bool Recurrence::calcIteratedUpdate(const UpdateMap &oldUpdate, const Expression &meterfunc, UpdateMap &newUpdate) {
assert(newUpdate.empty());
UpdateMap update = oldUpdate; //might be changed by dependencyOrder, so copy here
vector<VariableIndex> order = dependencyOrder(update);
assert(order.size() == update.size());
//in the given order try to solve the recurrence for every updated variable
for (VariableIndex vi : order) {
Expression res;
ExprSymbol target = itrs.getGinacSymbol(vi);
//use update rhs, but replace already processed variables with their recurrences
Expression todo = update.at(vi).subs(knownPreRecurrences);
if (!findUpdateRecurrence(todo,target,res)) {
return false;
}
//remember this recurrence to replace vi in the updates depending on vi
//note that updates need the value at n-1, e.g. x(n) = x(n-1) + vi(n-1) for the update x=x+vi
knownPreRecurrences[target] = res.subs(ginacN == ginacN-1);
//calcuate the final update using the loop's runtime
newUpdate[vi] = res.subs(ginacN == meterfunc);
}
return true;
}
//NOTE: very stupid and not very efficient; better use a graph for this problem
vector<VariableIndex> Recurrence::dependencyOrder(UpdateMap &update) {
vector<VariableIndex> ordering;
set<VariableIndex> orderedVars;
while (ordering.size() < update.size()) {
bool changed = false;
for (auto up : update) {
if (orderedVars.count(up.first) > 0) continue;
//check if all variables on update rhs are already processed
for (const string &varname : up.second.getVariableNames()) {
VariableIndex vi = itrs.getVarindex(varname);
if (vi != up.first && update.count(vi) > 0 && orderedVars.count(vi) == 0)
goto skipUpdate;
}
orderedVars.insert(up.first);
ordering.push_back(up.first);
changed = true;
skipUpdate: ;
}
if (changed) continue;
//if not all dependencies could be resolved, try to add constraints to the guard to make things easier
GiNaC::exmap subs;
ExprSymbol target;
bool has_target = false;
for (auto up : update) {
if (orderedVars.count(up.first) > 0) continue;
if (!has_target) {
target = itrs.getGinacSymbol(up.first);
has_target = true;
} else {
addGuard.push_back(target == itrs.getGinacSymbol(up.first));
subs[itrs.getGinacSymbol(up.first)] = target;
}
}
//assume all remaining variables are equal
for (auto &up : update) {
up.second = up.second.subs(subs);
}
}
return ordering;
}
