/// <remarks>
/// Constructor initializes the fields, and creaties the objective row.
/// </remarks>
public ClSimplexSolver()
{
_stayMinusErrorVars = new ArrayList();
_stayPlusErrorVars = new ArrayList();
_errorVars = new Hashtable();
_markerVars = new Hashtable();
_resolve_pair = new ArrayList(2);
_resolve_pair.Add(new ClDouble(0));
_resolve_pair.Add(new ClDouble(0));
_objective = new ClObjectiveVariable("Z");
_editVarMap = new Hashtable();
_slackCounter = 0;
_artificialCounter = 0;
_dummyCounter = 0;
_epsilon = 1e-8;
_cOptimizeAutomatically = true;
_cNeedsSolving = false;
ClLinearExpression e = new ClLinearExpression();
_rows.Add(_objective, e);
_stkCedcns = new Stack();
_stkCedcns.Push(0);
if (Trace)
TracePrint("objective expr == " + RowExpression(_objective));
}
/// <summary>
/// Minimize the value of the objective.
/// </summary>
/// <remarks>
/// The tableau should already be feasible.
/// </remarks>
private void Optimize(ClObjectiveVariable zVar)
/* throws ExClInternalError */
{
ClLinearExpression zRow = RowExpression(zVar);
if (zRow == null)
{
throw new CassowaryInternalException("Assertion failed: zRow != null");
}
ClAbstractVariable entryVar = null;
ClAbstractVariable exitVar = null;
while (true)
{
double objectiveCoeff = 0;
foreach (var kvp in zRow.Terms)
{
if (kvp.Key.IsPivotable && kvp.Value.Value < objectiveCoeff)
{
objectiveCoeff = kvp.Value.Value;
entryVar = kvp.Key;
}
}
if (objectiveCoeff >= -EPSILON || entryVar == null)
{
return;
}
double minRatio = Double.MaxValue;
foreach (ClAbstractVariable v in Columns[entryVar])
{
if (v.IsPivotable)
{
ClLinearExpression expr = RowExpression(v);
double coeff = expr.CoefficientFor(entryVar);
if (coeff < 0.0)
{
double r = -expr.Constant / coeff;
if (r < minRatio)
{
minRatio = r;
exitVar = v;
}
}
}
}
// ReSharper disable CompareOfFloatsByEqualityOperator
if (minRatio == Double.MaxValue)
// ReSharper restore CompareOfFloatsByEqualityOperator
{
throw new CassowaryInternalException("Objective function is unbounded in Optimize");
}
Pivot(entryVar, exitVar);
}
}
//// END PUBLIC INTERFACE ////
/// <summary>
/// Add the constraint expr=0 to the inequality tableau using an
/// artificial variable.
/// </summary>
/// <remarks>
/// To do this, create an artificial variable av and add av=expr
/// to the inequality tableau, then make av be 0 (raise an exception
/// if we can't attain av=0).
/// </remarks>
private void AddWithArtificialVariable(ClLinearExpression expr)
/* throws ExClRequiredFailure, ExClInternalError */
{
ClSlackVariable av = new ClSlackVariable(++_artificialCounter, "a");
ClObjectiveVariable az = new ClObjectiveVariable("az");
ClLinearExpression azRow = expr.Clone();
AddRow(az, azRow);
AddRow(av, expr);
Optimize(az);
ClLinearExpression azTableauRow = RowExpression(az);
if (!Approx(azTableauRow.Constant, 0.0))
{
RemoveRow(az);
RemoveColumn(av);
throw new CassowaryRequiredFailureException();
}
// see if av is a basic variable
ClLinearExpression e = RowExpression(av);
if (e != null)
{
// find another variable in this row and pivot,
// so that av becomes parametric
if (e.IsConstant)
{
// if there isn't another variable in the row
// then the tableau contains the equation av=0 --
// just delete av's row
RemoveRow(av);
RemoveRow(az);
return;
}
ClAbstractVariable entryVar = e.AnyPivotableVariable();
Pivot(entryVar, av);
}
Assert(RowExpression(av) == null, "RowExpression(av) == null)");
RemoveColumn(av);
RemoveRow(az);
}
//// END PUBLIC INTERFACE ////
/// <summary>
/// Add the constraint expr=0 to the inequality tableau using an
/// artificial variable.
/// </summary>
/// <remarks>
/// To do this, create an artificial variable av and add av=expr
/// to the inequality tableau, then make av be 0 (raise an exception
/// if we can't attain av=0).
/// </remarks>
protected void AddWithArtificialVariable(ClLinearExpression expr)
/* throws ExClRequiredFailure, ExClInternalError */
{
if (Trace)
FnEnterPrint("AddWithArtificialVariable: " + expr);
ClSlackVariable av = new ClSlackVariable(++_artificialCounter, "a");
ClObjectiveVariable az = new ClObjectiveVariable("az");
ClLinearExpression azRow = (ClLinearExpression) expr.Clone();
if (Trace)
TracePrint("before AddRows:\n" + this);
AddRow(az, azRow);
AddRow(av, expr);
if (Trace)
TracePrint("after AddRows:\n" + this);
Optimize(az);
ClLinearExpression azTableauRow = RowExpression(az);
if (Trace)
TracePrint("azTableauRow.Constant == " + azTableauRow.Constant);
if (!Cl.Approx(azTableauRow.Constant, 0.0))
{
RemoveRow(az);
RemoveColumn(av);
throw new ExClRequiredFailure();
}
// see if av is a basic variable
ClLinearExpression e = RowExpression(av);
if (e != null)
{
// find another variable in this row and pivot,
// so that av becomes parametric
if (e.IsConstant)
{
// if there isn't another variable in the row
// then the tableau contains the equation av=0 --
// just delete av's row
RemoveRow(av);
RemoveRow(az);
return;
}
ClAbstractVariable entryVar = e.AnyPivotableVariable();
Pivot(entryVar, av);
}
Assert(RowExpression(av) == null, "RowExpression(av) == null)");
RemoveColumn(av);
RemoveRow(az);
}
/// <summary>
/// Minimize the value of the objective.
/// </summary>
/// <remarks>
/// The tableau should already be feasible.
/// </remarks>
protected void Optimize(ClObjectiveVariable zVar)
/* throws ExClInternalError */
{
if (Trace)
{
FnEnterPrint("Optimize: " + zVar);
TracePrint(this.ToString());
}
ClLinearExpression zRow = RowExpression(zVar);
Assert(zRow != null, "zRow != null");
ClAbstractVariable entryVar = null;
ClAbstractVariable exitVar = null;
while (true)
{
double objectiveCoeff = 0;
Hashtable terms = zRow.Terms;
foreach (ClAbstractVariable v in terms.Keys)
{
double c = ((ClDouble) terms[v]).Value;
if (v.IsPivotable && c < objectiveCoeff)
{
objectiveCoeff = c;
entryVar = v;
}
}
if (objectiveCoeff >= -_epsilon || entryVar == null)
return;
if (Trace)
TracePrint("entryVar == " + entryVar + ", objectiveCoeff == " + objectiveCoeff);
double minRatio = Double.MaxValue;
Set columnVars = (Set) _columns[entryVar];
double r = 0.0;
foreach (ClAbstractVariable v in columnVars)
{
if (Trace)
TracePrint("Checking " + v);
if (v.IsPivotable)
{
ClLinearExpression expr = RowExpression(v);
double coeff = expr.CoefficientFor(entryVar);
if (Trace)
TracePrint("pivotable, coeff == " + coeff);
if (coeff < 0.0)
{
r = - expr.Constant / coeff;
if (r < minRatio)
{
if (Trace)
TracePrint("New minRatio == " + r);
minRatio = r;
exitVar = v;
}
}
}
}
if (minRatio == Double.MaxValue)
{
throw new ExClInternalError("Objective function is unbounded in Optimize");
}
Pivot(entryVar, exitVar);
if (Trace)
TracePrint(this.ToString());
}
}