利用最小二乘法拟合任意次函数曲线（C#）

///<summary>
    ///用最小二乘法拟合二元多次曲线
    ///</summary>
    ///<param name="arrX">已知点的x坐标集合</param>
    ///<param name="arrY">已知点的y坐标集合</param>
    ///<param name="length">已知点的个数</param>
    ///<param name="dimension">方程的最高次数</param>
   
    public static double[] MultiLine(double[] arrX, double[] arrY, int length, int dimension)//二元多次线性方程拟合曲线
    {
        int n = dimension + 1;                  //dimension次方程需要求 dimension+1个 系数
        double[,] Guass=new double[n,n+1];      //高斯矩阵 例如：y=a0+a1*x+a2*x*x
        for(int i=0;i<n;i++)
        {
            int j;
            for(j=0;j<n;j++)
            {
                Guass[i,j] = SumArr(arrX, j + i, length);
            }
            Guass[i,j] = SumArr(arrX,i,arrY,1,length);          
        }
       return ComputGauss(Guass,n);
    }
    public static double SumArr(double[] arr, int n, int length) //求数组的元素的n次方的和
    {
        double s = 0;
        for (int i = 0; i < length; i++)
        {
            if (arr[i] != 0 || n != 0)         
                s = s + Math.Pow(arr[i], n);
            else
                s = s + 1;
        }
        return s;
    }
    public static double SumArr(double[] arr1, int n1, double[] arr2, int n2, int length)
    {
        double s=0;
        for (int i = 0; i < length; i++)
        {
            if ((arr1[i] != 0 || n1 != 0) && (arr2[i] != 0 || n2 != 0))
                s = s + Math.Pow(arr1[i], n1) * Math.Pow(arr2[i], n2);
            else
                s = s + 1;
        }
        return s;
 
    }
    public static double[] ComputGauss(double[,] Guass,int n)
    {
        int i, j;
        int k,m;
        double temp;
        double max;
        double s;
        double[] x = new double[n];
        for (i = 0; i < n; i++)           x[i] = 0.0;//初始化
       
        for (j = 0; j < n; j++)
        {
            max = 0;         
            k = j;    
            for (i = j; i < n; i++)
            {
                if (Math.Abs(Guass[i, j]) > max)
                {
                    max = Guass[i, j];
                    k = i;
                }
            }

           
            if (k != j)
            {
                for (m = j; m < n + 1; m++)
                {
                    temp = Guass[j, m];
                    Guass[j, m] = Guass[k, m];
                    Guass[k, m] = temp;
                }
            }
            if (0 == max)
            {
                // "此线性方程为奇异线性方程" 
                return x;
            }
           
            for (i = j + 1; i < n; i++) 
            {
                s = Guass[i, j];
                for (m = j; m < n + 1; m++)
                {
                    Guass[i, m] = Guass[i, m] - Guass[j, m] * s / (Guass[j, j]);
                }
            }

        }//结束for (j=0;j<n;j++)
       
        for (i = n-1; i >= 0; i--)
        {           
            s = 0;
            for (j = i + 1; j < n; j++)
            {
                s = s + Guass[i,j] * x[j];
            }
            x[i] = (Guass[i,n] - s) / Guass[i,i];
        }
       return x;
    }//返回值是函数的系数
例如：y=a0+a1*x 返回值则为a0 a1
例如：y=a0+a1*x+a2*x*x 返回值则为a0 a1 a2