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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

double StepCalculator(double x1, double x2, double x3, double p_x1, double p_x2, double p_x3);
//Метод покоординатного спуска
void CoordinateDescent(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 покоординатного спуска
	CoordinateDescent(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 покоординатного спуска
void CoordinateDescent(double current_x1, double current_x2, double current_x3)
{
	//начальная установкаcurrent
	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 << " >> Покоординатный спуск:\n";
	cout << setw(11) << left << " Итерация" << setw(12) << left << "x1 " << setw(12) << left << "x2 " << setw(12) << left << "x3 "
		<< setw(18) << left << "||grad f(x1^k)|| " << setw(12) << left << " f(x1^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); // получение значения шага для x1
		next_x1 = current_x1 + step * p_x1; //расчет следующего значения переменной х
		//подсчет значений элементов вектора L
		p_x1 = -grad_x1(next_x1, current_x2, current_x3);
		p_x2 = -grad_x2(next_x1, current_x2, current_x3);
		p_x3 = -grad_x3(next_x1, current_x2, current_x3);

		step = StepCalculator(next_x1, current_x2, current_x3, p_x1, p_x2, p_x3);
		next_x2 = current_x2 + step * p_x2;
		p_x1 = -grad_x1(next_x1, next_x2, current_x3);
		p_x2 = -grad_x2(next_x1, next_x2, current_x3);
		p_x3 = -grad_x3(next_x1, next_x2, current_x3);

		step = StepCalculator(next_x1, next_x2, current_x3, p_x1, p_x2, p_x3);
		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;
}