package net.seninp.util;
// StdRandom.java
// Below is the syntax highlighted version of StdRandom.java from Standard Libraries.
// Copyright © 2000–2011, Robert Sedgewick and Kevin Wayne.
//Last updated: Tue Mar 25 20:35:06 EDT 2014.
/*************************************************************************
* Compilation: javac StdRandom.java
* Execution: java StdRandom
* Dependencies: StdOut.java
*
* A library of static methods to generate pseudo-random numbers from
* different distributions (bernoulli, uniform, gaussian, discrete,
* and exponential). Also includes a method for shuffling an array.
*
*
* % java StdRandom 5
* seed = 1316600602069
* 59 16.81826 true 8.83954 0
* 32 91.32098 true 9.11026 0
* 35 10.11874 true 8.95396 3
* 92 32.88401 true 8.87089 0
* 72 92.55791 true 9.46241 0
*
* % java StdRandom 5
* seed = 1316600616575
* 96 60.17070 true 8.72821 0
* 79 32.01607 true 8.58159 0
* 81 59.49065 true 9.10423 1
* 96 51.65818 true 9.02102 0
* 99 17.55771 true 8.99762 0
*
* % java StdRandom 5 1316600616575
* seed = 1316600616575
* 96 60.17070 true 8.72821 0
* 79 32.01607 true 8.58159 0
* 81 59.49065 true 9.10423 1
* 96 51.65818 true 9.02102 0
* 99 17.55771 true 8.99762 0
*
*
* Remark
* ------
* - Relies on randomness of nextDouble() method in java.util.Random
* to generate pseudorandom numbers in [0, 1).
*
* - This library allows you to set and get the pseudorandom number seed.
*
* - See http://www.honeylocust.com/RngPack/ for an industrial
* strength random number generator in Java.
*
*************************************************************************/
import java.util.Random;
/**
* <i>Standard random</i>. This class provides methods for generating random number from various
* distributions.
* <p>
* For additional documentation, see <a href="http://introcs.cs.princeton.edu/22library">Section
* 2.2</a> of <i>Introduction to Programming in Java: An Interdisciplinary Approach</i> by Robert
* Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public final class StdRandom {
private static Random random; // pseudo-random number generator
private static long seed; // pseudo-random number generator seed
// static initializer
static {
// this is how the seed was set in Java 1.4
seed = System.currentTimeMillis();
random = new Random(seed);
}
/**
* Disable the constructor, do not instantiate.
*/
private StdRandom() {
}
/**
* Sets the seed of the psedurandom number generator.
*
* @param s the seed value
*/
public static void setSeed(long s) {
seed = s;
random = new Random(seed);
}
/**
* Returns the seed of the psedurandom number generator.
*
* @return the seed value.
*/
public static long getSeed() {
return seed;
}
/**
* Return real number uniformly in [0, 1).
*
* @return the uniformly sampled random value.
*/
public static double uniform() {
return random.nextDouble();
}
/**
* Returns an integer uniformly between 0 (inclusive) and N (exclusive).
*
* @param N the upper bound.
* @return the next uniformly sampled value.
* @throws IllegalArgumentException if {@code N <= 0 }
*/
public static int uniform(int N) {
if (N <= 0)
throw new IllegalArgumentException("Parameter N must be positive");
return random.nextInt(N);
}
// /////////////////////////////////////////////////////////////////////////
// STATIC METHODS BELOW RELY ON JAVA.UTIL.RANDOM ONLY INDIRECTLY VIA
// THE STATIC METHODS ABOVE.
// /////////////////////////////////////////////////////////////////////////
/**
* Returns an integer uniformly in [a, b).
*
* @param a the sampling interval's start.
* @param b the sampling interval's end.
* @return the next uniformly sampled value.
* @throws IllegalArgumentException if {@code b <= a }
* @throws IllegalArgumentException if {@code b - a >= Integer.MAX_VALUE }
*/
public static int uniform(int a, int b) {
if (b <= a)
throw new IllegalArgumentException("Invalid range");
if ((long) b - a >= Integer.MAX_VALUE)
throw new IllegalArgumentException("Invalid range");
return a + uniform(b - a);
}
/**
* Returns a real number uniformly in [a, b).
*
* @param a the sampling interval's start.
* @param b the sampling interval's end.
*
* @return the next uniformly sampled value.
*
* @throws IllegalArgumentException unless {@code a < b }
*/
public static double uniform(double a, double b) {
if (!(a < b))
throw new IllegalArgumentException("Invalid range");
return a + uniform() * (b - a);
}
/**
* Returns a boolean, which is true with probability p, and false otherwise.
*
* @param p the probability.
* @throws IllegalArgumentException unless {@code p >= 0.0 } and {@code p <= 1.0 }
* @return the random value.
*/
public static boolean bernoulli(double p) {
if (!(p >= 0.0 && p <= 1.0))
throw new IllegalArgumentException("Probability must be between 0.0 and 1.0");
return uniform() < p;
}
/**
* Returns a boolean, which is true with probability .5, and false otherwise.
*
* @return the random value.
*/
public static boolean bernoulli() {
return bernoulli(0.5);
}
/**
* Returns a real number with a standard Gaussian distribution.
*
* @return the random value.
*/
public static double gaussian() {
// use the polar form of the Box-Muller transform
double r, x, y;
do {
x = uniform(-1.0, 1.0);
y = uniform(-1.0, 1.0);
r = x * x + y * y;
}
while (r >= 1 || r == 0);
return x * Math.sqrt(-2 * Math.log(r) / r);
// Remark: y * Math.sqrt(-2 * Math.log(r) / r)
// is an independent random gaussian
}
/**
* Returns a real number from a gaussian distribution with given mean and stddev
*
* @param mean the mean value to generate the distribution.
* @param stddev the standard deviation value.
* @return the random value.
*/
public static double gaussian(double mean, double stddev) {
return mean + stddev * gaussian();
}
/**
* Returns an integer with a geometric distribution with mean 1/p.
*
* @param p the value to configure the distribution.
* @throws IllegalArgumentException unless {@code p >= 0.0 } and {@code p <= 1.0 }
* @return the random value.
*/
public static int geometric(double p) {
if (!(p >= 0.0 && p <= 1.0))
throw new IllegalArgumentException("Probability must be between 0.0 and 1.0");
// using algorithm given by Knuth
return (int) Math.ceil(Math.log(uniform()) / Math.log(1.0 - p));
}
/**
* Return an integer with a Poisson distribution with mean lambda.
*
* @param lambda the value to configure the distribution.
* @throws IllegalArgumentException unless {@code lambda > 0.0 } and not infinite
* @return the random value.
*/
public static int poisson(double lambda) {
if (!(lambda > 0.0))
throw new IllegalArgumentException("Parameter lambda must be positive");
if (Double.isInfinite(lambda))
throw new IllegalArgumentException("Parameter lambda must not be infinite");
// using algorithm given by Knuth
// see http://en.wikipedia.org/wiki/Poisson_distribution
int k = 0;
double p = 1.0;
double L = Math.exp(-lambda);
do {
k++;
p *= uniform();
}
while (p >= L);
return k - 1;
}
/**
* Returns a real number with a Pareto distribution with parameter alpha.
*
* @param alpha the value to configure the distribution.
* @throws IllegalArgumentException unless {@code alpha > 0.0 }
* @return the random value.
*/
public static double pareto(double alpha) {
if (!(alpha > 0.0))
throw new IllegalArgumentException("Shape parameter alpha must be positive");
return Math.pow(1 - uniform(), -1.0 / alpha) - 1.0;
}
/**
* Returns a real number with a Cauchy distribution.
*
* @return the random value.
*/
public static double cauchy() {
return Math.tan(Math.PI * (uniform() - 0.5));
}
/**
* Returns a number from a discrete distribution: i with probability a[i]. throws
* IllegalArgumentException if sum of array entries is not (very nearly) equal to {@code 1.0 }
* throws IllegalArgumentException unless {@code a[i] >= 0.0 } for each index {@code i }
*
* @param a the value to configure the distribution.
* @return the random value.
*/
public static int discrete(double[] a) {
double EPSILON = 1E-14;
double sum = 0.0;
for (int i = 0; i < a.length; i++) {
if (!(a[i] >= 0.0))
throw new IllegalArgumentException("array entry " + i + " must be nonnegative: " + a[i]);
sum = sum + a[i];
}
if (sum > 1.0 + EPSILON || sum < 1.0 - EPSILON)
throw new IllegalArgumentException(
"sum of array entries does not approximately equal 1.0: " + sum);
// the for loop may not return a value when both r is (nearly) 1.0 and when the
// cumulative sum is less than 1.0 (as a result of floating-point roundoff error)
while (true) {
double r = uniform();
sum = 0.0;
for (int i = 0; i < a.length; i++) {
sum = sum + a[i];
if (sum > r)
return i;
}
}
}
/**
* Returns a real number from an exponential distribution with rate lambda.
*
* @param lambda the value to configure the distribution.
* @throws IllegalArgumentException unless {@code lambda > 0.0 }
* @return the random value.
*/
public static double exp(double lambda) {
if (!(lambda > 0.0))
throw new IllegalArgumentException("Rate lambda must be positive");
return -Math.log(1 - uniform()) / lambda;
}
/**
* Rearrange the elements of an array in random order.
*
* @param a the array to shuffle.
*/
public static void shuffle(Object[] a) {
int N = a.length;
for (int i = 0; i < N; i++) {
int r = i + uniform(N - i); // between i and N-1
Object temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
/**
* Rearrange the elements of a double array in random order.
*
* @param a the array to shuffle.
*/
public static void shuffle(double[] a) {
int N = a.length;
for (int i = 0; i < N; i++) {
int r = i + uniform(N - i); // between i and N-1
double temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
/**
* Rearrange the elements of an int array in random order.
*
* @param a the array to shuffle.
*/
public static void shuffle(int[] a) {
int N = a.length;
for (int i = 0; i < N; i++) {
int r = i + uniform(N - i); // between i and N-1
int temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
/**
* Rearrange the elements of the subarray a[lo..hi] in random order.
*
* @param a the array to shuffle.
* @param hi the upper bound.
* @param lo the lower bound.
*/
public static void shuffle(Object[] a, int lo, int hi) {
if (lo < 0 || lo > hi || hi >= a.length) {
throw new IndexOutOfBoundsException("Illegal subarray range");
}
for (int i = lo; i <= hi; i++) {
int r = i + uniform(hi - i + 1); // between i and hi
Object temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
/**
* Rearrange the elements of the subarray a[lo..hi] in random order.
*
* @param a the array to shuffle.
* @param hi the upper bound.
* @param lo the lower bound.
*/
public static void shuffle(double[] a, int lo, int hi) {
if (lo < 0 || lo > hi || hi >= a.length) {
throw new IndexOutOfBoundsException("Illegal subarray range");
}
for (int i = lo; i <= hi; i++) {
int r = i + uniform(hi - i + 1); // between i and hi
double temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
/**
* Rearrange the elements of the subarray a[lo..hi] in random order.
*
* @param a the array to shuffle.
* @param hi the upper bound.
* @param lo the lower bound.
*/
public static void shuffle(int[] a, int lo, int hi) {
if (lo < 0 || lo > hi || hi >= a.length) {
throw new IndexOutOfBoundsException("Illegal subarray range");
}
for (int i = lo; i <= hi; i++) {
int r = i + uniform(hi - i + 1); // between i and hi
int temp = a[i];
a[i] = a[r];
a[r] = temp;
}
}
// /**
// * Unit test.
// */
// public static void main(String[] args) {
// int N = Integer.parseInt(args[0]);
// if (args.length == 2)
// StdRandom.setSeed(Long.parseLong(args[1]));
// double[] t = { .5, .3, .1, .1 };
//
// StdOut.println("seed = " + StdRandom.getSeed());
// for (int i = 0; i < N; i++) {
// StdOut.printf("%2d ", uniform(100));
// StdOut.printf("%8.5f ", uniform(10.0, 99.0));
// StdOut.printf("%5b ", bernoulli(.5));
// StdOut.printf("%7.5f ", gaussian(9.0, .2));
// StdOut.printf("%2d ", discrete(t));
// StdOut.println();
// }
//
// String[] a = "A B C D E F G".split(" ");
// for (String s : a)
// StdOut.print(s + " ");
// StdOut.println();
// }
}