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Add docs of AutoSparseForwardDiff and matrix coloring #231

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Oct 9, 2023
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Add docs of AutoSparseForwardDiff and matrix coloring #231

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e4a181b
Add docs of AutoSparseForwardDiff and matrix coloring
ErikQQY Oct 8, 2023
af7654c
Add ArrayInterface
ErikQQY Oct 8, 2023
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2 changes: 2 additions & 0 deletions docs/Project.toml
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Original file line number Diff line number Diff line change
@@ -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"
Expand All @@ -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"
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27 changes: 26 additions & 1 deletion docs/src/tutorials/advanced.md
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Expand Up @@ -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)
Expand Down Expand Up @@ -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
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This seems a bit oddly placed since the parts above already did sparsity and matrix coloring. This is just a less manual route for it

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Avik said the above part https://docs.sciml.ai/NonlinearSolve/dev/tutorials/advanced/#Declaring-a-Sparse-Jacobian-with-Automatic-Sparsity-Detection didn't actually use sparsity, we still need to use sparse AD type for matrix coloring. Did I understand this wrong?

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@ErikQQY is right. Right now even if you have colorvecs and stuff but use a non-sparse AD type, we construct a dense jacobian based on how SparseDiffTools is setup. But this can be modified.

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Oh. We should change that. If you pass a sparse matrix into jac_prototype it should always use sparse diff on it. The SparseDiffTools stuff should only override it to force sparse in the case of jac_prototype=nothing, otherwise it should respect the user's type and color on-demand (since coloring is super cheap).


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)
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Aren't the color vectors done automatically so this step is unneccessary?

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Aren't the color vectors done automatically so this step is unneccessary?

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
```
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