C# ——计算线性关系kb值、R平方，类似于excel的趋势线线性关系功能
这些功能Excel上都有，原理一模一样，现在需要C#的实现代码；
各函数的线性拟合，相关系数、截距为0（即强制过原点）等等
源码：https://download.csdn.net/download/a1062484747/15769519
相关系数R²的公式引用：http://blog.csdn.net/huwei2003/article/details/18553775（验证过）
1.一次线性、二次曲线、指数、对数、幂等函数拟合及相关系数R²的代码实现（指数函数拟合的相关系数R²和Excel有出入）；
2.一次线性的截距为0（即强制过原点）的代码实现；
3.代码三次乃至多项以上的函数拟合有问题，不会改，望有大神补充修改一下；
4.有没有大神补充一下二次曲线、指数这2个函数拟合时截距为0（即强制过原点）的拟合代码或者数学公式。
代码实现在Excel验证过！
代码如下：
C#
using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace 高斯消元法 { class Program { static void Main(string[] args) { /* double[,] xArray = new double[,] { { 2.000000 ,-1.000000 , 3.000000, 1.000000}, { 4.000000 , 2.000000 , 5.000000, 4.000000}, { 1.000000 , 2.000000 , 0.000000 , 7.000000} };*/ System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch(); double[] y = new double[] { 29152.3, 47025.3, 86852.3, 132450.6, 200302.3, 284688.1, 396988.3 }; double[] x = new double[] { 1.24, 2.37, 5.12, 8.12, 12.19, 17.97, 24.99 }; // double[,] xArray; double[] ratio; double[] yy = new double[y.Length]; Console.WriteLine("一次拟合："); sw.Start(); ratio = FittingFunct.Linear(y, x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[0] + ratio[1] * x[i]; } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy) + "\r\n"); //Console.WriteLine("一次拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.WriteLine("一次拟合(截距为0，即强制过原点)："); sw.Start(); ratio = FittingFunct.LinearInterceptZero(y, x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[0] * x[i]; } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy) + "\r\n"); //Console.WriteLine("一次拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.WriteLine("二次拟合："); sw.Start(); ratio = FittingFunct.TowTimesCurve(y, x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[0] + ratio[1] * x[i] + ratio[2] * x[i] * x[i]; } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy) + "\r\n"); //Console.WriteLine("二次拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.WriteLine("对数拟合计算时间："); sw.Start(); ratio = FittingFunct.LOGEST(y, x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[1]*Math.Log10(x[i]) + ratio[0]; } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy) + "\r\n"); //Console.WriteLine("对数拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.WriteLine("幂级数拟合："); sw.Start(); ratio=FittingFunct.PowEST(y,x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[0] * Math.Pow(x[i], ratio[1]); } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy) + "\r\n"); //Console.WriteLine("幂级数拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.WriteLine("指数函数拟合："); sw.Start(); ratio = FittingFunct.IndexEST(y, x); sw.Stop(); foreach (double num in ratio) { Console.WriteLine(num); } for (int i = 0; i < x.Length; i++) { yy[i] = ratio[0] * Math.Exp(x[i] * ratio[1]); } Console.WriteLine("R²=: " + FittingFunct.Pearson(y, yy)); //Console.WriteLine("指数函数拟合计算时间："); //Console.WriteLine(sw.ElapsedMilliseconds); Console.ReadKey(); } } }
C#
using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace 高斯消元法 { class FittingFunct { #region 多项式拟合函数,输出系数是y=a0+a1*x+a2*x*x+.........，按a0,a1,a2输出 static public double[] Polyfit(double[] y, double[] x, int order) { double[,] guass = Get_Array(y, x, order); double[] ratio = Cal_Guass(guass, order + 1); return ratio; } #endregion #region 一次拟合函数，y=a0+a1*x,输出次序是a0,a1 static public double[] Linear(double[] y,double[] x) { double[] ratio = Polyfit(y, x, 1); return ratio; } #endregion #region 一次拟合函数，截距为0，y=a0x,输出次序是a0 static public double[] LinearInterceptZero(double[] y, double[] x) { double divisor = 0; //除数 double dividend = 0; //被除数 for (int i = 0; i < x.Length;i++ ) { divisor += x[i] * x[i]; dividend += x[i] * y[i]; } if (divisor == 0) { throw (new Exception("除数不为0！")); return null; } return new double[] { dividend / divisor }; } #endregion #region 二次拟合函数，y=a0+a1*x+a2x²,输出次序是a0,a1,a2 static public double[] TowTimesCurve(double[] y, double[] x) { double[] ratio = Polyfit(y, x, 2); return ratio; } #endregion #region 对数拟合函数,.y= c*(ln x)+b,输出为b,c static public double[] LOGEST(double[] y, double[] x) { double[] lnX = new double[x.Length]; for (int i = 0; i < x.Length; i++) { if (x[i] == 0 || x[i] < 0) { throw (new Exception("正对非正数取对数！")); return null; } lnX[i] = Math.Log(x[i]); } return Linear(y, lnX); } #endregion #region 幂函数拟合模型, y=c*x^b,输出为c,b static public double[] PowEST(double[] y, double[] x) { double[] lnX = new double[x.Length]; double[] lnY = new double[y.Length]; double[] dlinestRet; for (int i = 0; i < x.Length; i++) { lnX[i] = Math.Log(x[i]); lnY[i] = Math.Log(y[i]); } dlinestRet = Linear(lnY, lnX); dlinestRet[0] = Math.Exp(dlinestRet[0]); return dlinestRet; } #endregion #region 指数函数拟合函数模型，公式为 y=c*m^x;输出为 c,m static public double[] IndexEST(double[] y, double[] x) { double[] lnY = new double[y.Length]; double[] ratio; for (int i = 0; i < y.Length; i++) { lnY[i] = Math.Log(y[i]); } ratio = Linear(lnY, x); for (int i = 0; i < ratio.Length; i++) { if (i == 0) { ratio[i] = Math.Exp(ratio[i]); } } return ratio; } #endregion #region 相关系数R²部分 public static double Pearson(IEnumerable<double> dataA, IEnumerable<double> dataB) { int n = 0; double r = 0.0; double meanA = 0; double meanB = 0; double varA = 0; double varB = 0; int ii = 0; using (IEnumerator<double> ieA = dataA.GetEnumerator()) using (IEnumerator<double> ieB = dataB.GetEnumerator()) { while (ieA.MoveNext()) { if (!ieB.MoveNext()) { //throw new ArgumentOutOfRangeException("dataB", Resources.ArgumentArraysSameLength); } ii++; //Console.WriteLine("FF00:: " + ii + " -- " + meanA + " -- " + meanB + " -- " + varA + " --- " + varB); double currentA = ieA.Current; double currentB = ieB.Current; double deltaA = currentA - meanA; double scaleDeltaA = deltaA / ++n; double deltaB = currentB - meanB; double scaleDeltaB = deltaB / n; meanA += scaleDeltaA; meanB += scaleDeltaB; varA += scaleDeltaA * deltaA * (n - 1); varB += scaleDeltaB * deltaB * (n - 1); r += (deltaA * deltaB * (n - 1)) / n; //Console.WriteLine("FF00:: " + ii + " -- " + meanA + " -- " + meanB + " -- " + varA + " --- " + varB); } if (ieB.MoveNext()) { //throw new ArgumentOutOfRangeException("dataA", Resources.ArgumentArraysSameLength); } } return (r / Math.Sqrt(varA * varB)) * (r / Math.Sqrt(varA * varB)); } #endregion #region 最小二乘法部分 #region 计算增广矩阵 static private double[] Cal_Guass(double[,] guass,int count) { double temp; double[] x_value; for (int j = 0; j < count; j++) { int k = j; double min = guass[j,j]; for (int i = j; i < count; i++) { if (Math.Abs(guass[i, j]) < min) { min = guass[i, j]; k = i; } } if (k != j) { for (int x = j; x <= count; x++) { temp = guass[k, x]; guass[k, x] = guass[j, x]; guass[j, x] = temp; } } for (int m = j + 1; m < count; m++) { double div = guass[m, j] / guass[j, j]; for (int n = j; n <= count; n++) { guass[m, n] = guass[m, n] - guass[j, n] * div; } } /* System.Console.WriteLine("初等行变换："); for (int i = 0; i < count; i++) { for (int m = 0; m < count + 1; m++) { System.Console.Write("{0,10:F6}", guass[i, m]); } Console.WriteLine(); }*/ } x_value= Get_Value(guass, count); return x_value; /*if (x_value == null) Console.WriteLine("方程组无解或多解！"); else { foreach (double x in x_value) { Console.WriteLine("{0:F6}", x); } }*/ } #endregion #region 回带计算X值 static private double[] Get_Value(double[,] guass,int count) { double[] x = new double[count]; double[,] X_Array = new double[count, count]; int rank = guass.Rank;//秩是从0开始的 for (int i = 0; i < count; i++) for (int j = 0; j < count; j++) X_Array[i, j] = guass[i, j]; if (X_Array.Rank < guass.Rank)//表示无解 { return null; } if (X_Array.Rank < count-1)//表示有多解 { return null; } //回带计算x值 x[count - 1] = guass[count - 1, count] / guass[count-1, count-1]; for (int i = count - 2; i >= 0; i--) { double temp=0; for (int j = i; j < count; j++) { temp += x[j] * guass[i, j]; } x[i] = (guass[i, count] - temp) / guass[i, i]; } return x; } #endregion #region 得到数据的法矩阵,输出为发矩阵的增广矩阵 static private double[,] Get_Array(double[] y, double[] x, int n) { double[,] result = new double[n + 1, n + 2]; if (y.Length != x.Length) { throw (new Exception("两个输入数组长度不一！")); //return null; } for (int i = 0; i <= n; i++) { for (int j = 0; j <= n; j++) { result[i, j] = Cal_sum(x, i + j); } result[i, n + 1] = Cal_multi(y, x, i); } return result; } #endregion #region 累加的计算 static private double Cal_sum(double[] input,int order) { double result=0; int length = input.Length; for (int i = 0; i < length; i++) { result += Math.Pow(input[i], order); } return result; } #endregion #region 计算∑(x^j)*y static private double Cal_multi(double[] y,double[] x,int order) { double result = 0; int length = x.Length; for (int i = 0; i < length; i++) { result += Math.Pow(x[i], order) * y[i]; } return result; } #endregion #endregion } }
转http://www.skcircle.com/?id=362
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