protected override void Evaluate()
{
// here we could directly overwrite the existing matrix cells instead.
// note: values must then be initialized manually first, if null.
Value = RosenbrockFunction.Value(Point);
Gradient = RosenbrockFunction.Gradient(Point);
Hessian = RosenbrockFunction.Hessian(Point);
}
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 virtual ActionResult RosenbrockFunctionPlot(PlotViewModel model)
{
if (!ModelState.IsValid)
{
return(HttpNotFound());
}
var f = new RosenbrockFunction();
return(plot(f, model));
}
public void TestRosenbrockFunction()
{
var minimizer = new QNMinimizer();
var f = new RosenbrockFunction();
var x = minimizer.Minimize(f);
var minValue = f.ValueAt(x);
Assert.AreEqual(x[0], 1.0, 1e-5);
Assert.AreEqual(x[1], 1.0, 1e-5);
Assert.AreEqual(minValue, 0, 1e-10);
}
public void TestGradient()
{
var input = new DenseVector(new[] { -0.9, -0.5 });
var v1 = RosenbrockFunction.Value(input);
var g = RosenbrockFunction.Gradient(input);
var eps = 1e-5;
var eps0 = (new DenseVector(new[] { 1.0, 0.0 })) * eps;
var eps1 = (new DenseVector(new[] { 0.0, 1.0 })) * eps;
var g0 = (RosenbrockFunction.Value(input + eps0) - RosenbrockFunction.Value(input - eps0)) / (2 * eps);
var g1 = (RosenbrockFunction.Value(input + eps1) - RosenbrockFunction.Value(input - eps1)) / (2 * eps);
Assert.That(Math.Abs(g0 - g[0]) < 1e-3);
Assert.That(Math.Abs(g1 - g[1]) < 1e-3);
}
public void TestHessian()
{
var input = new DenseVector(new[] { -0.9, -0.5 });
var v1 = RosenbrockFunction.Value(input);
var h = RosenbrockFunction.Hessian(input);
var eps = 1e-5;
var eps0 = (new DenseVector(new[] { 1.0, 0.0 })) * eps;
var eps1 = (new DenseVector(new[] { 0.0, 1.0 })) * eps;
var epsuu = (new DenseVector(new[] { 1.0, 1.0 })) * eps;
var epsud = (new DenseVector(new[] { 1.0, -1.0 })) * eps;
var h00 = (RosenbrockFunction.Value(input + eps0) - 2 * RosenbrockFunction.Value(input) + RosenbrockFunction.Value(input - eps0)) / (eps * eps);
var h11 = (RosenbrockFunction.Value(input + eps1) - 2 * RosenbrockFunction.Value(input) + RosenbrockFunction.Value(input - eps1)) / (eps * eps);
var h01 = (RosenbrockFunction.Value(input + epsuu) - RosenbrockFunction.Value(input + epsud) - RosenbrockFunction.Value(input - epsud) + RosenbrockFunction.Value(input - epsuu)) / (4 * eps * eps);
Assert.That(Math.Abs(h00 - h[0, 0]) < 1e-3);
Assert.That(Math.Abs(h11 - h[1, 1]) < 1e-3);
Assert.That(Math.Abs(h01 - h[0, 1]) < 1e-3);
Assert.That(Math.Abs(h01 - h[1, 0]) < 1e-3);
}
protected override void EvaluateHessian()
{
Hessian = RosenbrockFunction.Hessian(Point);
}
protected override void EvaluateGradient()
{
Gradient = RosenbrockFunction.Gradient(Point);
}
protected override void EvaluateValue()
{
Value = RosenbrockFunction.Value(Point);
}
private static void CheckRosenbrock(double a, double b, double expectedMin)
{
var x = BfgsSolver.Solve(new DenseVector(new[] { a, b }), RosenbrockFunction.Value, RosenbrockFunction.Gradient);
Numerics.Precision.AlmostEqual(expectedMin, RosenbrockFunction.Value(x), Precision);
}
