/
Differentiate.mo
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Differentiate.mo
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/*
* This file is part of OpenModelica.
*
* Copyright (c) 1998-2014, Open Source Modelica Consortium (OSMC),
* c/o Linköpings universitet, Department of Computer and Information Science,
* SE-58183 Linköping, Sweden.
*
* All rights reserved.
*
* THIS PROGRAM IS PROVIDED UNDER THE TERMS OF GPL VERSION 3 LICENSE OR
* THIS OSMC PUBLIC LICENSE (OSMC-PL) VERSION 1.2.
* ANY USE, REPRODUCTION OR DISTRIBUTION OF THIS PROGRAM CONSTITUTES
* RECIPIENT'S ACCEPTANCE OF THE OSMC PUBLIC LICENSE OR THE GPL VERSION 3,
* ACCORDING TO RECIPIENTS CHOICE.
*
* The OpenModelica software and the Open Source Modelica
* Consortium (OSMC) Public License (OSMC-PL) are obtained
* from OSMC, either from the above address,
* from the URLs: http://www.ida.liu.se/projects/OpenModelica or
* http://www.openmodelica.org, and in the OpenModelica distribution.
* GNU version 3 is obtained from: http://www.gnu.org/copyleft/gpl.html.
*
* This program is distributed WITHOUT ANY WARRANTY; without
* even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE, EXCEPT AS EXPRESSLY SET FORTH
* IN THE BY RECIPIENT SELECTED SUBSIDIARY LICENSE CONDITIONS OF OSMC-PL.
*
* See the full OSMC Public License conditions for more details.
*
*/
encapsulated package Differentiate
" file: Differentiate.mo
package: Differentiate
description: Differentiation of equations from BackendDAE.BackendDAE
RCS: $Id$
This module is responsible for symbolic differentiation of equations and
expressions.
The symbolic differentiation is used in the Newton-Raphson method and in
index reduction."
// public imports
public import Absyn;
public import BackendDAE;
public import DAE;
public import DAEUtil;
public import Types;
// protected imports
protected import Algorithm;
protected import Array;
protected import BackendDump;
protected import BackendDAECreate;
protected import BackendDAEUtil;
protected import BackendEquation;
protected import BackendVariable;
protected import ClassInf;
protected import ComponentReference;
protected import DAEDump;
protected import Debug;
protected import Error;
protected import Expression;
protected import ExpressionSimplify;
protected import ExpressionDump;
protected import Flags;
protected import Inline;
protected import List;
protected import SCode;
protected import Util;
constant Integer defaultMaxIter = 20;
// =============================================================================
// differentiation interfaces
// - differentiateEquationTime
// - differentiateExpTime
// - differentiateExpSolve
//
// =============================================================================
public function differentiateEquationTime "function: differentiateEquationTime
Differentiates an equation with respect to the time variable."
input BackendDAE.Equation inEquation;
input BackendDAE.Variables inVariables;
input BackendDAE.Shared ishared;
output BackendDAE.Equation outEquation;
output BackendDAE.Shared oshared;
algorithm
(outEquation, oshared) := matchcontinue(inEquation, inVariables, ishared)
local
String msg;
DAE.ElementSource source;
BackendDAE.Shared shared;
BackendDAE.Equation deqn;
DAE.FunctionTree funcs;
BackendDAE.DifferentiateInputData diffData;
BackendDAE.Variables knvars;
case (_, _, _)
equation
funcs = BackendDAEUtil.getFunctions(ishared);
knvars = BackendDAEUtil.getknvars(ishared);
diffData = BackendDAE.DIFFINPUTDATA(NONE(), SOME(inVariables), SOME(knvars), SOME(inVariables), SOME({}), NONE(), NONE());
(deqn, funcs) = differentiateEquation(inEquation, DAE.crefTime, diffData, BackendDAE.DIFFERENTIATION_TIME(), funcs);
oshared = BackendDAEUtil.setSharedFunctionTree(ishared, funcs);
then (deqn, oshared);
else
equation
msg = "\nDifferentiate.differentiateEquationTime failed for " + BackendDump.equationString(inEquation) + "\n\n";
source = BackendEquation.equationSource(inEquation);
Error.addSourceMessage(Error.INTERNAL_ERROR, {msg}, DAEUtil.getElementSourceFileInfo(source));
then fail();
end matchcontinue;
end differentiateEquationTime;
public function differentiateExpTime "function: differentiateEquationTime
Differentiates an equation with respect to the time variable."
input DAE.Exp inExp;
input BackendDAE.Variables inVariables;
input BackendDAE.Shared ishared;
output DAE.Exp outExp;
output BackendDAE.Shared oshared;
algorithm
(outExp, oshared) := matchcontinue(inExp, inVariables, ishared)
local
String msg;
BackendDAE.Shared shared;
DAE.Exp dexp;
DAE.FunctionTree funcs;
BackendDAE.DifferentiateInputData diffData;
BackendDAE.Variables knvars;
case (_, _, _)
equation
funcs = BackendDAEUtil.getFunctions(ishared);
knvars = BackendDAEUtil.getknvars(ishared);
diffData = BackendDAE.DIFFINPUTDATA(NONE(), SOME(inVariables), SOME(knvars), SOME(inVariables), SOME({}), NONE(), NONE());
(dexp, funcs) = differentiateExp(inExp, DAE.crefTime, diffData, BackendDAE.DIFFERENTIATION_TIME(), funcs, defaultMaxIter, {});
(dexp,_) = ExpressionSimplify.simplify(dexp);
oshared = BackendDAEUtil.setSharedFunctionTree(ishared, funcs);
then (dexp, oshared);
else
equation
// expandDerOperator expectes sometime that differentiate fails,
// so the calling function need to take care of the error messages.
// TODO: change that in expandDerOperator
//Error.addSourceMessage(Error.INTERNAL_ERROR, {msg}, DAEUtil.getElementSourceFileInfo(DAE.emptyElementSource));
true = Flags.isSet(Flags.FAILTRACE);
msg = "\nDifferentiate.differentiateExpTime failed for " + ExpressionDump.printExpStr(inExp) + "\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then fail();
end matchcontinue;
end differentiateExpTime;
public function differentiateExpSolve
"function: differentiateEquationSolve
Differentiates an equation with respect to the cref variable."
input DAE.Exp inExp;
input DAE.ComponentRef inCref;
input Option<DAE.FunctionTree> functions;
output DAE.Exp outExp;
protected
list<DAE.Exp> fac = Expression.factors(inExp);
algorithm
({},_) := List.split1OnTrue(fac,Expression.expHasCrefInIf,inCref); // check: differentiateExpSolve is allowed
outExp := matchcontinue(inExp, inCref)
local
String msg;
DAE.Exp dexp;
BackendDAE.DifferentiateInputData diffData;
DAE.FunctionTree fun;
case (_,_)
equation
fun = match(functions)
local DAE.FunctionTree fun_;
case(SOME(fun_)) then fun_;
else DAE.emptyFuncTree;
end match;
diffData = BackendDAE.DIFFINPUTDATA(NONE(), NONE(), NONE(), NONE(), SOME({}), NONE(), NONE());
(dexp, _) = differentiateExp(inExp, inCref, diffData, BackendDAE.SIMPLE_DIFFERENTIATION(), fun, defaultMaxIter, {});
(dexp,_) = ExpressionSimplify.simplify(dexp);
then dexp;
else
equation
if Flags.isSet(Flags.FAILTRACE) then
msg = "\nDifferentiate.differentiateExpSolve failed for " + ExpressionDump.printExpStr(inExp) + "\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
end if;
then fail();
end matchcontinue;
end differentiateExpSolve;
public function differentiateExpCrefFullJacobian "function: differentiateEquationTime
Differentiates an equation with respect to the time variable."
input DAE.Exp inExp;
input DAE.ComponentRef inCref;
input BackendDAE.Variables inVariables;
input BackendDAE.Shared ishared;
output DAE.Exp outExp;
output BackendDAE.Shared oshared;
algorithm
(outExp, oshared) := matchcontinue(inExp, inCref, inVariables, ishared)
local
String msg;
BackendDAE.Shared shared;
DAE.Exp dexp;
DAE.FunctionTree funcs;
BackendDAE.DifferentiateInputData diffData;
BackendDAE.Variables knvars;
case (_, _, _, _)
equation
funcs = BackendDAEUtil.getFunctions(ishared);
knvars = BackendDAEUtil.getknvars(ishared);
diffData = BackendDAE.DIFFINPUTDATA(NONE(), SOME(inVariables), SOME(knvars), NONE(), SOME({}), NONE(), NONE());
(dexp, funcs) = differentiateExp(inExp, inCref, diffData, BackendDAE.DIFF_FULL_JACOBIAN(), funcs, defaultMaxIter, {});
(dexp,_) = ExpressionSimplify.simplify(dexp);
oshared = BackendDAEUtil.setSharedFunctionTree(ishared, funcs);
then (dexp, oshared);
else
equation
// expandDerOperator expectes sometime that differentiate fails,
// so the calling function need to take care of the error messages.
// TODO: change that in expandDerOperator
//Error.addSourceMessage(Error.INTERNAL_ERROR, {msg}, DAEUtil.getElementSourceFileInfo(DAE.emptyElementSource));
true = Flags.isSet(Flags.FAILTRACE);
msg = "\nDifferentiate.differentiateCrefFullJacobian failed for " + ExpressionDump.printExpStr(inExp) + "\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then fail();
end matchcontinue;
end differentiateExpCrefFullJacobian;
// =============================================================================
// further interface functions to differentiation
// - differentiateEquation
// - differentiateBackendDAE
//
// =============================================================================
protected function differentiateEquations "
Differentiates an equation with respect to a cref."
input list<BackendDAE.Equation> inEquations;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input list<BackendDAE.Equation> inEquationsAccum;
input DAE.FunctionTree inFunctionTree;
output list<BackendDAE.Equation> outEquations;
output DAE.FunctionTree outFunctionTree;
algorithm
(outEquations,outFunctionTree) := matchcontinue (inEquations, inDiffwrtCref, inInputData, inDiffType, inEquationsAccum, inFunctionTree)
local
DAE.FunctionTree funcs;
list<BackendDAE.Equation> rest, eqns;
BackendDAE.Equation eqn;
String msg;
DAE.ElementSource source;
list<Integer> ass, ass2;
case ({},_,_,_,_,_) then (listReverse(inEquationsAccum), inFunctionTree);
// equations
case (eqn::rest,_,_,_,_,_)
equation
(eqn, funcs) = differentiateEquation(eqn, inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
eqns = listAppend({eqn}, inEquationsAccum);
(eqns, funcs) = differentiateEquations(rest, inDiffwrtCref, inInputData, inDiffType, eqns, funcs);
then (eqns, funcs);
case (eqn::_,_,_,_,_,_)
equation
msg = "\nDifferentiate.differentiateEquations failed for " + BackendDump.equationString(eqn) + "\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then
fail();
end matchcontinue;
end differentiateEquations;
public function differentiateEquation
"Differentiates an equation with respect to a cref."
input BackendDAE.Equation inEquation;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input DAE.FunctionTree inFunctionTree;
output BackendDAE.Equation outEquation;
output DAE.FunctionTree outFunctionTree;
algorithm
(outEquation, outFunctionTree) := match(inEquation, inDiffwrtCref, inInputData, inDiffType, inFunctionTree)
local
DAE.Exp e1_1, e2_1, e1_2, e2_2, e1, e2;
DAE.ComponentRef cref;
BackendDAE.Variables timevars;
DAE.ElementSource source, sourceStmt;
Integer size;
list<DAE.Exp> out1, expExpLst, expExpLst1;
DAE.Type exptyp;
list<Integer> dimSize;
String msg, se1, dse1, se2, dse2;
DAE.SymbolicOperation op1, op2;
DAE.FunctionTree funcs;
DAE.Algorithm alg;
list<BackendDAE.Equation> eqns;
list<list<BackendDAE.Equation>> eqnslst;
list<DAE.Statement> statementLst;
DAE.Expand expand;
BackendDAE.WhenEquation whenEqn;
BackendDAE.EquationKind eqKind;
// equations
case (BackendDAE.EQUATION(exp=e1, scalar=e2, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(e1_1, funcs) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(e1_1, _) = ExpressionSimplify.simplify(e1_1);
(e2_1, funcs) = differentiateExp(e2, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
(e2_1, _) = ExpressionSimplify.simplify(e2_1);
op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e1_1);
op2 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e2, e2_1);
source = List.foldr({op1, op2}, DAEUtil.addSymbolicTransformation, source);
then
(BackendDAE.EQUATION(e1_1, e2_1, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// solved equations
case (BackendDAE.SOLVED_EQUATION(componentRef=cref, exp=e2, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
e1 = Expression.crefExp(cref);
(e1_1, funcs) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(e1_1, _) = ExpressionSimplify.simplify(e1_1);
(e2_1, funcs) = differentiateExp(e2, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
(e2_1, _) = ExpressionSimplify.simplify(e2_1);
op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e1_1);
op2 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e2, e2_1);
source = List.foldr({op1, op2}, DAEUtil.addSymbolicTransformation, source);
then
(BackendDAE.EQUATION(e1_1, e2_1, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// RESIDUAL_EQUATION
case (BackendDAE.RESIDUAL_EQUATION(exp=e1, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(e1_1, funcs) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(e1_1, _) = ExpressionSimplify.simplify(e1_1);
op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e1_1);
source = List.foldr({op1}, DAEUtil.addSymbolicTransformation, source);
then
(BackendDAE.RESIDUAL_EQUATION(e1_1, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// complex equations
case (BackendDAE.COMPLEX_EQUATION(size=size, left=e1, right=e2, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(e1_1, funcs) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(e1_1, _) = ExpressionSimplify.simplify(e1_1);
(e2_1, funcs) = differentiateExp(e2, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
(e2_1, _) = ExpressionSimplify.simplify(e2_1);
op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e1_1);
op2 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e2, e2_1);
source = List.foldr({op1, op2}, DAEUtil.addSymbolicTransformation, source);
then
(BackendDAE.COMPLEX_EQUATION(size, e1_1, e2_1, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// Array Equations
case (BackendDAE.ARRAY_EQUATION(dimSize=dimSize, left=e1, right=e2, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(e1_1, funcs) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(e1_1, _) = ExpressionSimplify.simplify(e1_1);
(e2_1, funcs) = differentiateExp(e2, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
(e2_1, _) = ExpressionSimplify.simplify(e2_1);
op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e1_1);
op2 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e2, e2_1);
source = List.foldr({op1, op2}, DAEUtil.addSymbolicTransformation, source);
then
(BackendDAE.ARRAY_EQUATION(dimSize, e1_1, e2_1, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// differentiate algorithm
case (BackendDAE.ALGORITHM(size=size, alg=DAE.ALGORITHM_STMTS(statementLst=statementLst), source=source, expand=expand, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
// get Allgorithm
(statementLst, funcs) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, defaultMaxIter, {});
alg = DAE.ALGORITHM_STMTS(statementLst);
//op1 = DAE.OP_DIFFERENTIATE(cr, before, after)
//op1 = DAE.OP_DIFFERENTIATE(inDiffwrtCref, e1, e2);
//source = DAEUtil.addSymbolicTransformation(source, op1);
then
(BackendDAE.ALGORITHM(size, alg, source, expand, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
// if-equations
case (BackendDAE.IF_EQUATION(conditions=expExpLst, eqnstrue=eqnslst, eqnsfalse=eqns, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(eqnslst, funcs) = differentiateEquationsLst(eqnslst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree);
(eqns, funcs) = differentiateEquations(eqns, inDiffwrtCref, inInputData, inDiffType, {}, funcs);
then
(BackendDAE.IF_EQUATION(expExpLst, eqnslst, eqns, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
case (BackendDAE.WHEN_EQUATION(size=size, whenEquation=whenEqn, source=source, attr=BackendDAE.EQUATION_ATTRIBUTES(kind=eqKind)), _, _, _, _)
equation
(whenEqn, funcs) = differentiateWhenEquations(whenEqn, inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
then
(BackendDAE.WHEN_EQUATION(size, whenEqn, source, BackendDAE.EQUATION_ATTRIBUTES(false, eqKind, BackendDAE.NO_LOOP())), funcs);
else
equation
msg = "\nDifferentiate.differentiateEquation failed for " + BackendDump.equationString(inEquation) + "\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then
fail();
end match;
end differentiateEquation;
protected function differentiateEquationsLst
" Differentiates a list of an equation list with respect to a cref.
Helper function to differentiate a IF-EQUATION."
input list<list<BackendDAE.Equation>> inEquationsLst;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input list<list<BackendDAE.Equation>> inEquationsLstAccum;
input DAE.FunctionTree inFunctionTree;
output list<list<BackendDAE.Equation>> outEquationsLst;
output DAE.FunctionTree outFunctionTree;
algorithm
(outEquationsLst, outFunctionTree) := matchcontinue (inEquationsLst, inDiffwrtCref, inInputData, inDiffType, inEquationsLstAccum, inFunctionTree)
local
DAE.FunctionTree funcs;
list<list<BackendDAE.Equation>> rest, eqnsLst;
list<BackendDAE.Equation> eqns;
String msg;
DAE.ElementSource source;
case ({},_,_,_,_,_) then (listReverse(inEquationsLstAccum), inFunctionTree);
// equations
case (eqns::rest,_,_,_,_,_)
equation
(eqns, funcs) = differentiateEquations(eqns, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree);
eqnsLst = listAppend({eqns}, inEquationsLstAccum);
(eqnsLst, funcs) = differentiateEquationsLst(rest, inDiffwrtCref, inInputData, inDiffType, eqnsLst, funcs);
then (eqnsLst, funcs);
case (_::_,_,_,_,_,_)
equation
msg = "\nDifferentiate.differentiateEquationsLst failed.\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then
fail();
end matchcontinue;
end differentiateEquationsLst;
protected function differentiateWhenEquations
"Differentiates a when equation with respect to a cref."
input BackendDAE.WhenEquation inWhenEquations;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input DAE.FunctionTree inFunctionTree;
output BackendDAE.WhenEquation outWhenEquations;
output DAE.FunctionTree outFunctionTree;
algorithm
(outWhenEquations, outFunctionTree) := matchcontinue (inWhenEquations, inDiffwrtCref, inInputData, inDiffType, inFunctionTree)
local
DAE.FunctionTree funcs;
String msg;
DAE.ElementSource source;
DAE.Exp condition;
DAE.ComponentRef left, dleft;
DAE.Exp right, dright, eleft;
BackendDAE.WhenEquation elsewhenPart, delsewhenPart;
// equations
case (BackendDAE.WHEN_EQ(condition=condition, left=left, right=right, elsewhenPart=NONE()) ,_,_,_,_)
equation
eleft = Expression.crefExp(left);
(eleft,funcs) = differentiateExp(eleft, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(dright,funcs) = differentiateExp(right, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
dleft = Expression.expCref(eleft);
then (BackendDAE.WHEN_EQ(condition, dleft, dright, NONE()), funcs);
case (BackendDAE.WHEN_EQ(condition=condition, left=left, right=right, elsewhenPart=SOME(elsewhenPart)) ,_,_,_,_)
equation
eleft = Expression.crefExp(left);
(eleft,funcs) = differentiateExp(eleft, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, defaultMaxIter, {});
(dright,funcs) = differentiateExp(right, inDiffwrtCref, inInputData, inDiffType, funcs, defaultMaxIter, {});
dleft = Expression.expCref(eleft);
(delsewhenPart, funcs) = differentiateWhenEquations(elsewhenPart, inDiffwrtCref, inInputData, inDiffType, funcs);
then (BackendDAE.WHEN_EQ(condition, dleft, dright, SOME(delsewhenPart)), funcs);
case (_,_,_,_,_)
equation
msg = "\nDifferentiate.differentiateWhenEquations failed.\n\n";
Error.addMessage(Error.NON_EXISTING_DERIVATIVE, {msg});
then
fail();
end matchcontinue;
end differentiateWhenEquations;
// =============================================================================
// main differentiation functions
// - differentiateExp
// - differentiateStatements
//
// =============================================================================
protected function differentiateExp
input DAE.Exp inExp;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input DAE.FunctionTree inFunctionTree;
input Integer maxIter;
input list<DAE.Exp> inExpStack;
output DAE.Exp outDiffedExp;
output DAE.FunctionTree outFunctionTree;
protected
list<DAE.Exp> expStack;
algorithm
/*
// This check does not seem to be necessary since looking through the stack of expression seems to stop iteration in most cases, and you get a spam of messages from this check.
if maxIter < 1 then
Error.addInternalError("Differentiation reached maximum number of iterations ("+String(defaultMaxIter)+"). Current expression is: " + ExpressionDump.printExpStr(inExp) + " w.r.t. " + ComponentReference.printComponentRefStr(inDiffwrtCref), sourceInfo());
fail();
end if;
*/
if listMember(inExp, inExpStack) then
Error.addInternalError("Differentiation failed due to recursion causing the same expression to need to be differentiated in order to calculate the derivative of itself: " + ExpressionDump.printExpStr(inExp) + " w.r.t. " + ComponentReference.printComponentRefStr(inDiffwrtCref) + ". The full stack of expressions to differentiate: " + sum("\n* " + ExpressionDump.printExpStr(e) for e in inExpStack), sourceInfo());
fail();
end if;
expStack := inExp :: inExpStack;
(outDiffedExp, outFunctionTree) :=
match(inExp, inDiffwrtCref, inInputData, inDiffType, inFunctionTree)
local
DAE.Exp e, e1, e2, e3, actual, simplified;
DAE.Exp res, res1, res2;
DAE.Type tp;
DAE.Operator op;
String s1,s2,serr;
String se1;
Integer i;
Boolean b;
list<DAE.Exp> sub, expl;
list<list<DAE.Exp>> matrix, dmatrix;
DAE.FunctionTree functionTree;
DAE.CallAttributes attr;
Absyn.Path p;
// constants => results in zero
case (DAE.BCONST(bool = b), _, _, _, _) then (DAE.BCONST(b), inFunctionTree);
case (DAE.ICONST(), _, _, _, _) then (DAE.ICONST(0), inFunctionTree);
case (DAE.RCONST(), _, _, _, _) then (DAE.RCONST(0.0), inFunctionTree);
// differentiate cref
case (e as DAE.CREF(), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-Cref\nDifferentiate exp: " + se1);
(res, functionTree) = differentiateCrefs(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then (res, functionTree);
/*/ differentiate homotopy
case( e as DAE.CALL(
path = p as Absyn.IDENT(name="homotopy"),
expLst = {actual,simplified},
attr = attr), _, _, _, _)
equation
(e1, functionTree) = differentiateExp(actual, inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
(e2, functionTree) = differentiateExp(simplified, inDiffwrtCref, inInputData, inDiffType, functionTree);
res = DAE.CALL(p, {e1, e2}, attr);
then
(res, functionTree);*/
// differentiate call
case( e as DAE.CALL(), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-Call\nDifferentiate exp: " + se1);
(res, functionTree) = differentiateCalls(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then (res, functionTree);
// differentiate binary
case( e as DAE.BINARY(), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-BINARY\nDifferentiate exp: " + se1);
(res, functionTree) = differentiateBinary(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then (res, functionTree);
// differentiate operator
case( DAE.UNARY(operator = op,exp = e1), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-UNARY\nDifferentiate exp: " + se1);
(res, functionTree) = differentiateExp(e1, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
res = DAE.UNARY(op,res);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then (res, functionTree);
// differentiate cast
case( DAE.CAST(ty = tp, exp = e), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-CAST\nDifferentiate exp: " + se1);
(res, functionTree) = differentiateExp(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then (DAE.CAST(tp, res), functionTree);
// differentiate asub
case (DAE.ASUB(exp = e,sub = sub), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-ASUB\nDifferentiate exp: " + se1);
(res1, functionTree) = differentiateExp(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
res = Expression.makeASUB(res1,sub);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
case (DAE.ARRAY(ty = tp,scalar = b,array = expl), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-ARRAY\nDifferentiate exp: " + se1);
(expl, functionTree) = List.map3Fold(expl, function differentiateExp(maxIter=maxIter-1, inExpStack=expStack), inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
res = DAE.ARRAY(tp, b, expl);
(res,_) = ExpressionSimplify.simplify1(res);
//(res,_) = ExpressionSimplify.simplify(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
case ((DAE.MATRIX(ty = tp, integer=i, matrix=matrix)), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-MARTIX\nDifferentiate exp: " + se1);
(dmatrix, functionTree) = List.map3FoldList(matrix, function differentiateExp(maxIter=maxIter-1, inExpStack=expStack), inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
res = DAE.MATRIX(tp, i, dmatrix);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(e);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
// differentiate tsub
case (DAE.TSUB(exp = e,ix = i, ty = tp), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-TSUB\nDifferentiate exp: " + se1);
(res1, functionTree) = differentiateExp(e, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
res = DAE.TSUB(res1, i, tp);
(res,_) = ExpressionSimplify.simplify1(res);
//(res,_) = ExpressionSimplify.simplify(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
// differentiate tuple
case (DAE.TUPLE(PR = expl), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-TUPLE\nDifferentiate exp: " + se1);
(expl, functionTree) = List.map3Fold(expl, function differentiateExp(maxIter=maxIter-1, inExpStack=expStack), inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
res = DAE.TUPLE(expl);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
case (DAE.IFEXP(expCond = e1, expThen = e2, expElse = e3), _, _, _, _)
equation
//se1 = ExpressionDump.printExpStr(e);
//print("\nExp-IF-EXP\nDifferentiate exp: " + se1);
(res1, functionTree) = differentiateExp(e2, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter-1, expStack);
(res2, functionTree) = differentiateExp(e3, inDiffwrtCref, inInputData, inDiffType, functionTree, maxIter-1, expStack);
res = DAE.IFEXP(e1, res1, res2);
(res,_) = ExpressionSimplify.simplify1(res);
//se1 = ExpressionDump.printExpStr(res);
//print("\nresults to exp: " + se1);
then
(res, functionTree);
// boolean expression e.g. relation are left as thes are
case (e as DAE.RELATION(), _, _, _, _)
then
(e, inFunctionTree);
case (e as DAE.LBINARY(), _, _, _, _)
then
(e, inFunctionTree);
case (e as DAE.LUNARY(), _, _, _, _)
then
(e, inFunctionTree);
else
equation
true = Flags.isSet(Flags.FAILTRACE);
s1 = ExpressionDump.printExpStr(inExp);
s2 = ComponentReference.printComponentRefStr(inDiffwrtCref);
serr = stringAppendList({"- differentiateExp ",s1," w.r.t: ",s2," failed\n"});
Debug.trace(serr);
then
fail();
end match;
end differentiateExp;
protected function differentiateStatements
input list<DAE.Statement> inStmts;
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input list<DAE.Statement> inStmtsAccum;
input DAE.FunctionTree inFunctionTree;
input Integer maxIter;
input list<DAE.Exp> expStack;
output list<DAE.Statement> outDiffedStmts;
output DAE.FunctionTree outFunctionTree;
algorithm
(outDiffedStmts, outFunctionTree) :=
match(inStmts, inDiffwrtCref, inInputData, inDiffType, inStmtsAccum, inFunctionTree)
local
DAE.ComponentRef cref;
DAE.ElementSource source;
DAE.Exp lhs, rhs, derivedLHS, derivedRHS;
DAE.FunctionTree functions;
DAE.Statement currStatement, stmt, dstmt;
DAE.Type type_;
BackendDAE.DifferentiateInputData inputData;
BackendDAE.Var controlVar;
Boolean iterIsArray,initialCall;
DAE.Ident ident;
DAE.Exp exp;
DAE.Exp elseif_exp;
DAE.Else elseif_else_;
list<DAE.Exp> expLst, dexpLst, expLstRHS;
Integer index;
list<tuple<DAE.Exp, DAE.Exp>> exptl;
list<DAE.Statement> statementLst, restStatements, derivedStatements1, derivedStatements2, else_statementLst, elseif_statementLst;
String s1,s2,serr;
case ({}, _, _, _, _, _) then (listReverse(inStmtsAccum), inFunctionTree);
case ((currStatement as DAE.STMT_ASSIGN(type_=type_, exp1=lhs, exp=rhs, source=source))::restStatements, _, _, _, _, _)
equation
(derivedLHS, functions) = differentiateExp(lhs, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter, expStack);
(derivedRHS, functions) = differentiateExp(rhs, inDiffwrtCref, inInputData, inDiffType, functions, maxIter, expStack);
(derivedRHS,_) = ExpressionSimplify.simplify(derivedRHS);
derivedStatements1 = {DAE.STMT_ASSIGN(type_, derivedLHS, derivedRHS, source), currStatement};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case ((currStatement as DAE.STMT_TUPLE_ASSIGN(expExpLst= expLst, exp=rhs, source=source))::restStatements, _, _, _, _, _)
equation
(dexpLst,functions) = List.map3Fold(expLst, function differentiateExp(maxIter=maxIter, inExpStack=expStack), inDiffwrtCref, inInputData, inDiffType, inFunctionTree);
(derivedRHS as DAE.TUPLE(expLstRHS), functions) = differentiateExp(rhs, inDiffwrtCref, inInputData, inDiffType, functions, maxIter, expStack);
(DAE.TUPLE(expLstRHS),_) = ExpressionSimplify.simplify(derivedRHS);
exptl = List.threadTuple(dexpLst, expLstRHS);
derivedStatements1 = List.map1(exptl, Algorithm.makeSimpleAssignment, source);
derivedStatements1 = listAppend(derivedStatements1, {currStatement});
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case ((currStatement as DAE.STMT_ASSIGN_ARR(lhs=lhs, exp=rhs, type_=type_, source=source))::restStatements, _, _, _, _, _)
equation
(derivedLHS, functions) = differentiateExp(lhs, inDiffwrtCref, inInputData, inDiffType, inFunctionTree, maxIter, expStack);
(derivedRHS, functions) = differentiateExp(rhs, inDiffwrtCref, inInputData, inDiffType, functions, maxIter, expStack);
(derivedRHS,_) = ExpressionSimplify.simplify(derivedRHS);
derivedStatements1 = {DAE.STMT_ASSIGN_ARR(type_, derivedLHS, derivedRHS, source), currStatement};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case (DAE.STMT_FOR(type_=type_, iterIsArray=iterIsArray, iter=ident, index=index, range=exp, statementLst=statementLst, source=source)::restStatements, _, _, _, _, _)
equation
cref = ComponentReference.makeCrefIdent(ident, DAE.T_INTEGER_DEFAULT, {});
controlVar = BackendDAE.VAR(cref, BackendDAE.DISCRETE(), DAE.BIDIR(), DAE.NON_PARALLEL(), DAE.T_REAL_DEFAULT, NONE(), NONE(), {}, DAE.emptyElementSource, NONE(), NONE(), NONE(), DAE.NON_CONNECTOR(), DAE.NOT_INNER_OUTER(), false);
inputData = addAllVars({controlVar}, inInputData);
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
derivedStatements1 = {DAE.STMT_FOR(type_, iterIsArray, ident, index, exp, derivedStatements1, source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_IF(exp=exp, statementLst=statementLst, else_=DAE.NOELSE(), source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
derivedStatements1 = {DAE.STMT_IF(exp, derivedStatements1, DAE.NOELSE(), source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_IF(exp=exp, statementLst=statementLst, else_=DAE.ELSEIF(exp=elseif_exp, statementLst=elseif_statementLst, else_=elseif_else_), source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
(derivedStatements2, functions) = differentiateStatements({DAE.STMT_IF(elseif_exp, elseif_statementLst, elseif_else_, source)}, inDiffwrtCref, inInputData, inDiffType, {}, functions, maxIter, expStack);
derivedStatements1 = {DAE.STMT_IF(exp, derivedStatements1, DAE.ELSE(derivedStatements2), source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_IF(exp=exp, statementLst=statementLst, else_=DAE.ELSE(statementLst=else_statementLst), source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
(derivedStatements2, functions) = differentiateStatements(else_statementLst, inDiffwrtCref, inInputData, inDiffType, {}, functions, maxIter, expStack);
derivedStatements1 = {DAE.STMT_IF(exp, derivedStatements1, DAE.ELSE(derivedStatements2), source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_WHILE(exp=exp, statementLst=statementLst, source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
derivedStatements1 = {DAE.STMT_WHILE(exp, derivedStatements1, source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_WHEN(exp=exp, initialCall=initialCall, statementLst=statementLst, elseWhen= NONE(), source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
derivedStatements1 = {DAE.STMT_WHEN(exp, {}, initialCall, derivedStatements1, NONE(), source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case(DAE.STMT_WHEN(exp=exp, initialCall=initialCall, statementLst=statementLst, elseWhen= SOME(stmt), source=source)::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(statementLst, inDiffwrtCref, inInputData, inDiffType, {}, inFunctionTree, maxIter, expStack);
({dstmt}, functions) = differentiateStatements({stmt}, inDiffwrtCref, inInputData, inDiffType, {}, functions, maxIter, expStack);
derivedStatements1 = {DAE.STMT_WHEN(exp, {}, initialCall, derivedStatements1, SOME(dstmt), source)};
derivedStatements1 = listAppend(derivedStatements1, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, functions, maxIter, expStack);
then (derivedStatements2, functions);
case((DAE.STMT_ASSERT())::restStatements, _, _, _, _, _)
equation
(derivedStatements1, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, inStmtsAccum, inFunctionTree, maxIter, expStack);
then (derivedStatements1, functions);
case((currStatement as DAE.STMT_TERMINATE())::restStatements, _, _, _, _, _)
equation
derivedStatements1 = listAppend({currStatement}, inStmtsAccum);
(derivedStatements2, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, inFunctionTree, maxIter, expStack);
then (derivedStatements2, functions);
case((currStatement as DAE.STMT_REINIT())::restStatements, _, _, _, _, _)
equation
derivedStatements1 = listAppend({currStatement}, inStmtsAccum);
(derivedStatements1, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, inFunctionTree, maxIter, expStack);
then (derivedStatements1, functions);
case((currStatement as DAE.STMT_NORETCALL())::restStatements, _, _, _, _, _)
equation
derivedStatements1 = listAppend({currStatement}, inStmtsAccum);
(derivedStatements1, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, inFunctionTree, maxIter, expStack);
then (derivedStatements1, functions);
case((currStatement as DAE.STMT_RETURN())::restStatements, _, _, _, _, _)
equation
derivedStatements1 = listAppend({currStatement}, inStmtsAccum);
(derivedStatements1, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, inFunctionTree, maxIter, expStack);
then (derivedStatements1, functions);
case((currStatement as DAE.STMT_BREAK())::restStatements, _, _, _, _, _)
equation
derivedStatements1 = listAppend({currStatement}, inStmtsAccum);
(derivedStatements1, functions) = differentiateStatements(restStatements, inDiffwrtCref, inInputData, inDiffType, derivedStatements1, inFunctionTree, maxIter, expStack);
then (derivedStatements1, functions);
else
equation
true = Flags.isSet(Flags.FAILTRACE);
(currStatement::_) = inStmts;
s1 = DAEDump.ppStatementStr(currStatement);
s2 = ComponentReference.printComponentRefStr(inDiffwrtCref);
serr = stringAppendList({"- differentiateStatements ",s1," w.r.t: ",s2," failed\n"});
Debug.trace(serr);
then
fail();
end match;
end differentiateStatements;
// =============================================================================
// help functions for differentation
// - differentiateCrefs
// - differentiateCalls
// - differentiateBinary (e.g.: ADD, SUB, MUL, DIV, POW, ...
//
// =============================================================================
protected function differentiateCrefs
"
function: differentiateCrefs
"
input DAE.Exp inExp; // in as DAE.CREF(_)
input DAE.ComponentRef inDiffwrtCref;
input BackendDAE.DifferentiateInputData inInputData;
input BackendDAE.DifferentiationType inDiffType;
input DAE.FunctionTree inFunctionTree;
input Integer maxIter;
input list<DAE.Exp> expStack;
output DAE.Exp outDiffedExp;
output DAE.FunctionTree outFunctionTree;
algorithm
(outDiffedExp, outFunctionTree) :=
matchcontinue(inExp, inDiffwrtCref, inInputData, inDiffType, inFunctionTree)
local
Absyn.Path path;
BackendDAE.Variables timevars;
BackendDAE.Variables knvars;
BackendDAE.Var var;
BackendDAE.VarKind kind;
list<BackendDAE.Var> vars;