Apache Commons Math3學習筆記（2） - 多項式曲線擬合(轉)

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

用法示例代碼：

 

// ... 創建並初始化輸入數據：
double[] x = new double[...];
double[] y = new double[...];
將原始的x-y數據序列合成帶權重的觀察點數據序列：
WeightedObservedPoints points = new WeightedObservedPoints();
// 將x-y數據元素調用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，結果保存於雙精度數組中，由常數項至最高次冪系數排列

 

首先要准備好待擬合的曲線數據x和y，這是兩個double數組，然后把這兩個數組合並到WeightedObservedPoints對象實例中，可以調用WeightedObservedPoints.add(x[i], y[i])將x和y序列中的數據逐個添加到觀察點序列對象中。隨后創建PolynomialCurveFitter對象，創建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。最后調用PolynomialCurveFitter的fit方法即可完成多項式曲線擬合，fit方法的參數通過WeightedObservedPoints.toList()獲得。擬合結果通過一個double數組返回，按元素順序依次是常數項、一次項、二次項、……。

完整的演示代碼如下：

package fitting;

import org.apache.commons.math3.fitting.PolynomialCurveFitter;
import org.apache.commons.math3.fitting.WeightedObservedPoints;

import java.util.ArrayList;
import java.util.List;

public class TimeCostCalculator {
    public static void main(String[] args) throws Exception {
        TimeCostCalculator tcc = new TimeCostCalculator();
        double timeCost = tcc.calcTimeCost(new CalcCurveFitting());
        System.out.println("--------------------------------------------------------------------------");
        System.out.println("time cost is: " + timeCost + "s");
        System.out.println("--------------------------------------------------------------------------");
    }

    /**
     * 計算指定對象的運行時間開銷。
     *
     * @param curveFitting 指定被測對象。
     * @return 返回sub.run的時間開銷，單位為s。
     * @throws Exception
     */
    public double calcTimeCost(CurveFitting curveFitting) throws Exception {
        List<Object> params = curveFitting.getParams();
        long startTime = System.nanoTime();
        Object result = curveFitting.run(params);
        long stopTime = System.nanoTime();
        curveFitting.printResult(result);
        System.out.println("start: " + startTime + " / stop: " + stopTime);
        return 1.0e-9 * (stopTime - startTime);
    }

}


interface CurveFitting {
    public List<Object> getParams();

    public Object run(List<Object> params) throws Exception;

    public void printResult(Object result);
}

class CalcCurveFitting implements CurveFitting {

    private WeightedObservedPoints points;

    private final int degree = 5;    // 階數

    public CalcCurveFitting() {
        int arrayLength = 200000;
        System.out.println(String.format("本算例用於計算多項式曲線擬合。正在初始化計算數據（%s點，%s階......", arrayLength, degree));
        double[] inputDataX = new double[arrayLength];
        //      inputDataX = new double[] {1, 2, 3, 4, 5, 6, 7};
        double[] inputDataY = new double[inputDataX.length];
        double[] factor = new double[degree + 1];    // N階多項式會有N+1個系數，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("init completely");
    }

    @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;
    }


}

http://blog.csdn.net/kingfox/article/details/44118319