多項式曲線擬合：org.apache.commons.math3.fitting.PolynomialCurveFitter類。

用法示例程式碼：

// ... 建立並初始化輸入資料：
double[] x = new double[...];
double[] y = new double[...];
將原始的x-y資料序列合成帶權重的觀察點資料序列：
WeightedObservedPoints points = new WeightedObservedPoints();
// 將x-y資料元素呼叫points.add(x[i], y[i])加入到觀察點序列中
// ...
PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);   // degree 指定多項式階數
double[] result = fitter.fit(points.toList());   // 曲線擬合，結果保存於雙精度陣列中，由常數項至最高次冪係數排列
 

首先要準備好待擬合的曲線資料x和y，這是兩個double陣列，然後把這兩個數組合併到WeightedObservedPoints物件例項中，可以呼叫WeightedObservedPoints.add(x[i], y[i])將x和y序列中的資料逐個新增到觀察點序列物件中。隨後建立PolynomialCurveFitter物件，建立時要指定擬合多項式的階數，注意階數要選擇適當，不是越高越好，否則擬合誤差會很大。最後呼叫PolynomialCurveFitter的fit方法即可完成多項式曲線擬合，fit方法的引數通過WeightedObservedPoints.toList()獲得。擬合結果通過一個double陣列返回，按元素順序依次是常數項、一次項、二次項、……。

完整的演示程式碼如下：

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("本算例用於計算多項式曲線擬合。正在初始化 計算資料(" + arrayLength + "點, " + degree + "階)... ...");
      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階多項式會有N+1個係數，其中之一為常數項
      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;    // 階數

}

public class TimeCostCalculator
{
   public TimeCostCalculator()
   {
   }

   /**
    * 計算指定物件的執行時間開銷。
    * 
    * @param testCase 指定被測物件。
    * @return 返回sub.run的時間開銷，單位為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("--------------------------------------------------------------------------");
   }

}