最小二乘法拟合三角函数C语言

可以使用最小二乘法来拟合三角函数。以下是一个使用C语言实现最小二乘法拟合三角函数的示例代码：

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

#define N 10  // 数据点个数

double func(double x) {
    return sin(x);  // 以sin函数为例
}

void leastSquaresFit(double x[], double y[], int n, double *a, double *b) {
    double sumX = 0, sumY = 0, sumXY = 0, sumX2 = 0;

    // 计算各个累加和
    for (int i = 0; i < n; i++) {
        sumX += x[i];
        sumY += y[i];
        sumXY += x[i] * y[i];
        sumX2 += x[i] * x[i];
    }

    // 计算拟合直线的系数
    double denominator = n * sumX2 - sumX * sumX;
    if (denominator == 0) {
        printf("Error: denominator is zero!");
        return;
    }
    *a = (n * sumXY - sumX * sumY) / denominator;
    *b = (sumX2 * sumY - sumX * sumXY) / denominator;
}

int main() {
    // 输入数据点的x和y值
    double x[N] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
    double y[N] = {0, 0.8415, 0.9093, 0.1411, -0.7568, -0.9589, -0.2794, 0.656, 0.989, 0.4121};

    // 计算拟合直线的系数
    double a, b;
    leastSquaresFit(x, y, N, &a, &b);

    printf("拟合直线的方程: y = %f * x + %f\n", a, b);

    // 输出拟合结果
    printf("实际值\t\t预测值\n");
    for (int i = 0; i < N; i++) {
        printf("%f\t%f\n", y[i], a * x[i] + b);
    }

    return 0;
}