///<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
