利用最小二乘法拟合任意次函数曲线（C#）

原文: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

剩下的就不用写了吧