Fix bug with complex roots

Author: fgittins

lib/BracketingNonlinearSolve/src/muller.jl

@@ -20,8 +20,8 @@ function CommonSolve.solve(prob::IntervalNonlinearProblem, alg::Muller, args...;
 
     xᵢ₊₁, fxᵢ₊₁ = xᵢ₋₂, fxᵢ₋₂
 
-    abstol = NonlinearSolveBase.get_tolerance(
-        xᵢ₋₂, abstol, promote_type(eltype(xᵢ₋₂), eltype(xᵢ)))
+    abstol = abs(NonlinearSolveBase.get_tolerance(
+        xᵢ₋₂, abstol, promote_type(eltype(xᵢ₋₂), eltype(xᵢ))))
 
     for _ ∈ 1:maxiters
         q = (xᵢ - xᵢ₋₁)/(xᵢ₋₁ - xᵢ₋₂)

lib/BracketingNonlinearSolve/test/muller_tests.jl

@@ -53,4 +53,20 @@
 
         @test sol.u ≈ π
     end
+
+    @testset "Complex roots" begin
+        f(u, p) = u^3 - 1
+
+        tspan = (-1.0, 1.0*im)
+        prob = IntervalNonlinearProblem{false}(f, tspan)
+        sol = solve(prob, Muller())
+
+        @test sol.u ≈ (-1 + √3*im)/2
+
+        tspan = (-1.0, -1.0*im)
+        prob = IntervalNonlinearProblem{false}(f, tspan)
+        sol = solve(prob, Muller())
+
+        @test sol.u ≈ (-1 - √3*im)/2
+    end
 end