feat: better handle loop opening defaults

Author: AayushSabharwal

src/systems/analysis_points.jl

@@ -486,14 +486,19 @@ struct Break <: AnalysisPointTransformation
     Whether to add a new input variable connected to all the outputs of `ap`.
     """
     add_input::Bool
+    """
+    Whether the default of the added input variable should be the input of `ap`. Only
+    applicable if `add_input == true`.
+    """
+    default_outputs_to_input::Bool
 end
 
 """
     $(TYPEDSIGNATURES)
 
-`Break` the given analysis point `ap` without adding an input.
+`Break` the given analysis point `ap`.
 """
-Break(ap::AnalysisPoint) = Break(ap, false)
+Break(ap::AnalysisPoint, add_input::Bool = false) = Break(ap, add_input, false)
 
 function apply_transformation(tf::Break, sys::AbstractSystem)
     modify_nested_subsystem(sys, tf.ap) do breaksys
@@ -517,7 +522,11 @@ function apply_transformation(tf::Break, sys::AbstractSystem)
             push!(breaksys_eqs, ap_var(outsys) ~ new_var)
         end
         defs = copy(get_defaults(breaksys))
-        defs[new_var] = new_def
+        defs[new_var] = if ap.default_outputs_to_input
+            ap_ivar
+        else
+            new_def
+        end
         @set! breaksys.defaults = defs
         unks = copy(get_unknowns(breaksys))
         push!(unks, new_var)
@@ -803,7 +812,7 @@ Given a list of analysis points, break the connection for each and set the outpu
 """
 function handle_loop_openings(sys::AbstractSystem, aps)
     for ap in canonicalize_ap(sys, aps)
-        sys, (outvar,) = apply_transformation(Break(ap, true), sys)
+        sys, (outvar,) = apply_transformation(Break(ap, true, true), sys)
         if Symbolics.isarraysymbolic(outvar)
             push!(get_eqs(sys), outvar ~ zeros(size(outvar)))
         else
@@ -815,7 +824,7 @@ end
 
 const DOC_LOOP_OPENINGS = """
     - `loop_openings`: A list of analysis points whose connections should be removed and
-      the outputs set to zero as a part of the linear analysis.
+      the outputs set to the input as a part of the linear analysis.
 """
 
 const DOC_SYS_MODIFIER = """