/// <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()); }