#include <stdio.h> #include <math.h> #define MAX_ITER 100000 // 最大迭代次数 #define TOL 1e-6 // 收敛精度 double f(double x, double y) { return 100 * pow(y - x * x, 2) + pow(1 - x, 2); } int main() { double x = 0, y = 0, tmp_x, tmp_y, fx, fy, diff, max_diff; int iter = 0; do { max_diff = 0; fx = f(x, y); fy = f(x, y); tmp_x = x; tmp_y = y; // 坐标轮换 x = (1 - sqrt(5)) / 2 * y; y = (1 - sqrt(5)) / 2 * tmp_x; diff = fabs(fx - f(x, y)); if (diff > max_diff) { max_diff = diff; } diff = fabs(fy - f(x, y)); if (diff > max_diff) { max_diff = diff; } iter++; } while (max_diff >= TOL && iter < MAX_ITER); printf("Minimum value of f(x,y) = %.6f\n", f(x, y)); printf("Optimal solution: x = %.6f, y = %.6f\n", x, y); return 0; }注释一下

以下是对代码的注释：

#include <stdio.h>
#include <math.h>

#define MAX_ITER 100000   // 最大迭代次数
#define TOL 1e-6          // 收敛精度

// 目标函数
double f(double x, double y) {
    return 100 * pow(y - x * x, 2) + pow(1 - x, 2);
}

int main() {
    double x = 0, y = 0, tmp_x, tmp_y, fx, fy, diff, max_diff;
    int iter = 0;

    do {
        max_diff = 0;
        fx = f(x, y);   // 保存当前点的函数值
        fy = f(x, y);   // 保存当前点的函数值
        tmp_x = x;      // 保存当前x坐标
        tmp_y = y;      // 保存当前y坐标

        // 坐标轮换
        x = (1 - sqrt(5)) / 2 * y;      // 优化x坐标
        y = (1 - sqrt(5)) / 2 * tmp_x;  // 优化y坐标

        // 计算当前点与上一次迭代点的函数值之差，并更新最大差值
        diff = fabs(fx - f(x, y));
        if (diff > max_diff) {
            max_diff = diff;
        }

        diff = fabs(fy - f(x, y));
        if (diff > max_diff) {
            max_diff = diff;
        }

        iter++;     // 迭代次数加1
    } while (max_diff >= TOL && iter < MAX_ITER);   // 当最大差值小于收敛精度或达到最大迭代次数时停止迭代

    // 输出最小值和最优解
    printf("Minimum value of f(x,y) = %.6f\n", f(x, y));
    printf("Optimal solution: x = %.6f, y = %.6f\n", x, y);

    return 0;
}