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///<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

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