test: add tests for HomotopyContinuation.jl interface

Author: AayushSabharwal

test/extensions/Project.toml

@@ -3,10 +3,12 @@ BifurcationKit = "0f109fa4-8a5d-4b75-95aa-f515264e7665"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
 LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 SciMLStructures = "53ae85a6-f571-4167-b2af-e1d143709226"
 SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

test/extensions/homotopy_continuation.jl

@@ -0,0 +1,62 @@
+using ModelingToolkit, NonlinearSolve, SymbolicIndexingInterface
+using LinearAlgebra
+using Test
+import HomotopyContinuation
+
+@testset "No parameters" begin
+    @variables x y z
+    eqs = [0 ~ x^2 + y^2 + 2x * y
+           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], [])
+    @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
+end
+
+struct Wrapper
+    x::Matrix{Float64}
+end
+
+@testset "Parameters" begin
+    wrapper(w::Wrapper) = det(w.x)
+    @register_symbolic wrapper(w::Wrapper)
+
+    @variables x y z
+    @parameters p q::Int r::Wrapper
+
+    eqs = [0 ~ x^2 + y^2 + p * x * y
+           0 ~ x^2 + 4x + q
+           0 ~ y * z + 4x^2 + wrapper(r)]
+
+    @mtkbuild sys = NonlinearSystem(eqs)
+    prob = HomotopyContinuationProblem(sys, [x => 1.0, y => 1.0, z => 1.0],
+        [p => 2.0, q => 4, r => Wrapper([1.0 1.0; 0.0 0.0])])
+    @test prob.ps[p] == 2.0
+    @test prob.ps[q] == 4
+    @test prob.ps[r].x == [1.0 1.0; 0.0 0.0]
+    @test prob.ps[p * q] == 8.0
+    sol = solve(prob; threading = false)
+    @test SciMLBase.successful_retcode(sol)
+    @test norm(sol.resid)≈0.0 atol=1e-10
+end
+
+@testset "Array variables" begin
+    @variables x[1:3]
+    @parameters p[1:3]
+    _x = collect(x)
+    eqs = collect(0 .~ vec(sum(_x * _x'; dims = 2)) + collect(p))
+    @mtkbuild sys = NonlinearSystem(eqs)
+    prob = HomotopyContinuationProblem(sys, [x => ones(3)], [p => 1:3])
+    @test prob[x] == ones(3)
+    @test prob[p + x] == [2, 3, 4]
+    prob[x] = 2ones(3)
+    @test prob[x] == 2ones(3)
+    prob.ps[p] = [2, 3, 4]
+    @test prob.ps[p] == [2, 3, 4]
+    sol = @test_nowarn solve(prob; threading = false)
+    @test sol.retcode == ReturnCode.ConvergenceFailure
+end

test/runtests.jl

@@ -110,6 +110,7 @@ end
     if GROUP == "All" || GROUP == "Extensions"
         activate_extensions_env()
         @safetestset "BifurcationKit Extension Test" include("extensions/bifurcationkit.jl")
+        @safetestset "HomotopyContinuation Extension Test" include("extensions/homotopy_continuation.jl")
         @safetestset "Auto Differentiation Test" include("extensions/ad.jl")
         @safetestset "LabelledArrays Test" include("labelledarrays.jl")
     end