#include<iostream.h>#include<math.h>#include<stdlib.h>#include <windows.h>double f(int n,double x){ //f(n,x)用来返回x的n次方double y=1.0;if(n==0)return 1.0;else{for(int i=0;i<n;i++)y*=x;return y;}}int xianxingfangchengzu(double **a,int n,double *b,double *p,double dt)//用高斯列主元法来求解法方程组 { int i,j,k,l; double c,t; for(k=1;k<=n;k++) { c=0.0; for(i=k;i<=n;i++) if(fabs(a[i-1][k-1])>fabs(c)) { c=a[i-1][k-1]; l=i; }if(fabs(c)<=dt) return(0); if(l!=k) { for(j=k;j<=n;j++) { t=a[k-1][j-1]; a[k-1][j-1]=a[l-1][j-1]; a[l-1][j-1]=t; } t=b[k-1]; b[k-1]=b[l-1]; b[l-1]=t; } c=1/c; for(j=k+1;j<=n;j++) { a[k-1][j-1]=a[k-1][j-1]*c; for(i=k+1;i<=n;i++) a[i-1][j-1]-=a[i-1][k-1]*a[k-1][j-1]; } b[k-1]*=c; for(i=k+1;i<=n;i++)b[i-1]-=b[k-1]*a[i-1][k-1]; } for(i=n;i>=1;i--) for(j=i+1;j<=n;j++) b[i-1]-=b[j-1]*a[i-1][j-1]; cout.precision(12); for(i=0;i<n;i++)p[i]=b[i];}double** create(int a,int b)//动态生成数组{double **P=new double *[a];for(int i=0;i<b;i++)P[i]=new double[b];return P;}void zuixiaoerchengnihe(double x[],double y[],int n,double a[],int m){int i,j,k,l;double **A,*B;A=create(m,m);B=new double[m];for(i=0;i<m;i++)for(j=0;j<m;j++)A[i][j]=0.0;for(k=0;k<m;k++)for(l=0;l<m;l++)for(j=0;j<n;j++)A[k][l]+=f(k,x[j])*f(l,x[j]);//计算法方程组系数矩阵A[k][l]cout<<"法方程组的系数矩阵为:"<<endl;for(i=0;i<m;i++)for(j=0,k=1;j<m;j++,k++){cout<<A[i][j]<<'\t';if(k&&k%m==0)cout<<endl;} for(i=0;i<m;i++)B[i]=0.0;for(i=0;i<m;i++)for(j=0;j<n;j++)B[i]+=y[j]*f(i,x[j]);for(i=0;i<m;i++)cout<<"B["<<i<<"]="<<B[i]<<endl;//记录B[n]xianxingfangchengzu(A,m,B,a,1e-6);delete[]A;delete B;}double pingfangwucha(double x[],double y[],int n,double a[],int m)//计算最小二乘解的平方误差{double deta,q=0.0,r=0.0;int i,j;double *B;B=new double[m];for(i=0;i<m;i++)B[i]=0.0;for(i=0;i<m;i++)for(j=0;j<n;j++)B[i]+=y[j]*f(i,x[j]);for(i=0;i<n;i++)q+=y[i]*y[i];for(j=0;j<m;j++)r+=a[j]*B[j];deta=fabs(q-r);return deta;delete B;}void main(void){int i,n,m;double *x,*y,*a;char ch='y';do{system("cls");cout<<"请输入所给拟合数据点的个数n=";cin>>n;cout<<"请输入所要拟合多项式的项数m=";cin>>m;while(n<=m){ cout<<"你所输入的数据点无法确定拟合项数，请重新输入"<<endl; Sleep(1000); system("cls"); cout<<"请输入所给拟合数据点的个数n="; cin>>n; cout<<"请输入所要拟合多项式的项数m="; cin>>m; }x=new double[n]; //存放数据点xy=new double[n]; //存放数据点ya=new double[m]; //存放拟合多项式的系数cout<<"请输入所给定的"<<n<<"个数据x"<<endl;for(i=0;i<n;i++){cout<<"x["<<i+1<<"]=";cin>>x[i];}cout<<"请输入所给定的"<<n<<"个数据y"<<endl;for(i=0;i<n;i++){cout<<"y["<<i+1<<"]=";cin>>y[i];}zuixiaoerchengnihe(x,y,n,a,m+1); cout<<endl;cout<<"拟合多项式的系数为:"<<endl;for(i=0;i<=m;i++)cout<<"a["<<i<<"]="<<a[i]<<'\t';cout<<endl;cout<<"平方误差为："<<pingfangwucha(x,y,n,a,m+1)<<endl;delete x; delete y;cout<<"按y继续，按其他字符退出"<<endl;cin>>ch;}while(ch=='y'||ch=='Y');cout<<"~~~~~~~~~~~~~~~~~~~~~~~谢谢使用！~~~~~~~~~~~~~~~~~~~~~~~"<<endl;}
