转载于:https://blog.csdn.net/c914620529/article/details/50393238
高斯拟合(Gaussian Fitting)即使用形如:
的高斯函数对数据点集进行函数逼近的拟合方法。
其实可以跟多项式拟合类比起来,不同的是多项式拟合是用幂函数系,
而高斯拟合是用高斯函数系。
使用高斯函数来进行拟合,优点在于计算积分十分简单快捷。这一点
在很多领域都有应用,特别是计算化学。著名的化学软件Gaussian98
就是建立在高斯基函数拟合的数学基础上的。
- double[,] a = new double[fitDatas.Count, 3];
- double[] b = new double[fitDatas.Count];
- double[] X = new double[3] { 0, 0, 0 };
- for (int i = 0; i < fitDatas.Count; i++)
- {
- b[i] = Math.Log(fitDatas[i].Intensity);
- a[i, 0] = 1;
- a[i, 1] = fitDatas[i].WaveLength;
- a[i, 2] = a[i, 1] * a[i, 1];
- }
- // Matrix.Equation(datas.Count, 3, a, b, X);
- MathNet.Numerics.LinearAlgebra.Matrix matrixA = new MathNet.Numerics.LinearAlgebra.Matrix(a);
- MathNet.Numerics.LinearAlgebra.Matrix matrixB = new MathNet.Numerics.LinearAlgebra.Matrix(b, b.Length);
- MathNet.Numerics.LinearAlgebra.Matrix matrixC = matrixA.Solve(matrixB);
- X = matrixC.GetColumnVector(0);
- double S = -1 / X[2];
- double xMax = X[1] * S / 2.0;
- double yMax = Math.Exp(X[0] + xMax * xMax / S);
运用c++实现方案
- #include<iostream.h>
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- #include<math.h>
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- #include<stdlib.h>
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- #include <windows.h>
-
- double f(int n,double x){ //f(n,x)用来返回x的n次方
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- double y=1.0;
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- 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;
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- 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);
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- 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];
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- 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;
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- 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]
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- cout<<"法方程组的系数矩阵为:"<<endl;
-
- for(i=0;i<m;i++)
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- for(j=0,k=1;j<m;j++,k++){
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- cout<<A[i][j]<<'\t';
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- if(k&&k%m==0)cout<<endl;
-
- }
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- for(i=0;i<m;i++)B[i]=0.0;
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- for(i=0;i<m;i++)
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- for(j=0;j<n;j++)B[i]+=y[j]*f(i,x[j]);
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- for(i=0;i<m;i++)cout<<"B["<<i<<"]="<<B[i]<<endl;//记录B[n]
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- xianxingfangchengzu(A,m,B,a,1e-6);
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- 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;
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- double *x,*y,*a;
-
- char ch='y';
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- do{
-
- system("cls");
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- cout<<"请输入所给拟合数据点的个数n=";
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- cin>>n;
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- cout<<"请输入所要拟合多项式的项数m=";
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- cin>>m;
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- 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);
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- system("cls");
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- cout<<"请输入所给拟合数据点的个数n=";
-
- cin>>n;
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- 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
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- y=new double[n]; //存放数据点y
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- a=new double[m]; //存放拟合多项式的系数
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- 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;
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- cout<<"拟合多项式的系数为:"<<endl;
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- for(i=0;i<=m;i++)cout<<"a["<<i<<"]="<<a[i]<<'\t';
-
- cout<<endl;
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- 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');
文章来源: https://blog.csdn.net/Du_Shuang/article/details/91399864