optimizationMethods

#include <iostream>
#include <locale>
#include <iomanip>
using namespace std;

const double a = -1.;
const double b = 1.;
const double delta = 0.005;
const double e = 0.01;

double f(double x)
{
    return (fabs(x) + (x - 1.)*(x - 1.));
}
void coutRes(int type)
{
    switch (type)
    {
    case 1:
        cout << setw(2) << "n";
        cout << setw(11) << "a_n";
        cout << setw(11) << "x_(2n-1)";
        cout << setw(11) << "x_2n";
        cout << setw(11) << "b_n";
        cout << setw(11) << "f(x_(2n-1))";
        cout << setw(11) << "f(x_2n)";
        cout << setw(11) << "b_n - a_n";
        break;
    case 2:
        cout << setw(2) << "n";
        cout << setw(11) << "a_n";
        cout << setw(11) << "x_(n+1)";
        cout << setw(11) << "x_n";
        cout << setw(11) << "b_n";
        cout << setw(11) << "f(x_(n+1))";
        cout << setw(11) << "f(x_n)";
        cout << setw(11) << "b_n - a_n";
        break;
    case 3:
        cout << setw(2) << "n";
        cout << setw(11) << "a_n";
        cout << setw(11) << "b_n";
        cout << setw(11) << "u_n";
        cout << setw(11) << "v_n";
        cout << setw(11) << "f(u_n)";
        cout << setw(11) << "f(v_n)";
        break;
    }
    cout << endl;
}
void coutRes(int a1, double a2, double a3, double a4, double a5, double a6, double a7, double a8, int type)
{
    switch (type)
    {
    case 1: case 2:
        cout << setw(2) << a1;
        cout << setw(11) << a2;
        cout << setw(11) << a3;
        cout << setw(11) << a4;
        cout << setw(11) << a5;
        cout << setw(11) << a6;
        cout << setw(11) << a7;
        cout << setw(11) << a8;
        break;
    case 3:
        cout << setw(2) << a1;
        cout << setw(11) << a2;
        cout << setw(11) << a3;
        cout << setw(11) << a4;
        cout << setw(11) << a5;
        cout << setw(11) << a6;
        cout << setw(11) << a7;
        break;
    }
    cout << endl;
}

void halfDivision()
{
    int k;
    double a_k = a;
    double b_k = b;
    double x_1, x_2;
    coutRes(1);
    for (k = 1; (b_k - a_k) >= e; k++)
    {
        x_1 = (a_k + b_k - delta) / 2.;
        x_2 = (a_k + b_k + delta) / 2.;
        coutRes(k, a_k, x_1, x_2, b_k, f(x_1), f(x_2), b_k - a_k, 1);
        if (f(x_1) <= f(x_2))
            b_k = x_2;
        else
            a_k = x_1;
    }
    coutRes(k, a_k, x_1, x_2, b_k, f(x_1), f(x_2), b_k - a_k, 1);
    cout << "количество шагов = " << k << endl;
    cout << "x = " << (a_k + b_k) / 2. << endl;
    cout << "y(x) = " << f((a_k + b_k) / 2.) << endl;
}

void goldenSection()
{
    int n;
    double a_n, b_n;
    a_n = a;
    b_n = b;
    double x_1, x_2;
    double func_x1, func_x2;
    x_1 = a_n + ((3 - sqrt(5)) / 2.)*(b_n - a_n);
    x_2 = a_n + ((sqrt(5) - 1) / 2.)*(b_n - a_n);
    func_x1 = f(x_1);
    func_x2 = f(x_2);
    coutRes(2);
    for (n = 1; (b_n - a_n) * 10 >= e * 10; n++)
    {
        coutRes(n, a_n, x_2, x_1, b_n, func_x2, func_x1, b_n - a_n, 2);
        if (func_x1 < func_x2)
        {
            b_n = x_2;
            x_2 = x_1;
            func_x2 = func_x1;
            x_1 = a_n + ((3 - sqrt(5)) / 2.)*(b_n - a_n);
            func_x1 = f(x_1);
        }
        else
        {
            a_n = x_1;
            x_1 = x_2;
            func_x1 = func_x2;
            x_2 = a_n + ((sqrt(5) - 1) / 2.)*(b_n - a_n);
            func_x2 = f(x_2);
        }
    }
    coutRes(n, a_n, x_2, x_1, b_n, func_x2, func_x1, b_n - a_n, 2);
    cout << "количество шагов = " << n << endl;
    cout << "x = " << (a_n + b_n) / 2. << endl;
    cout << "y(x) = " << f((a_n + b_n) / 2.) << endl;
}

void Fibonacci(int &F_k, int &F_k_1, int &k)
{
    int F_k_2 = F_k_1 + F_k;
    while (!((F_k_1 <= ((b - a) / e)) && (((b - a) / e) <= F_k_2)))
    {
        F_k = F_k_1;
        F_k_1 = F_k_2;
        F_k_2 = F_k_1 + F_k;
        k++;
    }
}
int Fib(int end)
{
    int F_i = 1;
    int F_i_1 = 1;
    int F_i_2 = F_i_1 + F_i;
    int i = 1;
    while (i != end)
    {
        F_i = F_i_1;
        F_i_1 = F_i_2;
        F_i_2 = F_i_1 + F_i;
        i++;
    }
    return F_i;
}
void FibonacciMethod()
{
    int F_n, F_n_1, F_n_2, n, k;
    double a_n, b_n, func_u, func_v;
    double u, v;
    F_n = F_n_1 = n = 1;
    a_n = a;
    b_n = b;


    Fibonacci(F_n, F_n_1, n);
    F_n_2 = F_n_1 + F_n;

    u = a_n + ((double)F_n / F_n_2) * (b_n - a_n);
    v = a_n + ((double)F_n_1 / F_n_2) * (b_n - a_n);
    func_u = f(u);
    func_v = f(v);

    coutRes(3);
    coutRes(1, a_n, b_n, u, v, func_u, func_v, 0, 3);

    for (k = 2; k < n; k++)
    {
        if (func_u <= func_v)
            b_n = v;
        else
            a_n = u;
        if (func_u <= func_v)
        {
            v = u;
            u = a_n + ((double)Fib(n - k + 1) / F_n_2)*(b - a);
            func_v = func_u;
            func_u = f(u);
        }
        else
        {
            u = v;
            func_u = func_v;
            v = a_n + ((double)Fib(n - k + 2) / F_n_2)*(b - a);
            func_v = f(v);
        }
        coutRes(k, a_n, b_n, u, v, func_u, func_v, 0, 3);
    }
    coutRes(k, a_n, b_n, u, v, func_u, func_v, 0, 3);
    cout << "количество шагов = " << n << endl;
    cout << "x = " << (a_n + b_n) / 2. << endl;
    cout << "y(x) = " << f((a_n + b_n) / 2.) << endl;
}

int main()
{
    setlocale(LC_ALL, "russian");
    cout << "Метод половинного деления" << endl << endl;
    halfDivision();
    cout << endl << endl << "Метод золотого сечения" << endl << endl;
    goldenSection();
    cout << endl << endl << "Метод Фибоначчи" << endl << endl;
    FibonacciMethod();

    system("pause");
    return 0;
}