Apache Commons Math3学习笔记（2） - 多项式曲线拟合(转)

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

用法示例代码：

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1. // ... 创建并初始化输入数据：  
2. double[] x = new double[...];  
3. double[] y = new double[...];  
4. 将原始的x-y数据序列合成带权重的观察点数据序列：  
5. WeightedObservedPoints points = new WeightedObservedPoints();  
6. // 将x-y数据元素调用points.add(x[i], y[i])加入到观察点序列中  
7. // ...  
8. PolynomialCurveFitter fitter = PolynomialCurveFitter.create(degree);   // degree 指定多项式阶数  
9. 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：

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

    /**
     * 计算指定对象的运行时间开销。
     *
     * @param curveFitting 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(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;    // 阶数

    public CalcCurveFitting() {
        int arrayLength = 200000;
        System.out.println(String.format("本算例用于计算多项式曲线拟合。正在初始化计算数据（%s点，%s阶......", 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("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;
    }

}

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