/// <summary>
/// Find vector x that minimizes the function f(x) using the Newton algorithm.
/// For more options and diagnostics consider to use <see cref="NewtonMinimizer"/> directly.
/// </summary>
public static Vector <double> OfFunctionGradientHessian(Func <Vector <double>, Tuple <double, Vector <double>, Matrix <double> > > functionGradientHessian, Vector <double> initialGuess, double gradientTolerance = 1e-8, int maxIterations = 1000)
{
var objective = ObjectiveFunction.GradientHessian(functionGradientHessian);
var result = NewtonMinimizer.Minimum(objective, initialGuess, gradientTolerance, maxIterations);
return(result.MinimizingPoint);
}
public void FindMinimum_Rosenbrock_Easy()
{
var obj = ObjectiveFunction.GradientHessian(RosenbrockFunction.Value, RosenbrockFunction.Gradient, RosenbrockFunction.Hessian);
var solver = new NewtonMinimizer(1e-5, 1000);
var result = solver.FindMinimum(obj, new DenseVector(new[] { 1.2, 1.2 }));
Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
Assert.That(Math.Abs(result.MinimizingPoint[1] - 1.0), Is.LessThan(1e-3));
}
public void FindMinimum_Linesearch_Rosenbrock_Overton()
{
var obj = new LazyRosenbrockObjectiveFunction();
var solver = new NewtonMinimizer(1e-5, 1000, true);
var result = solver.FindMinimum(obj, new DenseVector(new[] { -0.9, -0.5 }));
Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
Assert.That(Math.Abs(result.MinimizingPoint[1] - 1.0), Is.LessThan(1e-3));
}
public void FindMinimum_Rosenbrock_Hard()
{
var obj = ObjectiveFunction.GradientHessian(point => Tuple.Create(RosenbrockFunction.Value(point), RosenbrockFunction.Gradient(point), RosenbrockFunction.Hessian(point)));
var solver = new NewtonMinimizer(1e-5, 1000);
var result = solver.FindMinimum(obj, new DenseVector(new[] { -1.2, 1.0 }));
Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
Assert.That(Math.Abs(result.MinimizingPoint[1] - 1.0), Is.LessThan(1e-3));
}
public void BoxBod_Newton_Der()
{
var obj = ObjectiveFunction.NonlinearFunction(BoxBodModel, BoxBodPrime, BoxBodX, BoxBodY);
var solver = new NewtonMinimizer(1e-10, 100);
var result = solver.FindMinimum(obj, BoxBodStart2);
for (int i = 0; i < result.MinimizingPoint.Count; i++)
{
AssertHelpers.AlmostEqualRelative(BoxBodPbest[i], result.MinimizingPoint[i], 6);
}
}
public double NewtonPerpendicular(GeoPoint2D fromHere, double position)
{
NewtonMinimizer nm = new NewtonMinimizer(1e-6, 10);
IObjectiveFunction iof = ObjectiveFunction.GradientHessian(
new Func <Vector <double>, Tuple <double, Vector <double>, Matrix <double> > >(delegate(Vector <double> vd)
{
// vd[0] is the 0..1 parameter of the curve
TryPointDeriv3At(vd[0], out GeoPoint2D point, out GeoVector2D deriv1, out GeoVector2D deriv2, out GeoVector2D deriv3);
GeoVector2D toPoint = fromHere - point;
double s1 = toPoint * deriv1;
double s2 = (toPoint * deriv2 - deriv1 * deriv1);
double val = sqr(s1);
Vector <double> gradient = new DenseVector(new double[] { 2 * s1 * s2 });
Matrix <double> hessian = new DenseMatrix(1, 1);
hessian[0, 0] = 2 * s1 * (toPoint * deriv3 - 3 * deriv1 * deriv2) + 2 * sqr(s2);
return(new Tuple <double, Vector <double>, Matrix <double> >(val, gradient, hessian));
}));
/// <summary>
/// Find the (u,v)-position for the provided point on a surface. Using the NewtonMinimizer from MathNet. Faster than LevenbergMarquardtMinimizer. Surfaces need second derivatives.
/// </summary>
/// <param name="surface"></param>
/// <param name="p3d"></param>
/// <param name="res"></param>
/// <param name="mindist"></param>
/// <returns></returns>
public static bool PositionOfMN(ISurface surface, GeoPoint p3d, ref GeoPoint2D res, out double mindist)
{
NewtonMinimizer nm = new NewtonMinimizer(1e-12, 30);
IObjectiveFunction iof = ObjectiveFunction.GradientHessian(
new Func <Vector <double>, Tuple <double, Vector <double>, Matrix <double> > >(delegate(Vector <double> vd)
{
GeoPoint2D uv = new GeoPoint2D(vd[0], vd[1]);
surface.Derivation2At(uv, out GeoPoint loc, out GeoVector du, out GeoVector dv, out GeoVector duu, out GeoVector dvv, out GeoVector duv);
double val = (p3d.x - loc.x) * (p3d.x - loc.x) + (p3d.y - loc.y) * (p3d.y - loc.y) + (p3d.z - loc.z) * (p3d.z - loc.z);
double u = -2 * du.x * (p3d.x - loc.x) - 2 * du.y * (p3d.y - loc.y) - 2 * du.z * (p3d.z - loc.z);
double v = -2 * dv.x * (p3d.x - loc.x) - 2 * dv.y * (p3d.y - loc.y) - 2 * dv.z * (p3d.z - loc.z);
Vector <double> gradient = new DenseVector(new double[] { u, v });
Matrix <double> hessian = new DenseMatrix(2, 2);
hessian[0, 0] = -2 * duu.z * (p3d.z - loc.z) - 2 * duu.y * (p3d.y - loc.y) - 2 * duu.x * (p3d.x - loc.x) + 2 * du.z * du.z + 2 * du.y * du.y + 2 * du.x * du.x;
hessian[1, 1] = -2 * dvv.z * (p3d.z - loc.z) - 2 * dvv.y * (p3d.y - loc.y) - 2 * dvv.x * (p3d.x - loc.x) + 2 * dv.z * dv.z + 2 * dv.y * dv.y + 2 * dv.x * dv.x;
hessian[0, 1] = hessian[1, 0] = -2 * duv.z * (p3d.z - loc.z) - 2 * duv.y * (p3d.y - loc.y) - 2 * duv.x * (p3d.x - loc.x) + 2 * du.z * dv.z + 2 * du.y * dv.y + 2 * du.x * dv.x;
return(new Tuple <double, Vector <double>, Matrix <double> >(val, gradient, hessian));
}));
public void Mgh_Tests(TestFunctions.TestCase test_case)
{
var obj = new MghObjectiveFunction(test_case.Function, true, true);
var result = NewtonMinimizer.Minimum(obj, test_case.InitialGuess, 1e-8, 1000, useLineSearch: false);
if (test_case.MinimizingPoint != null)
{
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
}
var val1 = result.FunctionInfoAtMinimum.Value;
var val2 = test_case.MinimalValue;
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
var abs_err = Math.Abs(val1 - val2);
var rel_err = abs_err / abs_min;
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
Assert.That(success, "Minimal function value is not as expected.");
}