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#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

//Метод градиентного спуска с дроблением шага
void GradDescentStep(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 градиентного спуска с дроблением шага
    GradDescentStep(x1, x2, x3);
    cout << endl;
    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));
}


//Метод градиентного спуска с дроблением шага
void GradDescentStep(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 = 1;        //шаг
    int iterations = 0;     //количество итераций
    double eps = 0.0001;     //точность

    double f = 0;
    double f_delta = 0;

    cout << " >> Градиентный спуск с дроблением шага:\n";
    cout << setw(11) << left << " Итерация" << setw(12) << left << "x1 " << setw(12) << left << "x2 " << setw(12) << left << "x3 "
        << setw(16) << left << "||gradf(x^k)|| " << setw(12) << left << " f(x^k)\n" << endl;

    while (grad(next_x1, next_x2, next_x3) > eps)
    {
        current_x1 = next_x1;   //определение переменных текущей итерации
        current_x2 = next_x2;
        current_x3 = next_x3;

        //получение значений функции и функции с учетом градиента
        f = function(next_x1, next_x2, next_x3);
        f_delta = function(next_x1 - step * grad_x1(current_x1, current_x2, current_x3), next_x2 - step * grad_x2(current_x1, current_x2, current_x3), next_x3 - step * grad_x3(current_x1, current_x2, current_x3));

        if (f > f_delta)
        {
            next_x1 = current_x1 - step * grad_x1(current_x1, current_x2, current_x3);
            next_x2 = current_x2 - step * grad_x2(current_x1, current_x2, current_x3);
            next_x3 = current_x3 - step * grad_x3(current_x1, current_x2, current_x3);
        }
        else
            step = step * 0.5; //уменьшение шага

        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;
}