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);
}
所以，这是一个老问题，但我最近遇到了同样的问题，最后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 的文档记录非常差，但是在当前版本的 Apache Common Math (3.3+) 中，有两个部分，假设您有一个带有多个参数的变量：要拟合的函数（实现 ParametricUnivariateFunction）和曲线拟合器（它扩展了 AbstractCurveFitter）。
适合的功能
public double value(double t, double... parameters)
fnc逻辑的地方。public double[] gradient(double t, double... parameters)
曲线拟合器
protected LeastSquaresProblem getProblem(Collection<WeightedObservedPoint> points)
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));
}
}
我知道这个问题已经很老了，而且i80回答这个问题做得很好，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用 Apache Math 计算导数或偏导数（所以你没有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，您所要做的就是：
// 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。