public Tuple <Matrix, double> NewtonsMethod(Matrix x0, double eps, double a = 1, int steps = 100)
{
int n = function.Variables.Count;
FunctionParser[] gradFunctional = new FunctionParser[n];
for (int i = 0; i < n; ++i)
{
gradFunctional[i] = function.DifferentiateBy(function.Variables[i]);//.Optimize();
}
FunctionParser[,] HessianFunctional = new FunctionParser[n, n];
for (int i = 0; i < n; ++i)
{
for (int j = i; j < n; ++j)
{
FunctionParser tmp = function.DifferentiateBy(function.Variables[i]);
tmp = tmp.DifferentiateBy(function.Variables[j]);
tmp = tmp.Optimize();
HessianFunctional[i, j] = HessianFunctional[j, i] = tmp; //function.DifferentiateBy(function.Variables[i]).DifferentiateBy(function.Variables[j]).Optimize();
}
}
Matrix x = (Matrix)x0.Clone(),
grad = CountGrad(x, gradFunctional),
HessianMatrix;
int step = steps;
while (Norm(grad) >= eps && step-- > 0)
{
HessianMatrix = CountHessian(x, HessianFunctional);
Matrix invertedH;
if (!HessianMatrix.TryInvert(out invertedH))
{
throw new ArgumentException("Ошибка в поиске обратной матрицы!");
}
Matrix a_grad = a * grad,
mult = a_grad * invertedH;
x = x - mult;
grad = CountGrad(x, gradFunctional);
}
if (step < 0)
{
throw new MethodDivergencyException($"Методу не удалось найти решение за {steps} шагов.");
}
return(new Tuple <Matrix, double>(x, f(x.ToVector())));
}