C#求多元回归方程系数，java求多元回归方程系数，有详细注释

Class GA{ /// <summary> /// 求自变量x与因变量y的回归方程系数 /// </summary> /// <param name="x"></param> /// <param name="y"></param> /// <param name="n">自变量个数</param> /// <param name="m">自变量数据组数个数</param> /// <param name="b">返回b1，b2，b3...bn即：回归系数</param> /// <param name="b0">方程组中b0的值</param> public string DYHGFC(float[,] x, float[] y, int n, int m, ref float[] b, ref float b0) { //实现公式Y=B0+B1*X1+B2*X2+B3*X3+...+Bn*Xn //设有n个自变量，m组数据 //L12=L21=自变量X11*自变量X21+自变量X12*自变量X22+自变量X13*自变量X23+...+自变量X1m*自变量X2m //-(自变量X11+自变量X12+自变量X13+...+自变量X1m)*(自变量X21+自变量X22+自变量X23+...+自变量X2m)/x.length //B0=Yavg-(B1*X1avg+B2*X2avg+B3*X3avg+...+Bn*Xnavg) float[,] xx = new float[n + 1, n + 1];//建立一个离差矩阵 for (int i = 0; i <= n; i++) { float v1 = 0;//设v1的结果为：自变量X11*自变量X21+自变量X12*自变量X22+自变量X13*自变量X23+...+自变量X1m*自变量X2m float v2 = 0;//设v2的结果为：(自变量X11+自变量X12+自变量X13+...+自变量X1m) float v3 = 0;//设v3的结果为：(自变量X21+自变量X22+自变量X23+...+自变量X2m) for (int j = 0; j <= n; j++) { for (int k = 0; k < m; k++) { v1 += x[i, k] * x[j, k]; v2 += x[i, k]; v3 += x[j, k]; } //Console.WriteLine(v1 - v2 * v3 / m); xx[i, j] = v1 - v2 * v3 / m; v1 = v2 = v3 = 0; } } //解方程组，求各个变量x的系数 b = Gause(xx, n); float[] xAvg = new float[n]; float yAvg = 0; for (int i = 0; i < n; i++) { float avg = 0; for (int j = 0; j < m; j++) { avg += x[i, j]; } xAvg[i] = avg / m; } yAvg = y.Average(); float t = 0;//定义一个临时变量保存：B1*X1avg+B2*X2avg+B3*X3avg+...+Bn*Xnavg 的值 for (int i = 0; i < n; i++) { t += b[i] * xAvg[i]; } b0 = yAvg - (t); string fc = b0.ToString("0.0000"); for (int i = 0; i < n; i++) { string fh = " + "; fh = Math.Round(b[i], 4) < 0 ? "" : " + "; fc += fh + Math.Round(b[i], 4) + " * X" + (i + 1).ToString(); } return fc; } /// <summary> /// 高斯消元求解方程组的解 /// </summary> /// <param name="a"></param> /// <param name="n"></param> /// <returns></returns> static float[] Gause(float[,] a, int n) { int i, j, k; int rank, columm; float temp, l, s; float[] x = new float[n]; for (i = 0; i <= n - 2; i++) { rank = i; columm = i; for (j = i + 1; j <= n - 1; j++) //选主元 if (a[j, i] > a[i, i]) { rank = j; columm = i; } for (k = 0; k <= n; k++) //主元行变换 { temp = a[i, k]; a[i, k] = a[rank, k]; a[rank, k] = temp; } for (j = i + 1; j <= n - 1; j++) //解线性方程 { l = a[j, i] / a[i, i]; for (k = i; k <= n; k++) a[j, k] = a[j, k] - l * a[i, k]; } } x[n - 1] = a[n - 1, n] / a[n - 1, n - 1]; //回代方程求解x for (i = n - 2; i >= 0; i--) { s = 0; for (j = i + 1; j <= n - 1; j++) s = s + a[i, j] * x[j]; x[i] = (a[i, n] - s) / a[i, i]; } return x; } }