public void DeterminDuality()
{
originalLP.DisplayCurrentTable();
LinearProgram duality = (LinearProgram)originalLP.Clone();
if (originalLP.Type == LPType.Max)
{
duality.Type = LPType.Min;
}
else
{
duality.Type = LPType.Max;
}
duality.LinearProgramMatrix = new double[originalLP.CountX + 1, originalLP.RowCount];
//Fill X Values
for (int i = 1; i < originalLP.RowCount; i++)
{
for (int j = 0; j <= originalLP.CountX; j++)
{
duality.LinearProgramMatrix[j, i] = originalLP.LinearProgramMatrix[i, j];
}
}
double[] rhs = new double[originalLP.CountX + 1];
//Fill RHS
for (int i = 1; i <= originalLP.CountX; i++)
{
rhs[i] = originalLP.LinearProgramMatrix[0, i];
}
duality.CountA = 0;
duality.CountS = 0;
duality.CountE = originalLP.CountX;
duality.CountX = originalLP.RowCount - 1;
double[,] eArray = new double[duality.CountE + 1, duality.CountE];
//Handle URS
for (int i = 0; i < eArray.GetLength(1); i++)
{
eArray[i + 1, i] = 1;
}
double[,] finalLP = new double[duality.RowCount, duality.ColumnCount + eArray.GetLength(0)];
for (int i = 0; i < finalLP.GetLength(0); i++)
{
int mainCol = 0;
//Saves the LP
for (int orgCol = 0; orgCol < duality.ColumnCount; orgCol++)
{
finalLP[i, orgCol] = duality.LinearProgramMatrix[i, orgCol] * -1;
mainCol++;
}
//Saves the E's
for (int eCol = 0; eCol < duality.CountE; eCol++)
{
finalLP[i, mainCol] = eArray[i, eCol];
mainCol++;
}
//Saves the RHS
finalLP[i, duality.ColumnCount + duality.CountE] = rhs[i];
}
for (int i = 1; i < originalLP.RowCount; i++)
{
finalLP[0, i] = originalLP.LinearProgramMatrix[i, originalLP.ColumnCount - 1] * -1;
}
duality.LinearProgramMatrix = finalLP;
duality.LinearProgramMatrix[0, 0] = 1;
Console.WriteLine("Duality Initial Table");
duality.DisplayCurrentTable();
Console.WriteLine();
Dual dual = new Dual(duality);
duality = dual.Solve();
Console.WriteLine();
if (optimalSoltution.GetBasicVariables()[0] == duality.GetBasicVariables()[0])
{
Console.WriteLine("Strong Duality");
}
else
{
Console.WriteLine("Weak Duality");
}
}
//TODO: WILL BREAK IF SOLUTION IS NOT YET SOLVED OR IF YOU ADD CONSTRAINT TO A COLUMN WITH NO X SOLUTION
public static LinearProgram AddBasicConstraint
(LinearProgram linearProgram, int column, int ConstraintType, int rhs)
{
if (ConstraintType != GREATER_THAN && ConstraintType != LESS_THAN)
{
throw new ArgumentException
("The argument passed to AddBasicConstraint for ConstraintType does not match the expected value");
}
LinearProgram tempLp = (LinearProgram)linearProgram.Clone();
int constraintRow = linearProgram.RowCount;
double[,] newArray = new double[linearProgram.RowCount + 1, linearProgram.ColumnCount + 1];
for (int c = 0; c < linearProgram.ColumnCount - 1; c++)
{
for (int r = 0; r < linearProgram.RowCount; r++)
{
newArray[r, c] = linearProgram.LinearProgramMatrix[r, c];
}
}
for (int i = 0; i < linearProgram.RowCount; i++)
{
newArray[i, linearProgram.ColumnCount] = linearProgram.LinearProgramMatrix[i, linearProgram.ColumnCount - 1];
}
for (int i = 0; i < linearProgram.RowCount; i++)
{
newArray[i, linearProgram.ColumnCount - 1] = 0;
}
newArray[constraintRow, column] = 1;
newArray[constraintRow, linearProgram.ColumnCount] = rhs;
newArray[constraintRow, linearProgram.ColumnCount - 1] = 1;
//Constraint has been added, now check vilidity
int conflictingRow = 0;
for (int i = 0; i < linearProgram.RowCount; i++)
{
if (newArray[i, column] == 1)
{
conflictingRow = i;
break;
}
}
if (ConstraintType == GREATER_THAN)
{
tempLp.CountE++;
for (int i = 0; i < linearProgram.ColumnCount + 1; i++)
{
newArray[constraintRow, i] = newArray[constraintRow, i] - newArray[conflictingRow, i];
}
newArray[constraintRow, linearProgram.ColumnCount - 1] *= -1;
}
else
{
tempLp.CountS++;
for (int i = 0; i < linearProgram.ColumnCount + 1; i++)
{
newArray[constraintRow, i] = newArray[constraintRow, i] - newArray[conflictingRow, i];
}
}
if (newArray[constraintRow, linearProgram.ColumnCount - 1] < 0)
{
for (int i = 0; i < linearProgram.ColumnCount + 1; i++)
{
newArray[constraintRow, i] *= -1;
}
}
tempLp.LinearProgramMatrix = newArray;
tempLp.DisplayCurrentTable();
return(tempLp);
}
//Loop this?
public static void SensitivityAnalysisMenu()
{
try
{
//Sensitivity Analysis Menu
Console.WriteLine(@"
IP SOLVER
________________________________________________________________________________________
SENSITIVITY ANALYSIS
1. Display the range of a selected Non-Basic Variable.
2. Apply and display a change of a selected Non-Basic Variable.
3. Display the range of a selected Basic Variable.
4. Apply and display a change of a selected Basic Variable.
5. Display the range of a selected constraint right-hand-side value.
6. Apply and display a change of a selected constraint right-hand-side value.
7. Display the range of a selected variable in a Non-Basic Variable column.
8. Apply and display a change of a selected variable in a Non-Basic Variable column.
9. Add a new activity to an optimal solution.
10. Add a new constraint to an optimal solution.
11. Display the shadow prices.
12. Duality
");
Console.WriteLine("\nSolved LP\n");
linearProgram.DisplayCurrentTable();
Console.WriteLine();
int userInputSensitivityAnalysis = int.Parse(Console.ReadLine());
SensitivityMenu smenu = (SensitivityMenu)userInputSensitivityAnalysis;
switch (smenu)
{
case SensitivityMenu.display1:
//TODO Display the range of a selected Non-Basic Variable.
//SensivitityAnalysis.GetNonBasicVariables(linearProgram);
Console.WriteLine("Enter the column Number: (Z Column = Column 0)");
int rowNumber = int.Parse(Console.ReadLine());
Console.WriteLine("Ranges for Non Basic Variables");
SensivitityAnalysis.GetNBVRange(SensivitityAnalysis.GetFormatedSensistivityMatrix(linearProgram.LinearProgramMatrix), rowNumber);
Console.ReadKey();
break;
case SensitivityMenu.display2:
//TODO Display the range of a selected Non-Basic Variable.
Console.WriteLine("Enter the column Number: (Z Column = Column 0)");
int columnNumber = int.Parse(Console.ReadLine());
Console.WriteLine("Enter the row Number: (Z Column = Column 0)");
rowNumber = int.Parse(Console.ReadLine());
if (linearProgram.GetBasicVariables()[columnNumber] != 0)
{
Console.WriteLine("Not NBV");
}
else
{
Console.WriteLine("ENter NEw Value:");
int valuenew = int.Parse(Console.ReadLine());
linearProgram.LinearProgramMatrix[rowNumber, columnNumber] = valuenew;
linearProgram.DisplayCurrentTable();
if (LpTools.CheckIfIPIsSolved(linearProgram))
{
Console.WriteLine("No Change");
Console.ReadKey();
}
else
{
LinearProgram linearProgramNew = (LinearProgram)linearProgram.Clone();
Dual dual2 = new Dual(linearProgramNew);
dual2.Solve();
if (LpTools.CheckIfIPIsSolved(linearProgramNew))
{
linearProgramNew.DisplaySolution();
}
else
{
Console.WriteLine("No solution");
Console.ReadKey();
}
}
}
break;
case SensitivityMenu.display3:
//TODO Display the range of a selected Basic Variable.
Console.WriteLine("Enter the column Number: (Z Column = Column 0)");
rowNumber = int.Parse(Console.ReadLine());
Console.WriteLine("Ranges for Basic variables");
SensivitityAnalysis.GetRangesForSelectedBV(SensivitityAnalysis.GetFormatedSensistivityMatrix(linearProgram.LinearProgramMatrix), rowNumber);
Console.ReadKey();
break;
case SensitivityMenu.display4:
//TODO Apply and display a change of a selected Basic Variable.
break;
case SensitivityMenu.display5:
//TODO Display the range of a selected constraint right-hand-side value.
//Console.WriteLine("Enter the row Number: (Z Row = Row 0)");
//rowNumber = int.Parse(Console.ReadLine());
Console.WriteLine("Ranges for RHS variables");
SensivitityAnalysis.GetRangesForRHS(SensivitityAnalysis.GetFormatedSensistivityMatrix(linearProgram.LinearProgramMatrix), linearProgram);
Console.ReadKey();
break;
case SensitivityMenu.display6:
//TODO Apply and display a change of a selected constraint right-hand-side value.
break;
case SensitivityMenu.display7:
//TODO Display the range of a selected variable in a Non-Basic Variable column.
break;
case SensitivityMenu.display8:
//TODO Apply and display a change of a selected variable in a Non-Basic Variable column.
Console.WriteLine("Under Construction");
Console.ReadKey();
break;
case SensitivityMenu.display9:
//TODO Add a new activity to an optimal solution.
break;
case SensitivityMenu.display10:
//TODO Add a new constraint to an optimal solution.
Console.WriteLine("Enter the X Number: (Z Row = Row 0)");
rowNumber = int.Parse(Console.ReadLine());
Console.WriteLine("Type:\n1. <= \n2 . >=");
int sign = int.Parse(Console.ReadLine());
Console.WriteLine("RHS:");
int rhs = int.Parse(Console.ReadLine());
linearProgram = LpTools.AddBasicConstraint(linearProgram, rowNumber, sign - 1, rhs);
Console.WriteLine("New Table");
linearProgram.DisplayCurrentTable();
LinearProgram newLP = (LinearProgram)linearProgram.Clone();
Dual dual = new Dual(newLP);
dual.Solve();
if (LpTools.CheckIfIPIsSolved(newLP))
{
linearProgram.DisplaySolution();
}
else
{
Console.WriteLine("No solution");
Console.ReadKey();
}
break;
case SensitivityMenu.display11:
//TODO Display the shadow prices.
Console.WriteLine("shadow prices.");
SensivitityAnalysis.GetShadowPrices(SensivitityAnalysis.GetFormatedSensistivityMatrix(linearProgram.LinearProgramMatrix), linearProgram);
Console.ReadKey();
break;
case SensitivityMenu.display12:
//TODO Duality
Duality duality = new Duality(linearProgram);
duality.DeterminDuality();
Console.ReadKey();
break;
default:
break;
}
}
catch (FormatException)
{
Console.WriteLine("Invalid Input");
}
}