feat: implement ImplicitDiscreteProblem, ImplicitDiscreteFunction for System

Author: AayushSabharwal

src/problems/compatibility.jl

@@ -123,3 +123,11 @@ function check_is_explicit(sys::System, T, altT)
         """))
     end
 end
+
+function check_is_implicit(sys::System, T, altT)
+    if !has_alg_equations(sys)
+        throw(SystemCompatibilityError("""
+        `$T` expects an implicit system. Consider a `$altT` instead.
+        """))
+    end
+end

src/problems/implicitdiscreteproblem.jl

@@ -0,0 +1,62 @@
+@fallback_iip_specialize function SciMLBase.ImplicitDiscreteFunction{iip, spec}(
+        sys::System, _d = nothing, u0 = nothing, p = nothing;
+        t = nothing, eval_expression = false, eval_module = @__MODULE__,
+        checkbounds = false, analytic = nothing, simplify = false, cse = true,
+        initialization_data = nothing, check_compatibility = true, kwargs...) where {
+        iip, spec}
+    check_complete(sys, ImplicitDiscreteFunction)
+    check_compatibility && check_compatible_system(ImplicitDiscreteFunction, sys)
+
+    iv = get_iv(sys)
+    dvs = unknowns(sys)
+    ps = parameters(sys)
+    f = generate_rhs(sys, dvs, ps; expression = Val{false}, implicit_dae = true,
+        eval_expression, eval_module, checkbounds = checkbounds, cse,
+        kwargs...)
+
+    if spec === SciMLBase.FunctionWrapperSpecialize && iip
+        if u0 === nothing || p === nothing || t === nothing
+            error("u0, p, and t must be specified for FunctionWrapperSpecialize on ImplicitDiscreteFunction.")
+        end
+        f = SciMLBase.wrapfun_iip(f, (u0, u0, u0, p, t))
+    end
+
+    observedfun = ObservedFunctionCache(
+        sys; steady_state = false, eval_expression, eval_module, checkbounds, cse)
+
+    ImplicitDiscreteFunction{iip, spec}(f;
+        sys = sys,
+        observed = observedfun,
+        analytic = analytic,
+        initialization_data)
+end
+
+@fallback_iip_specialize function SciMLBase.ImplicitDiscreteProblem{iip, spec}(
+        sys::System, u0map, tspan, parammap = SciMLBase.NullParameters();
+        check_compatibility = true, kwargs...) where {iip, spec}
+    check_complete(sys, ImplicitDiscreteProblem)
+    check_compatibility && check_compatible_system(ImplicitDiscreteProblem, sys)
+
+    dvs = unknowns(sys)
+    u0map = to_varmap(u0map, dvs)
+    u0map = shift_u0map_forward(sys, u0map, defaults(sys))
+    f, u0, p = process_SciMLProblem(
+        ImplicitDiscreteFunction{iip, spec}, sys, u0map, parammap;
+        t = tspan !== nothing ? tspan[1] : tspan, check_compatibility, kwargs...)
+
+    kwargs = process_kwargs(sys; kwargs...)
+    # Call `remake` so it runs initialization if it is trivial
+    return remake(ImplicitDiscreteProblem{iip}(f, u0, tspan, p; kwargs...))
+end
+
+function check_compatible_system(
+        T::Union{Type{ImplicitDiscreteFunction}, Type{ImplicitDiscreteProblem}}, sys::System)
+    check_time_dependent(sys, T)
+    check_not_dde(sys)
+    check_no_cost(sys, T)
+    check_no_constraints(sys, T)
+    check_no_jumps(sys, T)
+    check_no_noise(sys, T)
+    check_is_discrete(sys, T)
+    check_is_implicit(sys, T, DiscreteProblem)
+end