Java中Math3 各种随机数生成器的使用(Random Generator)

た入场券 2022-01-29 18:59 1202阅读 0赞

本文作者：合肥工业大学 管理学院 钱洋 email：1563178220@qq.com 内容可能有不到之处，欢迎交流。  
**未经本人允许禁止转载**。

### 文章目录 ###

*  背景
 *  python中numpy生成随机数
 *   *  产生一组随机数
     *  产生二维随机数
     *  归一化随机数
     *  标准正太分布随机数
     *  多元正太分布随机数
 *  Java中math3产生各种随机数
 *   *  CorrelatedRandomVectorGenerator
     *   *  使用案例
     *  GaussianRandomGenerator
     *   *  使用案例
     *  HaltonSequenceGenerator
     *   *  使用案例
     *  JDKRandomGenerator
     *   *  使用案例
     *  SobolSequenceGenerator
     *   *  使用案例
     *  UniformRandomGenerator
     *   *  使用案例

# 背景 #

在编写机器学习算法时，经常需要对各类参数进行初始化，例如**一些使用变分推断算法的模型**。无论是在Java中，还是Python中，随机数生成器使用都非常重要。

在Python中，我们可以使用numpy中的函数产生各类随机数。以下将先介绍numpy产生随机数的方式，之后介绍Java中Math3 如何产生用户想要的随机数。

# python中numpy生成随机数 #

## 产生一组随机数 ##

import numpy as np
    a1 = np.random.sample(3)
    print(a1)

程序输出结果为：

[0.894403   0.75327423 0.0598    ]

## 产生二维随机数 ##

import numpy as np
    a2 = np.random.random([3, 5])
    print(a2)

程序输出结果为：

[[0.74259942 0.14265614 0.39788471 0.24822603 0.70212864]
     [0.24499887 0.10752136 0.87938368 0.66949099 0.60077382]
     [0.93464286 0.12540026 0.23024034 0.01755745 0.1791168 ]]

## 归一化随机数 ##

import numpy as np
    a2 = np.random.random([3, 5])
    a2 = a2 / a2.sum(1)[:, np.newaxis]  # normalize
    print(a2)

程序输出结果为：

[[0.20371704 0.13704266 0.07736116 0.07489164 0.50698749]
     [0.16472605 0.10869033 0.44036911 0.10437194 0.18184257]
     [0.12031567 0.04564694 0.0950007  0.33511749 0.40391919]]

## 标准正太分布随机数 ##

import numpy as np
    c = np.random.normal(size=(3,4))
    print(c)

程序输出结果为：

[[-0.3369725  -1.05351817 -0.84444184  0.43715886]
     [-0.56812588  0.15303606  0.50248202  0.95384482]
     [-0.63582981  0.44559096 -1.91725906 -0.70182715]]

## 多元正太分布随机数 ##

import numpy as np
    V = np.random.multivariate_normal(np.zeros(5), np.identity(5) * (5),size=3)
    print(V)

即均值为0，协方差为5的多元正太分布中，产生随机数，输出结果为：

[[ 2.91755746 -1.67030031 -1.0542531   0.13214101 -2.03207468]
     [-1.86659205  0.14574427 -4.24525326 -3.91111677 -2.81316827]
     [-1.57533411  2.54300223 -0.69052118 -3.19566595  3.21427621]]

# Java中math3产生各种随机数 #

Math3中的选择器有：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9xaWFueWFuZy1oZnV0LmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70_pic_center]  
即：

## CorrelatedRandomVectorGenerator ##

*  CorrelatedRandomVectorGenerator：这个选择器用于从**多元正太分布中抽取随机数**，其中的方法包括：

通过源码可以看到，CorrelatedRandomVectorGenerator中的构造方法有两个，分别是：

/** * Builds a correlated random vector generator from its mean * vector and covariance matrix. * * @param mean Expected mean values for all components. * @param covariance Covariance matrix. * @param small Diagonal elements threshold under which column are * considered to be dependent on previous ones and are discarded * @param generator underlying generator for uncorrelated normalized * components. * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException * if the covariance matrix is not strictly positive definite. * @throws DimensionMismatchException if the mean and covariance * arrays dimensions do not match. */
        public CorrelatedRandomVectorGenerator(double[] mean,
                                               RealMatrix covariance, double small,
                                               NormalizedRandomGenerator generator) { 
            int order = covariance.getRowDimension();
            if (mean.length != order) { 
                throw new DimensionMismatchException(mean.length, order);
            }
            this.mean = mean.clone();
    
            final RectangularCholeskyDecomposition decomposition =
                new RectangularCholeskyDecomposition(covariance, small);
            root = decomposition.getRootMatrix();
    
            this.generator = generator;
            normalized = new double[decomposition.getRank()];
    
        }

从这个构造方法中，可以看到其输入是均值数组，协方差矩阵，一个double类型的值，和实例化的NormalizedRandomGenerator。在后面会介绍这个构造方法的使用。  
另外一个构造方法是：

/** * Builds a null mean random correlated vector generator from its * covariance matrix. * * @param covariance Covariance matrix. * @param small Diagonal elements threshold under which column are * considered to be dependent on previous ones and are discarded. * @param generator Underlying generator for uncorrelated normalized * components. * @throws org.apache.commons.math3.linear.NonPositiveDefiniteMatrixException * if the covariance matrix is not strictly positive definite. */
 public CorrelatedRandomVectorGenerator(RealMatrix covariance, double small,
 NormalizedRandomGenerator generator) { 
 int order = covariance.getRowDimension();
 mean = new double[order];
 for (int i = 0; i < order; ++i) { 
 mean[i] = 0;
 }
 
 final RectangularCholeskyDecomposition decomposition =
 new RectangularCholeskyDecomposition(covariance, small);
 root = decomposition.getRootMatrix();
 
 this.generator = generator;
 normalized = new double[decomposition.getRank()];
 
 }

使用多元正太分布，产生一组随机数，需要使用这里面的一个方法：

/** Generate a correlated random vector. * @return a random vector as an array of double. The returned array * is created at each call, the caller can do what it wants with it. */
 public double[] nextVector() { 
 
 // generate uncorrelated vector
 for (int i = 0; i < normalized.length; ++i) { 
 normalized[i] = generator.nextNormalizedDouble();
 }
 
 // compute correlated vector
 double[] correlated = new double[mean.length];
 for (int i = 0; i < correlated.length; ++i) { 
 correlated[i] = mean[i];
 for (int j = 0; j < root.getColumnDimension(); ++j) { 
 correlated[i] += root.getEntry(i, j) * normalized[j];
 }
 }
 
 return correlated;
 
 }

### 使用案例 ###

下面以具体的案例讲解如何使用CorrelatedRandomVectorGenerator。

import org.apache.commons.math3.linear.MatrixUtils;
    import org.apache.commons.math3.linear.RealMatrix;
    import org.apache.commons.math3.random.CorrelatedRandomVectorGenerator;
    import org.apache.commons.math3.random.GaussianRandomGenerator;
    import org.apache.commons.math3.random.JDKRandomGenerator;
    import org.apache.commons.math3.random.RandomGenerator;
    
    public class MultivariateGaussianGeneratorTest2 { 
    
    	public static void main(String[] args) { 
    		RandomGenerator rg = new JDKRandomGenerator();
    		rg.setSeed(17399225432l);  // 随机种子
    		GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    		double[] mean = { 1, 2, 5};
    		double[][] arrA = { { 1, 2, 3}, { 3, 4, 5}, { 4, 5, 6}};
    		RealMatrix matrixA = MatrixUtils.createRealMatrix(arrA); 
    		//生成协方差矩阵
    		RealMatrix covariance = matrixA.multiply (matrixA.transpose());
    		// 调用函数
    		CorrelatedRandomVectorGenerator generator = 
    		    new CorrelatedRandomVectorGenerator(mean, covariance, 1.0e-12 * covariance.getNorm(), rawGenerator);
    		double[] randomVector = generator.nextVector();
    		for(double d : randomVector){ 
    			System.out.println(d);
    		}
    	}
    }

如上面程序所示，设置了均值数组，通过矩阵和矩阵的逆相乘得到协方差，以此作为输入产生一组来自多元正太分布的随机数。  
上面程序的输出结果为：

Array2DRowRealMatrix{
       {14.0,26.0,32.0},{26.0,50.0,62.0},{32.0,62.0,77.0}}
    8.241122654913196
    15.481679575594983
    21.601958035935876

## GaussianRandomGenerator ##

这个类，在上面的代码中已有使用。该类用于从标准正太分布中产生一个值。其中，该类的构造方法如下：

/** Create a new generator. * @param generator underlying random generator to use */
        public GaussianRandomGenerator(final RandomGenerator generator) { 
            this.generator = generator;
        }

该类中产生，产生一个随机数的方法如下：

/** Generate a random scalar with null mean and unit standard deviation. * @return a random scalar with null mean and unit standard deviation */
        public double nextNormalizedDouble() { 
            return generator.nextGaussian();
        }

### 使用案例 ###

下面以一个案例讲解其使用：

import org.apache.commons.math3.random.GaussianRandomGenerator;
 import org.apache.commons.math3.random.JDKRandomGenerator;
 import org.apache.commons.math3.random.RandomGenerator;
 
 public class GaussianRandomTest { 
 
 	public static void main(String[] args) { 
 		RandomGenerator rg = new JDKRandomGenerator();
 // rg.setSeed(17399225432l); // 随机种子
 		GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
 		for (int i = 0; i < 10; i++) { 
 			double g = rawGenerator.nextNormalizedDouble();
 			System.out.println(g);
 		}
 	}
 }

执行该程序，会在控制台输出10个随机数，如下所示：  
![在这里插入图片描述][20190530084154807.png_pic_center]

## HaltonSequenceGenerator ##

Halton sequences常用于 Monte Carlo估计中。其产生随机数的原理是以一个质数为基，例如2或者3等，然后开始在0-1之间进行划分。例如：

1⁄2, 1⁄4, 3⁄4, 1⁄8, 5⁄8, 3⁄8, 7⁄8, 1⁄16, 9⁄16,...

1⁄3, 2⁄3, 1⁄9, 4⁄9, 7⁄9, 2⁄9, 5⁄9, 8⁄9, 1⁄27,...

在math3中，HaltonSequenceGenerator类中的构造方法有：

/** * Construct a new Halton sequence generator for the given space dimension. * * @param dimension the space dimension * @throws OutOfRangeException if the space dimension is outside the allowed range of [1, 40] */
        public HaltonSequenceGenerator(final int dimension) throws OutOfRangeException { 
            this(dimension, PRIMES, WEIGHTS);
        }

即设置产生随机数的维度。  
另外，一个构造方法是：

/** * Construct a new Halton sequence generator with the given base numbers and weights for each dimension. * The length of the bases array defines the space dimension and is required to be > 0. * * @param dimension the space dimension * @param bases the base number for each dimension, entries should be (pairwise) prime, may not be null * @param weights the weights used during scrambling, may be null in which case no scrambling will be performed * @throws NullArgumentException if base is null * @throws OutOfRangeException if the space dimension is outside the range [1, len], where * len refers to the length of the bases array * @throws DimensionMismatchException if weights is non-null and the length of the input arrays differ */
 public HaltonSequenceGenerator(final int dimension, final int[] bases, final int[] weights)
 throws NullArgumentException, OutOfRangeException, DimensionMismatchException { 
 
 MathUtils.checkNotNull(bases);
 
 if (dimension < 1 || dimension > bases.length) { 
 throw new OutOfRangeException(dimension, 1, PRIMES.length);
 }
 
 if (weights != null && weights.length != bases.length) { 
 throw new DimensionMismatchException(weights.length, bases.length);
 }
 
 this.dimension = dimension;
 this.base = bases.clone();
 this.weight = weights == null ? null : weights.clone();
 count = 0;
 }

即需要产生数据的维度，以及所使用的基(质素数组)以及权重。  
其中，在该类中，默认的基有：

/** The first 40 primes. */
        private static final int[] PRIMES = new int[] {
            2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
            71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
            149, 151, 157, 163, 167, 173
        };

默认的权重为：

/** The optimal weights used for scrambling of the first 40 dimension. */
        private static final int[] WEIGHTS = new int[] {
            1, 2, 3, 3, 8, 11, 12, 14, 7, 18, 12, 13, 17, 18, 29, 14, 18, 43, 41,
            44, 40, 30, 47, 65, 71, 28, 40, 60, 79, 89, 56, 50, 52, 61, 108, 56,
            66, 63, 60, 66
        };

如果需要产生一组随机数，需要调用该类中的两个方法：

/** {@inheritDoc} */
 public double[] nextVector() { 
 final double[] v = new double[dimension];
 for (int i = 0; i < dimension; i++) { 
 int index = count;
 double f = 1.0 / base[i];
 
 int j = 0;
 while (index > 0) { 
 final int digit = scramble(i, j, base[i], index % base[i]);
 v[i] += f * digit;
 index /= base[i]; // floor( index / base )
 f /= base[i];
 }
 }
 count++;
 return v;
 }
 /** * Skip to the i-th point in the Halton sequence. * * This operation can be performed in O(1). * * @param index the index in the sequence to skip to * @return the i-th point in the Halton sequence * @throws NotPositiveException if index < 0 */
 public double[] skipTo(final int index) throws NotPositiveException { 
 count = index;
 return nextVector();
 }

### 使用案例 ###

下面将以具体的案例讲解HaltonSequenceGenerator的使用。

import org.apache.commons.math3.random.HaltonSequenceGenerator;
 public class HaltonSequenceTest { 
 
 	public static void main(String[] args) { 
 		/*****第一种方式产生一组随机数*****/
 		HaltonSequenceGenerator randomVectorGenerator = new HaltonSequenceGenerator(3);
 		//设置
 		randomVectorGenerator.skipTo(999999); 
 		//产生一组随机数
 		double[] b = randomVectorGenerator.nextVector();
 		for (int i = 0; i < b.length; i++) { 
 			System.out.println(b[i]);
 		}
 		/*****第二种方式产生一组随机数*****/
 		System.out.println(".......第二种构造方法产生随机数.........");
 		HaltonSequenceGenerator randomVectorGenerator1 = new HaltonSequenceGenerator(4, new int[] { 3, 5, 7,11, 13 }, null);
 		//设置
 		randomVectorGenerator1.skipTo(999999); 
 		//产生一组随机数
 		double[] b1 = randomVectorGenerator1.nextVector();
 		for (int i = 0; i < b1.length; i++) { 
 			System.out.println(b1[i]);
 		}
 	}
 }

执行该程序，输出结果为：  
![在这里插入图片描述][20190530103755657.png_pic_center]

调整skipTo()方法中的数字，可以产生不同的随机数。

## JDKRandomGenerator ##

JDKRandomGenerator类继承了java.util中的Random类，其使用方式较为简单。其构造方法主要有：

/** * Create a new JDKRandomGenerator with a default seed. */
        public JDKRandomGenerator() { 
            super();
        }
    
        /** * Create a new JDKRandomGenerator with the given seed. * * @param seed initial seed * @since 3.6 */
        public JDKRandomGenerator(int seed) {

另外，其还包括两个方法，用于设置随机数种子。

该类可以调用Random类中的next, nextBoolean, nextBytes, nextDouble, nextFloat, nextGaussian, nextInt, nextInt, nextLong, setSeed方法。

### 使用案例 ###

下面为使用案例：

import org.apache.commons.math3.random.JDKRandomGenerator;
 import org.apache.commons.math3.random.RandomGenerator;
 
 public class JDKRandomTest { 
 
 	public static void main(String[] args) { 
 		RandomGenerator rg = new JDKRandomGenerator();
 		for (int i = 0; i < 2; i++) { 
 			System.out.println("double:" + rg.nextDouble());
 			System.out.println("boolean:" + rg.nextBoolean());
 			System.out.println("float:" + rg.nextFloat());
 			System.out.println("gaussian:" + rg.nextGaussian());
 			System.out.println("int:" + rg.nextInt());
 			System.out.println("long:" + rg.nextLong());
 		}
 		
 	}
 }

执行该程序，输出结果为：  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9xaWFueWFuZy1oZnV0LmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70_pic_center 1]

## SobolSequenceGenerator ##

SobolSequenceGenerator类的构造方法有两种，常使用第一种：

/** * Construct a new Sobol sequence generator for the given space dimension. * * @param dimension the space dimension * @throws OutOfRangeException if the space dimension is outside the allowed range of [1, 1000] */
 public SobolSequenceGenerator(final int dimension) throws OutOfRangeException { 
 if (dimension < 1 || dimension > MAX_DIMENSION) { 
 throw new OutOfRangeException(dimension, 1, MAX_DIMENSION);
 }
 
 // initialize the other dimensions with direction numbers from a resource
 final InputStream is = getClass().getResourceAsStream(RESOURCE_NAME);
 if (is == null) { 
 throw new MathInternalError();
 }
 
 this.dimension = dimension;
 
 // init data structures
 direction = new long[dimension][BITS + 1];
 x = new long[dimension];
 
 try { 
 initFromStream(is);
 } catch (IOException e) { 
 // the internal resource file could not be read -> should not happen
 throw new MathInternalError();
 } catch (MathParseException e) { 
 // the internal resource file could not be parsed -> should not happen
 throw new MathInternalError();
 } finally { 
 try { 
 is.close();
 } catch (IOException e) { // NOPMD
 // ignore
 }
 }
 }
 
 /** * Construct a new Sobol sequence generator for the given space dimension with * direction vectors loaded from the given stream. * * The expected format is identical to the files available from * <a href="http://web.maths.unsw.edu.au/~fkuo/sobol/">Stephen Joe and Frances Kuo</a>. * The first line will be ignored as it is assumed to contain only the column headers. * The columns are: * <ul> * <li>d: the dimension</li> * <li>s: the degree of the primitive polynomial</li> * <li>a: the number representing the coefficients</li> * <li>m: the list of initial direction numbers</li> * </ul> * Example: * <pre> * d s a m_i * 2 1 0 1 * 3 2 1 1 3 * </pre> * * The input stream must be an ASCII text containing one valid direction vector per line. * * @param dimension the space dimension * @param is the stream to read the direction vectors from * @throws NotStrictlyPositiveException if the space dimension is < 1 * @throws OutOfRangeException if the space dimension is outside the range [1, max], where * max refers to the maximum dimension found in the input stream * @throws MathParseException if the content in the stream could not be parsed successfully * @throws IOException if an error occurs while reading from the input stream */
 public SobolSequenceGenerator(final int dimension, final InputStream is)
 throws NotStrictlyPositiveException, MathParseException, IOException { 
 
 if (dimension < 1) { 
 throw new NotStrictlyPositiveException(dimension);
 }
 
 this.dimension = dimension;
 
 // init data structures
 direction = new long[dimension][BITS + 1];
 x = new long[dimension];
 
 // initialize the other dimensions with direction numbers from the stream
 int lastDimension = initFromStream(is);
 if (lastDimension < dimension) { 
 throw new OutOfRangeException(dimension, 1, lastDimension);
 }
 }

使用该方法产生的随机数如下图所示：

![在这里插入图片描述][2019053010554247.png_pic_center]

### 使用案例 ###

以下为一个使用案例：

import java.util.ArrayList;
 import java.util.List;
 import org.apache.commons.math3.linear.Array2DRowRealMatrix;
 import org.apache.commons.math3.linear.RealMatrix;
 import org.apache.commons.math3.random.SobolSequenceGenerator;
 
 public class SobolSequenceTest { 
 
 	public static void main(String[] args) { 
 		//产生一组随机数---测试案例
 		SobolSequenceGenerator generator = new SobolSequenceGenerator(5);
 	 generator.skipTo(999999); //这里必须使用，否则产生的全部是0
 	 System.out.println("..............................");
 	 double[] vector = generator.nextVector();
 	 for (int i = 0; i < vector.length; i++) { 
 	 	System.out.println(vector[i]);
 		}
 	 System.out.println("...........SobolSequenceGenerator产生一组随机数.......");
 	 //产生多组随机数，并添加到矩阵中
 	 System.out.println(".............生成随机数矩阵...............");
 	 List<RealMatrix> points = new ArrayList<RealMatrix>();
 	 for (double i = 0; i < 3; i++) { 
 	 double[] vector1 = generator.nextVector();
 	 RealMatrix pointMatrix = new Array2DRowRealMatrix(vector1);
 	 points.add(pointMatrix);
 	 }
 	 for (int i = 0; i < points.size(); i++) { 
 			System.out.println(points.get(i));
 		}
 	}
 }

程序的输出结果为：

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9xaWFueWFuZy1oZnV0LmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70_pic_center 2]

## UniformRandomGenerator ##

从均匀分布中产生随机数。UniformRandomGenerator类实现了NormalizedRandomGenerator接口。UniformRandomGenerator类的构造方法为：

/** Create a new generator. * @param generator underlying random generator to use */
        public UniformRandomGenerator(RandomGenerator generator) { 
            this.generator = generator;
        }

下面为其部分源码：

/** Generate a random scalar with null mean and unit standard deviation. * The number generated is uniformly distributed between -&sqrt;(3) * and +&sqrt;(3). * @return a random scalar with null mean and unit standard deviation */
 public double nextNormalizedDouble() { 
 return SQRT3 * (2 * generator.nextDouble() - 1.0);
 }

从该源码中可以看到， nextNormalizedDouble()方法产生的随机数在 \[-√3, +√3\].之间，因为SQRT3 设置为√3，generator.nextDouble()产生的值范围是\[0-1\]。

### 使用案例 ###

import org.apache.commons.math3.random.JDKRandomGenerator;
 import org.apache.commons.math3.random.RandomGenerator;
 import org.apache.commons.math3.random.UniformRandomGenerator;
 
 public class UniformRandomTest { 
 
 	public static void main(String[] args) { 
 		RandomGenerator rg = new JDKRandomGenerator();
 		rg.setSeed(10);
 		UniformRandomGenerator generator = new UniformRandomGenerator(rg);
 		double[] sample = new double[10];
 		for (int i = 0; i < sample.length; ++i) { 
 			sample[i] = generator.nextNormalizedDouble();
 			System.out.println(sample[i]);
 		}
 	}
 }

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9xaWFueWFuZy1oZnV0LmJsb2cuY3Nkbi5uZXQ_size_16_color_FFFFFF_t_70_pic_center]: /images/20220126/f293c00828c2454191467d14b18f4e87.png
[20190530084154807.png_pic_center]: /images/20220126/b370106c2f6a4117bfc0a8017552fb3e.png
[20190530103755657.png_pic_center]: /images/20220126/dce80445f7514d0c9005b68d5b038115.png
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[2019053010554247.png_pic_center]: /images/20220126/5ab60716a3c54cb48a641aa497e579ca.png
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