c语言 顺序最小二乘法

顺序最小二乘法是一种求解线性回归问题的方法，其基本思想是通过最小化残差平方和来求解回归系数。下面是一个简单的 C 语言程序，实现了顺序最小二乘法：

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

#define N 10

struct Point {
    double x;
    double y;
};

void least_squares(struct Point *points, int n, double *a, double *b) {
    double sum_x = 0, sum_y = 0, sum_xy = 0, sum_x2 = 0;
    for (int i = 0; i < n; i++) {
        sum_x += points[i].x;
        sum_y += points[i].y;
        sum_xy += points[i].x * points[i].y;
        sum_x2 += points[i].x * points[i].x;
    }
    double denominator = n * sum_x2 - sum_x * sum_x;
    if (fabs(denominator) < 1e-6) {
        printf("Error: denominator is zero.\n");
        exit(1);
    }
    *a = (n * sum_xy - sum_x * sum_y) / denominator;
    *b = (sum_x2 * sum_y - sum_xy * sum_x) / denominator;
}

int main() {
    struct Point points[N] = {{1, 10}, {2, 20}, {3, 30}, {4, 40}, {5, 50}, {6, 60}, {7, 70}, {8, 80}, {9, 90}, {10, 100}};
    double a, b;
    least_squares(points, N, &a, &b);
    printf("The linear equation is y = %.2fx + %.2f\n", a, b);
    return 0;
}

在这个程序中，我们定义了一个 `Point` 结构体，用来存储二维坐标系中的点。`least_squares` 函数接收一个 `Point` 数组和数组大小作为参数，然后计算出回归系数 `a` 和 `b`。最后在 `main` 函数中输出线性方程的解。