public static List <Double> Fitting(List <PointF> point_list, bool zeroPassage)
{
if ((point_list == null) || (point_list.Count == 0))
{
return(null);
}
List <PointF> _log_point_list = new List <PointF>();
foreach (PointF _point in point_list)
{
_log_point_list.Add(new PointF((float)Math.Log10(_point.X), (float)Math.Log10(_point.Y)));
}
CoeffMatrix _coeff_matrix = CreateCoeffMatrix(_log_point_list, 1, zeroPassage);
List <double> _coefficients = GaussianElimination(_coeff_matrix, zeroPassage);
return(_coefficients);
}
/// <summary> 建立超定方程组和法方程组</summary>
/// <param name="pList">数据点列表</param>
/// <param name="order">待拟合的多项式次数</param>
/// <param name="zeroPassage">是否过零点</param>
/// <returns>返回建立的方程组系数矩阵</returns>
protected static CoeffMatrix CreateCoeffMatrix(List <PointF> point_list, int order, bool zeroPassage)
{
if (point_list == null)
{
return(null);
}
if (order < 1)
{
return(null);
}
CoeffMatrix _coeff_matrix = new CoeffMatrix();
if (zeroPassage == false)
{
order += 1;
}
_coeff_matrix.AA = new double[point_list.Count, order];
_coeff_matrix.MM = new double[order, order];
_coeff_matrix.eq = new double[order];
//构建超定方程组系数矩阵
if (zeroPassage)
{
for (int i = 0; i < point_list.Count; i++)
{
_coeff_matrix.AA[i, 0] = point_list[i].X;
}
}
else
{
for (int i = 0; i < point_list.Count; i++)
{
_coeff_matrix.AA[i, 0] = 1.0;
}
}
for (int j = 1; j < order; j++)
{
for (int i = 0; i < point_list.Count; i++)
{
_coeff_matrix.AA[i, j] = _coeff_matrix.AA[i, j - 1] * point_list[i].X;
}
}
//构建法方程系数矩阵
double _sum;
for (int i = 0; i < order; i++)
{
//计算系数矩阵
for (int j = 0; j <= i; j++)
{
_sum = 0.0;
for (int l = 0; l < point_list.Count; l++)
{
_sum += (_coeff_matrix.AA[l, i] * _coeff_matrix.AA[l, j]);
}
_coeff_matrix.MM[i, j] = _sum;
_coeff_matrix.MM[j, i] = _sum;
}
//计算右端向量
_sum = 0.0;
for (int l = 0; l < point_list.Count; l++)
{
_sum += (_coeff_matrix.AA[l, i] * point_list[l].Y);
}
_coeff_matrix.eq[i] = _sum;
}
return(_coeff_matrix);
}
/// <summary>
/// 建立超定方程组和法方程组
/// </summary>
/// <param name="pList">数据点列表</param>
/// <param name="rank">待拟合的多项式次数</param>
/// <param name="isZero">是否过零点</param>
/// <param name="r2">线性拟合度</param>
/// <returns>返回拟合系数</returns>
public static List <Double> Fitting(List <PointF> point_list, int order, bool zeroPassage)
{
CoeffMatrix _coeff_matrix = CreateCoeffMatrix(point_list, order, zeroPassage);
return(GaussianElimination(_coeff_matrix, zeroPassage));
}
/// <summary>高斯消元法解线性方程组</summary>
/// <param name="A">线性方程组系数矩阵/法方程构造矩阵</param>
/// <param name="xx">解向量</param>
/// <param name="isZero">是否过零点</param>
/// <returns>是否有解</returns>
protected static List <double> GaussianElimination(CoeffMatrix coeff_matrix, bool zeroPassage)
{
if ((coeff_matrix == null) || (coeff_matrix.MM == null) || (coeff_matrix.eq == null))
{
return(null);
}
//系数矩阵维数
int lengthRow = coeff_matrix.MM.GetLength(0);
int lengthColumn = coeff_matrix.MM.GetLength(1);
int lengthSolution = coeff_matrix.eq.Length;
#region 矩阵打印，测试时使用
//高斯消元前打印矩阵
for (int i = 0; i < lengthRow; i++)
{
for (int j = 0; j < lengthColumn; j++)
{
Debug.Write(coeff_matrix.MM[i, j].ToString().PadLeft(10));
}
Debug.WriteLine("\n");
}
//打印解向量
for (int i = 0; i < lengthSolution; i++)
{
Debug.Write(coeff_matrix.eq[i].ToString().PadLeft(10));
}
Debug.WriteLine("\n");
#endregion
//是否超定方程
if (lengthRow < lengthColumn)
{
Debug.WriteLine("The linear equalitions are no solution!");
}
for (int k = 0; k < lengthRow; k++)
{
if (coeff_matrix.MM[k, k] == 0)
{
Debug.WriteLine("The linear equalitions are no solution!");
}
for (int i = k + 1; i < lengthRow; i++)
{
coeff_matrix.MM[i, k] = coeff_matrix.MM[i, k] / coeff_matrix.MM[k, k];
for (int j = k + 1; j < lengthColumn; j++)
{
coeff_matrix.MM[i, j] = coeff_matrix.MM[i, j] - coeff_matrix.MM[i, k] * coeff_matrix.MM[k, j];
}
coeff_matrix.eq[i] = coeff_matrix.eq[i] - coeff_matrix.MM[i, k] * coeff_matrix.eq[k];
}
}
coeff_matrix.eq[lengthSolution - 1] = coeff_matrix.eq[lengthSolution - 1] / coeff_matrix.MM[lengthRow - 1, lengthColumn - 1];
for (int i = lengthColumn - 2; i >= 0; i--)
{
for (int j = i + 1; j < lengthRow; j++)
{
coeff_matrix.eq[i] = coeff_matrix.eq[i] - coeff_matrix.MM[i, j] * coeff_matrix.eq[j];
}
coeff_matrix.eq[i] = coeff_matrix.eq[i] / coeff_matrix.MM[i, i];
}
List <double> _coeff_list = new List <double>();
if (zeroPassage)
{
_coeff_list.Add(0);
}
for (int i = 0; i < lengthColumn; i++)
{
_coeff_list.Add(coeff_matrix.eq[i]);
}
#region 矩阵打印，测试时使用
Debug.WriteLine("高斯消元后矩阵：");
for (int i = 0; i < lengthRow; i++)
{
for (int j = 0; j < lengthColumn; j++)
{
Debug.Write(coeff_matrix.MM[i, j].ToString().PadLeft(20));
}
Debug.WriteLine("\n");
}
//打印解向量
for (int i = 0; i < coeff_matrix.eq.Length; i++)
{
Debug.WriteLine(coeff_matrix.eq[i]);
}
#endregion
return(_coeff_list);
}
