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);
}
/// <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 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 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 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);
}
}