line_fit

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#include <stdio.h>#include <stdlib.h>#include <math.h>#define POINTS_NUM       6typedef struct {double x;double y;}typePoints;typePoints points[POINTS_NUM] = {{0   , 0.002},{0.1 , 0.082},{0.2 , 0.162},{0.5 , 0.407},{1   , 0.805},{1.5 , 1.185}};/* * 最小二乘法直线拟合（不是常见的一元线性回归算法） * 将离散点拟合为  a x + b y + c = 0 型直线 * 假设每个点的 X Y 坐标的误差都是符合 0 均值的正态分布的。 * 与一元线性回归算法的区别：一元线性回归算法假定 X 是无误差的，只有 Y 有误差。 */void lineFit(double *a , double *b , double *c){  int i;     double x_mean = 0;     double y_mean = 0;          for(i = 0; i < POINTS_NUM; i++)     {         x_mean += points[i].x;         y_mean += points[i].y;     }     x_mean /= POINTS_NUM;     y_mean /= POINTS_NUM; //至此，计算出了 x y 的均值     double Dxx = 0, Dxy = 0, Dyy = 0;     for(i = 0; i < POINTS_NUM; i++)     {         Dxx += (points[i].x - x_mean) * (points[i].x - x_mean);         Dxy += (points[i].x - x_mean) * (points[i].y - y_mean);         Dyy += (points[i].y - y_mean) * (points[i].y - y_mean);     }          double lambda = ( (Dxx + Dyy) - sqrt( (Dxx - Dyy) * (Dxx - Dyy) + 4 * Dxy * Dxy) ) / 2.0;     double den = sqrt( Dxy * Dxy + (lambda - Dxx) * (lambda - Dxx) );          *a = Dxy / den;     *b = (lambda - Dxx) / den;     *c = - (*a) * x_mean - (*b) * y_mean;} int main(int argc, char *argv[]) {double a , b , c;lineFit(&a,&b,&c);printf("slope = %f;intercept = %f",(-a/b),(-c/b));system("pause");return 0;}
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