public Tuple <Matrix, double> SpeedestDescentMethod(Matrix x0, double epsilon, double a = 1, int steps = 100)
{
int n = function.Variables.Count,
accuracy = 10;// Regex.Match(epsilon.ToString(), @"(?<=[,])\d+").Value.Count();
//заполняем градиент
FunctionParser[] gradFunctional = new FunctionParser[n];
for (int i = 0; i < n; ++i)
{
gradFunctional[i] = function.DifferentiateBy(function.Variables[i]).Optimize();
}
//вычисляем градиент в точке x_0
Matrix x = (Matrix)x0.Clone(),
grad = CountGrad(x, gradFunctional);
int step = steps;
//пока ||grad f(x_0)|| >= e
while (Norm(grad) >= epsilon && step-- > 0)
{
string func = function.ToString();
//заменяем цифры в скобках просто цифрами
func = Regex.Replace(func, @"[(](\d+)[)]", "$1");
//заменяем переменные x_i на x_i - x * grad_i, чтобы получить функцию одной переменной x
for (int i = 0; i < function.Variables.Count; ++i)
{
string replacedVariable = function.Variables[i],
//replacement = grad[i] > 0 ? $"{Math.Round(x[i], accuracy)}-{Math.Round(grad[i], accuracy)}a" : $"{Math.Round(x[i], accuracy)}+{Math.Abs(Math.Round(grad[i], accuracy))}a";
replacement = grad[i] > 0 ? $"{x[i]:f10}-{grad[i]:f10}a" : $"{x[i]:f10}+{Math.Abs(grad[i]):f10}a";
func = Regex.Replace(func, $@"(?<=[(]){replacedVariable}(?=[)])", replacement);
func = Regex.Replace(func, replacedVariable, $"({replacement})");
}
FunctionParser Ф = new FunctionParser(func);
Matrix A = new Matrix(1);
A[0] = a;
Optimizer support = new Optimizer(Ф);
var min = support.NewtonsMethod(A, epsilon);
x = x - min.Item1[0] * grad;
grad = CountGrad(x, gradFunctional);
}
if (step < 0)
{
throw new MethodDivergencyException($"Методу не удалось найти решение за {steps} шагов.");
}
return(new Tuple <Matrix, double>(x, f(x.ToVector())));
}