public void VideoLecture01()
{
var lp = new LinearProgram
{
M = 4,
N = 2,
BasicIndices = new[] { 0, 1, 4, 2, 6 },
NonBasicIndices = new[] { 0, 3, 5 },
Coefficients = new[]
{
new[] { 0.0, 0.0, 0.0 },
new[] { 2.0, 2.0 / 3.0, 1.0 / 3.0 },
new[] { 2.0, -1.0 / 3.0, -2.0 / 3.0 },
new[] { 2.0, 1.0 / 3.0, 2.0 / 3.0 },
new[] { 2.0, -2.0 / 3.0, -1.0 / 3.0 }
},
ObjectiveCoefficients = new[] { 9.0, 9.0, 9.0 }
};
var restorer = new SimpleRestoreObjective();
restorer.Restore(lp, new[] { 0.0, 1.0, 2.0 }, new[] { 0, 1, 2 });
lp.ObjectiveCoefficients.ShouldEqual(new[] { 6.0, 4.0 / 3.0, 5.0 / 3.0 }, .000001);
}
/// <summary>
/// Reads the file provided and load in into the Liner Program Business Object. It will also filter out the header and not process it.
/// </summary>
/// <param name="filepath"></param>
public virtual void LoadLinearProgramFileContent(string filepath)
{
//TODO:Dynamic type??? overkill??
using (StreamReader _reader = new StreamReader(filepath))
{
string _line = null;
while (null != (_line = _reader.ReadLine()))
{
string[] _values = _line.Split(',');
//bypass the header - both files the first column header starts with Meter
if (_values[0].ToString().ToLower().Substring(0, 5) != "meter")
{
LinearProgram _tempLinearProgram = new LinearProgram();
_tempLinearProgram.FileName = Path.GetFileName(filepath);
_tempLinearProgram.MeterPointCode = _values[0].ToString();
_tempLinearProgram.SerialNumber = _values[1].ToString();
_tempLinearProgram.PlantCode = _values[2].ToString();
_tempLinearProgram.Timestamp = Convert.ToDateTime(_values[3].ToString());
_tempLinearProgram.DataType = _values[4].ToString();
_tempLinearProgram.DataValue = Convert.ToDecimal(_values[5].ToString());
_tempLinearProgram.Units = (UnitType)Enum.Parse(typeof(UnitType), _values[6].ToString(), true);
_tempLinearProgram.Status = _values[7].ToString();
_filteredLinearProgramList.Add(_tempLinearProgram);
}
}
}
}
private static void VerifyDual(LinearProgram primal, DualLinearProgram dual)
{
//verify coefficients
dual.Coefficients.Length.ShouldEqual(primal.Coefficients[0].Length);
//verify orig objective
dual.OriginalObjectiveCoefficients.ShouldEqual(primal.ObjectiveCoefficients, Tolerance);
for (var m = 1; m <= dual.M; m++)
{
dual.Coefficients[m][0].ShouldEqual(1, Tolerance);
for (var n = 1; n <= dual.N; n++)
{
dual.Coefficients[m][n].ShouldEqual(-primal.Coefficients[n][m], Tolerance);
}
}
//verify objective coeficients
dual.ObjectiveCoefficients[0].ShouldEqual(0.0);
for (var n = 1; n <= dual.N; n++)
{
dual.ObjectiveCoefficients[n].ShouldEqual(-primal.Coefficients[n][0]);
}
//verify objective
dual.ObjectiveValue.ShouldEqual(0.0);
}
public LinearProgamSolution Solve(LinearProgram linearProgram)
{
var pivotCount = 0;
while (true)
{
//do this until no entering, or stop if unbounded
_analyze.Analyze(linearProgram);
//no entering, must be solved
if (_analyze.Entering == 0)
{
break;
}
//if unbounded
if (_analyze.Leaving == 0)
{
return(new LinearProgamSolution(0, 0, LinearProgramSolutionType.Unbounded));
}
//if here, we can pivot
++pivotCount;
_pivotor.Pivot(_analyze.Entering, _analyze.Leaving, linearProgram);
}
return(new LinearProgamSolution(linearProgram.ObjectiveValue, pivotCount, LinearProgramSolutionType.Solved));
}
static void Main(string[] args)
{
LinearProgram[] linearProgrammes = new LinearProgram[6];
LPParser parser = new LPParser();
parser.SetObjectiveFunction("8x + 10y + 7z");
parser.AddConstraint("x + 3y + 2z < 10");
parser.AddConstraint("x + 5y + z < 8");
linearProgrammes[0] = parser.LinearProgram;
parser = new LPParser();
parser.SetObjectiveFunction("x + 2y - z");
parser.AddConstraint("2x + y + z < 14");
parser.AddConstraint("4x + 2y + 3z < 28");
parser.AddConstraint("2x + 5y + 5z < 30");
linearProgrammes[1] = parser.LinearProgram;
parser = new LPParser();
parser.SetObjectiveFunction("3x + 4y");
parser.AddConstraint("x + y < 4");
parser.AddConstraint("2x + y < 5");
linearProgrammes[2] = parser.LinearProgram;
parser = new LPParser();
parser.SetObjectiveFunction("-2x + y");
parser.AddConstraint("x + 2y < 6");
parser.AddConstraint("3x + 2y < 12");
linearProgrammes[3] = parser.LinearProgram;
parser = new LPParser();
parser.SetObjectiveFunction("2x + 3y");
parser.AddConstraint("x + y < 2000");
parser.AddConstraint("8x + 14y < 20000");
linearProgrammes[4] = parser.LinearProgram;
parser = new LPParser();
parser.SetObjectiveFunction("x + 0.8y");
parser.AddConstraint("x + y < 1000");
parser.AddConstraint("2x + y < 1500");
parser.AddConstraint("3x + 2y < 2400");
linearProgrammes[5] = parser.LinearProgram;
for (int i = 0; i < linearProgrammes.Length; i++)
{
Console.WriteLine("----------------------------------");
Console.WriteLine($"LP { i + 1 }");
linearProgrammes[i].Output();
Console.WriteLine();
Console.WriteLine("Solution:");
new Simplex(linearProgrammes[i]).Solve().Output();
}
Console.WriteLine("----------------------------------");
Console.ReadKey();
}
//[Line 1] m n
//[Line 2] B1 B2 ... Bm [the list of basic indices m integers]
//[Line 3] N1 N2 ... Nn [the list of non-basic indices n integers]
//[Line 4] b1 .. bm (m floating point numbers)
//[Line 5] a11 ... a1n (first row coefficients. See dictionary notation above.)
//....
//[Line m+4] am1 ... amn (mth row coefficients. See dictionary notation above.)
//[Line m+5] z0 c1 .. cn (objective coefficients (n+1 floating point numbers))
public LinearProgram Map(DualLinearProgram dual)
{
var primal = new LinearProgram();
primal.M = dual.N;
primal.N = dual.M;
primal.BasicIndices = new int[dual.NonBasicIndices.Length];
primal.NonBasicIndices = new int[dual.BasicIndices.Length];
//set basic / non basic indices
dual.NonBasicIndices.CopyTo(primal.BasicIndices, 0);
dual.BasicIndices.CopyTo(primal.NonBasicIndices, 0);
//set coefficients
primal.Coefficients = new double[dual.Coefficients[0].Length][];
primal.ObjectiveCoefficients = new double[dual.BasicIndices.Length];
//map dual coefficients to primal coefficients
var a = dual.Coefficients.Length;
for (var i = 0; i < primal.Coefficients.Length; i++)
{
primal.Coefficients[i] = new double[a];//empty row for 1-based indexes
if (i == 0)
{
continue;
}
for (var k = 1; k < dual.Coefficients.Length; k++)
{
primal.Coefficients[i][k] = -dual.Coefficients[k][i];
}
}
//map dual objective coefficients to primal b-values
for (var i = 1; i < dual.ObjectiveCoefficients.Length; i++)
{
primal.Coefficients[i][0] = -dual.ObjectiveCoefficients[i];
}
//map dual b-values to primal objective coefficients
for (var i = 1; i < dual.Coefficients.Length; i++)
{
primal.ObjectiveCoefficients[i] = -dual.Coefficients[i][0];
}
primal.ObjectiveCoefficients[0] = -dual.ObjectiveCoefficients[0];
return(primal);
}
public void TestSimplex()
{
double[,] A = new double[, ]
{
{ 0, -1, -1 },
{ -2, -1, -2 },
{ -2, 1, -2 }
//{0,1,1 },
//{2,1,2 },
//{0,-1,2}
};
double[] B = new double[] { -4, -6, -2 };
double[] Z = new double[] { 3, 2, 1 };
ILinearAlgoritm simplex = LinearProgram.GetDoubleSimplex(A, B, Z);
simplex.Run();
}
public void TestJordanGayss()
{
double[,] A = new double[, ] {
{ 4, -7, 8 }, { 2, -4, 5 }, { -3, 11, 1 }
};
double[] B = new double[] { -23, -13, 16 };
ILinearAlgoritm jordan = LinearProgram.GetJourdanGayssLinearAlgoritm(A, B);
jordan.Run();
var test = jordan.Value;
double[,] expecteDoubles = new double[, ] {
{ 1, 0, 0, -2 }, { 0, 1, 0, 1 }, { 0, 0, 1, -1 }
};
for (int rowIndex = 0; rowIndex < test.GetLength(0); rowIndex++)
{
for (int columIndex = 0; columIndex < test.GetLength(1); columIndex++)
{
Assert.AreEqual(expecteDoubles[rowIndex, columIndex], test[rowIndex, columIndex], delta: jordan.Delta);
}
}
A = new double[, ] {
{ 3, 4 }, { 8, -10 }
};
B = new double[] { 4, 5 };
expecteDoubles = new double[, ] {
{ 1, 0, 0.967 }, { 0, 1, 0.274 }
};
jordan = LinearProgram.GetJourdanGayssLinearAlgoritm();
jordan.A = A;
jordan.B = B;
jordan.Run();
test = jordan.Value;
for (int rowIndex = 0; rowIndex < test.GetLength(0); rowIndex++)
{
for (int columIndex = 0; columIndex < test.GetLength(1); columIndex++)
{
Assert.AreEqual(expecteDoubles[rowIndex, columIndex], test[rowIndex, columIndex], delta: jordan.Delta);
}
}
}
static void Main(string[] args)
{
// This QuickStart Sample illustrates the three ways to create a Linear Program.
// The first is in terms of matrices. The coefficients
// are supplied as a matrix. The cost vector, right-hand side
// and constraints on the variables are supplied as a vector.
// The cost vector:
var c = Vector.Create(-1.0, -3.0, 0.0, 0.0, 0.0, 0.0);
// The coefficients of the constraints:
var A = Matrix.Create(4, 6, new double[]
{
1, 1, 1, 0, 0, 0,
1, 1, 0, -1, 0, 0,
1, 0, 0, 0, 1, 0,
0, 1, 0, 0, 0, 1
}, MatrixElementOrder.RowMajor);
// The right-hand sides of the constraints:
var b = Vector.Create(1.5, 0.5, 1.0, 1.0);
// We're now ready to call the constructor.
// The last parameter specifies the number of equality
// constraints.
LinearProgram lp1 = new LinearProgram(c, A, b, 4);
// Now we can call the Solve method to run the Revised
// Simplex algorithm:
var x = lp1.Solve();
// The GetDualSolution method returns the dual solution:
var y = lp1.GetDualSolution();
Console.WriteLine("Primal: {0:F1}", x);
Console.WriteLine("Dual: {0:F1}", y);
// The optimal value is returned by the Extremum property:
Console.WriteLine("Optimal value: {0:F1}", lp1.OptimalValue);
// The second way to create a Linear Program is by constructing
// it by hand. We start with an 'empty' linear program.
LinearProgram lp2 = new LinearProgram();
// Next, we add two variables: we specify the name, the cost,
// and optionally the lower and upper bound.
lp2.AddVariable("X1", -1.0, 0, 1);
lp2.AddVariable("X2", -3.0, 0, 1);
// Next, we add constraints. Constraints also have a name.
// We also specify the coefficients of the variables,
// the lower bound and the upper bound.
lp2.AddLinearConstraint("C1", Vector.Create(1.0, 1.0), 0.5, 1.5);
// If a constraint is a simple equality or inequality constraint,
// you can supply a LinearProgramConstraintType value and the
// right-hand side of the constraint.
// We can now solve the linear program:
x = lp2.Solve();
y = lp2.GetDualSolution();
Console.WriteLine("Primal: {0:F1}", x);
Console.WriteLine("Dual: {0:F1}", y);
Console.WriteLine("Optimal value: {0:F1}", lp2.OptimalValue);
// Finally, we can create a linear program from an MPS file.
// The MPS format is a standard format.
LinearProgram lp3 = MpsReader.Read(@"..\..\..\..\data\sample.mps");
// We can go straight to solving the linear program:
x = lp3.Solve();
y = lp3.GetDualSolution();
Console.WriteLine("Primal: {0:F1}", x);
Console.WriteLine("Dual: {0:F1}", y);
Console.WriteLine("Optimal value: {0:F1}", lp3.OptimalValue);
Console.Write("Press Enter key to exit...");
Console.ReadLine();
}
