最小二乘法及其c++的实现

//最小二乘法的实现
#include
#include
#include "source.h"
#define Length 10
using namespace std;
double fun(int n, double array[Length][Length])
{int ii, jj, k, u;int iter = 0;  //记录行变换的次数（交换）double det1 = 1, yin;for (ii = 0; ii < n; ii++){for (k = ii + 1; k < n; k++){yin = -1 * array[k][ii] / array[ii][ii];for (u = 0; u < n; u++){array[k][u] = array[k][u] + array[ii][u] * yin;}}}for (ii = 0; ii < n; ii++)  //求对角线的积 即 行列式的值det1 = det1 * array[ii][ii];//行变换偶数次符号不变if (iter % 2 == 1)det1 = -det1;return (det1);
}
void  LeastSquareMethod(int n,int m, double* x, double* y) {int i, j;double temp[Length][Length];double d[Length], arr[Length][Length];double tempsumx, tempsumy;double sumx[Length] = { 0.0 }, sumy[Length] = { 0.0 };for (i = 0; i <2*m; i++) {tempsumx = 0.0;tempsumy = 0.0;for (j = 0; j < n; j++) {tempsumx += pow(x[j], i + 1);tempsumy += pow(x[j], i) * y[j];}sumx[i] = tempsumx;sumy[i] = tempsumy;}int a=0;//上三角for (i = 1; i < m + 1; i++) {temp[0][0] = n;for (j = 0; j <= i; j++) {temp[j][i - j] = sumx[i - 1];a = i - 1;}}//下三角for (j = 1; j <= m; j++) {for (i = 0; i <= m - j; i++) {temp[i + j][m - i] = sumx[a + j];}}//临时赋值for (i = 0; i <= m; i++) {for (j = 0; j <= m; j++) {arr[i][j] = temp[i][j];}}for (i = 0; i <= m; i++) {for (j = 0; j <= m; j++) {arr[j][i] = sumy[j];}d[i + 1] = fun(m+1, arr);//求行列式的值for (int p = 0; p <= m; p++) {for (int q = 0; q <= m; q++) {arr[p][q] = temp[p][q];//恢复被改变过的arr}}}d[0] = fun(m + 1, temp);double z[Length];for (i = 0; i <= m; i++) {z[i] = d[i + 1] / d[0];}char cha = '+';cout << "拟合数据的" << m << "次多项式为:P" << m << "(x)=" << z[0];for (i = 1; i <= m; i++) {if (z[i] < 0)cha = ' ';cout << cha << z[i] << "x^" << i;}cout << endl;
}
int main() {int n, m, xi, i;double x[Length], y[Length];cout << "请输入x和f(x)的个数:";cin >> n;cout << "----------录入数据----------\n" << endl;for (i = 0; i < n; i++) {cout << "x[" << i << "]=";cin >> x[i];cout << "y[" << i << "]=";cin >> y[i];}cout << "\n----------录入完毕----------" << endl;cout << "请输入所求多项式的次数:";cin >> m;LeastSquareMethod(n, m, x, y);system("pause");return 0;
}

本文来自互联网用户投稿，文章观点仅代表作者本人，不代表本站立场，不承担相关法律责任。如若转载，请注明出处。 如若内容造成侵权/违法违规/事实不符，请点击【内容举报】进行投诉反馈！