Update sparsity detection docs

Author: adrhill

docs/Project.toml

@@ -1,4 +1,5 @@
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 AlgebraicMultigrid = "2169fc97-5a83-5252-b627-83903c6c433c"
 BSON = "fbb218c0-5317-5bc6-957e-2ee96dd4b1f0"
 BVProblemLibrary = "ded0fc24-dfea-4565-b1d9-79c027d14d84"
@@ -31,12 +32,13 @@ RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SDEProblemLibrary = "c72e72a9-a271-4b2b-8966-303ed956772e"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
+ADTypes = "1.7"
 AlgebraicMultigrid = "0.5, 0.6"
 BSON = "0.3"
 BVProblemLibrary = "0.1.2"
@@ -68,7 +70,7 @@ RecursiveArrayTools = "2, 3"
 SDEProblemLibrary = "0.1"
 SciMLBase = "2"
 SciMLOperators = "0.3"
+SparseConnectivityTracer = "0.6"
 StaticArrays = "1"
 Sundials = "4.11.3"
-Symbolics = "4, 5, 6"
 Unitful = "1"

docs/src/tutorials/advanced_ode_example.md

@@ -145,23 +145,30 @@ Note that you should only do this if the sparsity is high, for example, 0.1%
 of the matrix is non-zeros, otherwise the overhead of sparse matrices can be higher
 than the gains from sparse differentiation!
 
-One of the useful companion tools for DifferentialEquations.jl is
-[Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl).
-This allows for automatic declaration of Jacobian sparsity types. To see this
-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`.
+[ADTypes.jl](https://github.com/SciML/ADTypes.jl) provides a [common interface for automatic sparsity detection](https://sciml.github.io/ADTypes.jl/stable/#Sparsity-detector) 
+via its function `jacobian_sparsity`.
+This function can be called using sparsity detectors from [SparseConnectivityTracer.jl](https://github.com/adrhill/SparseConnectivityTracer.jl) 
+or [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl).
+
+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`.
+
+Let's try SparseConnectivityTracer's [`TracerSparsityDetector`](https://adrianhill.de/SparseConnectivityTracer.jl/stable/user/api/#SparseConnectivityTracer.TracerSparsityDetector):
 
 ```@example stiff1
-using Symbolics
+using SparseConnectivityTracer, ADTypes
+detector = TracerSparsityDetector()
 du0 = copy(u0)
-jac_sparsity = Symbolics.jacobian_sparsity((du, u) -> brusselator_2d_loop(du, u, p, 0.0),
-    du0, u0)
+jac_sparsity = ADTypes.jacobian_sparsity(
+    (du, u) -> brusselator_2d_loop(du, u, p, 0.0), du0, u0, detector)
 ```
 
-Notice that Julia gives a nice print out of the sparsity pattern. That's neat, and
-would be tedious to build by hand! Now we just pass it to the `ODEFunction`
-like as before:
+Using a different backend for sparsity detection just requires swapping out the detector,
+e.g. for Symbolics' [`SymbolicsSparsityDetector`](https://docs.sciml.ai/Symbolics/stable/manual/sparsity_detection/#Symbolics.SymbolicsSparsityDetector).
+
+Notice that Julia gives a nice print out of the sparsity pattern. 
+That's neat, and would be tedious to build by hand! 
+Now we just pass it to the `ODEFunction` like as before:
 
 ```@example stiff1
 f = ODEFunction(brusselator_2d_loop; jac_prototype = float.(jac_sparsity))