高斯擬合(Gaussian Fitting)即使用形如：
    
          Gi(x)=Ai*exp((x-Bi)^2/Ci^2)

        的高斯函式對資料點集進行函式逼近的擬合方法。其實可以跟多項式擬合類比起來，不同的是多項式擬合是用冪函式系，而高斯擬合是用高斯函式系。使用高斯函式來進行擬合，優點在於計算積分十分簡單快捷。這一點在很多領域都有應用，特別是計算化學。著名的化學軟體Gaussian98
        就是建立在高斯基函式擬合的數學基礎上的。

c#中用mathnet 驚醒矩陣運算  實現方案

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);
 

運用c++實現方案

#include<iostream.h>

#include<math.h>

#include<stdlib.h>

#include <windows.h>

double f(int n,double x){             //f(n,x)用來返回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)//用高斯列主元法來求解法方程組

 {

   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)//動態生成陣列

{

        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]);//計演算法方程組係數矩陣A[k][l]

        cout<<"法方程組的係數矩陣為:"<<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;//記錄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)//計算最小二乘解的平方誤差

{

        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<<"請輸入所給擬合數據點的個數n=";

        cin>>n;

        cout<<"請輸入所要擬合多項式的項數m=";

        cin>>m;

        while(n<=m){

           cout<<"你所輸入的資料點無法確定擬合項數，請重新輸入"<<endl;

           Sleep(1000);

           system("cls");

           cout<<"請輸入所給擬合數據點的個數n=";

           cin>>n;

           cout<<"請輸入所要擬合多項式的項數m=";

           cin>>m;

           }

        x=new double[n];                             //存放資料點x

        y=new double[n];                             //存放資料點y

        a=new double[m];                             //存放擬合多項式的係數

        cout<<"請輸入所給定的"<<n<<"個數據x"<<endl;

        for(i=0;i<n;i++)

        {

               cout<<"x["<<i+1<<"]=";

               cin>>x[i];

        }

        cout<<"請輸入所給定的"<<n<<"個數據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<<"擬合多項式的係數為:"<<endl;

        for(i=0;i<=m;i++)cout<<"a["<<i<<"]="<<a[i]<<'\t';

        cout<<endl;

        cout<<"平方誤差為："<<pingfangwucha(x,y,n,a,m+1)<<endl;

        delete x;   delete y;

        cout<<"按y繼續，按其他字元退出"<<endl;

        cin>>ch;

    }while(ch=='y'||ch=='Y');