/// <summary>
/// Create the tableau by itself.
/// </summary>
/// <param name="maximize">if true, goal is to maximize the objective function</param>
/// <returns>created tableau</returns>
protected Matrix <T, TPolicy> CreateTableau(bool maximize)
{
// create a matrix of the correct size
int width = numDecisionVariables + numSlackVariables +
numArtificialVariables + NumObjectiveFunctions + 1; // + 1 is for RHS
int height = constraints.Count + NumObjectiveFunctions;
var matrix = new Matrix <T, TPolicy>(width, height);
var minusOne = Policy.Sub(Policy.Zero(), Policy.One());
// initialize the objective function rows
if (NumObjectiveFunctions == 2)
{
matrix[0, 0] = minusOne;
}
int zIndex = (NumObjectiveFunctions == 1) ? 0 : 1;
matrix[zIndex, zIndex] = maximize ? Policy.One() : minusOne;
Vector <T, TPolicy> objectiveCoefficients = maximize ? f.Coefficients * minusOne : f.Coefficients;
var rowData = matrix.GetRow(zIndex);
CopyArray(objectiveCoefficients.Data, rowData);
matrix.SetRow(zIndex, rowData);
matrix[width - 1, zIndex] = maximize ? f.ConstantTerm : Policy.Mul(minusOne, f.ConstantTerm);
if (!restrictToNonNegative)
{
matrix[SlackVariableOffset - 1, zIndex] = InvertedCoefficientSum(objectiveCoefficients);
}
// initialize the constraint rows
int slackVar = 0;
int artificialVar = 0;
for (int i = 0; i < constraints.Count; i++)
{
var constraint = constraints[i];
int row = NumObjectiveFunctions + i;
rowData = matrix.GetRow(row);
// decision variable coefficients
CopyArray(constraint.Coefficients.Data, rowData);
matrix.SetRow(row, rowData);
// x-
if (!restrictToNonNegative)
{
matrix[SlackVariableOffset - 1, row] =
InvertedCoefficientSum(constraint.Coefficients);
}
// RHS
matrix[width - 1, row] = constraint.Value;
// slack variables
if (constraint.Relationship == Relationship.LEQ)
{
matrix[SlackVariableOffset + slackVar++, row] = Policy.One(); // slack
}
else if (constraint.Relationship == Relationship.GEQ)
{
matrix[SlackVariableOffset + slackVar++, row] = minusOne; // excess
}
// artificial variables
if ((constraint.Relationship == Relationship.EQ) ||
(constraint.Relationship == Relationship.GEQ))
{
matrix[ArtificialVariableOffset + artificialVar, 0] = Policy.One();
matrix[ArtificialVariableOffset + artificialVar++, row] = Policy.One();
matrix.SetRowVector(0, matrix.GetRowVector(0) - matrix.GetRowVector(row));
}
}
return(matrix);
}
/// <summary>
/// Multiply and normalize
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static Rational <T, TPolicy> operator *(Rational <T, TPolicy> a, Rational <T, TPolicy> b)
{
return(new Rational <T, TPolicy>(Policy.Mul(a.Numerator, b.Numerator), Policy.Mul(a.Denominator, b.Denominator)).Normalize());
}
