public void GoldfarbIdnaniParseTest()
{
var s = CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;
String strObjective = "0" + s + "5x² + 0" + s + "2y² + 0" + s + "3xy";
String[] strConstraints =
{
"0" + s + "01x + 0" + s + "02y - 0" + s + "03 = 0",
"x + y = 100"
};
// Now we can start creating our function:
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective, CultureInfo.CurrentCulture);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
{
cst.Add(new LinearConstraint(function, tmpCst, CultureInfo.CurrentCulture));
}
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void GoldfarbIdnaniParseGlobalizationTest2()
{
String strObjective = 0.5.ToString(CultureInfo.InvariantCulture)
+ "x² +" + 0.2.ToString(CultureInfo.InvariantCulture) + "y² +"
+ 0.3.ToString(CultureInfo.InvariantCulture) + "xy";
String[] strConstraints =
{
0.01.ToString(CultureInfo.InvariantCulture) + "x" + " + " +
0.02.ToString(CultureInfo.InvariantCulture) + "y - " +
0.03.ToString(CultureInfo.InvariantCulture) + " = 0",
"x + y = 100"
};
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
{
cst.Add(new LinearConstraint(function, tmpCst));
}
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void GoldfarbIdnaniParseGlobalizationTestBase()
{
// minimize 0.5x² + 0.2y² + 0.3xy s.t. 0.01x + 0.02y - 0.03 = 0 AND x + y = 100
// http://www.wolframalpha.com/input/?i=minimize+0.5x%C2%B2+%2B+0.2y%C2%B2+%2B+0.3xy+s.t.+0.01x+%2B+0.02y+-+0.03+%3D+0+AND+x+%2B+y+%3D+100
String strObjective = "0.5x² + 0.2y² + 0.3xy";
String[] strConstraints =
{
"0.01x + 0.02y - 0.03 = 0",
"x + y = 100"
};
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
{
cst.Add(new LinearConstraint(function, tmpCst));
}
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void solve_vectors()
{
#region doc_vector
// Suppose we would like to minimize the following function:
//
// f(x,y) = min 100(y-x²)²+(1-x)²
//
// Subject to the constraints
//
// x >= 0 (x must be positive)
// y >= 0 (y must be positive)
//
// Now, we can create an objective function using vectors
var f = new NonlinearObjectiveFunction(numberOfVariables: 2,
// This is the objective function: f(x,y) = min 100(y-x²)²+(1-x)²
function: (x) => 100 * Math.Pow(x[1] - x[0] * x[0], 2) + Math.Pow(1 - x[0], 2),
// And this is the vector gradient for the same function:
gradient: (x) => new[]
{
2 * (200 * Math.Pow(x[0], 3) - 200 * x[0] * x[1] + x[0] - 1), // df/dx = 2(200x³-200xy+x-1)
200 * (x[1] - x[0] * x[0]) // df/dy = 200(y-x²)
}
);
// As before, we state the constraints. However, to illustrate the flexibility
// of the AugmentedLagrangian, we shall use LinearConstraints to constrain the problem.
double[,] a = Matrix.Identity(2); // Set up the constraint matrix...
double[] b = Vector.Zeros(2); // ...and the values they must be greater than
int numberOfEqualities = 0;
var linearConstraints = LinearConstraintCollection.Create(a, b, numberOfEqualities);
// Finally, we create the non-linear programming solver
var solver = new AugmentedLagrangian(f, linearConstraints);
// And attempt to find a minimum
bool success = solver.Minimize();
// The solution found was { 1, 1 }
double[] solution = solver.Solution;
// with the minimum value zero.
double minValue = solver.Value;
#endregion
Assert.IsTrue(success);
Assert.AreEqual(0, minValue, 1e-10);
Assert.AreEqual(1, solver.Solution[0], 1e-6);
Assert.AreEqual(1, solver.Solution[1], 1e-6);
Assert.IsFalse(double.IsNaN(minValue));
Assert.IsFalse(double.IsNaN(solver.Solution[0]));
Assert.IsFalse(double.IsNaN(solver.Solution[1]));
}
public void GoldfarbIdnaniMinimizeTest1()
{
// This test reproduces Issue #33 at Google Code Tracker
// https://code.google.com/p/accord/issues/detail?id=33
// Create objective function using the
// Hessian Q and linear terms vector d.
double[,] Q =
{
{ 0.12264004, 0.011579293, 0.103326825, 0.064073439 },
{ 0.011579293, 0.033856, 0.014311947, 0.014732381 },
{ 0.103326825, 0.014311947, 0.17715681, 0.067615114 },
{ 0.064073439, 0.014732381, 0.067615114, 0.11539609 }
};
Assert.IsTrue(Q.IsPositiveDefinite());
double[] d = { 0, 0, 0, 0 };
var f = new QuadraticObjectiveFunction(Q, d, "a", "b", "c", "d");
// Now, create the constraints
var constraints = new LinearConstraintCollection();
constraints.Add(new LinearConstraint(f, "0.0732 * a + 0.0799 * b + 0.1926 * c + 0.0047 * d = 0.098"));
constraints.Add(new LinearConstraint(f, "a + b + c + d = 1"));
constraints.Add(new LinearConstraint(f, "a >= 0"));
constraints.Add(new LinearConstraint(f, "b >= 0"));
constraints.Add(new LinearConstraint(f, "c >= 0"));
constraints.Add(new LinearConstraint(f, "d >= 0"));
constraints.Add(new LinearConstraint(f, "a >= 0.5"));
double[] b;
int eq;
double[,] A = constraints.CreateMatrix(4, out b, out eq);
// Now we create the quadratic programming solver for 2 variables, using the constraints.
GoldfarbIdnaniQuadraticSolver solver = new GoldfarbIdnaniQuadraticSolver(4, constraints);
// And attempt to solve it.
double minValue = solver.Minimize(f);
double[] expected = { 0.5, 0.336259542, 0.163740458, 0 };
double[] actual = solver.Solution;
for (int i = 0; i < expected.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a);
}
}
/// <summary>
/// Constructs a new <see cref="GoldfarbIdnani" /> class.
/// </summary>
/// <param name="function">The objective function to be optimized.</param>
/// <param name="constraints">The problem's constraints.</param>
public GoldfarbIdnani(QuadraticObjectiveFunction function, LinearConstraintCollection constraints)
: base(function.NumberOfVariables, function.Function, function.Gradient)
{
int equalities;
// Create the constraint matrix A from the specified constraint list
var A = constraints.CreateMatrix(function.NumberOfVariables,
out constraintValues, out constraintTolerances, out equalities);
Debug.Assert(A.GetLength(1) == function.NumberOfVariables);
initialize(function.NumberOfVariables,
function.QuadraticTerms, function.LinearTerms,
A, constraintValues, equalities);
}
private static void DoSv(Tuple<double[], double>[] classified)
{
var stripped = classified.Select(t => new Tuple<double[], double>(t.Item1.Skip(1).ToArray(), t.Item2))
.ToArray();
var q = GetQ(stripped);
//all are 0 or more
var lcc = new LinearConstraintCollection(
Enumerable.Range(0, stripped.Length)
.Select(i => new LinearConstraint(1)
{
VariablesAtIndices = new[] { i },
ShouldBe = ConstraintType.GreaterThanOrEqualTo,
Value = 0.0,
CombinedAs= new []{1.0} //???
}));
//and they zero out with the classificaiton
lcc.Add(
//new LinearConstraint(stripped.Select(t => t.Item2).ToArray()) { Value = 0, ShouldBe = ConstraintType.EqualTo }
new LinearConstraint(stripped.Length)
{
Value = 0,
ShouldBe = ConstraintType.EqualTo,
VariablesAtIndices = Enumerable.Range(0, stripped.Length).ToArray(),
CombinedAs = stripped.Select(t => t.Item2).ToArray()
} );
var solver = new GoldfarbIdnaniQuadraticSolver(stripped.Length, lcc);
solver.Minimize(q, neg1Array(stripped.Length));
//b = 1/y - w_*x_
var tmp = solver.Solution.Zip(stripped, (alpha, s) => s.Item1.Select(x => x * alpha * s.Item2))
.Aggregate(VAdd).ToList();
var support = solver.Solution.Zip(stripped, (alpha, s) => Math.Abs(alpha) > 0.0001 ? s : null).Where(x => x != null).ToArray();
var offset = GetOffset(support, tmp); //I'm pretty sure this calculation for b is wrong: you get a different one for each of elements...
tmp.Insert(0, offset);
var wSupp = Norm( tmp.ToArray());
}
/// <summary>
/// Constructs a new <see cref="GoldfarbIdnaniQuadraticSolver"/> class.
/// </summary>
///
/// <param name="numberOfVariables">The number of variables.</param>
/// <param name="constraints">The problem's constraints.</param>
///
public GoldfarbIdnaniQuadraticSolver(int numberOfVariables, LinearConstraintCollection constraints)
{
int equalities;
// Create the constraint matrix A from the specified constraint list
double[,] A = constraints.CreateMatrix(numberOfVariables, out constraintValues, out equalities);
System.Diagnostics.Debug.Assert(A.GetLength(1) == numberOfVariables);
initialize(numberOfVariables, A, constraintValues, equalities);
}
public void ConstructorTest2()
{
// https://github.com/accord-net/framework/issues/171
int n = 21;
var Q = Matrix.Diagonal(n, 2.0);
var d = Vector.Create(3132.0, 6264, 15660, 18792, 21924, 6264, 18792, 21924, 9396, 3132, 12528, 6264, 9396, 18792, 21924, 9396, 3132, 3132, 6264, 15660, 18792);
int m = 44;
var b = Vector.Create(
703.999, -704.001,
1267.999, -1268.001,
1565.999, -1566.001,
471.999, -472.001,
1425.999, -1426.001,
-107.001,
-1164.001,
-57.001,
-311.001,
-1433.001,
-0.001,
-0.001,
-788.001,
-472.001,
-850.001,
-273.001,
-0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001, -0.001,
-0.001, -0.001, -0.001, -0.001);
var A = Matrix.Create(m, n,
1.0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1,
0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0,
0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0,
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0,
0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1);
var aa = A.Reshape();
var qq = Q.Reshape();
var r = Quadprog.Compute(n, m, aa, b, 0, qq, d);
double[] expected = r.Item2;
var constraints = LinearConstraintCollection.FromMatrix(A, b, 0);
double[] expectedViolation = constraints.Apply(x => x.GetViolation(r.Item2));
for (int i = 0; i < expectedViolation.Length; i++)
{
Assert.IsTrue(expectedViolation[i] <= 1e-3);
}
var solver = new GoldfarbIdnani(Q, d.Multiply(-1), A, b, 0);
Assert.IsTrue(solver.Minimize());
double[] actual = solver.Solution;
Assert.IsTrue(actual.IsEqual(expected, 1e-3));
double[] actualViolation = constraints.Apply(x => x.GetViolation(solver.Solution));
Assert.IsTrue(actualViolation.IsEqual(expectedViolation, 1e-3));
}
public void GoldfarbIdnaniMinimizeTest1()
{
// This test reproduces Issue #33 at Google Code Tracker
// https://code.google.com/p/accord/issues/detail?id=33
// Create objective function using the
// Hessian Q and linear terms vector d.
double[,] Q =
{
{ 0.12264004, 0.011579293, 0.103326825, 0.064073439 },
{ 0.011579293, 0.033856, 0.014311947, 0.014732381 },
{ 0.103326825, 0.014311947, 0.17715681, 0.067615114 },
{ 0.064073439, 0.014732381, 0.067615114, 0.11539609 }
};
Assert.IsTrue(Q.IsPositiveDefinite());
double[] d = { 0, 0, 0, 0 };
var f = new QuadraticObjectiveFunction(Q, d, "a", "b", "c", "d");
// Now, create the constraints
var constraints = new LinearConstraintCollection();
constraints.Add(new LinearConstraint(f, "0.0732 * a + 0.0799 * b + 0.1926 * c + 0.0047 * d = 0.098"));
constraints.Add(new LinearConstraint(f, "a + b + c + d = 1"));
constraints.Add(new LinearConstraint(f, "a >= 0"));
constraints.Add(new LinearConstraint(f, "b >= 0"));
constraints.Add(new LinearConstraint(f, "c >= 0"));
constraints.Add(new LinearConstraint(f, "d >= 0"));
constraints.Add(new LinearConstraint(f, "a >= 0.5"));
double[] b;
int eq;
double[,] A = constraints.CreateMatrix(4, out b, out eq);
// Now we create the quadratic programming solver for 2 variables, using the constraints.
GoldfarbIdnaniQuadraticSolver solver = new GoldfarbIdnaniQuadraticSolver(4, constraints);
// And attempt to solve it.
double minValue = solver.Minimize(f);
double[] expected = { 0.5, 0.336259542, 0.163740458, 0 };
double[] actual = solver.Solution;
for (int i = 0; i < expected.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a);
}
}
public void GoldfarbIdnaniParseGlobalizationTestBase()
{
// minimize 0.5x² + 0.2y² + 0.3xy s.t. 0.01x + 0.02y - 0.03 = 0 AND x + y = 100
// http://www.wolframalpha.com/input/?i=minimize+0.5x%C2%B2+%2B+0.2y%C2%B2+%2B+0.3xy+s.t.+0.01x+%2B+0.02y+-+0.03+%3D+0+AND+x+%2B+y+%3D+100
String strObjective = "0.5x² + 0.2y² + 0.3xy";
String[] strConstraints =
{
"0.01x + 0.02y - 0.03 = 0",
"x + y = 100"
};
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
cst.Add(new LinearConstraint(function, tmpCst));
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void GoldfarbIdnaniMinimizeLessThanWithEqualityTest()
{
// This test reproduces Issue #33 at Google Code Tracker
// https://code.google.com/p/accord/issues/detail?id=33
// Create objective function using the
// Hessian Q and linear terms vector d.
double[,] Q =
{
{ 0.12264004, 0.011579293, 0.103326825, 0.064073439 },
{ 0.011579293, 0.033856, 0.014311947, 0.014732381 },
{ 0.103326825, 0.014311947, 0.17715681, 0.067615114 },
{ 0.064073439, 0.014732381, 0.067615114, 0.11539609 }
};
Assert.IsTrue(Q.IsPositiveDefinite());
double[] d = { 0, 0, 0, 0 };
var f = new QuadraticObjectiveFunction(Q, d, "a", "b", "c", "d");
// Now, create the constraints
var constraints = new LinearConstraintCollection();
constraints.Add(new LinearConstraint(f, "0.0732 * a + 0.0799 * b + 0.1926 * c + 0.0047 * d = 0.098"));
constraints.Add(new LinearConstraint(f, "a + b + c + d = 1"));
constraints.Add(new LinearConstraint(f, "-a <= 0"));
constraints.Add(new LinearConstraint(f, "-b <= 0"));
constraints.Add(new LinearConstraint(f, "-c <= 0"));
constraints.Add(new LinearConstraint(f, "-d <= 0"));
constraints.Add(new LinearConstraint(f, "-a + 0.5 <= 0.0"));
Assert.AreEqual(-1, constraints[6].CombinedAs[0]);
Assert.AreEqual(-0.5, constraints[6].Value);
Assert.AreEqual(0.1, constraints[6].GetViolation(new double[] { 0.6 }), 1e-10);
Assert.AreEqual(-0.1, constraints[6].GetViolation(new double[] { 0.4 }), 1e-10);
bool psd = Q.IsPositiveDefinite();
double[] b;
int eq;
double[,] A = constraints.CreateMatrix(4, out b, out eq);
// Now we create the quadratic programming solver for 2 variables, using the constraints.
GoldfarbIdnani solver = new GoldfarbIdnani(f, constraints);
// And attempt to solve it.
Assert.IsTrue(solver.Minimize());
double minValue = solver.Value;
double[] expected = { 0.50000000000000, 0.30967169476486, 0.19032830523514, 0 };
double[] actual = solver.Solution;
for (int i = 0; i < constraints.Count; i++)
{
double error = constraints[i].GetViolation(actual);
Assert.IsTrue(error >= 0);
}
for (int i = 0; i < expected.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a, 1e-10);
}
}
public void GoldfarbIdnaniParseTest()
{
var s = CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator;
String strObjective = "0" + s + "5x² + 0" + s + "2y² + 0" + s + "3xy";
String[] strConstraints =
{
"0" + s + "01x + 0" + s + "02y - 0" + s + "03 = 0",
"x + y = 100"
};
// Now we can start creating our function:
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective, CultureInfo.CurrentCulture);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
cst.Add(new LinearConstraint(function, tmpCst, CultureInfo.CurrentCulture));
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void GoldfarbIdnaniParseGlobalizationTest2()
{
String strObjective = 0.5.ToString(CultureInfo.InvariantCulture)
+ "x² +" + 0.2.ToString(CultureInfo.InvariantCulture) + "y² +"
+ 0.3.ToString(CultureInfo.InvariantCulture) + "xy";
String[] strConstraints =
{
0.01.ToString(CultureInfo.InvariantCulture) + "x" + " + " +
0.02.ToString(CultureInfo.InvariantCulture) + "y - " +
0.03.ToString(CultureInfo.InvariantCulture) + " = 0",
"x + y = 100"
};
QuadraticObjectiveFunction function = new QuadraticObjectiveFunction(strObjective);
LinearConstraintCollection cst = new LinearConstraintCollection();
foreach (var tmpCst in strConstraints)
cst.Add(new LinearConstraint(function, tmpCst));
var classSolver = new Accord.Math.Optimization.GoldfarbIdnani(function, cst);
bool status = classSolver.Minimize();
double result = classSolver.Value;
Assert.IsTrue(status);
Assert.AreEqual(15553.60, result, 1e-10);
}
public void GoldfarbIdnaniMinimizeLessThanWithEqualityTest()
{
// This test reproduces Issue #33 at Google Code Tracker
// https://code.google.com/p/accord/issues/detail?id=33
// Create objective function using the
// Hessian Q and linear terms vector d.
double[,] Q =
{
{ 0.12264004, 0.011579293, 0.103326825, 0.064073439 },
{ 0.011579293, 0.033856, 0.014311947, 0.014732381 },
{ 0.103326825, 0.014311947, 0.17715681, 0.067615114 },
{ 0.064073439, 0.014732381, 0.067615114, 0.11539609 }
};
Assert.IsTrue(Q.IsPositiveDefinite());
double[] d = { 0, 0, 0, 0 };
var f = new QuadraticObjectiveFunction(Q, d, "a", "b", "c", "d");
// Now, create the constraints
var constraints = new LinearConstraintCollection();
constraints.Add(new LinearConstraint(f, "0.0732 * a + 0.0799 * b + 0.1926 * c + 0.0047 * d = 0.098"));
constraints.Add(new LinearConstraint(f, "a + b + c + d = 1"));
constraints.Add(new LinearConstraint(f, "-a <= 0"));
constraints.Add(new LinearConstraint(f, "-b <= 0"));
constraints.Add(new LinearConstraint(f, "-c <= 0"));
constraints.Add(new LinearConstraint(f, "-d <= 0"));
constraints.Add(new LinearConstraint(f, "-a + 0.5 <= 0.0"));
Assert.AreEqual(-1, constraints[6].CombinedAs[0]);
Assert.AreEqual(-0.5, constraints[6].Value);
Assert.AreEqual(0.1, constraints[6].GetViolation(new double[] { 0.6 }), 1e-10);
Assert.AreEqual(-0.1, constraints[6].GetViolation(new double[] { 0.4 }), 1e-10);
bool psd = Q.IsPositiveDefinite();
double[] b;
int eq;
double[,] A = constraints.CreateMatrix(4, out b, out eq);
// Now we create the quadratic programming solver for 2 variables, using the constraints.
GoldfarbIdnani solver = new GoldfarbIdnani(f, constraints);
// And attempt to solve it.
Assert.IsTrue(solver.Minimize());
double minValue = solver.Value;
double[] expected = { 0.50000000000000, 0.30967169476486, 0.19032830523514, 0 };
double[] actual = solver.Solution;
for (int i = 0; i < constraints.Count; i++)
{
double error = constraints[i].GetViolation(actual);
Assert.IsTrue(error >= 0);
}
for (int i = 0; i < expected.Length; i++)
{
double e = expected[i];
double a = actual[i];
Assert.AreEqual(e, a, 1e-10);
}
}