feat: use HomotopyContinuationProblem in NonlinearProblem if possible

Author: AayushSabharwal

src/systems/nonlinear/nonlinearsystem.jl

@@ -492,10 +492,14 @@ end
 
 function DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem, u0map,
         parammap = DiffEqBase.NullParameters();
-        check_length = true, kwargs...) where {iip}
+        check_length = true, use_homotopy_continuation = true, kwargs...) where {iip}
     if !iscomplete(sys)
         error("A completed `NonlinearSystem` is required. Call `complete` or `structural_simplify` on the system before creating a `NonlinearProblem`")
     end
+    prob = safe_HomotopyContinuationProblem(sys, u0map, parammap; check_length, kwargs...)
+    if prob isa HomotopyContinuationProblem
+        return prob
+    end
     f, u0, p = process_SciMLProblem(NonlinearFunction{iip}, sys, u0map, parammap;
         check_length, kwargs...)
     pt = something(get_metadata(sys), StandardNonlinearProblem())

test/extensions/homotopy_continuation.jl

@@ -22,12 +22,19 @@ import HomotopyContinuation
            0 ~ x^2 + 4x + 4
            0 ~ y * z + 4x^2]
     @mtkbuild sys = NonlinearSystem(eqs)
-    prob = HomotopyContinuationProblem(sys, [x => 1.0, y => 1.0, z => 1.0], [])
+    u0 = [x => 1.0, y => 1.0, z => 1.0]
+    prob = HomotopyContinuationProblem(sys, u0)
     @test prob[x] == prob[y] == prob[z] == 1.0
     @test prob[x + y] == 2.0
     sol = solve(prob; threading = false)
     @test SciMLBase.successful_retcode(sol)
     @test norm(sol.resid)≈0.0 atol=1e-10
+
+    prob2 = NonlinearProblem(sys, u0)
+    @test prob2 isa HomotopyContinuationProblem
+    sol = solve(prob2; threading = false)
+    @test SciMLBase.successful_retcode(sol)
+    @test norm(sol.resid)≈0.0 atol=1e-10
 end
 
 struct Wrapper
@@ -92,36 +99,44 @@ end
         "Exponent", "not an integer", "not a polynomial"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
+
     @mtkbuild sys = NonlinearSystem([x^x - x ~ 0])
     @test_throws ["Cannot convert", "Unable", "symbolically solve",
         "Exponent", "unknowns", "not a polynomial"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
     @mtkbuild sys = NonlinearSystem([((x^2) / sin(x))^2 + x ~ 0])
     @test_throws ["Cannot convert", "both polynomial", "non-polynomial",
         "recognized", "sin", "not a polynomial"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
 
     @variables y = 2.0
     @mtkbuild sys = NonlinearSystem([x^2 + y^2 + 2 ~ 0, y ~ sin(x)])
     @test_throws ["Cannot convert", "recognized", "sin", "not a polynomial"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
 
     @mtkbuild sys = NonlinearSystem([x^2 + y^2 - 2 ~ 0, sin(x + y) ~ 0])
     @test_throws ["Cannot convert", "function of multiple unknowns"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
 
     @mtkbuild sys = NonlinearSystem([sin(x)^2 + 1 ~ 0, cos(y) - cos(x) - 1 ~ 0])
     @test_throws ["Cannot convert", "multiple non-polynomial terms", "same unknown"] HomotopyContinuationProblem(
         sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
 
     @mtkbuild sys = NonlinearSystem([sin(x^2)^2 + sin(x^2) - 1 ~ 0])
     @test_throws ["import Nemo"] HomotopyContinuationProblem(sys, [])
     @test MTK.safe_HomotopyContinuationProblem(sys, []) isa MTK.NotPolynomialError
+    @test NonlinearProblem(sys, []) isa NonlinearProblem
 end
 
 import Nemo