// MO_Powell.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <iostream>
#include <cmath>

double f(double p1, double p2, double x, double y, double alpha)
{
    return pow((p1 + x*alpha - 2.0), 2.0) + pow((p2 + y*alpha + 1.0), 2.0) - 0.5*(p1 + x*alpha)*(p2 + y*alpha) + 4.0;
    //return  sin(p1 + x*alpha + 0.8) *sin(p1 + x*alpha + 0.8) + sin(p2 + y*alpha - 0.2)* sin(p2 + y*alpha - 0.2);

}

int main()
{

    double a = -1.0, b = 3.0; //interval
    double e[2] = { 1.0,0 }; //direction
    double x_init[2] = { 0,0 }; //
    double x_second[2] = { 0,0 };
    double accuracy = 0.01;
    double x1, x2;

    //25% method

    x1 = a + (b - a)*0.25;
    x2 = b - (b - a)*0.25;

    std::cout << x1;
    std::cout << x2;
    double min;

    while (abs(x2-x1)>accuracy)
    {
        if (f(x_init[0], x_init[1], e[0], e[1], x1) >= f(x_init[0], x_init[1], e[0], e[1], x2))
        {
            min = f(x_init[0], x_init[1], e[0], e[1], x2);
            a = x1;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;
        }

        else if (f(x_init[0], x_init[1], e[0], e[1], x2) > f(x_second[0], x_second[1], e[0], e[1], x1))
        {
            min = f(x_init[0], x_init[1], e[0], e[1], x1);
            b = x2;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;
        }
        else continue;
    }

    std::cout << "local min at" << (x1 + x2) / 2.0 << " with value " <<min<<std::endl;

    x_second[0] = (x1 + x2) / 2.0;
    e[0] = 0;
    e[1] = 1;
    a = -1.0;
    b = 3.0;

    x1 = a + (b - a)*0.25;
    x2 = b - (b - a)*0.25;

    std::cout << "second iteration: "<<std::endl;

    while (abs(x2 - x1)>accuracy)
    {
        if (f(x_second[0], x_second[1], e[0], e[1], x1) >= f(x_second[0], x_second[1], e[0], e[1], x2))
        {
            min = f(x_init[0], x_init[1], e[0], e[1], x2);
            b = x2;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;
        }
        else if (f(x_init[0], x_init[1], e[0], e[1], x2) > f(x_second[0], x_second[1], e[0], e[1], x1))
        {
            min = f(x_second[0], x_second[1], e[0], e[1], x1);
            b = x2;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;
        }
        else continue;
    }

    std::cout << "local min at: " << (x1 + x2) / 2.0 << " with value " << min<<std::endl;

    e[0] = x_second[0] - x_init[0];
    e[1] = x_second[1] - x_init[1];
    a = -1.0;
    b = 3.0;
    x1 = a + (b - a)*0.25;
    x2 = b - (b - a)*0.25;
    std::cout << x1 << "," << x2 << "," << e[0] << "," << e[1] << "," << a << "," << b << std::endl;
    std::cout << "third iteration: " << std::endl;

    while (abs(x2 - x1)>=accuracy)
    {

        if (f(x_second[0], x_second[1], e[0], e[1], x1) >= f(x_second[0], x_second[1], e[0], e[1], x2))
        {
            min = f(x_init[0], x_init[1], e[0], e[1], x2);
            b = x2;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;

        }
        else if (f(x_init[0], x_init[1], e[0], e[1], x2) > f(x_second[0], x_second[1], e[0], e[1], x1))
        {
            min = f(x_second[0], x_second[1], e[0], e[1], x1);
            b = x2;
            x1 = a + (b - a)*0.25;
            x2 = b - (b - a)*0.25;

        }
    }

    std::cout << "local min at: " << (x1 + x2) / 2.0 << " with value " << min;

    system("pause");

    return 0;
}