其中引用到了apache的common-math的jar包，主要用于矩阵运算，下载地址： http://commons.apache.org/proper/commons-math/userguide/fitting.html import org.apache.commons.math3.fitting.PolynomialCurveFitter; import org.apache.commons.math3.fitting.WeightedObservedPoints; import org.apache.commons.math3.linear.ArrayRealVector; import org.apache.commons.math3.linear.DecompositionSolver; import org.apache.commons.math3.linear.LUDecomposition; import org.apache.commons.math3.linear.MatrixUtils; import org.apache.commons.math3.linear.RealMatrix; import org.apache.commons.math3.linear.RealVector; public class MathUtil { /** * 一元线性拟合 * y = a + b*x * @param x * @param y * reuslt[0] = a * result[1] = b * result[2] 相关系数 * result[3] 决定系数 * result[4] 点数量(长度) * result[5] 自由度 */ public static double[] lineFitting(double x[], double y[]) { int size = x.length; double xmean = 0.0; double ymean = 0.0; double xNum = 0.0; double yNum = 0.0; double xyNum = 0; double xNum2 = 0; double yNum2 = 0; double rss = 0; double tss = 0; double result[] = new double[6]; for (int i = 0; i < size; i++) { xmean += x[i]; ymean += y[i]; xNum2 += x[i] * x[i]; yNum2 += y[i] * y[i]; xyNum += x[i] * y[i]; } xNum = xmean; yNum = ymean; xmean /= size; ymean /= size; double sumx2 = 0.0f; double sumxy = 0.0f; for (int i = 0; i < size; i++) { sumx2 += (x[i] - xmean) * (x[i] - xmean); sumxy += (y[i] - ymean) * (x[i] - xmean); } double b = sumxy / sumx2; double a = ymean - b * xmean; result[0] = a; result[1] = b; System.out.println("a = " + a + ", b=" + b); double correlation = (xyNum - xNum * yNum / size) / Math.sqrt((xNum2 - xNum * xNum / size) * (yNum2 - yNum * yNum / size)); System.out.println("相关系数：" + correlation); result[2] = correlation; for (int i = 0; i < size; i++) { rss += (y[i] - (a + b * x[i])) * (y[i] - (a + b * x[i])); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - 1 - 1)) / (tss/ (size - 1)); result[3] = r2; System.out.println("决定系数" + r2); result[4] = x.length; result[5] = x.length - 1 - 1; return result; } /** * 多元线性拟合 * y = a + b*x1 + c*x2 * @param x * @param y * result[0] = a * result[b] = b * . * . * . * result[len - 4] 点数 * result[len - 3] 自由度 * result[len - 2] 残差平方和 * result[len - 1] 确定系数 */ public static double[] lineFitting2(double x[][], double y[]) { double[] a = new double[x.length + 1]; double[] v = new double[2]; // 这里的2为m double[] dt = new double[4]; line2sqt(x, y, 2, 11, a, dt, v); int i; System.out.println("残差平方和：" + dt[0]); double temp = a[a.length - 1]; // 更换输出位置，把常数放到第一位 for(i = a.length - 1; i > 0; i--) { a[i] = a[i - 1]; } a[0] = temp; double[] result = new double[x.length + 5]; for (i = 0; i <= x.length; i++) { result[i] = a[i]; } result[x.length + 1] = y.length; result[x.length + 2] = y.length - x.length; result[x.length + 3] = dt[0]; result[x.length + 4] = getLine2R(x, y, a, x.length); System.out.println("校正确定系数：" + result[x.length + 4]); return result; } /** * 多项式拟合 * y = a + b*x1 + c*x1^2…… * result[0] = a * result[1] = b * . * . * . * result[n + 1] 点数 * result[n + 2] 自由度 * result[n + 3] 确定系数 * @param n 几级 * @return */ public static double[] dxsFitting(double x[], double y[], int n) { double result[] = new double[n + 4]; WeightedObservedPoints obs = new WeightedObservedPoints(); for(int i = 0; i < x.length; i++) { obs.add(x[i], y[i]); } // Instantiate a third-degree polynomial fitterm. final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(n); // Retrieve fitted parameters (coefficients of the polynomial function). final double[] coeff = fitter.fit(obs.toList()); for(int i = 0; i < coeff.length; i++) { result[i] = coeff[i]; } double s = getDxsR(x, y, coeff, 5); System.out.println("确定系数:" + s); result[n + 1] = x.length; result[n + 2] = x.length - n - 1; result[n + 3] = s; return result; } /** * 指数拟合 * y = b*exp(ax) * result[0] = a * result[1] = b * result[2] 数据点数 * result[3] 自由度 * result[4] 确定系数 * @param x * @param y * @return */ public static double[] expFitting(double x[], double y[]) { int size = x.length; double xmean = 0.0; double ymean = 0.0; double rss = 0; double tss = 0; double result[] = new double[5]; for (int i = 0; i < size; i++) { xmean += x[i]; y[i] = Math.log(y[i]); ymean += y[i]; } xmean /= size; ymean /= size; double sumx2 = 0.0f; double sumxy = 0.0f; for (int i = 0; i < size; i++) { sumx2 += (x[i] - xmean) * (x[i] - xmean); sumxy += (y[i] - ymean) * (x[i] - xmean); } double b = sumxy / sumx2; double a = ymean - b * xmean; for (int i = 0; i < size; i++) { rss += (y[i] - (a + b * x[i])) * (y[i] - (a + b * x[i])); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - 1 - 1)) / (tss/ (size - 1)); System.out.println("决定系数" + r2); a = Math.exp(a); System.out.println("a = " + a + ";b= " + b); result[0] = a; result[1] = b; result[2] = x.length; result[3] = x.length - 2; result[4] = r2; return result; } /** * 对数拟合 * y = ln(a * x + b) * result[0] = a * result[1] = b * result[2] 数据点数 * result[3] 自由度 * result[4] 确定系数 * @param x * @param y */ public static double[] logFitting(double x[], double y[]) { int size = x.length; double xmean = 0.0; double ymean = 0.0; double rss = 0; double tss = 0; double result[] = new double[5]; for (int i = 0; i < size; i++) { xmean += x[i]; y[i] = Math.exp(y[i]); ymean += y[i]; } xmean /= size; ymean /= size; double sumx2 = 0.0f; double sumxy = 0.0f; for (int i = 0; i < size; i++) { sumx2 += (x[i] - xmean) * (x[i] - xmean); sumxy += (y[i] - ymean) * (x[i] - xmean); } double b = sumxy / sumx2; double a = ymean - b * xmean; for (int i = 0; i < size; i++) { rss += (y[i] - (b + a * x[i])) * (y[i] - (b + a * x[i])); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - 1 - 1)) / (tss/ (size - 1)); System.out.println("决定系数" + r2); System.out.println("a = " + a + ";b= " + b); result[0] = a; result[1] = b; result[2] = x.length; result[3] = x.length - 2; result[4] = r2; return result; } /** * 参考网址：http://wenku.baidu.com/link?url=T-xy9CUR_hVlCpA5o6xjqWb-Z1o5jraGEg-OHEtDgFLEynf6HedV68wMwC5u7RTs7PN5kiYq3qjyiddMveDFywLiuXai11MisNrNvv4KjAW&qq-pf-to=pcqq.c2c * 峰拟合 * y = y(max) * exp[-(x - x(max))^2/S] * @param x * @param y * result[0] = x(max) * result[1] = y(max) * result[2] = S * result[3] 点数 * result[4] 自由度 * result[5] 确定系数 */ public static double[] peakFitting(double x[], double y[]) { int size = x.length; double maxX = 0; double maxY = 0; double minY = Integer.MAX_VALUE; double result[] = new double[6]; double[][] left = new double[x.length][3]; double[][] right = new double[x.length][1]; for (int i = 0; i < size; i++) { if(y[i] > maxY) { maxX = x[i]; maxY = y[i]; } if(y[i] < minY) { minY = y[i]; } for(int j = 0; j < 3; j++) { left[i][j] = getPeakValue(j, x[i]); } right[i][0] = Math.log(y[i]); } RealMatrix leftMatrix = MatrixUtils.createRealMatrix(left); RealMatrix rightMatrix = MatrixUtils.createRealMatrix(right); RealMatrix leftMatrix1 = leftMatrix.transpose(); RealMatrix m = leftMatrix1.multiply(leftMatrix); RealMatrix tMatrix = new LUDecomposition(m).getSolver().getInverse().multiply(leftMatrix1).multiply(rightMatrix); result[0] = maxX; result[1] = maxY; result[2] = - 1.0 / tMatrix.getEntry(2, 0); System.out.println(result[0] + " " + result[1] + " " + result[2]); double aaaa = getPearR(x, y, result, 2); System.out.println("确定系数:" + aaaa); result[3] = x.length; result[4] = x.length - 1 - 2; result[5] = aaaa; return result; } /** * 用户自定义拟合 * @param x * @param y * @param sf 算法 * <input type="checkbox" value="0" />常数 <input type="checkbox" value="1" />x <input type="checkbox" value="2" />x^2 <input type="checkbox" value="3" />x^3 <input type="checkbox" value="4" />exp(x) <input type="checkbox" value="5" />ln(x) <input type="checkbox" value="6" />sin(x) <input type="checkbox" value="7" />cos(x) * * result[0] = 第一项系数 * result[1] = 第二项系数 * . * . * . * result[n] = 第N项系数 * result[sf.length] 点数 * result[sf.length+1] 自由度 * result[sf.length+2] 确定系数 * @return */ public static double[] userDefineFitting(double x[], double y[], int sf[]) { double[][] left = new double[sf.length][sf.length]; double[] right = new double[sf.length]; double[] result = new double[sf.length + 3]; result[sf.length] = x.length; boolean containZero = false; for(int i = 0; i < sf.length; i++) { double yValue = 0; // 数值中包括0 if(sf[i] == 0) { containZero = true; } for(int j = 0; j < sf.length; j++) { double xValue = 0; // 计算X的的司格马 for(int k = 0; k < x.length; k++) { xValue += getUserDefineValue(sf[i], x[k]) * getUserDefineValue(sf[j], x[k]); } left[i][j] = xValue; } // 计算Y的的司格马 for(int k = 0; k < x.length; k++) { yValue += y[k] * getUserDefineValue(sf[i], x[k]); } right[i] = yValue; } // 计算自由度 result[sf.length + 1] = x.length - sf.length - 1; // 计算自由度 if(containZero) { result[sf.length + 1] = x.length - sf.length; } // 矩阵求解 RealMatrix leftMatrix = MatrixUtils.createRealMatrix(left); DecompositionSolver solver = new LUDecomposition(leftMatrix).getSolver(); RealVector constants = new ArrayRealVector(right, false); RealVector solution = solver.solve(constants); System.out.println(solution); // 获得系数值 for(int i = 0; i < solution.getDimension(); i++) { result[i] = solution.getEntry(i); } double rss = 0, tss = 0, ymean = 0; for (int i = 0; i < x.length; i++) { ymean += y[i]; } ymean /= x.length; for (int i = 0; i < x.length; i++) { rss += (y[i] - getUserDefineValueByX(sf, x[i], solution)) * (y[i] - getUserDefineValueByX(sf, x[i], solution)); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / result[sf.length + 1]) / (tss / (x.length - 1)); System.out.println("决定系数" + r2); result[sf.length + 2] = r2; return result; } /** * 用户自定义函数，传入X值获得Y值 * @param n * @param x * @param solution * @return */ private static double getUserDefineValueByX(int[] n, double x, RealVector solution) { double value = 0; for(int i = 0; i < n.length; i++) { value += getUserDefineValue(n[i], x) * solution.getEntry(i); } return value; } /** * 获得用户自定义的值， * <input type="checkbox" value="0" />常数 <input type="checkbox" value="1" />x <input type="checkbox" value="2" />x^2 <input type="checkbox" value="3" />x^3 <input type="checkbox" value="4" />exp(x) <input type="checkbox" value="5" />ln(x) <input type="checkbox" value="6" />sin(x) <input type="checkbox" value="7" />cos(x) * @param i * @param x * @return */ private static double getUserDefineValue(int i, double x) { // 常数 if(i == 0) { return 1; }else if(i == 1) { // x return x; }else if(i == 2) { // x^2 return x * x; }else if(i == 3) { // x^3 return x * x * x; }else if(i == 4) { //exp(x) return Math.pow(Math.E, x); }else if(i == 5) { // ln(x) return Math.log(x); }else if(i == 6) { // sin(x) return Math.sin(x); }else if(i == 7) { // cos(x) return Math.cos(x); } return 0; } /** * 获得决定系数 * @param coeff * @return */ private static double getPearR(double x[], double y[], double coeff[], int n) { int size = x.length; double ymean = 0.0; double rss = 0; double tss = 0; for (int i = 0; i < size; i++) { ymean += y[i]; } ymean /= size; for (int i = 0; i < size; i++) { rss += (y[i] - getPeakValueByX(x[i], coeff)) * (y[i] - getPeakValueByX(x[i], coeff)); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - n - 1)) / (tss / (size - 1)); return r2; } /** * 通过X获得Y的值 * y = y(max) * exp[-(x - x(max))^2/S] * @param x * @param y * result[0] = x(max) * result[1] = y(max) * result[2] = S * @return */ private static double getPeakValueByX(double x, double result[]) { double b = Math.exp(-Math.pow((x - result[0]), 2) / result[2]) * result[1]; return b; } private static double getPeakValue(int i, double x) { // 常数 if(i == 0) { return 1; }else if(i == 1) { return x; }else if(i == 2) { // x^2 return x * x; } return 0; } /** * 获得决定系数 * @param coeff * @return */ private static double getDxsR(double x[], double y[], double coeff[], int n) { int size = x.length; double ymean = 0.0; double rss = 0; double tss = 0; for (int i = 0; i < size; i++) { ymean += y[i]; } ymean /= size; for (int i = 0; i < size; i++) { rss += (y[i] - getDxsValueByX(x[i], coeff)) * (y[i] - getDxsValueByX(x[i], coeff)); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - n - 1)) / (tss / (size - 1)); return r2; } /** * 通过X获得Y的值 * @param x * @param coeff * @return */ private static double getDxsValueByX(double x, double coeff[]) { int size = coeff.length; double result = coeff[0]; for(int i = 1; i < size; i++) { result += coeff[i] * Math.pow(x, i); } return result; } /** * 多元线性回归分析 * * @param x[m][n] * 每一列存放m个自变量的观察值 * @param y[n] * 存放随即变量y的n个观察值 * @param m * 自变量的个数 * @param n * 观察数据的组数 * @param a * 返回回归系数a0,...,am * @param dt[4] * dt[0]偏差平方和q,dt[1] 平均标准偏差s dt[2]返回复相关系数r dt[3]返回回归平方和u * @param v[m] * 返回m个自变量的偏相关系数 */ private static void line2sqt(double[][] x, double[] y, int m, int n, double[] a, double[] dt, double[] v) { int i, j, k, mm; double q, e, u, p, yy, s, r, pp; double[] b = new double[(m + 1) * (m + 1)]; mm = m + 1; b[mm * mm - 1] = n; for (j = 0; j <= m - 1; j++) { p = 0.0; for (i = 0; i <= n - 1; i++) p = p + x[j][i]; b[m * mm + j] = p; b[j * mm + m] = p; } for (i = 0; i <= m - 1; i++) for (j = i; j <= m - 1; j++) { p = 0.0; for (k = 0; k <= n - 1; k++) p = p + x[i][k] * x[j][k]; b[j * mm + i] = p; b[i * mm + j] = p; } a[m] = 0.0; for (i = 0; i <= n - 1; i++) a[m] = a[m] + y[i]; for (i = 0; i <= m - 1; i++) { a[i] = 0.0; for (j = 0; j <= n - 1; j++) a[i] = a[i] + x[i][j] * y[j]; } chlk(b, mm, 1, a); yy = 0.0; for (i = 0; i <= n - 1; i++) yy = yy + y[i] / n; q = 0.0; e = 0.0; u = 0.0; for (i = 0; i <= n - 1; i++) { p = a[m]; for (j = 0; j <= m - 1; j++) p = p + a[j] * x[j][i]; q = q + (y[i] - p) * (y[i] - p); e = e + (y[i] - yy) * (y[i] - yy); u = u + (yy - p) * (yy - p); } s = Math.sqrt(q / n); r = Math.sqrt(1.0 - q / e); for (j = 0; j <= m - 1; j++) { p = 0.0; for (i = 0; i <= n - 1; i++) { pp = a[m]; for (k = 0; k <= m - 1; k++) if (k != j) pp = pp + a[k] * x[k][i]; p = p + (y[i] - pp) * (y[i] - pp); } v[j] = Math.sqrt(1.0 - q / p); } dt[0] = q; dt[1] = s; dt[2] = r; dt[3] = u; } private static int chlk(double[] a, int n, int m, double[] d) { int i, j, k, u, v; if ((a[0] + 1.0 == 1.0) || (a[0] < 0.0)) { System.out.println("fail "); return (-2); } a[0] = Math.sqrt(a[0]); for (j = 1; j <= n - 1; j++) a[j] = a[j] / a[0]; for (i = 1; i <= n - 1; i++) { u = i * n + i; for (j = 1; j <= i; j++) { v = (j - 1) * n + i; a[u] = a[u] - a[v] * a[v]; } if ((a[u] + 1.0 == 1.0) || (a[u] < 0.0)) { System.out.println("fail "); return (-2); } a[u] = Math.sqrt(a[u]); if (i != (n - 1)) { for (j = i + 1; j <= n - 1; j++) { v = i * n + j; for (k = 1; k <= i; k++) a[v] = a[v] - a[(k - 1) * n + i] * a[(k - 1) * n + j]; a[v] = a[v] / a[u]; } } } for (j = 0; j <= m - 1; j++) { d[j] = d[j] / a[0]; for (i = 1; i <= n - 1; i++) { u = i * n + i; v = i * m + j; for (k = 1; k <= i; k++) d[v] = d[v] - a[(k - 1) * n + i] * d[(k - 1) * m + j]; d[v] = d[v] / a[u]; } } for (j = 0; j <= m - 1; j++) { u = (n - 1) * m + j; d[u] = d[u] / a[n * n - 1]; for (k = n - 1; k >= 1; k--) { u = (k - 1) * m + j; for (i = k; i <= n - 1; i++) { v = (k - 1) * n + i; d[u] = d[u] - a[v] * d[i * m + j]; } v = (k - 1) * n + k - 1; d[u] = d[u] / a[v]; } } return (2); } /** * 获得相关系数 * @param coeff * @return */ private static double getLine2R(double x[][], double y[], double a[], int n) { int size = x[0].length; double ymean = 0.0; double rss = 0; double tss = 0; for (int i = 0; i < size; i++) { ymean += y[i]; } ymean /= size; for (int i = 0; i < size; i++) { rss += (y[i] - getLine2ValueByX(x, a, i)) * (y[i] - getLine2ValueByX(x, a, i)); tss += (y[i] - ymean) * (y[i] - ymean); } double r2 = 1 - (rss / (size - n - 1)) / (tss / (size - 1)); return r2; } /** * 通过X获得Y的值 * @param x * @return */ private static double getLine2ValueByX(double x[][], double a[], int n) { int size = a.length; double result = a[0]; for(int i = 1; i < size; i++) { result += x[i - 1][n] * a[i]; } return result; } }