Merge pull request #244 from avik-pal/ap/defaults

Better Defaults: Auto AD Selection for Newton Methods

Author: ChrisRackauckas

Project.toml

@@ -50,7 +50,7 @@ PrecompileTools = "1"
 RecursiveArrayTools = "2"
 Reexport = "0.2, 1"
 SciMLBase = "2.4"
-SimpleNonlinearSolve = "0.1"
+SimpleNonlinearSolve = "0.1.22"
 SparseDiffTools = "2.6"
 StaticArraysCore = "1.4"
 UnPack = "1.0"

docs/pages.jl

@@ -2,8 +2,7 @@
 
 pages = ["index.md",
     "tutorials/getting_started.md",
-    "Tutorials" => Any[
-        "tutorials/code_optimization.md",
+    "Tutorials" => Any["tutorials/code_optimization.md",
         "tutorials/large_systems.md",
         "tutorials/small_compile.md",
         "tutorials/termination_conditions.md",

docs/src/solvers/NonlinearSystemSolvers.md

@@ -16,7 +16,7 @@ it will make sure to work.
 
 If one is looking for more robustness then `RobustMultiNewton` is a good choice.
 It attempts a set of the most robust methods in succession and only fails if
-all of the methods fail to converge. Additionally, `DynamicSS` can be a good choice 
+all of the methods fail to converge. Additionally, `DynamicSS` can be a good choice
 for high stability.
 
 As a balance, `NewtonRaphson` is a good choice for most problems that aren't too
@@ -25,13 +25,13 @@ but more stable. If the problem is well-conditioned, `Klement` or `Broyden`
 may be faster, but highly dependent on the eigenvalues of the Jacobian being
 sufficiently small.
 
-`NewtonRaphson` and `TrustRegion` are designed for for large systems. 
+`NewtonRaphson` and `TrustRegion` are designed for for large systems.
 They can make use of sparsity patterns for sparse automatic differentiation
 and sparse linear solving of very large systems. Meanwhile,
 `SimpleNewtonRaphson` and `SimpleTrustRegion` are implementations which is specialized for
 small equations. They are non-allocating on static arrays and thus really well-optimized
 for small systems, thus usually outperforming the other methods when such types are
-used for `u0`. 
+used for `u0`.
 
 ## Full List of Methods
 
@@ -57,7 +57,7 @@ features, but have a bit of overhead on very small problems.
     large-scale and numerically-difficult nonlinear systems.
   - `RobustMultiNewton()`: A polyalgorithm that mixes highly robust methods (line searches and
     trust regions) in order to be as robust as possible for difficult problems. If this method
-    fails to converge, then one can be pretty certain that most (all?) other choices would 
+    fails to converge, then one can be pretty certain that most (all?) other choices would
     likely fail.
   - `FastShortcutNonlinearPolyalg`: The default method. A polyalgorithm that mixes fast methods
     with fallbacks to robust methods to allow for solving easy problems quickly without sacrificing

docs/src/tutorials/code_optimization.md

@@ -55,4 +55,4 @@ prob = NonlinearProblem(f!, u0, p)
 
 linsolve = LinearSolve.KrylovJL_GMRES()
 sol = solve(prob, NewtonRaphson(; linsolve), reltol = 1e-9)
-```
+```

docs/src/tutorials/getting_started.md

@@ -9,19 +9,19 @@ to understanding the deeper parts of the documentation.
 
 There are three types of nonlinear systems:
 
-1. The "standard nonlinear system", i.e. the `NonlinearProblem`. This is a
-   system of equations with an initial condition where you want to satisfy
-   all equations simultaniously.
-2. The "interval rootfinding problem", i.e. the `IntervalNonlinearProblem`.
-   This is the case where you're given an interval `[a,b]` and need to find
-   where `f(u) = 0` for `u` inside the bounds.
-3. The "steady state problem", i.e. find the `u` such that `u' = f(u) = 0`.
-   While related to (1), it's not entirely the same because there's a uniquely
-   defined privledged root.
-4. The nonlinear least squares problem, which is an overconstrained nonlinear
-   system (i.e. more equations than states) which might not be satisfiable, i.e.
-   there may be no `u` such that `f(u) = 0`, and thus we find the `u` which
-   minimizes `||f(u)||` in the least squares sense.
+ 1. The "standard nonlinear system", i.e. the `NonlinearProblem`. This is a
+    system of equations with an initial condition where you want to satisfy
+    all equations simultaniously.
+ 2. The "interval rootfinding problem", i.e. the `IntervalNonlinearProblem`.
+    This is the case where you're given an interval `[a,b]` and need to find
+    where `f(u) = 0` for `u` inside the bounds.
+ 3. The "steady state problem", i.e. find the `u` such that `u' = f(u) = 0`.
+    While related to (1), it's not entirely the same because there's a uniquely
+    defined privledged root.
+ 4. The nonlinear least squares problem, which is an overconstrained nonlinear
+    system (i.e. more equations than states) which might not be satisfiable, i.e.
+    there may be no `u` such that `f(u) = 0`, and thus we find the `u` which
+    minimizes `||f(u)||` in the least squares sense.
 
 For now let's focus on the first two. The other two are covered in later tutorials,
 but from the first two we can show the general flow of the NonlinearSolve.jl package.
@@ -105,7 +105,7 @@ For a complete list of solver choices, see [the nonlinear system solvers page](@
 Next we can modify the tolerances. Here let's set some really low tolerances to force a tight solution:
 
 ```@example 1
-solve(prob, TrustRegion(), reltol=1e-12, abstol=1e-12)
+solve(prob, TrustRegion(), reltol = 1e-12, abstol = 1e-12)
 ```
 
 There are many more options for doing this configuring. Specifically for handling termination conditions,
@@ -139,10 +139,10 @@ sol = solve(prob_int, ITP(), abstol = 0.01)
 Congrats, you now know how to use the basics of NonlinearSolve.jl! However, there is so much more to
 see. Next check out:
 
-- [Some code optimization tricks to know about with NonlinearSolve.jl](@ref code_optimization)
-- [An iterator interface which lets you step through the solving process step by step](@ref iterator)
-- [How to handle large systems of equations efficiently](@ref large_systems)
-- [Ways to use NonlinearSolve.jl that is faster to startup and can statically compile](@ref fast_startup)
-- [More detailed termination conditions](@ref termination_conditions_tutorial)
+  - [Some code optimization tricks to know about with NonlinearSolve.jl](@ref code_optimization)
+  - [An iterator interface which lets you step through the solving process step by step](@ref iterator)
+  - [How to handle large systems of equations efficiently](@ref large_systems)
+  - [Ways to use NonlinearSolve.jl that is faster to startup and can statically compile](@ref fast_startup)
+  - [More detailed termination conditions](@ref termination_conditions_tutorial)
 
-And also check out the rest of the manual.
+And also check out the rest of the manual.

docs/src/tutorials/iterator_interface.md

@@ -1,7 +1,7 @@
 # [Nonlinear Solver Iterator Interface](@id iterator)
 
 !!! warn
-
+    
     This iterator interface will be expanded with a `step!` function soon!
 
 There is an iterator form of the nonlinear solver which mirrors the DiffEq integrator interface:

docs/src/tutorials/large_systems.md

@@ -209,8 +209,7 @@ function incompletelu(W, du, u, p, t, newW, Plprev, Prprev, solverdata)
 end
 
 @btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = incompletelu,
-        concrete_jac = true));
+    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = incompletelu, concrete_jac = true));
 nothing # hide
 ```
 
@@ -275,28 +274,3 @@ 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
-@btime 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)
-
-@btime solve(prob_brusselator_2d_sparse,
-    NewtonRaphson(linsolve = KrylovJL_GMRES(), precs = incompletelu, concrete_jac = true,
-        autodiff = AutoSparseForwardDiff()));
-nothing # hide
-```

docs/src/tutorials/small_compile.md

@@ -1,3 +1,3 @@
 # Faster Startup and and Static Compilation
 
-This is a stub article to be completed soon.
+This is a stub article to be completed soon.

docs/src/tutorials/termination_conditions.md

@@ -1,3 +1,3 @@
 # [More Detailed Termination Conditions](@id termination_conditions_tutorial)
 
-This is a stub article to be completed soon.
+This is a stub article to be completed soon.