From 9a763fcb9358fa02ab21cdd2ea10f70354937af8 Mon Sep 17 00:00:00 2001
From: phannebohm <phannebohm@hsbi.de>
Date: Sat, 10 Feb 2024 13:54:52 +0100
Subject: [PATCH] [NB] Differentiate delay (#11945)

---
 .../Compiler/NBackEnd/Util/NBDifferentiate.mo | 24 +++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/OMCompiler/Compiler/NBackEnd/Util/NBDifferentiate.mo b/OMCompiler/Compiler/NBackEnd/Util/NBDifferentiate.mo
index a2b415a5266..12a1b551cb0 100644
--- a/OMCompiler/Compiler/NBackEnd/Util/NBDifferentiate.mo
+++ b/OMCompiler/Compiler/NBackEnd/Util/NBDifferentiate.mo
@@ -846,6 +846,30 @@ public
         Expression ret, ret1, ret2, arg1, arg2, arg3, diffArg1, diffArg2, diffArg3;
         list<Expression> rest;
         Type ty;
+        DifferentiationType diffType;
+
+      // DELAY
+      // d/dz delay(x, delta) = (dt/dz - d delta/dz) * delay(der(x), delta)
+      case (Expression.CALL()) guard(name == "delay")
+      algorithm
+        {arg1, arg2, arg3} := Call.arguments(exp.call);
+        // if z = t then dt/dz = 1 else dt/dz = 0
+        ret1 := Expression.REAL(if diffArguments.diffType == DifferentiationType.TIME then 1.0 else 0.0);
+        // d delta/dz
+        (ret2, diffArguments) := differentiateExpression(arg2, diffArguments);
+        // dt/dz - d delta/dz
+        ret2 := SimplifyExp.simplify(Expression.MULTARY({ret1}, {ret2}, addOp));
+        if Expression.isZero(ret2) then
+          ret := Expression.makeZero(Expression.typeOf(arg1));
+        else
+          diffType := diffArguments.diffType;
+          diffArguments.diffType := DifferentiationType.TIME;
+          (ret1, diffArguments) := differentiateExpression(arg1, diffArguments);
+          diffArguments.diffType := diffType;
+          exp.call := Call.setArguments(exp.call, {ret1, arg2, arg3});
+          ret := Expression.MULTARY({ret2, exp}, {}, mulOp);
+        end if;
+      then ret;
 
       // SMOOTH
       case (Expression.CALL()) guard(name == "smooth")