private ResultType SolveTableau(ref Tableau t)
{
Variable head;
Variable row;
var prevTargetVal = 0d;
var isCircular = false;
while (t.FindPivot(out head, out row))
{
t = NextTableau(t, head, row);
//check cycles
if (Math.Abs(t.TargetEquation.Coefficient - prevTargetVal) <= double.Epsilon)
{
isCircular = true;
break;
}
prevTargetVal = t.TargetEquation.Coefficient;
}
ResultFactors = (from e in t.Equations where e.LeftTerm.Type != VariableType.Slack select new VariableFactor(e.LeftTerm, e.Coefficient)).ToArray();
if (isCircular)
{
return(ResultType.InfinitResults);
}
return(ResultType.OneResult);
}
public ResultType Solve()
{
var tableau = new Tableau(_equations);
tableau = PreprocessTableau(tableau);
return(SolveTableau(ref tableau));
}
private Tableau PreprocessTableau(Tableau t)
{
//check if there is no need to preprocess the table
if (t.Equations.All(e => e.LeftTerm.Type == VariableType.Target || e.Coefficient >= 0))
{
return(t);
}
var eqs = new Equation[t.Equations.Length];
var tVar = Variable.Problem(0);
for (var i = 0; i < eqs.Length - 1; i++)
{
eqs[i] = t.Equations[i].AddFactor(new VariableFactor(tVar, 1));
}
var f = new VariableFactor[t.Equations[0].Factors.Length];
for (var i = 0; i < f.Length; i++)
{
f[i] = new VariableFactor(t.Equations[0].Factors[i].Variable, 0);
}
var target = new Equation(Variable.Target(), f, 0);
target = target.AddFactor(new VariableFactor(tVar, -1));
eqs[eqs.Length - 1] = target;
t = new Tableau(eqs);
for (var i = 0; i < eqs.Length; i++)
{
if (t[i].LeftTerm.Type != VariableType.Target && t[i].Coefficient < 0)
{
t = NextTableau(t, tVar, t[i].LeftTerm);
}
}
SolveTableau(ref t);
var mainEquations = new Equation[t.Equations.Length];
for (var i = 0; i < mainEquations.Length - 1; i++)
{
mainEquations[i] = t.Equations[i].RemoveFactor(tVar);
}
var mainTarget = target.RemoveFactor(tVar);
mainEquations[mainEquations.Length - 1] = mainTarget;
return(new Tableau(mainEquations));
}
public static Tableau NextTableau(Tableau t, Variable pHead, Variable pRow)
{
var pIndex = t.IndexOf(pRow);
var pEq = t[pRow].Switch(pHead);
var equations = new Equation[t.Equations.Length];
for (int i = 0; i < equations.Length; i++)
{
if (i == pIndex)
{
equations[i] = pEq;
}
else
{
equations[i] = t[i].Resolve(pEq);
}
}
return(new Tableau(equations));
}