chore: apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: avik-pal

docs/src/basics/sparsity_detection.md

@@ -9,30 +9,30 @@ Notation wise we are trying to solve for `x` such that `nlfunc(x) = 0`.
 ## Big Table for Determining Sparsity Detection and Coloring Algorithms
 
 | `f.sparsity`               | `f.jac_prototype` | `f.colorvec` | Sparsity Detection                               | Coloring Algorithm                        |
-| :------------------------- | :---------------- | :----------- | :----------------------------------------------- | :---------------------------------------- |
-| ❌                         | ❌                | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
-| ❌                         | Not Structured    | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
-| ❌                         | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
-| ❌                         | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+|:-------------------------- |:----------------- |:------------ |:------------------------------------------------ |:----------------------------------------- |
+| ❌                          | ❌                 | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                          | Not Structured    | `Any`        | `NoSparsityDetector()`                           | `NoColoringAlgorithm()`                   |
+| ❌                          | Structured        | ✅            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+| ❌                          | Structured        | ❌            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
 | -                          | -                 | -            | -                                                | -                                         |
-| `AbstractMatrix`           | ❌                | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractMatrix`           | ❌                | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractMatrix`           | Not Structured    | ✅           | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractMatrix`           | Not Structured    | ❌           | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractMatrix`           | Structured        | `Any`        | 🔴                                               | 🔴                                        |
+| `AbstractMatrix`           | ❌                 | ✅            | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | ❌                 | ❌            | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Not Structured    | ✅            | `KnownJacobianSparsityDetector(f.sparsity)`      | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractMatrix`           | Not Structured    | ❌            | `KnownJacobianSparsityDetector(f.sparsity)`      | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractMatrix`           | Structured        | `Any`        | 🔴                                                | 🔴                                         |
 | -                          | -                 | -            | -                                                | -                                         |
-| `AbstractSparsityDetector` | ❌                | `Any`        | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractSparsityDetector` | Not Structured    | ✅           | `f.sparsity`                                     | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractSparsityDetector` | Not Structured    | ❌           | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
-| `AbstractSparsityDetector` | Structured        | ✅           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `ConstantColoringAlgorithm(f.colorvec)`   |
-| `AbstractSparsityDetector` | Structured        | ❌           | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
-
-1. `Structured` means either a `AbstractSparseMatrix` or `ArrayInterface.isstructured(x)` is true.
-2. ❌ means not provided (default)
-3. ✅ means provided
-4. 🔴 means an error will be thrown
-5. Providing a colorvec without specifying either sparsity or jac_prototype with a sparse or structured matrix will cause us to ignore the colorvec.
-6. The function calls demonstrated above are simply pseudo-code to show the general idea.
+| `AbstractSparsityDetector` | ❌                 | `Any`        | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Not Structured    | ✅            | `f.sparsity`                                     | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Not Structured    | ❌            | `f.sparsity`                                     | `GreedyColoringAlgorithm(LargestFirst())` |
+| `AbstractSparsityDetector` | Structured        | ✅            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `ConstantColoringAlgorithm(f.colorvec)`   |
+| `AbstractSparsityDetector` | Structured        | ❌            | `KnownJacobianSparsityDetector(f.jac_prototype)` | `GreedyColoringAlgorithm(LargestFirst())` |
+
+ 1. `Structured` means either a `AbstractSparseMatrix` or `ArrayInterface.isstructured(x)` is true.
+ 2. ❌ means not provided (default)
+ 3. ✅ means provided
+ 4. 🔴 means an error will be thrown
+ 5. Providing a colorvec without specifying either sparsity or jac_prototype with a sparse or structured matrix will cause us to ignore the colorvec.
+ 6. The function calls demonstrated above are simply pseudo-code to show the general idea.
 
 ## Case I: Sparse Jacobian Prototype is Provided
 
@@ -55,7 +55,7 @@ prob = NonlinearProblem(
 If the `colorvec` is not provided, then it is computed on demand.
 
 !!! note
-
+    
     One thing to be careful about in this case is that `colorvec` is dependent on the
     autodiff backend used. `ADTypes.mode(ad) isa ADTypes.ForwardMode` will assume that the
     colorvec is the column colorvec, otherwise we will assume that the colorvec is the
@@ -80,7 +80,7 @@ for more information on sparsity detection algorithms.
 ## Case III: Sparse AD Type is being Used
 
 !!! warning
-
+    
     This is now deprecated. Please use the previous two cases instead.
 
 If you constructed a Nonlinear Solver with a sparse AD type, for example