/// <summary>
/// Solve the linear equation system Ax = b with Jacobi
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="init">initial solution</param>
/// <param name="reach"></param>
/// <param name="allRowVars"></param>
/// <param name="allColVars"></param>
/// <param name="omega">jor parameter</param>
/// <returns></returns>
public static CUDDNode Jacobi(CUDDNode a, CUDDNode b, CUDDNode init, CUDDNode reach, CUDDVars allRowVars, CUDDVars allColVars, double omega)
{
DateTime startTime = DateTime.Now;
int numberOfIterations = 0;
CUDDNode id = CUDD.Matrix.Identity(allRowVars, allColVars);
CUDD.Ref(reach);
id = CUDD.Function.And(id, reach);
CUDD.Ref(id, a);
CUDDNode diags = CUDD.Function.Times(id, a);
diags = CUDD.Abstract.SumAbstract(diags, allColVars);
//
CUDD.Ref(id, a);
CUDDNode newA = CUDD.Function.ITE(id, CUDD.Constant(0), a);
newA = CUDD.Function.Times(CUDD.Constant(-1), newA);
// divide a,b by diagonal
CUDD.Ref(diags);
newA = CUDD.Function.Divide(newA, diags);
CUDD.Ref(b, diags);
CUDDNode newB = CUDD.Function.Divide(b, diags);
// print out some memory usage
Debug.WriteLine("Iteration matrix MTBDD... [nodes = " + CUDD.GetNumNodes(newA) + "]");
Debug.WriteLine("Diagonals MTBDD... [nodes = " + CUDD.GetNumNodes(diags) + "]");
CUDD.Ref(init);
CUDDNode sol = init;
while(true)
{
numberOfIterations++;
CUDDNode tmp = CUDD.Matrix.MatrixMultiplyVector(newA, sol, allRowVars, allColVars);
CUDD.Ref(newB);
tmp = CUDD.Function.Plus(tmp, newB);
if(omega != 1)
{
tmp = CUDD.Function.Times(tmp, CUDD.Constant(omega));
CUDD.Ref(sol);
tmp = CUDD.Function.Plus(tmp, CUDD.Function.Times(sol, CUDD.Constant(1 - omega)));
}
if(CUDD.IsEqual(tmp, sol))
{
CUDD.Deref(tmp);
break;
}
CUDD.Deref(sol);
sol = tmp;
}
CUDD.Deref(id, diags, newA, newB);
DateTime endTime = DateTime.Now;
double runningTime = (endTime - startTime).TotalSeconds;
Debug.WriteLine("Jacobi: " + numberOfIterations + " iterations in " + runningTime + " seconds");
return sol;
}
/// <summary>
/// Check whether destination is reachable from source
/// [ REFS: '', DEREFS:]
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="transitions"></param>
/// <returns></returns>
public bool Path(CUDDNode source, CUDDNode destination, List <CUDDNode> transitions)
{
CUDD.Ref(source, destination);
CUDDNode temp = CUDD.Function.And(source, destination);
//In case source already satisfies destination
if (!temp.Equals(CUDD.ZERO))
{
CUDD.Deref(temp);
return(true);
}
//
bool reachable = false;
CUDDNode allReachabeToGoal, currentReachableToGoal;
CUDD.Ref(destination, destination);
allReachabeToGoal = currentReachableToGoal = destination;
CUDDNode allReachableFromInit, currentReachableFromInit;
CUDD.Ref(source, source);
allReachableFromInit = currentReachableFromInit = source;
int nextStep = 0;
int forwardStep = 0;
int numberOfForwardNodes = 0;
int backwardSteps = 0;
int numberOfBackwardNodes = 0;
int numberOfLoop = 0;
CUDDNode commonNode = CUDD.Constant(0);
do
{
if (nextStep != GoForward)
{
//backward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
//to find source state, now the currentReachableToGoal must be in column form (target state)
currentReachableToGoal = this.Predecessors(currentReachableToGoal, transitions);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableToGoal, allReachabeToGoal);
CUDDNode allReachabeToGoalTemp = CUDD.Function.Or(allReachabeToGoal, currentReachableToGoal);
backwardSteps++;
numberOfBackwardNodes = CUDD.GetNumNodes(allReachabeToGoalTemp);
if (allReachabeToGoalTemp.Equals(allReachabeToGoal))
{
reachable = false;
CUDD.Deref(allReachabeToGoalTemp);
break;
}
else
{
currentReachableToGoal = CUDD.Function.Different(currentReachableToGoal, allReachabeToGoal);
allReachabeToGoal = allReachabeToGoalTemp;
}
}
if (nextStep != GoBackward)
{
//forward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
currentReachableFromInit = this.Successors(currentReachableFromInit, transitions);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableFromInit, allReachableFromInit);
CUDDNode allReachabeFromInitTemp = CUDD.Function.Or(currentReachableFromInit, allReachableFromInit);
forwardStep++;
numberOfForwardNodes = CUDD.GetNumNodes(allReachabeFromInitTemp);
if (allReachabeFromInitTemp.Equals(allReachableFromInit))
{
reachable = false;
CUDD.Deref(allReachabeFromInitTemp);
break;
}
else
{
currentReachableFromInit = CUDD.Function.Different(currentReachableFromInit, allReachableFromInit);
allReachableFromInit = allReachabeFromInitTemp;
}
}
nextStep = GetNextStep(forwardStep, numberOfForwardNodes, backwardSteps, numberOfBackwardNodes);
} while (true);
Debug.WriteLine("\nPath: " + numberOfLoop + " loops.");
CUDD.Deref(allReachabeToGoal, currentReachableToGoal, allReachableFromInit, currentReachableFromInit, commonNode);
//
return(reachable);
}
public void ShowInfo()
{
Console.WriteLine("Domain name: {0}", DomainName);
Console.WriteLine(Domain.BarLine);
Console.WriteLine("Problem Name: {0}", ProblemName);
Console.WriteLine(Domain.BarLine);
Globals.TermInterpreter.ShowInfo();
Console.WriteLine("Predicates:");
foreach (var pair in _predicateDict)
{
Console.WriteLine(" Name: {0}, PreCuddIndex: {1}, SucCuddIndex: {2}", pair.Key,
pair.Value.PreviousCuddIndex, pair.Value.SuccessiveCuddIndex);
}
Console.WriteLine(Domain.BarLine);
//Console.WriteLine("Initial state:");
//foreach (var pred in TruePredSet)
//{
// Console.WriteLine(" {0}", pred);
//}
List <string> eventNameArray = new List <string>
{
"leftFail(a1)",
"rightSuc2(a2,-2)",
"leftSuc2(a1,0)",
"leftSuc1(a1)",
"leftSuc1(a2)",
"rightSuc1(a1)",
"rightSuc1(a2)",
"dropFail(a1)",
"dropSuc(a1)",
"pickSuc(a2)",
"learn(a1,1,-1)",
"learn(a1,1,0)"
};
Console.WriteLine("Events:");
for (int i = 0; i < eventNameArray.Count; i++)
{
string eventName = eventNameArray[i];
Console.WriteLine(eventName);
Event e = _eventDict[eventName];
Console.WriteLine(" Name: {0}", eventNameArray[i]);
Console.WriteLine(" Cudd index: {0}", e.CuddIndex);
Console.WriteLine(" Precondition:");
Console.WriteLine(" Number of nodes: {0}", CUDD.GetNumNodes(e.Precondition));
//Console.WriteLine(" CondEffect:");
////Console.WriteLine(" Count:{0}", e.CondEffect.Count);
//for (int j = 0; j < e.CondEffect.Count; j++)
//{
// Console.WriteLine(" Index: {0}", j);
// //Console.WriteLine(" Condition:");
// //CUDD.Print.PrintMinterm(e.CondEffect[j].Item1);
// Console.Write(" Literals: ");
// foreach (var literal in e.CondEffect[j].Item2)
// {
// string format = literal.Item2 ? "{0} " : "!{0} ";
// Console.Write(format, literal.Item1);
// }
// Console.WriteLine();
//}
Console.WriteLine(" Partial successor state axiom:");
Console.WriteLine(" Number of nodes: {0}", CUDD.GetNumNodes(e.PartialSsa));
Console.WriteLine();
}
Console.WriteLine(Domain.BarLine);
Console.WriteLine("Actions:");
foreach (var action in _actionDict.Values)
{
Console.WriteLine(" Name: {0}", action.FullName);
Console.WriteLine(" Response:");
foreach (var response in action.ResponseDict.Values)
{
Console.WriteLine(" Name: {0}", response.FullName);
Console.Write(" Believe Event list: ");
foreach (var e in response.EventModel.BelieveEventList)
{
Console.Write("{0} ", e.FullName);
}
Console.WriteLine();
Console.Write(" Know Event list: ");
foreach (var e in response.EventModel.KnowEventList)
{
Console.Write("{0} ", e.FullName);
}
Console.WriteLine();
}
Console.WriteLine();
}
Console.WriteLine(Domain.BarLine);
Console.WriteLine("Observations:");
foreach (var observation in _obervationDict.Values)
{
Console.WriteLine(" Name: {0}", observation.FullName);
Console.Write(" Believe Event list: ");
foreach (var e in observation.EventModel.BelieveEventList)
{
Console.Write("{0} ", e.FullName);
}
Console.WriteLine();
Console.Write(" Know Event list: ");
foreach (var e in observation.EventModel.KnowEventList)
{
Console.Write("{0} ", e.FullName);
}
Console.WriteLine();
}
Console.WriteLine(Domain.BarLine);
}
/// <summary>
/// Return the path from source to destination. If reachable, return true and path contains the path from source to destination
/// [ REFS: '', DEREFS:]
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="transitions"></param>
/// <param name="model"></param>
/// <param name="path">not include the init state</param>
/// <param name="isEmptyPathAllowed">if false, then the path must be not empty though the source satisfies the destination</param>
/// <returns></returns>
public bool Path(CUDDNode source, CUDDNode destination, List <CUDDNode> transitions, List <CUDDNode> path, bool isEmptyPathAllowed)
{
if (isEmptyPathAllowed)
{
CUDD.Ref(source, destination);
CUDDNode temp = CUDD.Function.And(source, destination);
//In case source already satisfies destination
if (!temp.Equals(CUDD.ZERO))
{
CUDD.Deref(temp);
return(true);
}
}
//
bool reachable = false;
List <CUDDNode> backtrackingReachability = new List <CUDDNode>();
List <CUDDNode> forwardReachability = new List <CUDDNode>();
CUDDNode allReachabeToGoal, currentReachableToGoal;
CUDD.Ref(destination, destination);
allReachabeToGoal = currentReachableToGoal = destination;
CUDDNode allReachableFromInit, currentReachableFromInit;
CUDD.Ref(source, source);
allReachableFromInit = currentReachableFromInit = source;
int nextStep = 0;
int forwardStep = 0;
int numberOfForwardNodes = 0;
int backwardSteps = 0;
int numberOfBackwardNodes = 0;
int numberOfLoop = 0;
CUDDNode commonNode = CUDD.Constant(0);
do
{
if (nextStep != GoForward)
{
//Backward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
//to find source state, now the currentReachableToGoal must be in column form (target state)
currentReachableToGoal = this.SwapRowColVars(currentReachableToGoal);
CUDD.Ref(transitions);
currentReachableToGoal = CUDD.Function.And(currentReachableToGoal, transitions);
CUDD.Ref(currentReachableToGoal);
backtrackingReachability.Add(currentReachableToGoal);
//get source state, but in row-form
currentReachableToGoal = CUDD.Abstract.ThereExists(currentReachableToGoal, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableToGoal, allReachabeToGoal);
CUDDNode allReachabeToGoalTemp = CUDD.Function.Or(allReachabeToGoal, currentReachableToGoal);
backwardSteps++;
numberOfBackwardNodes = CUDD.GetNumNodes(allReachabeToGoalTemp);
if (allReachabeToGoalTemp.Equals(allReachabeToGoal))
{
reachable = false;
CUDD.Deref(allReachabeToGoalTemp);
break;
}
else
{
currentReachableToGoal = CUDD.Function.Different(currentReachableToGoal, allReachabeToGoal);
allReachabeToGoal = allReachabeToGoalTemp;
}
}
if (nextStep != GoBackward)
{
//forward
numberOfLoop++;
Debug.Write(numberOfLoop + " ");
CUDD.Ref(transitions);
currentReachableFromInit = CUDD.Function.And(currentReachableFromInit, transitions);
//Must reference because current value of currentReachableDD belonging to backtrackingReachability
CUDD.Ref(currentReachableFromInit);
forwardReachability.Add(currentReachableFromInit);
currentReachableFromInit = this.SwapRowColVars(currentReachableFromInit);
//get target state, in row-form
currentReachableFromInit = CUDD.Abstract.ThereExists(currentReachableFromInit, AllColVars);
//Check 2 directions have intersection
CUDD.Ref(currentReachableToGoal, currentReachableFromInit);
CUDD.Deref(commonNode);
commonNode = CUDD.Function.And(currentReachableToGoal, currentReachableFromInit);
if (!commonNode.Equals(CUDD.ZERO))
{
reachable = true;
break;
}
//find fixpoint
CUDD.Ref(currentReachableFromInit, allReachableFromInit);
CUDDNode allReachabeFromInitTemp = CUDD.Function.Or(currentReachableFromInit, allReachableFromInit);
forwardStep++;
numberOfForwardNodes = CUDD.GetNumNodes(allReachabeFromInitTemp);
if (allReachabeFromInitTemp.Equals(allReachableFromInit))
{
reachable = false;
CUDD.Deref(allReachabeFromInitTemp);
break;
}
else
{
currentReachableFromInit = CUDD.Function.Different(currentReachableFromInit, allReachableFromInit);
allReachableFromInit = allReachabeFromInitTemp;
}
}
nextStep = GetNextStep(forwardStep, numberOfForwardNodes, backwardSteps, numberOfBackwardNodes);
} while (true);
Debug.WriteLine("\nPath: " + numberOfLoop + " loops.");
if (!reachable)
{
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, currentReachableFromInit, allReachableFromInit, commonNode);
CUDD.Deref(backtrackingReachability);
CUDD.Deref(forwardReachability);
//
backtrackingReachability.Clear();
forwardReachability.Clear();
}
else
{
//
CUDD.Deref(currentReachableToGoal, allReachabeToGoal, currentReachableFromInit, allReachableFromInit);
//in column form
commonNode = this.SwapRowColVars(commonNode);
for (int i = forwardReachability.Count - 1; i >= 0; i--)
{
//Kill commonNode
CUDDNode correctTransition = CUDD.Function.And(forwardReachability[i], commonNode);
CUDD.Ref(correctTransition);
backtrackingReachability.Add(correctTransition);
//in column form
commonNode = CUDD.Abstract.ThereExists(correctTransition, AllColVars);
commonNode = this.SwapRowColVars(commonNode);
}
CUDD.Deref(commonNode);
//backtrackingReachability contains transitions from source to destination
if (backtrackingReachability.Count > 0)
{
CUDDNode currentStateDD = source;
CUDD.Ref(currentStateDD);
for (int i = backtrackingReachability.Count - 1; i >= 0; i--)
{
//find the intersection
currentStateDD = CUDD.Function.And(backtrackingReachability[i], currentStateDD);
//remove all boolean variables in the row-form, it is now set of all reachable backward state
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, AllRowVars);
currentStateDD = CUDD.RestrictToFirst(currentStateDD, this.AllColVars);
currentStateDD = CUDD.Abstract.ThereExists(currentStateDD, this.GetAllEventVars());
//swap to row-variable form
currentStateDD = this.SwapRowColVars(currentStateDD);
CUDD.Ref(currentStateDD);
path.Add(currentStateDD);
}
//
CUDD.Deref(currentStateDD);
}
}
//
return(reachable);
}
