Question

我制作了一个测试程序，通过NewtonRaphsonSolver库试用Apache Commons Math课程。牛顿的方法用于查找给定函数的根。

我写的测试程序引用了cos（x）函数（我有一个更难分析的函数，我首先看cos（x）函数）。

测试程序的代码是

import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.solvers.*;
import org.apache.commons.math3.exception.DimensionMismatchException;

public class Test3 {

    public static void main(String args[]) {
        NewtonRaphsonSolver test = new NewtonRaphsonSolver();
        UnivariateDifferentiableFunction f = new UnivariateDifferentiableFunction() {

            public double value(double x) {
                return Math.cos(x);
            }

            @Override
            public DerivativeStructure value(DerivativeStructure t) throws DimensionMismatchException {
                return t.cos();
            }
        };

        for (int i = 1; i <= 500; i++) {
            System.out.println(test.solve(1000, f, i, i+0.1));
        }
    }
}

不确定我是否需要两次引用Math.cos（x）和t.cos（）

public double value(double x) {
                return Math.cos(x);
            }

            @Override
            public DerivativeStructure value(DerivativeStructure t) throws DimensionMismatchException {
                return t.cos();
            }

Newton的方法找到所有零并将它们显示给用户。

1.5707963267948966
1.5707963267948966
-7.853981633974483
4.71238898038469
4.71238898038469
1.5707963267948966
7.853981633974483
7.853981633974483
10.995574287564276
10.995574287564276
10.995574287564276
10.995574287564276
14.137166941154069
14.137166941154069
14.137166941154069
127.23450247038663
17.278759594743864
17.278759594743864
23.56194490192345
20.420352248333657
20.420352248333657
39.269908169872416
23.56194490192345
23.56194490192345
14.137166941154069
26.703537555513243
26.703537555513243
23.56194490192345
29.845130209103036
29.845130209103036
26.703537555513243
32.98672286269283
32.98672286269283
32.98672286269283
36.12831551628262
36.12831551628262
36.12831551628262
23.56194490192345
39.269908169872416
39.269908169872416
45.553093477052
42.411500823462205
42.411500823462205

有没有办法防止打印出重复的零？例如，上面的输出将读取

1.5707963267948966
4.71238898038469
7.853981633974483
10.995574287564276
14.137166941154069
17.278759594743864
20.420352248333657
23.56194490192345
26.703537555513243
29.845130209103036
32.98672286269283
36.12831551628262
39.269908169872416
42.411500823462205
45.553093477052

这可以在for循环中进行，还是通过只打印出不重复的值的数组来完成？

Answer 1

第一个问题是，什么是相同的零。我会上课：

class SolutionForZero{
    public final double value;
    final int hash;
    static double tolerance = 1e-6;
    public SolutionForZero(double value){
        this.value = value;
        hash = 1;
    }
    public boolean equals(Object other){
        if( other instanceof SolutionForZero ){
           double v = value - other.value;
           return (v < 0) ? (-v > tolerance) : (v > tolerance);
        }
        return false;
    }
    public int hashCode(){
        return hash;
    }
}

本课程将比较双打。要使用这个类：

Set<SolutionForZero> resultSet = new HashSet<>();
for(double d: yourAnswers){
    if(resultSet.add(new SolutionForZero(d))){
        System.out.println("'unique' zero at: " + d);
    };
}

现在，您的resultSet将仅包含至少相差的值。

哈希码有点棘手。只要公差小于1.0，我提供的方式就会起作用。我希望有所改进。

Answer 2

import java.util.TreeSet;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.solvers.*;
import org.apache.commons.math3.exception.DimensionMismatchException;

public class Test5 {

    public static void main(String args[]) {
        NewtonRaphsonSolver test = new NewtonRaphsonSolver(1E-10);

        UnivariateDifferentiableFunction f = new UnivariateDifferentiableFunction() {

            public double value(double x) {
                return Math.sin(x);
            }

            public DerivativeStructure value(DerivativeStructure t) throws
                    DimensionMismatchException {
                return t.sin();
            }
        };

        double EPSILON = 1e-6;
        TreeSet<Double> set = new TreeSet<>();
        for (int i = 1; i <= 5000; i++) {
            set.add(test.solve(1000, f, i, i + EPSILON));
        }
        for (Double s : set) {
            if (s > 0) {
                System.out.println(s);
            }
        }
    }
}

使用Math.Commons库的{Newton-Raphson方法

2 个答案: