feat: make system index zero when initializing DAEProblems

Author: AayushSabharwal

src/systems/nonlinear/initializesystem.jl

@@ -11,9 +11,35 @@ function generate_initializesystem(sys::ODESystem;
         default_dd_guess = 0.0,
         algebraic_only = false,
         check_units = true, check_defguess = false,
+        implicit_dae = false,
         name = nameof(sys), kwargs...)
     trueobs, eqs = unhack_observed(observed(sys), equations(sys))
     vars = unique([unknowns(sys); getfield.(trueobs, :lhs)])
+
+    if implicit_dae
+        pre_simplification_sys = sys
+        while get_parent(pre_simplification_sys) !== nothing
+            pre_simplification_sys = get_parent(pre_simplification_sys)
+        end
+        schedule = get_schedule(sys)
+        if schedule === nothing
+            throw(ArgumentError("The system must be structurally simplified to create an initialization system for an implicit DAE."))
+        end
+        old_eqs = equations(pre_simplification_sys)
+        inv_dummy_sub = Dict()
+        for (k, v) in schedule.dummy_sub
+            if isequal(default_toterm(k), v)
+                inv_dummy_sub[v] = k
+            end
+        end
+        new_eqs = Symbolics.fast_substitute.([trueobs; eqs], (inv_dummy_sub,))
+        filter!(eq -> !isequal(eq.lhs, eq.rhs), new_eqs)
+        new_sys = ODESystem(new_eqs, get_iv(sys); name = nameof(sys))
+        new_sys = dummy_derivative(new_sys; to_index_zero = true, array_hack = false, cse_hack = false)
+        trueobs = observed(new_sys)
+        eqs = equations(new_sys)
+        vars = unique([unknowns(new_sys); getfield.(trueobs, :lhs)])
+    end
     vars_set = Set(vars) # for efficient in-lookup
 
     idxs_diff = isdiffeq.(eqs)