chore: apply suggestions from code review

Author: avik-pal

docs/src/basics/sparsity_detection.md

@@ -37,7 +37,8 @@ If the `colorvec` is not provided, then it is computed on demand.
 
     Previously you could provide a `sparsity` argument to `NonlinearFunction` to specify
     the jacobian prototype. However, to avoid confusion, this is now deprecated. Instead,
-    use the `jac_prototype` argument.
+    use the `jac_prototype` argument. `sparsity` must be used to exclusively specify the
+    sparsity detection algorithm.
 
 ## Case II: Sparsity Detection algorithm is provided
 
@@ -46,14 +47,14 @@ algorithm you want to use, then you can create your problem as follows:
 
 ```julia
 prob = NonlinearProblem(
-    NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetection()), x0)  # Remember to have Symbolics.jl loaded
+    NonlinearFunction(nlfunc; sparsity = SymbolicsSparsityDetector()), x0)  # Remember to have Symbolics.jl loaded
 # OR
 prob = NonlinearProblem(
     NonlinearFunction(nlfunc; sparsity = TracerSparsityDetector()), x0) # From SparseConnectivityTracer.jl
 ```
 
-Refer to the documentation of DifferentiationInterface.jl for more information on
-sparsity detection algorithms.
+Refer to the documentation of DifferentiationInterface.jl and SparseConnectivityTracer.jl
+for more information on sparsity detection algorithms.
 
 ## Case III: Sparse AD Type is being Used
 

src/NonlinearSolve.jl

@@ -57,7 +57,8 @@ using SparseConnectivityTracer: TracerSparsityDetector # This can be dropped in
 using SparseDiffTools: SparseDiffTools, JacPrototypeSparsityDetection,
                        PrecomputedJacobianColorvec, init_jacobian, sparse_jacobian,
                        sparse_jacobian!, sparse_jacobian_cache
-using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm
+using SparseMatrixColorings: ConstantColoringAlgorithm, GreedyColoringAlgorithm,
+                             LargestFirst
 
 @reexport using SciMLBase, SimpleNonlinearSolve
 

src/internal/jacobian.jl

@@ -64,7 +64,7 @@ function JacobianCache(prob, alg, f::F, fu_, u, p; stats, autodiff = nothing,
     if !has_analytic_jac && needs_jac
         autodiff = construct_concrete_adtype(f, autodiff)
         using_sparsedifftools = autodiff isa StructuredMatrixAutodiff
-        # DI can't handle structured matrices
+        # SparseMatrixColorings can't handle structured matrices
         if using_sparsedifftools
             di_extras = nothing
             uf = JacobianWrapper{iip}(f, p)
@@ -249,7 +249,7 @@ function construct_concrete_adtype(f::NonlinearFunction, ad::AbstractADType)
             return AutoSparse(
                 ad;
                 sparsity_detector,
-                coloring_algorithm = GreedyColoringAlgorithm()
+                coloring_algorithm = GreedyColoringAlgorithm(LargestFirst())
             )
         else
             if ArrayInterface.isstructured(f.jac_prototype)
@@ -304,7 +304,7 @@ function select_fastest_structured_matrix_autodiff(
             JacPrototypeSparsityDetection(; jac_prototype = prototype)
         end
     end
-    return StructuredMatrixAutodiff(ad, sparsity_detection)
+    return StructuredMatrixAutodiff(AutoSparse(ad), sparsity_detection)
 end
 
 function select_fastest_coloring_algorithm(
@@ -314,7 +314,7 @@ function select_fastest_coloring_algorithm(
             ADTypes.mode(ad) isa ADTypes.ReverseMode, :row, :column)}(
             prototype, f.colorvec)
     end
-    return GreedyColoringAlgorithm()
+    return GreedyColoringAlgorithm(LargestFirst())
 end
 
 function construct_concrete_adtype(f::NonlinearFunction, ad::AutoSparse)