public LPSolution Solve()
{
LinearProgram.VerifyVariables();
Tableau previousTableau = new Tableau();
ConstraintRow[] constraints = new ConstraintRow[LinearProgram.Constraints.Length];
for (int i = 0; i < constraints.Length; i++)
{
constraints[i] = new ConstraintRow(i, constraints.Length, LinearProgram.Constraints[i].GetVars(), LinearProgram.Constraints[i].Constant);
}
previousTableau.Constraints = constraints;
previousTableau.ObjectiveRow = new ObjectiveRow(constraints.Length, LinearProgram.ObjectiveFunction.GetVars());
Variable[] emptyVars = previousTableau.ObjectiveRow.Vars.Where(var => !var.IsSlack).Select(var => var.Empty).ToArray();
Tableau currentTableau = Tableau.EmptyTableau(previousTableau.Constraints.Length, emptyVars);
while (MostNegitive(previousTableau, out Variable mostNegitive))
{
int index = 0;
double leastPositive = previousTableau.Constraints.Length > 0 ? previousTableau.Constraints[index].RatioTest(mostNegitive) : -1;
for (int i = 0; i < previousTableau.Constraints.Length; i++)
{
double rt = previousTableau.Constraints[i].RatioTest(mostNegitive);
if (rt > 0 && rt < leastPositive)
{
leastPositive = rt; index = i;
}
}
if (leastPositive == 0)
{
throw new Exception("Least Positive is Unchanged");
}
currentTableau.Constraints[index] = previousTableau.Constraints[index].PivotRow(mostNegitive.Index);
currentTableau.ObjectiveRow = previousTableau.ObjectiveRow.Normalize(mostNegitive.Index, currentTableau.Constraints[index].Vars, currentTableau.Constraints[index].RHS);
for (int i = 0; i < currentTableau.Constraints.Length; i++)
{
if (i != index)
{
currentTableau.Constraints[i] = previousTableau.Constraints[i].Normalize(mostNegitive.Index, currentTableau.Constraints[index].Vars, currentTableau.Constraints[index].RHS);
}
}
previousTableau = currentTableau.Copy();
currentTableau = Tableau.EmptyTableau(previousTableau.Constraints.Length, emptyVars);
}
Console.WriteLine(previousTableau);
return(new LPSolution(previousTableau));
}
private bool MostNegitive(Tableau tablar, out Variable mostNegitive)
{
mostNegitive = new Variable {
Index = -1, Value = 0
};
foreach (Variable var in tablar.ObjectiveRow.Vars)
{
if (var.Value < mostNegitive.Value)
{
mostNegitive = var;
}
}
return(mostNegitive.Index != -1);
}
public LPSolution(Tableau finalTableau)
{
Results = finalTableau.BasicVariableAnalysis();
Maximum = finalTableau.ObjectiveRow.RHS;
FinalTableau = finalTableau;
}
