Measure the first homotopy contraction

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: ChrisRackauckas

lib/NonlinearSolveBase/src/homotopy_sweep.jl

@@ -401,8 +401,7 @@ function _homotopy_corrector!(
         return sol, zero(T), zero(T), false, false
     end
 
-    residualnormprev = zero(L2_NORM(get_fu(cache)))
-    observations = 0
+    residualnormprev = L2_NORM(get_fu(cache))
     first_Θ = zero(T)
     rejected_Θ = zero(T)
     has_Θ = false
@@ -412,19 +411,16 @@ function _homotopy_corrector!(
     while not_terminated(cache)
         CommonSolve.step!(cache)
         residualnorm = L2_NORM(get_fu(cache))
-        if observations > 0
-            Θ = iszero(residualnormprev) ? zero(T) : T(residualnorm / residualnormprev)
-            if !has_Θ
-                first_Θ = Θ
-                has_Θ = true
-            end
-            if !contraction_rejected && !(Θ <= Θreject)
-                rejected_Θ = Θ
-                contraction_rejected = true
-            end
+        Θ = iszero(residualnormprev) ? zero(T) : T(residualnorm / residualnormprev)
+        if !has_Θ
+            first_Θ = Θ
+            has_Θ = true
+        end
+        if !contraction_rejected && !(Θ <= Θreject)
+            rejected_Θ = Θ
+            contraction_rejected = true
         end
         residualnormprev = residualnorm
-        observations += 1
     end
 
     sol = CommonSolve.solve!(cache)

test/Core/kantorovich_homotopy_tests__item1.jl

@@ -139,6 +139,16 @@ function CommonSolve.solve!(cache::SlowContractionCache)
     )
 end
 
+corrector_prob = NonlinearProblem((u, p) -> [u[1] - 1], [0.0])
+corrector_cache = init(corrector_prob, SlowContractionAlgorithm(); maxiters = 2)
+corrector_sol, first_Θ, rejected_Θ, has_Θ, contraction_rejected =
+    NonlinearSolveBase._homotopy_corrector!(corrector_cache, alg, Float64)
+@test SciMLBase.successful_retcode(corrector_sol)
+@test has_Θ
+@test first_Θ ≈ 0.99
+@test rejected_Θ ≈ 0.99
+@test contraction_rejected
+
 slowprob = HomotopyProblem((u, p, λ) -> [u[1] - λ], [0.0]; λspan = (0.0, 0.1))
 strictsol = solve(
     slowprob,