Simple Linear System

[Marcelo Lopes (mlopes)]

Dear all,

I am trying to solve a basic linear system, but I am getting the wrong constraints when I run the code below.

The system (with solution [1, 2, 3]) is:

| 2 1 1 |   | A |   |  7 |

| 1 1 4 | * | B | = | 15 |

| 0 3 2 |   | C |   | 12 |

The constraints I am getting are:
0 <= 2*A + A + A - 7 <= 0

0 <= B + B + 4*B - 15 <= 0

0 <= 0*C + 3*C + 2*C - 12 <= 0

Instead of:

0 <= 2*A + B + C - 7 <= 0

0 <= A + B + 4*C - 15 <= 0

0 <= 0*A + 3*B + 2*C - 12 <= 0

The code I am using to set up the solver is presented below:

         using (var scope = new ModelScope())
         {
            var model = new OPTANO.Modeling.Optimization.Model();

            double[,] mtxA = new double[,] {
                                           { 2, 1, 1 },
                                           { 1, 1, 4 },
                                           { 0, 3, 2 },
                                           };

            var indices = Enumerable.Range(0, 3).ToList();

            double[] vecB = new double[] { 7, 15, 12 };
            // Variável de decisão
            var vecX = new VariableCollection<int>(
               model,
               indices,
               "x",
               (x) => $"var_{x}",
               null, // use default lower bound.
               null, // use default upper bound.
               (x) => VariableType.Continuous
            );

           // Constraints
            foreach (var row in indices)
            {
               model.AddConstraint(Expression.Sum(indices.Select(col => mtxA[row, col] * vecX[row])) == vecB[row]);
            }

            // Objetivo
            var objective = new Objective(Expression.Sum(indices.Select(col => vecX[col])), "meta", ObjectiveSense.Minimize);
            model.AddObjective(objective);

            using (var solver = new OPTANO.Modeling.GLPK.GLPKSolver())
            {
               var solution = solver.Solve(model);

               foreach (var entry in solution.ObjectiveValues)
               {
                  string straux = string.Format("Objetivo: {0}, Valor {1}", entry.Key, entry.Value);
                  MessageBox.Show(straux);
               }
            }
         }
      }

Could you please shed some light on this?

Thank you for your attention,

Marcelo.

[Marcelo Lopes (mlopes)]

Dear all,

I found the issue: 

model.AddConstraint(Expression.Sum(indices.Select(col => mtxA[row, col] * vecX[col])) == vecB[row])

Thank you for your attention,

Marcelo.