如何使用Java Math Commons CurveFitter？

Question

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);
}

Answer 1

所以,这是一个老问题,但我最近遇到了同样的问题,最终不得不深入研究邮件列表和Apache Commons Math源代码来解决这个问题.

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:要适应的函数(实现ParametricUnivariateFunction)和曲线拟合器(扩展了AbstractCurveFitter).

适合的功能

• public double value(double t, double... parameters)
  • 你的等式.这是您放置fnc逻辑的地方.
• public double[] gradient(double t, double... parameters)
  • 返回上面关于每个参数的偏导数的数组. 如果(像我一样)你的微积分生锈了,这个计算器可能会有所帮助,但任何好的计算机代数系统都可以计算这些值.

曲线钳工

• protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points)
  • 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,
            1.0);
        points.add(point);

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

Answer 2

我知道这个问题已经很老了并且在i80上做得很好，但是我只是想补充一下（对于将来的SO-ers），有一种非常简单的方法可以使用Apache Math计算导数或偏导数（因此您没有为雅各比矩阵做自己的微分）。这是DerivativeStructure。

扩展i80and的答案以使用DerivativeStructure类：

//Everything stays the same except for the Jacobian Matrix

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;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;

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];

        // Jacobian Matrix Edit

        // Using Derivative Structures...
        // constructor takes 4 arguments - the number of parameters in your
        // equation to be differentiated (3 in this case), the order of
        // differentiation for the DerivativeStructure, the index of the
        // parameter represented by the DS, and the value of the parameter itself
        DerivativeStructure aDev = new DerivativeStructure(3, 1, 0, a);
        DerivativeStructure bDev = new DerivativeStructure(3, 1, 1, b);
        DerivativeStructure cDev = new DerivativeStructure(3, 1, 2, c);

        // define the equation to be differentiated using another DerivativeStructure
        DerivativeStructure y = aDev.multiply(DerivativeStructure.pow(t, bDev))
                .multiply(cDev.negate().multiply(t).exp());

        // then return the partial derivatives required
        // notice the format, 3 arguments for the method since 3 parameters were
        // specified first order derivative of the first parameter, then the second, 
        // then the third
        return new double[] {
                y.getPartialDerivative(1, 0, 0),
                y.getPartialDerivative(0, 1, 0),
                y.getPartialDerivative(0, 0, 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,
                1.0);
        points.add(point);

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

就是这样。我知道这是一个令人费解的/令人困惑的类，但是当您处理非常复杂的方程式而要手工获取部分导数会很麻烦时（这在我不久前就发生了），它肯定会派上用场当您想导出偏导数时，请说出二阶或三阶。

对于二阶，三阶等等的导数，您要做的就是：

// specify the required order as the second argument, say second order so 2
DerivativeStructure aDev = new DerivativeStructure(3, 2, 0, a);        
DerivativeStructure bDev = new DerivativeStructure(3, 2, 1, b);
DerivativeStructure cDev = new DerivativeStructure(3, 2, 2, c);

// and then specify the order again here
y.getPartialDerivative(2, 0, 0),
y.getPartialDerivative(0, 2, 0),
y.getPartialDerivative(0, 0, 2)

希望这对某人有所帮助。