chislMethods

#include<iostream>
#include<cmath>
#include<ctime>
#include<iomanip>
using namespace std;

double myfunc(double t);
double myfunc1(double t);
double myfunc2(double t);
void coutPromFirst(int n, double c, double a, double b);
void coutPromSecond(int n, double x, char c);
void coutPromThird(int n, double x, double xLast, double sigma, char c);
void coutPromSecond(int n, double x, char c);
void coutPromFourth(int n, double x, double xLast, double gamma, char c);
int sign(double t);
double min(double first, double second);
double max(double first, double second);
void HalfDis();
void SimpleIteration();
void Newton();
void ModifyNewton();
void Chords();
double TransFunc(double t);
double TransFunc1(double t);
double TransFunc2(double t);
void TransModifyNewton(double a, double b);
void TransNewton(double a, double b);
void main()
{
    setlocale(LC_ALL, "rus");
    HalfDis();
    SimpleIteration();
    Newton();
    ModifyNewton();
    Chords();
    cout << "========================================================================"<<endl;
    TransModifyNewton(19,20);
    TransModifyNewton(18, 18.5);
    TransModifyNewton(0.1, 0.2);
    TransModifyNewton(-0.01, 0.1);
    TransModifyNewton(-15, -15.3);
    TransNewton(-16.2, -16.5);
    TransModifyNewton(-21, -21.1);
    TransNewton(-22.5, -23);
    system("pause");
}
void HalfDis()
    {

        double a = -1;
        double b = 0;
        double  c, eps = 0.00001;
        cout << "1) Метод половинного деления." << endl;

        int iterator = 0;
        while (fabs(b - a) >= eps)
        {
            c = (a + b) / 2.;
            coutPromFirst(iterator, c, a, b);
            if (myfunc(a)*myfunc(c) < 0)
                b = c;
            else
                a = c;
            iterator++;
        }

        cout << "Уточненный корень уравнения: x=" << setprecision(5) << fixed << c << endl;
        cout << "Итераций: " << iterator << endl;
    }
void SimpleIteration()
{

    double a = -1.;
    double b = 0.;
    double  eps = 0.00001;
    double x, xLast, alpha, m1, M1;
    cout << "2)Метод простой итерации." << endl;
    x = xLast = 2;

    if (sign(myfunc2(a)) == sign(myfunc2(b)))
    {
        M1 = fabs(myfunc1(max(a, b)));
        m1 = fabs(myfunc1(min(a, b)));
    }
    else
    {
        M1 = m1 = fabs(myfunc1(a));
        for (double count = a; count <= b; count += 0.05)
        {
            if (fabs(myfunc1(count)) > M1)
                M1 = fabs(myfunc1(count));
            if (fabs(myfunc1(count)) < m1)
                m1 = fabs(myfunc1(count));
        }
    }
    alpha = 2. / (m1 + M1);
    if (!(myfunc1(a) > 0 && myfunc1(b) > 0))
        alpha *= (-1);
    int n;
    for (n = 0; fabs(myfunc(x)) / m1 >= eps; n++)
    {
        coutPromSecond(n, x, '-');
        xLast = x;
        x = xLast - alpha*myfunc(xLast);
    }
    coutPromSecond(n, x, '+');
    cout << "Уточненный корень уравнения: x=" << setprecision(5) << fixed << x << endl;
    cout << "Итераций:" << n << endl;
}

void Newton()
{
    double a = -1.;
    double b = 0.;
    double  eps = 0.00001, x0, x1;
    cout << "3) Метод касательных." << endl;
    int iterator = 0;

    x0 = a;
    x1 = x0 - myfunc(x0) / myfunc1(x0);
    while (fabs(x1 - x0) > eps)
    {
        coutPromThird(iterator, x1, x0, eps, '-');
        x0 = x1;
        x1 = x0 - myfunc(x0) / myfunc1(x0);
        iterator++;
    }
    coutPromThird(iterator++, x1, x0, eps, '+');

    cout << "Уточненный корень уравнения: x=" << setprecision(5) << fixed << x1 << endl;
    cout << "Итераций:" << iterator << endl;
}

void ModifyNewton()
{
    double a = -1.;
    double b = 0.;
    double  eps = 0.00001, x0;
    double x, xLast, m1;
    int n = 0;
    cout << "3.1) Модифицированный метод касательных." << endl;
    xLast = 0;
    m1 = min(fabs(myfunc1(a)), fabs(myfunc1(b)));

    for (x = a; myfunc(x)*myfunc2(x) <= 0; x += 0.05);
    x0 = x;

    for (n = 0; (fabs(myfunc(x)) / m1) >= eps; n++)
    {
        coutPromSecond(n, x, '-');
        xLast = x;
        x = xLast - (myfunc(xLast) / myfunc1(x0));
    }

    coutPromSecond(n++, x, '+');
    cout << "Уточненный корень уравнения: x=" << setprecision(6) << fixed << x << endl;
    cout << "Итераций:" << n << endl;
}
void Chords()
{
    double a = -1;
    double b = 0.;
    double  eps = 0.00001;
    double x, xLast, M1, m1, gamma;
    int n = 0;
    cout << "4) Метод хорд." << endl;

    M1 = fabs(myfunc1(max(a, b)));
    m1 = fabs(myfunc1(min(a, b)));
    gamma = (m1 * eps) / (M1 - m1);

    if (myfunc(a)*myfunc2(a) < 0)
        for (xLast = 1, x = a; fabs(x - xLast) >= fabs(gamma);n++)
        {
            coutPromFourth(n, x, xLast, gamma, '-');
            xLast = x;
            x = xLast - (myfunc(xLast) / (myfunc(b) - myfunc(xLast))*(b - xLast));
        }
    else
        for (xLast = 1, x = b; fabs(x - xLast) >= fabs(gamma);n++)
        {
            coutPromFourth(n, x, xLast, gamma, '-');
            xLast = x;
            x = xLast - (myfunc(xLast) / (myfunc(a) - myfunc(xLast))*(a - xLast));
        }
    coutPromFourth(n++, x, xLast, gamma, '+');
    cout << "Уточненный корень уравнения: x=" << setprecision(6) << fixed << x << endl;
    cout << "Итераций:" << n << endl;
}


double myfunc(double t)
{
    double res;
    res = t*t*t - t*t + 2 * t + 3;
    return res;
}

double myfunc1(double t)
{
    double res;
    res = 3*t*t - 2*t + 2;
    return res;
}

double myfunc2(double t)
{
    double res;
    res = 6 * t - 2;
    return res;
}

int sign(double t)
{
    if (t > 0)
        return 1;
    else
        if (t < 0)
            return -1;
    return 0;
}
double min(double first, double second)
{
    if (first < second)
        return first;
    return second;
}
double max(double first, double second)
{
    if (first > second)
        return first;
    return second;
}

void coutPromFirst(int n, double c, double a, double b)
{
    if (n == 0)
        cout << setw(5) << "n" << setw(10) << "a" << setw(10) << "x" << setw(10) << "b" << setw(15) << "f(a)" << setw(15) << "f(x)" << setw(12) << "f(b)" << endl << endl;
    cout << setw(5) << n + 1 << setw(10) << a << setw(10) << c << setw(10) << b << setw(15) << myfunc(a) << setw(15) << myfunc(c) << setw(12) << myfunc(b) << endl;
}
void coutPromSecond(int n, double x, char c)
{
    double eps = 0.00001;
    if (n == 0)
        cout << setw(5) << "n" << setw(10) << "x" << setw(15) << "|f(x)|/m_1" << setw(25) << "|f(x)|/m_1 < " << eps << endl << endl;
    cout << setw(5) << n + 1 << setw(10) << x << setw(15) << fabs(myfunc(x)) / 6 << setw(25) << c << endl;
}
void coutPromThird(int n, double x, double xLast, double sigma, char c)
{
    if (n == 0)
        cout << setw(5) << "n" << setw(12) << "x_n" << setw(20) << "|x_n - x_(n-1)|" << setw(20) << "|x_n - x_(n-1)| < " << sigma << endl << endl;
    cout << setw(5) << n + 1 << setw(7) << x << setw(14);
    if (n == 0)
        cout << "---";
    else
        cout << fabs(x - xLast);
    cout << setw(25) << c << endl;
}
void coutPromFourth(int n, double x, double xLast, double gamma, char c)
{
    cout.precision(8);
    coutPromThird(n, x, xLast, gamma, c);
    cout.precision(6);
}
double TransFunc(double t)
{
    return(pow((t - 1), 3)*cos(t) + 1 - 14 * pow(t, 2));
}
double TransFunc1(double t)
{
    return(-28 * t - pow((t - 1), 3)*sin(t) + 3 * pow((t - 1), 2)*cos(t));
}
double TransFunc2(double t)
{
    return(-pow((t - 1), 3)*cos(t) - 6 * pow((t - 1), 2)*sin(t) + 6 * (t - 1)*cos(t) - 28);

}

void TransModifyNewton(double a, double b)
{

    //double a;
    //double b;
    double  eps = 0.00001, x0;
    double x, xLast, m1;
    int n = 0;
    cout << "3.1) Модифицированный метод касательных." << endl;
    /*cout << "Введите начало и конец отрезка:" << endl;
    cout << "a="; cin >> a;
    cout << "b="; cin >> b;*/
    xLast = 0;
    m1 = min(fabs(TransFunc1(a)), fabs(TransFunc1(b)));

    for (x = a; TransFunc(x)*TransFunc2(x) <= 0; x += 0.05);
    x0 = x;

    for (n = 0; (fabs(TransFunc(x)) / m1) >= eps; n++)
    {
        coutPromSecond(n, x, '-');
        xLast = x;
        x = xLast - (TransFunc(xLast) / TransFunc1(x0));
    }

    coutPromSecond(n++, x, '+');
    cout << "Уточненный корень уравнения: x=" << setprecision(5) << fixed << x << endl;
    cout << "Итераций:" << n << endl;
}
void TransNewton(double a, double b)
{
    double  eps = 0.00001, x0, x1;
    cout << "3) Метод касательных." << endl;
    int iterator = 0;

    x0 = a;
    x1 = x0 - TransFunc(x0) / TransFunc1(x0);
    while (fabs(x1 - x0) > eps)
    {
        coutPromThird(iterator, x1, x0, eps, '-');
        x0 = x1;
        x1 = x0 - TransFunc(x0) / TransFunc1(x0);
        iterator++;
    }
    coutPromThird(iterator++, x1, x0, eps, '+');

    cout << "Уточненный корень уравнения: x=" << setprecision(5) << fixed << x1 << endl;
    cout << "Итераций:" << iterator << endl;
}