lab2

#include <cstdio>
#include <cmath>
#include <vector>

double a = -2;
double b = 2;

double function(double x) {
    return sin(2.0 * x) + pow(cos(x), 2) - x * 0.5;
}

double derivative(double x) {
    return 2.0 * cos(2.0 * x) - 2.0 * sin(x) * cos(x) - 0.5;
}

std::vector<int> iteration(double x, double step) {
    std::vector<int> iterations;

    double a = x;
    double b = x + step;
    double da = derivative(a);
    double db = derivative(b);
    double alpha = 1.0 / ((abs(da) > abs(db)) ? da : db);
    double q = 1.0 - abs((abs(da) > abs(db) ? (db / da) : (da / db)));
    double k = 1.0 / q - 1.0;

    printf("|  eps  |     equation root     | accuracy estimation I |\n");
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3) {
        double sigma = k * eps;
        double x0 = (a + b) * 0.5;
        double x1 = x0;
        int count = 0;
        do {
            x0 = x1;
            x1 = x0 - alpha * function(x0);
            count++;
        } while (abs(x1 - x0) > sigma);
        iterations.push_back(count);
        printf("| %.0E | %21.18f | %.15E |\n", eps, x1, abs(x1 - x0) / k);
    }
    printf("\n");

    return iterations;
}

std::vector<int> bisection(double x, double step) {
    std::vector<int> iterations;
    printf("|  eps  |     equation root     | accuracy estimation B |\n");
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3) {
        double a = x;
        double b = x + step;
        int count = 0;
        do {
            double c = (a + b) * 0.5;

            double fa = function(a);
            double fb = function(b);
            double fc = function(c);

            if (fa * fc < 0) b = c;
            if (fb * fc < 0) a = c;
            count++;
        } while (abs(b - a) >= 2 * eps);
        iterations.push_back(count);
        printf("| %.0E | %21.18f | %.15E |\n", eps, (a + b) * 0.5, abs((b - a) * 0.5));
    }
    printf("\n");

    return iterations;
}

std::vector<double> findroots() {
    std::vector<double> X;
    for (double x = a; x <= b; x += 0.1) {
        if (function(x) * function(x + 0.1) < 0) {
            X.push_back(x);
        }
    }
    return X;
}

int main() {
    auto roots = findroots();

    auto ii = iteration(roots[0], 0.1);
    for (int i = 1; i < 3; i++) {
        iteration(roots[i], 0.1);
    }

    auto ib = bisection(roots[0], 0.1);
    for (int i = 1; i < 3; i++) {
        bisection(roots[i], 0.1);
    }

    printf("|  eps  | iteration | bisection |\n");
    int index = 0;
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3, index++) {
        printf("| %.0E | %9i | %9i |\n", eps, ii[index], ib[index]);
    }
    return 0;
}