Same environment for ill conditioned nlprob

Signed-off-by: ErikQQY <[email protected]>

Author: ErikQQY

docs/Project.toml

@@ -1,4 +1,5 @@
 [deps]
+AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
@@ -13,6 +14,7 @@ Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
+AlgebraicMultigrid = "0.5"
 BenchmarkTools = "1"
 Documenter = "0.27"
 IncompleteLU = "0.2"

docs/src/tutorials/advanced.md

@@ -54,7 +54,7 @@ are then applied at each point in space (they are broadcast). Use `dx=dy=1/32`.
 
 The resulting `NonlinearProblem` definition is:
 
-```@example
+```@example ill_conditioned_nlprob
 using NonlinearSolve, LinearAlgebra, SparseArrays, LinearSolve
 
 const N = 32
@@ -130,7 +130,7 @@ in action, we can give an example `du` and `u` and call `jacobian_sparsity`
 on our function with the example arguments, and it will kick out a sparse matrix
 with our pattern, that we can turn into our `jac_prototype`.
 
-```@example
+```@example ill_conditioned_nlprob
 using Symbolics
 du0 = copy(u0)
 jac_sparsity = Symbolics.jacobian_sparsity((du, u) -> brusselator_2d_loop(du, u, p),
@@ -141,19 +141,19 @@ Notice that Julia gives a nice print out of the sparsity pattern. That's neat, a
 would be tedious to build by hand! Now we just pass it to the `NonlinearFunction`
 like as before:
 
-```@example
+```@example ill_conditioned_nlprob
 ff = NonlinearFunction(brusselator_2d_loop; jac_prototype = float.(jac_sparsity))
 ```
 
 Build the `NonlinearProblem`:
 
-```@example
+```@example ill_conditioned_nlprob
 prob_brusselator_2d_sparse = NonlinearProblem(ff, u0, p)
 ```
 
 Now let's see how the version with sparsity compares to the version without:
 
-```@example
+```@example ill_conditioned_nlprob
 using BenchmarkTools # for @btime
 @btime solve(prob_brusselator_2d, NewtonRaphson());
 @btime solve(prob_brusselator_2d_sparse, NewtonRaphson());
@@ -172,7 +172,7 @@ matrices is to use a Krylov subspace method. This requires choosing a linear
 solver for changing to a Krylov method. To swap the linear solver out, we use
 the `linsolve` command and choose the GMRES linear solver.
 
-```@example
+```@example ill_conditioned_nlprob
 @btime solve(prob_brusselator_2d, NewtonRaphson(linsolve = KrylovJL_GMRES()));
 nothing # hide
 ```
@@ -197,7 +197,7 @@ approximate the inverse of `W = I - gamma*J` used in the solution of the ODE.
 An example of this with using [IncompleteLU.jl](https://github.com/haampie/IncompleteLU.jl)
 is as follows:
 
-```@example
+```@example ill_conditioned_nlprob
 using IncompleteLU
 function incompletelu(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
     if newW === nothing || newW
@@ -233,7 +233,7 @@ requires a well-tuned `τ` parameter. Another option is to use
 [AlgebraicMultigrid.jl](https://github.com/JuliaLinearAlgebra/AlgebraicMultigrid.jl)
 which is more automatic. The setup is very similar to before:
 
-```@example
+```@example ill_conditioned_nlprob
 using AlgebraicMultigrid
 function algebraicmultigrid(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
     if newW === nothing || newW
@@ -252,7 +252,7 @@ nothing # hide
 
 or with a Jacobi smoother:
 
-```@example
+```@example ill_conditioned_nlprob
 function algebraicmultigrid2(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
     if newW === nothing || newW
         A = convert(AbstractMatrix, W)