void slack_matrix::init_geqz_constraints(Matrix& m)
{
geqz_constraints = new bool[m.num_vars()];
memset(geqz_constraints, 0, m.num_vars()*sizeof(bool));
Matrix::iterator it = m.begin();
for(; it!= m.end(); it++)
{
bignum constant = it->second;
if(constant > 0) continue;
int index = -1;
Equation* eq = it->first;
for(int c=0; c<eq->num_entries(); c++)
{
bignum e = eq->get(c);
if(e > 0){
index = -1;
break;
}
else if(e<0 && index != -1)
{
index = -1;
break;
}
else if(e<0)
index = c;
}
// Mark entry as 1 if var has non-negativity constraint
if(index != -1)
geqz_constraints[index] = true;
}
}
// -----------Private methods ------------------//
void slack_matrix::populate_slack_matrix(Matrix& m)
{
/*
* If the initial system is Ax <= b,
* the slack matrix will contain it in the form
* -x0 + y +Ax -b
* and the last row is the objective function, initially -x0.
*/
Matrix::iterator it = m.begin();
int last = m.size()-1;
/*
vector<int> rows;
std::set<int> used;
for(int i=0; i <= last; i++)
{
int cur = rand()%(last+1);
while(used.count(cur) > 0){
cur++;
cur = cur%(last+1);
}
used.insert(cur);
rows.push_back(cur);
}
*/
int r = 0;
int i = 0;
for(; it!=m.end(); it++, r++, i++)
{
r = i;//rows[i];
// s0 entry is initially -1 for all rows
sm->set(r, 0, -1);
// In row r, set the corresponding slack variable to 1.
sm->set(r, i+1, 1);
Equation *eq = it->first;
for(int c=0; c < eq->num_entries(); c++) {
int start_index = index_mapping[c];
bignum coef = eq->get(c);
sm->set(r, start_index, coef);
/* Figure out whether we needed to split
* x as x1-x2 for missing non-negative constraints
*/
if(geqz_constraints[c]) continue;
sm->set(r, start_index+1, -coef);
}
//Deal with original constant
sm->set_constant(r, -it->second);
//Fill last slot with index of pivot variable for this row
sm->set_pivot(r, i+1);
}
/*
* Populate objective function row: Initially we want
* to maximize -x0
*/
sm->set(last+1, 0, -1);
}
