Apache Commons Math3学习笔记（2） - 多项式曲线拟合

多项式曲线拟合：org.apache.commons.math3.fitting.PolynomialCurveFitter类。

用法示例代码：

// ... 创建并初始化输入数据：double[] x = new double[...];double[] y = new double[...];将原始的x-y数据序列合成带权重的观察点数据序列：WeightedObservedPoints points = new WeightedObservedPoints();// 将x-y数据元素调用points.add(x[i], y[i])加入到观察点序列中// ...PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);   // degree 指定多项式阶数double[] result = fitter.fit(points.toList());   // 曲线拟合，结果保存于双精度数组中，由常数项至最高次幂系数排列

首先要准备好待拟合的曲线数据x和y，这是两个double数组，然后把这两个数组合并到WeightedObservedPoints对象实例中，可以调用WeightedObservedPoints.add(x[i], y[i])将x和y序列中的数据逐个添加到观察点序列对象中。随后创建PolynomialCurveFitter对象，创建时要指定拟合多项式的阶数，注意阶数要选择适当，不是越高越好，否则拟合误差会很大。最后调用PolynomialCurveFitter的fit方法即可完成多项式曲线拟合，fit方法的参数通过WeightedObservedPoints.toList()获得。拟合结果通过一个double数组返回，按元素顺序依次是常数项、一次项、二次项、……。

完整的演示代码如下：

interface TestCase{   public Object run(List<Object> params) throws Exception;   public List<Object> getParams();   public void printResult(Object result);}class CalcCurveFitting implements TestCase{   public CalcCurveFitting()   {      System.out.print("本算例用于计算多项式曲线拟合。正在初始化 计算数据(" + arrayLength + "点, " + degree + "阶)... ...");      inputDataX = new double[arrayLength];      //      inputDataX = new double[] {1, 2, 3, 4, 5, 6, 7};      inputDataY = new double[inputDataX.length];      double[] factor = new double[degree + 1];    // N阶多项式会有N+1个系数，其中之一为常数项      for(int index = 0; index < factor.length; index ++)      {         factor[index] = index + 1;      }      for(int index = 0; index < inputDataY.length; index ++)      {         inputDataX[index] = index * 0.00001;         inputDataY[index] = calcPoly(inputDataX[index], factor);    // y = sum(x[n) * fact[n])         // System.out.print(inputDataY[index] + ", ");      }      points = new WeightedObservedPoints();      for(int index = 0; index < inputDataX.length; index ++)      {         points.add(inputDataX[index], inputDataY[index]);      }      System.out.println("初始化完成");   }   @Override   public List<Object> getParams()   {      List<Object> params = new ArrayList<Object>();      params.add(points);      return params;   }   @Override   public Object run(List<Object> params) throws Exception   {      PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);      WeightedObservedPoints points = (WeightedObservedPoints)params.get(0);      double[] result = fitter.fit(points.toList());      return result;   }   @Override   public void printResult(Object result)   {      for(double data : (double[])result)      {         System.out.println(data);      }   }   private double calcPoly(double x, double[] factor)   {      double y = 0;      for(int deg = 0; deg < factor.length; deg ++)      {         y += Math.pow(x, deg) * factor[deg];      }      return y;   }   private double[] inputDataX = null;   private double[] inputDataY = null;   private WeightedObservedPoints points = null;   private final int arrayLength = 200000;   private final int degree = 5;    // 阶数}public class TimeCostCalculator{   public TimeCostCalculator()   {   }   /**    * 计算指定对象的运行时间开销。    *     * @param testCase 指定被测对象。    * @return 返回sub.run的时间开销，单位为s。    * @throws Exception    */   public double calcTimeCost(TestCase testCase) throws Exception   {      List<Object> params = testCase.getParams();      long startTime = System.nanoTime();      Object result = testCase.run(params);      long stopTime = System.nanoTime();      testCase.printResult(result);      System.out.println("start: " + startTime + " / stop: " + stopTime);      double timeCost = (stopTime - startTime) * 1.0e-9;      return timeCost;   }   public static void main(String[] args) throws Exception   {      TimeCostCalculator tcc = new TimeCostCalculator();      double timeCost;      System.out.println("--------------------------------------------------------------------------");      timeCost = tcc.calcTimeCost(new CalcCurveFitting());      System.out.println("time cost is: " + timeCost + "s");      System.out.println("--------------------------------------------------------------------------");   }}