#include <stdio.h>
#include <math.h>
 
#define EPSILON 1e-5 // Adjusted to match the slide requirement
#define MAX_ITER 100
 
double f1(double x, double y) { return x * x + y * y - 4; }
double f2(double x, double y) { return pow(x, 4) + x - y * y + 1; }
 
double df1_dx(double x, double y) { return 2 * x; }
double df1_dy(double x, double y) { return 2 * y; }
double df2_dx(double x, double y) { return 4 * x * x * x + 1; }
double df2_dy(double x, double y) { return -2 * y; }
 
void solve(double x0, double y0) {
    double x = x0, y = y0;
    int iter = 0;
 
    printf("\n--- Starting Guess: x=%.2f, y=%.2f ---\n", x0, y0);
    printf("Iter\tX\t\tY\n");
 
    while (iter <= MAX_ITER) {
        double F1 = f1(x, y);
        double F2 = f2(x, y);
 
        // Print current iteration values
        printf("%d\t%.10f\t%.10f\n", iter, x, y);
 
        // Check convergence based on slides
        if (fabs(F1) < EPSILON && fabs(F2) < EPSILON) {
            printf("Converged to solution.\n");
            return;
        }
 
        double J11 = df1_dx(x, y);
        double J12 = df1_dy(x, y);
        double J21 = df2_dx(x, y);
        double J22 = df2_dy(x, y);
 
        double det = J11 * J22 - J12 * J21;
        if (fabs(det) < 1e-12) {
            printf("Jacobian determinant too small. Method fails.\n");
            return;
        }
 
        x += (-F1 * J22 + F2 * J12) / det;
        y += (-J11 * F2 + J21 * F1) / det;
        iter++;
    }
    printf("Did not converge.\n");
}
 
int main() {
    // Define 3 sets of initial values as required
    double initial_x[] = {1.0, -1.5, 0.5};
    double initial_y[] = {1.0, 1.0, -1.5};
 
    for (int i = 0; i < 3; i++) {
        solve(initial_x[i], initial_y[i]);
    }
 
    return 0;
}
 

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