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| // Secant method for root finding | |
| // Iterative method using finite differences (no derivatives needed) | |
| // Test functions | |
| double f1(double x) { | |
| return x * x * x - x - 2.0; // Root near 1.52 | |
| } | |
| double f2(double x) { | |
| return exp(x) - 3.0 * x; // Root near 0.619 | |
| } | |
| double f3(double x) { | |
| return sin(x) - 0.5 * x; // Root near 1.896 | |
| } | |
| double secant(double (*f)(double), double x0, double x1, double tol, int max_iter) { | |
| for (int i = 0; i < max_iter; i++) { | |
| double f0 = f(x0); | |
| double f1_val = f(x1); | |
| if (fabs(f1_val) < tol) { | |
| return x1; | |
| } | |
| if (fabs(f1_val - f0) < 1e-15) { | |
| return NAN; // Division by zero | |
| } | |
| double x2 = x1 - f1_val * (x1 - x0) / (f1_val - f0); | |
| if (fabs(x2 - x1) < tol) { | |
| return x2; | |
| } | |
| x0 = x1; | |
| x1 = x2; | |
| } | |
| return x1; | |
| } | |
| int main() { | |
| clock_t start = clock(); | |
| double sum = 0.0; | |
| int found = 0; | |
| for (int iter = 0; iter < NUM_TRIALS; iter++) { | |
| double root; | |
| if (iter % 3 == 0) { | |
| root = secant(f1, 1.0, 2.0, TOL, MAX_ITER); | |
| } else if (iter % 3 == 1) { | |
| root = secant(f2, 0.0, 1.0, TOL, MAX_ITER); | |
| } else { | |
| root = secant(f3, 1.0, 2.0, TOL, MAX_ITER); | |
| } | |
| if (!isnan(root)) { | |
| sum += root; | |
| found++; | |
| } | |
| } | |
| clock_t end = clock(); | |
| double time_spent = (double)(end - start) / CLOCKS_PER_SEC; | |
| printf("Secant method: %d trials, %.6f seconds\n", | |
| NUM_TRIALS, time_spent); | |
| printf("Found %d roots, average: %.10f\n", found, sum / found); | |
| return 0; | |
| } | |