public void ScalarFunctonSecondDerivativeTest()
{
// d2/dx2((2x)^2) = 8
Func<double, double> f = x => Math.Pow(2 * x, 2);
var J = new NumericalHessian();
var jeval = J.Evaluate(f, 2);
Assert.AreEqual((double)8, jeval[0], 1e-7);
}
public void OneEquationTwoVarVectorFunctionTest()
{
Func<double[], double> f = x => 4 * Math.Pow(x[0], 2) + 3 * Math.Pow(x[1], 3);
var H = new NumericalHessian();
var heval = H.Evaluate(f, new double[] { 1, 1 });
var solution = new double[,] { { 8, 0 }, { 0, 18 } };
Assert.AreEqual(solution, heval);
Assert.AreEqual(12, H.FunctionEvaluations);
H.ResetFunctionEvaluations();
Assert.AreEqual(0, H.FunctionEvaluations);
}
public void RosenbrockFunctionHessianTest()
{
Func<double[], double> f = x => Math.Pow((1 - x[0]), 2) + 100 * Math.Pow(x[1] - Math.Pow(x[0], 2), 2);
var H = new NumericalHessian(5, 2);
var heval = H.Evaluate(f, new double[] { 2, 3 });
var solution = new double[,] { { 3602, -800 }, { -800, 200 } };
for (int row = 0; row < solution.Rank; row++)
{
for (int col = 0; col < solution.Rank; col++)
{
Assert.AreEqual(solution[row, col], heval[row, col], 1e-7);
}
}
}
public override void Execute()
{
var varCount = Fh.Point.Count;
//Подготовка
_hessian = new DenseMatrix(varCount, varCount);
//начальная точка
var x1 = Fh.Point;
Func<double[], double> castFunc = doubles => Fh.Y(new DenseVector(doubles));
var hessianCalculator = new NumericalHessian();
//Альфа метод
if (AlphaMethod == null) AlphaMethod = new BoostedDavidon(Fh.AlphaFunction, Fh.AlphaDiffFunction, Eps);
IterationCount = 0;
//Основной этап
do
{
if (!Kop1(Fh.Grad(Fh.Point))) break;
//Находим ньютоновское направление - p TODO
var temp = hessianCalculator.Evaluate(castFunc, x1.ToArray());
for (var i = 0; i < varCount; i++)
for (var j = 0; j < varCount; j++)
_hessian[i, j] = temp[i, j];
var p = -(_hessian.Inverse())*Fh.Grad(x1);
Fh.Dir = p;
//Альфа метод
AlphaMethod.SetSvenInterval();
AlphaMethod.Execute();
var alpha1 = AlphaMethod.Answer;
//Переходим на новую точку
x1 = x1 + Fh.Dir*alpha1;
Fh.Point = x1;
IterationCount++;
} while (Kop1(Fh.Dir) && Kop1(Fh.Grad(Fh.Point)));
Answer = Fh.Point;
}