c# 数学拟合公式类(非原创)
using System; using System.Collections.Generic; using System.Drawing; using System.Linq; using System.Text; namespace Oprations { public class cNIHE { #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 } }