最小二乘法拟合任意次曲线.docx
最小二乘法拟合任意次曲线最小二乘法拟合任意次曲线 说明： 代码较为简洁没有过多的说明，如有不明白之处可查阅相关最小二乘法计算步骤资料和求解线性方程组的资料。另外该方法只能实现二元N次拟合，多元方程不适用。 以下是最小二乘法类的实现： public class MatrixEquation private double, gaussMatrix; private int coe; public MatrixEquation public MatrixEquation(double arrX, double arrY, int n) coe = n; gaussMatrix= GetGauss(GetXPowSum(arrX, n), GetXPowYSum(arrX, arrY, n), n); public double, GetGaussMatrix return gaussMatrix; public double GetResult return ComputeGauss(gaussMatrix, coe); / <summary> / 计算获取x散点的幂次和数组 / </summary> / <param name="arrX">x散点序列</param> / <param name="n">函数拟合次数</param> / <returns></returns> protected double GetXPowSum(double arrX, int n) int m = arrX.Length;/X散点的个数 double xPow = new double2 * n + 1; /存储X散点的幂次值 for (int i = 0; i < xPow.Length; i+) if (i = 0) xPowi = m; else /计算x的i次方和 double max = 0; for (int j = 0; j < m; j+) if (arrXj = 0) max = max + 1; else max = max + Math.Pow(arrXj, i); xPowi =Math.Round( max,4); return xPow; / <summary> / 计算获取xy的幂次和序列 / </summary> / <param name="arrX">x散点序列</param> / <param name="arrY">y散点序列</param> / <param name="n">拟合曲线次数</param> / <returns></returns> protected double GetXPowYSum(double arrX, double arrY, int n) int m = arrX.Length;/X散点的个数 double xyPow = new doublen + 1; /仓储X散点的幂次值 for (int i = 0; i < xyPow.Length; i+) /计算xy的i次方和 double max = 0; for (int j = 0; j < m; j+) if (arrXj = 0) max = max + 1; else max = max + Math.Pow(arrXj, i) * arrYj; xyPowi =Math.Round( max,4); return xyPow; / <summary> / 获取高斯矩阵(增广矩阵) / </summary> / <param name="arrX">X的幂次和</param> / <param name="arrXY">XY的幂次和</param> / <param name="n">拟合曲线次数</param> / <returns></returns> protected double, GetGauss(double arrX, double arrXY, int n) double, gauss = new doublen+1, n + 2; for (int i = 0; i < n + 1; i+) int j; int m = i; for (j = 0; j < n + 1; j+) gaussi, j = arrXm; m+; gaussi,j = arrXYi; return gauss; / <summary> / 求解拟合曲线的系数 / </summary> / <param name="gauss">线性方程的增广矩阵</param> / <param name="n">方程次数</param> / <returns></returns> protected double ComputeGauss(double, gauss, int n) double a = new doublen + 1; double s; int matrixLine = n + 1; for (int i = 0; i < n + 1; i+) ai = 0; /循环每列 for (int j = 0; j < matrixLine; j+) /每列J行以后的绝对值最大值 double max = 0; int k = j; for (int i = j; i < matrixLine; i+) if (Math.Abs(gaussi, j) > max) max = gaussi, j; k = i; /判断j行否为最大值行 若不是将j行调换为最大值行 if (k != j) double temp; for (int m = j; m < matrixLine+1; m+) temp = gaussj, m; gaussj, m = gaussk, m; gaussk, m = temp; if (max = 0) /奇异矩阵无解 return a; /进行初等行变换 得到上三角矩阵 for (int i = j + 1; i < matrixLine; i+) s = gaussi, j; for (int m = j; m < matrixLine + 1; m+) gaussi, m =Math.Round( gaussi, m - gaussj, m * s / gaussj, j,6); /根据倒推方式一次计算现行方程的解 for (int i = matrixLine - 1; i >= 0; i-) s = 0; for (int j = i + 1; j < matrixLine; j+) s += gaussi, j * aj; ai =Math.Round( (gaussi, matrixLine - s) / gaussi, i,6); /返回方程的解 即拟合曲线的系数 return a;
