高斯拟合算法
请问，如何用c++实现高斯拟合算法？
[解决办法]
#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x
y=new double[n]; //存放数据点y
a=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'
[解决办法]
ch=='Y');
cout<<"~~~~~~~~~~~~~~~~~~~~~~~谢谢使用！~~~~~~~~~~~~~~~~~~~~~~~"<<endl;
}
