3

#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

double function(double x1, double x2, double x3); // исходная функция
double grad_x1(double x1, double x2, double x3);  // чп по х1
double grad_x2(double x1, double x2, double x3);  // чп по х2
double grad_x3(double x1, double x2, double x3);  // чп по х3
double grad(double x1, double x2, double x3);     // градиент функции

//Подсчет значения шага
double StepCalculator(double x1, double x2, double x3, double p_x1, double p_x2, double p_x3);

//Метод наискорейшего спуска
void FastestGradDescent(double current_x1, double current_x2, double current_x3);

int main()
{
    setlocale(LC_ALL, "RUSSIAN");
    double x1 = 1;
    double x2 = 2;
    double x3 = 3;
    //Метод наискорейшего спуска
    FastestGradDescent(x1, x2, x3);
    system("pause");
    return 0;
}

double function(double x1, double x2, double x3)
{
    return 3 * pow(x1, 2) + 4 * pow(x2, 2) + 6 * pow(x3, 2) + 2 * x1 * x2 + 2 * x1 - 3 * x2 + 5 * x3;
}
double grad_x1(double x1, double x2, double x3)
{
    return 6 * x1 + 2 * x2 + 2;
}
double grad_x2(double x1, double x2, double x3)
{
    return 8 * x2 + 2 * x1 - 3;
}
double grad_x3(double x1, double x2, double x3)
{
    return 12 * x3 + 5;
}

double grad(double x1, double x2, double x3)
{
    double gr_x1 = grad_x1(x1, x2, x3);
    double gr_x2 = grad_x2(x1, x2, x3);
    double gr_x3 = grad_x3(x1, x2, x3);

    return sqrt(pow(gr_x1, 2) + pow(gr_x2, 2) + pow(gr_x3, 2));
}

//Подсчет значения шага
double StepCalculator(double x1, double x2, double x3, double p_x1, double p_x2, double p_x3)
{
    double step = 0;
    double numerator = 0;
    double denominator = 0;
    //подсчет выражения для определения шага
    numerator = 6 * x1 * p_x1 + 8 * x2 * p_x2 + 12 * x3 * p_x3 + 2 * x1 * p_x2 + 2 * x2 * p_x1 + 2 * p_x1 - 3 * p_x2 + 5 * p_x3;
    denominator = 6 * pow(p_x1, 2) + 8 * pow(p_x2, 2) + 12 * pow(p_x3, 2) + 4 * p_x1 * p_x2;
    step = -numerator / denominator;
    return step;
}
//Метод наискорейшего спуска
void FastestGradDescent(double current_x1, double current_x2, double current_x3)
{
    //начальная установка
    double next_x1 = current_x1;
    double next_x2 = current_x2;
    double next_x3 = current_x3;
    double step = 0; //шаг
    int iterations = 0; //количество итераций
    double eps = 0.0001; //точность
    //элементы вектора P
    double p_x1 = 0;
    double p_x2 = 0;
    double p_x3 = 0;
    cout << " >> Наискорейший спуск:\n";
    cout << setw(11) << left << " Итерация" << setw(12) << left << "x1 " << setw(12) << left << "x2 " << setw(12) << left << "x3 "
        << setw(16) << left << "||grad f(x^k)|| " << setw(12) << left << " f(x^k)\n" << endl;
    while (grad(next_x1, next_x2, next_x3) > eps)
    {
        //определение переменных текущей итерации
        current_x1 = next_x1;
        current_x2 = next_x2;
        current_x3 = next_x3;
        //подсчет значений элементов вектора P
        p_x1 = -grad_x1(current_x1, current_x2, current_x3);
        p_x2 = -grad_x2(current_x1, current_x2, current_x3);
        p_x3 = -grad_x3(current_x1, current_x2, current_x3);
        step = StepCalculator(current_x1, current_x2, current_x3, p_x1, p_x2, p_x3);
        //расчет следующих значений переменных
        next_x1 = current_x1 + step * p_x1;
        next_x2 = current_x2 + step * p_x2;
        next_x3 = current_x3 + step * p_x3;
        iterations++;
        cout << " " << setw(10) << left << iterations << setw(12) << left << next_x1 << setw(12) << left << next_x2 << setw(12) << left << next_x3
            << setw(16) << left << grad(next_x1, next_x2, next_x3) << setw(12) << left << function(next_x1, next_x2, next_x3) << endl;
    }
    cout << "\nПолученная точка минимума: (" << next_x1 << ", " << next_x2 << ", " << next_x3 << ")" << endl;
    cout << "Количество итераций: " << iterations << endl;

}