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？有人告诉我将 CurveFitter 与 LevenbergMarquardtOptimizer 和 ParametricUnivariateFunction 一起使用，但我不知道在 ParametricUnivariateFunction 梯度和值方法中要写什么。另外，写完之后，如何获取拟合的函数参数呢？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。

此 API 的文档记录非常差，但在 当前 版本的 Apache Common Math (3.3+) 中，假设您有一个带有多个参数的变量，则分为两部分：要拟合的函数with（实现 ParametricUnivariateFunction）和曲线拟合器（扩展 AbstractCurveFitter）。

适合的功能

• public double value(double t, double... parameters)
  • 你的方程式。这是您放置 fnc 逻辑的地方。
• public double[] gradient(double t, double... parameters)
  • 返回上述关于每个参数的偏导数数组。 This calculator 如果您（像我一样）对微积分不熟悉，可能会有所帮助，但是任何好的计算机代数系统都可以计算这些值。

曲线拟合器

• protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points)
  • 设置一堆样板废话，并返回一个最小二乘问题供装配工使用。

综上所述，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，i80and 很好地回答了这个问题，但我只是想补充一下（对于未来的 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（所以你不必为雅可比矩阵做你自己的微分）。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。我知道这是一个使用起来非常复杂/令人困惑的类，但是当您处理非常复杂的方程时，它肯定会派上用场，而手动获得偏导数会很麻烦（这发生在我不久前），或者当您想导出偏导数时，请说二阶或三阶。

对于二阶、三阶等阶导数，您只需：

// 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)

希望这对某些人有所帮助。