╡ 69a3e7b5-bf52-408b-bd33-80e0618b539b
+alg = NLS.NewtonRaphson(
+    linesearch = missing,
+    forcing = NLS.EisenstatWalkerForcing2(),
+    linsolve = NLS.KrylovJL()
+)
+
+# ╔═╡ aa53ea6f-9d39-43ea-b130-f0c98f187958
+alg2 = NLS.NewtonRaphson(
+    linesearch = NLS.BackTracking(),
+    forcing = NLS.EisenstatWalkerForcing2(),
+    linsolve = NLS.KrylovJL()
+)
+
+# ╔═╡ 08473c35-a4f6-4115-8db5-03b13f4a2cce
+let
+    sol = NLS.solve(prob, alg, reltol = 1.0e-6, abstol = 1.0e-12, verbose = false)
+    sol.stats
+end
+
+# ╔═╡ 9cea0413-f915-4784-a2c0-9b041c71b649
+let
+    sol = NLS.solve(prob, alg2, reltol = 1.0e-6, abstol = 1.0e-12, verbose = false)
+    sol.stats
+end
+
+# ╔═╡ Cell order:
+# ╠═eb792fe6-3cbe-11f1-2eca-0bd287486337
+# ╠═869833fd-ee32-4469-ad9f-ef6489f68811
+# ╠═0aa45e3b-433b-4385-aa8c-e71e8acf725a
+# ╟─fa13b4ca-a809-43c4-979d-e0864874d8f6
+# ╠═edf5d7a1-4f17-484a-aebf-729ea149b580
+# ╠═078b6618-f037-44b1-9c17-4a1785170bfc
+# ╠═80cde332-fbd1-49a0-bd61-944720f885fe
+# ╟─4bb5bf4b-a37b-4d02-97a6-00bece7dc9f8
+# ╠═772047e4-debd-4871-a659-f91d15c3ea45
+# ╠═42a30e51-8cf7-49fa-8348-159803d4a1c3
+# ╟─4ec97f25-7af2-4138-9203-f933d8e593d9
+# ╠═eafb63ff-857d-4cc3-84eb-19ad4dd5755a
+# ╠═58fbc259-aa11-49a4-8252-7c9d8acd1dcc
+# ╠═69a3e7b5-bf52-408b-bd33-80e0618b539b
+# ╠═aa53ea6f-9d39-43ea-b130-f0c98f187958
+# ╠═08473c35-a4f6-4115-8db5-03b13f4a2cce
+# ╠═9cea0413-f915-4784-a2c0-9b041c71b649

docs/src/notebooks/heat_1D_DG.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.20.8
+# v0.20.24
 
 using Markdown
 using InteractiveUtils