3元最小二乘拟合C语言代码 格式：z=ax+by+c

以下是使用3元最小二乘法拟合的C语言代码，格式为z = ax + by + c：

#include <stdio.h>

void least_square_fit(double x[], double y[], double z[], int n, double *a, double *b, double *c) {
    double sum_x = 0.0, sum_y = 0.0, sum_z = 0.0; // 存储x、y、z的和
    double sum_xx = 0.0, sum_xy = 0.0, sum_xz = 0.0; // 存储x^2、xy、xz的和
    double sum_yy = 0.0, sum_yz = 0.0; // 存储y^2、yz的和

    // 计算各个和的值
    for (int i = 0; i < n; ++i) {
        sum_x += x[i];
        sum_y += y[i];
        sum_z += z[i];
        sum_xx += x[i] * x[i];
        sum_xy += x[i] * y[i];
        sum_xz += x[i] * z[i];
        sum_yy += y[i] * y[i];
        sum_yz += y[i] * z[i];
    }

    // 求解3元方程组
    double det = sum_xx * sum_yy * n + 2 * sum_x * sum_y * sum_xy - sum_x * sum_x * sum_yy - sum_y * sum_y * sum_xx - n * sum_xy * sum_xy;
    double det_a = sum_xz * sum_yy * n + sum_x * sum_y * sum_yz + sum_z * sum_xy * n - sum_x * sum_yz * sum_y - sum_z * sum_xx * n;
    double det_b = sum_xx * sum_yz * n + sum_xz * sum_y * n + sum_x * sum_y * sum_z - sum_x * sum_yz * sum_x - sum_xy * sum_z * n;
    double det_c = sum_xx * sum_yy * sum_z + sum_x * sum_y * sum_yz + sum_xy * sum_xz * n - sum_xz * sum_yy * sum_x - sum_xy * sum_xy * sum_z - sum_xx * sum_yz * sum_y;

    // 计算a、b、c
    *a = det_a / det;
    *b = det_b / det;
    *c = det_c / det;
}

int main() {
    double x[] = {1.0, 2.0, 3.0, 4.0, 5.0}; // x的数据
    double y[] = {2.0, 3.0, 4.0, 5.0, 6.0}; // y的数据
    double z[] = {3.0, 4.0, 5.0, 6.0, 7.0}; // z的数据
    int n = 5; // 数据长度
    double a, b, c; // 存储拟合结果

    least_square_fit(x, y, z, n, &a, &b, &c);

    printf("z = %.2fx + %.2fy + %.2f\n", a, b, c);

    return 0;
}

请注意，此代码仅适用于数据点的数量为3或更多的情况。如果只有两个数据点，则无法使用3元最小二乘法进行拟合。