feat: enable OverrideInit to solve for du0 of DAEProblems

Author: AayushSabharwal

src/initialization.jl

@@ -3,7 +3,7 @@
 
 A collection of all the data required for `OverrideInit`.
 """
-struct OverrideInitData{IProb, UIProb, IProbMap, IProbPmap}
+struct OverrideInitData{IProb, UIProb, IProbMap, IProbPmap, IProbDu0Map}
     """
     The `AbstractNonlinearProblem` to solve for initialization.
     """
@@ -29,12 +29,18 @@ struct OverrideInitData{IProb, UIProb, IProbMap, IProbPmap}
     initialized will be returned as-is.
     """
     initializeprobpmap::IProbPmap
+    """
+    A function which takes the solution of `initializeprob` and returns the
+    `du0` vector of the original problem.
+    """
+    initializeprob_du0map::IProbDu0Map
 
     function OverrideInitData(initprob::I, update_initprob!::J, initprobmap::K,
-            initprobpmap::L) where {I, J, K, L}
+            initprobpmap::L, initprob_du0map::M = nothing) where {I, J, K, L, M}
         @assert initprob isa
                 Union{SCCNonlinearProblem, NonlinearProblem, NonlinearLeastSquaresProblem}
-        return new{I, J, K, L}(initprob, update_initprob!, initprobmap, initprobpmap)
+        return new{I, J, K, L, M}(
+            initprob, update_initprob!, initprobmap, initprobpmap, initprob_du0map)
     end
 end
 
@@ -171,9 +177,12 @@ Keyword arguments:
   provided to the `OverrideInit` constructor takes priority over this keyword argument.
   If the former is `nothing`, this keyword argument will be used. If it is also not provided,
   an error will be thrown.
+- `return_du0`: Whether to use `initializeprob_du0map` (if present) and return
+  `du0, u0, p, success`.
 """
 function get_initial_values(prob, valp, f, alg::OverrideInit,
-        iip::Union{Val{true}, Val{false}}; nlsolve_alg = nothing, abstol = nothing, reltol = nothing, kwargs...)
+        iip::Union{Val{true}, Val{false}}; nlsolve_alg = nothing, abstol = nothing,
+        reltol = nothing, return_du0 = false, kwargs...)
     u0 = state_values(valp)
     p = parameter_values(valp)
 
@@ -214,5 +223,10 @@ function get_initial_values(prob, valp, f, alg::OverrideInit,
         p = initdata.initializeprobpmap(valp, nlsol)
     end
 
+    if return_du0
+        du0 = initdata.initializeprob_du0map === nothing ? nothing : initdata.initializeprob_du0map(nlsol)
+        return du0, u0, p, SciMLBase.successful_retcode(nlsol)
+    end
+
     return u0, p, SciMLBase.successful_retcode(nlsol)
 end

test/initialization.jl

@@ -229,4 +229,66 @@ end
         @test p ≈ 0.0
         @test success
     end
+
+    @testset "DAEProblem" begin
+        function daerhs(du, u, p, t)
+            return [u[1] * t + p, u[1]^2 - u[2]^2]
+        end
+        # unknowns are u[2], p, D(u[1]), D(u[2]). Parameters are u[1], t
+        initprob = NonlinearProblem([1.0, 1.0, 1.0, 1.0], [1.0, 0.0]) do x, _p
+            u2, p, du1, du2 = x
+            u1, t = _p
+            return [u1^3 - u2^3, p^2 - 2p + 1, du1 - u1 * t - p, 2u1 * du1 - 2u2 * du2]
+        end
+
+        update_initializeprob! = function (iprob, integ)
+            iprob.p[1] = integ.u[1]
+            iprob.p[2] = integ.t
+        end
+        initprobmap = function (nlsol)
+            return [parameter_values(nlsol)[1], nlsol.u[1]]
+        end
+        initprobpmap = function (_, nlsol)
+            return nlsol.u[2]
+        end
+        initprob_du0map = function (nlsol)
+            return nlsol.u[3:4]
+        end
+        initialization_data = SciMLBase.OverrideInitData(
+            initprob, update_initializeprob!, initprobmap, initprobpmap, initprob_du0map)
+        fn = DAEFunction(daerhs; initialization_data)
+        prob = DAEProblem(fn, [0.0, 0.0], [2.0, 0.0], (0.0, 1.0), 0.0)
+        integ = init(prob, DImplicitEuler(); initializealg = NoInit())
+
+        initialization_data2 = SciMLBase.OverrideInitData(
+            initprob, update_initializeprob!, initprobmap, initprobpmap)
+        fn2 = DAEFunction(daerhs; initialization_data = initialization_data2)
+        prob2 = DAEProblem(fn2, [0.0, 0.0], [2.0, 0.0], (0.0, 1.0), 0.0)
+        integ2 = init(prob2, DImplicitEuler(); initializealg = NoInit())
+
+        nlsolve_alg = FastShortcutNonlinearPolyalg()
+        @testset "Doesn't return `du0` by default" begin
+            @test length(SciMLBase.get_initial_values(
+                prob, integ, fn, SciMLBase.OverrideInit(),
+                Val(false); nlsolve_alg, abstol, reltol)) == 3
+        end
+        @testset "`du0 === nothing` if missing `du0map`" begin
+            du0, u0, p, success = SciMLBase.get_initial_values(
+                prob2, integ2, fn2, SciMLBase.OverrideInit(), Val(false);
+                nlsolve_alg, abstol, reltol, return_du0 = true)
+            @test du0 === nothing
+            @test u0 ≈ [2.0, 2.0]
+            @test p ≈ 1.0
+            @test success
+        end
+        @testset "With `return_du0 = true`" begin
+            du0, u0, p, success = SciMLBase.get_initial_values(
+                prob, integ, fn, SciMLBase.OverrideInit(), Val(false);
+                nlsolve_alg, abstol, reltol, return_du0 = true)
+            @test du0 ≈ [1.0, 1.0]
+            @test u0 ≈ [2.0, 2.0]
+            @test p ≈ 1.0
+            @test success
+        end
+    end
 end