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("--------------------------------------------------------------------------");
   }

}