[NB] Mark algebraic loops using homotopy (#15535)

TODO structural reduction on homotopy system

Author: phannebohm

OMCompiler/Compiler/NBackEnd/Classes/NBStrongComponent.mo

@@ -1056,6 +1056,18 @@ public
     end match;
   end isAlgebraicLoop;
 
+  function setHomotopy
+    input output StrongComponent comp;
+    input Boolean homotopy;
+  algorithm
+    comp := match comp
+      case ALGEBRAIC_LOOP() algorithm
+        comp.homotopy := homotopy;
+      then comp;
+      else comp;
+    end match;
+  end setHomotopy;
+
   function createPseudoScalar
     input list<Integer> comp_indices;
     input array<Integer> eqn_to_var;

OMCompiler/Compiler/NBackEnd/Classes/NBackendDAE.mo

@@ -331,7 +331,8 @@ public
       (function Tearing.main(kind = kind),    "Tearing"),
       (Partitioning.categorize,               "Categorize"),
       (Solve.main,                            "Solve"),
-      (function Jacobian.main(kind = kind),   "Jacobian")
+      (function Jacobian.main(kind = kind),   "Jacobian"),
+      (Initialization.minimizeHomotopySystem, "Minimize Homotopy System")
     };
 
     (bdae, preOptClocks)  := applyModules(bdae, preOptModules, eq_filter_opt, ClockIndexes.RT_CLOCK_NEW_BACKEND_MODULE);

OMCompiler/Compiler/NBackEnd/Modules/1_Main/NBInitialization.mo

@@ -70,6 +70,7 @@ protected
   import Replacements = NBReplacements;
   import BPartition = NBPartition;
   import NBPartition.Partition;
+  import StrongComponent = NBStrongComponent;
   import Tearing = NBTearing;
 
   // Util imports
@@ -804,6 +805,22 @@ public
     end if;
   end containsLambda0;
 
+  function minimizeHomotopySystem
+    extends Module.wrapper;
+  algorithm
+    bdae := match bdae
+      case BackendDAE.MAIN() algorithm
+        if isSome(bdae.init_0) then
+          // for now all strong components have homotopy if init_0 exists
+          // TODO reduced analysis on what needs to be computed for homotopy
+          bdae.init := list(Partition.mapStrongComponents(par, function StrongComponent.setHomotopy(homotopy = true)) for par in bdae.init);
+        end if;
+      then bdae;
+
+      else bdae;
+    end match;
+  end minimizeHomotopySystem;
+
   function removeWhenEquation
     "this function checks if an equation has to be removed before initialization.
     true for: when branch without condition initial()"

testsuite/simulation/modelica/NBackend/initialization/Makefile

@@ -2,6 +2,7 @@ TEST = ../../../../rtest -v
 
 TESTFILES = \
 experimental_initialSimplified.mos \
+homotopy_indirect.mos \
 homotopy_no_loop.mos \
 init_if_eq.mos \
 init_if_exp.mos \