From e4a181b4ad86655cd99ed9a4df7cd204e205db88 Mon Sep 17 00:00:00 2001
From: ErikQQY <2283984853@qq.com>
Date: Sun, 8 Oct 2023 21:13:34 +0800
Subject: [PATCH 1/2] Add docs of AutoSparseForwardDiff and matrix coloring

Signed-off-by: ErikQQY <2283984853@qq.com>
---
 docs/src/tutorials/advanced.md | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/docs/src/tutorials/advanced.md b/docs/src/tutorials/advanced.md
index ca8ca0bd3..b86232901 100644
--- a/docs/src/tutorials/advanced.md
+++ b/docs/src/tutorials/advanced.md
@@ -55,7 +55,7 @@ are then applied at each point in space (they are broadcast). Use `dx=dy=1/32`.
 The resulting `NonlinearProblem` definition is:
 
 ```@example ill_conditioned_nlprob
-using NonlinearSolve, LinearAlgebra, SparseArrays, LinearSolve
+using NonlinearSolve, LinearAlgebra, SparseArrays, LinearSolve, Symbolics
 
 const N = 32
 const xyd_brusselator = range(0, stop = 1, length = N)
@@ -275,3 +275,28 @@ nothing # hide
 
 For more information on the preconditioner interface, see the
 [linear solver documentation](https://docs.sciml.ai/LinearSolve/stable/basics/Preconditioners/).
+
+## Speed up Jacobian computation with sparsity exploitation and matrix coloring
+
+To cut down the of Jacobian building overhead, we can choose to exploit the sparsity pattern and deploy matrix coloring during Jacobian construction. With NonlinearSolve.jl, we can simply use ```autodiff=AutoSparseForwardDiff()``` to automatically exploit the sparsity pattern of Jacobian matrices:
+
+```@example ill_conditioned_nlprob
+@benchmark solve(prob_brusselator_2d,
+    NewtonRaphson(linsolve=KrylovJL_GMRES(), precs=incompletelu, concrete_jac=true,
+        autodiff=AutoSparseForwardDiff()));
+nothing # hide
+```
+
+To setup matrix coloring for the jacobian sparsity pattern, we can simply get the coloring vector by using [ArrayInterface.jl](https://github.com/JuliaArrays/ArrayInterface.jl) for the sparsity pattern of `jac_prototype`:
+
+```@example ill_conditioned_nlprob
+using ArrayInterface
+colorvec = ArrayInterface.matrix_colors(jac_sparsity)
+ff = NonlinearFunction(brusselator_2d_loop; jac_prototype=float.(jac_sparsity), colorvec)
+prob_brusselator_2d_sparse = NonlinearProblem(ff, u0, p)
+
+@benchmark solve(prob_brusselator_2d_sparse,
+    NewtonRaphson(linsolve=KrylovJL_GMRES(), precs=incompletelu, concrete_jac=true,
+        autodiff=AutoSparseForwardDiff()));
+nothing # hide
+```
\ No newline at end of file

From af7654c1778589e82fc27d7f20e920dd6d10c3a6 Mon Sep 17 00:00:00 2001
From: ErikQQY <2283984853@qq.com>
Date: Sun, 8 Oct 2023 21:54:01 +0800
Subject: [PATCH 2/2] Add ArrayInterface

Signed-off-by: ErikQQY <2283984853@qq.com>
---
 docs/Project.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/Project.toml b/docs/Project.toml
index 1cb355487..fbc6a4185 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,6 @@
 [deps]
 AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
+ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
@@ -15,6 +16,7 @@ Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
 AlgebraicMultigrid = "0.5, 0.6"
+ArrayInterface = "6, 7"
 BenchmarkTools = "1"
 Documenter = "1"
 IncompleteLU = "0.2"