如何使用Java Math Commons CurveFitter？

如何使用Math Commons CurveFitter将函数拟合到一组数据？有人告诉我使用带有LevenbergMarquardtOptimizer和ParametricUnivariateFunction的CurveFitter,但我不知道在ParametricUnivariateFunction梯度和值方法中要写什么.另外,在写完之后,如何获得拟合的函数参数？我的功能：

public static double fnc(double t,double a,double b,double c){
  return a * Math.pow(t,b) * Math.exp(-c * t);
}

解决方法

这个API的文档记录非常少,但是在当前版本的Apache Common Math(3.3)中,有两个部分,假设你有一个带有多个参数的变量：拟合的函数(实现ParametricUnivariateFunction)和曲线拟合器(它扩展了AbstractCurveFitter).

适合的功能

>公共双值(双t,双…参数)

>你的等式.这是您放置fnc逻辑的地方.

> public double [] gradient(double t,double …参数)

>根据每个参数返回上述偏导数的数组.如果(像我一样)你的微积分生锈了,但是任何好的计算机代数系统都可以计算出这些值,This calculator可能会有所帮助.

曲线钳工

>受保护的LeastSquaresProblem getProblem(集合< WeightedObservedPoint>点)

>设置一堆样板垃圾,并返回最小二乘问题供装配工使用.

总而言之,这是您特定情况下的示例解决方案：

import java.util.*;
import org.apache.commons.math3.analysis.ParametricUnivariateFunction;
import org.apache.commons.math3.fitting.AbstractCurveFitter;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresBuilder;
import org.apache.commons.math3.fitting.leastsquares.LeastSquaresProblem;
import org.apache.commons.math3.fitting.WeightedObservedPoint;
import org.apache.commons.math3.linear.DiagonalMatrix;

class MyFunc implements ParametricUnivariateFunction {
    public double value(double t,double... parameters) {
        return parameters[0] * Math.pow(t,parameters[1]) * Math.exp(-parameters[2] * t);
    }

    // Jacobian matrix of the above. In this case,this is just an array of
    // partial derivatives of the above function,with one element for each parameter.
    public double[] gradient(double t,double... parameters) {
        final double a = parameters[0];
        final double b = parameters[1];
        final double c = parameters[2];

        return new double[] {
            Math.exp(-c*t) * Math.pow(t,b),a * Math.exp(-c*t) * Math.pow(t,b) * Math.log(t),a * (-Math.exp(-c*t)) * Math.pow(t,b+1)
        };
    }
}

public class MyFuncFitter extends AbstractCurveFitter {
    protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points) {
        final int len = points.size();
        final double[] target  = new double[len];
        final double[] weights = new double[len];
        final double[] initialGuess = { 1.0,1.0,1.0 };

        int i = 0;
        for(WeightedObservedPoint point : points) {
            target[i]  = point.getY();
            weights[i] = point.getWeight();
            i += 1;
        }

        final AbstractCurveFitter.TheoreticalValuesFunction model = new
            AbstractCurveFitter.TheoreticalValuesFunction(new MyFunc(),points);

        return new LeastSquaresBuilder().
            maxEvaluations(Integer.MAX_VALUE).
            maxIterations(Integer.MAX_VALUE).
            start(initialGuess).
            target(target).
            weight(new DiagonalMatrix(weights)).
            model(model.getModelFunction(),model.getModelFunctionJacobian()).
            build();
    }

    public static void main(String[] args) {
        MyFuncFitter fitter = new MyFuncFitter();
        ArrayList<WeightedObservedPoint> points = new ArrayList<WeightedObservedPoint>();

        // Add points here; for instance,WeightedObservedPoint point = new WeightedObservedPoint(1.0,1.0);
        points.add(point);

        final double coeffs[] = fitter.fit(points);
        System.out.println(Arrays.toString(coeffs));
    }
}

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