/*************************************************************************
* 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);
} // don't instantiate
private StdRandom() { } /**
* Sets the seed of the psedurandom number generator.
*/
public static void setSeed(long s) {
seed = s;
random = new Random(seed);
} /**
* Returns the seed of the psedurandom number generator.
*/
public static long getSeed() {
return seed;
} /**
* Return real number uniformly in [0, 1).
*/
public static double uniform() {
return random.nextDouble();
} /**
* Returns an integer uniformly between 0 (inclusive) and N (exclusive).
* @throws IllegalArgumentException if <tt>N <= 0</tt>
*/
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 a real number uniformly in [0, 1).
* @deprecated clearer to use {@link #uniform()}
*/
public static double random() {
return uniform();
} /**
* Returns an integer uniformly in [a, b).
* @throws IllegalArgumentException if <tt>b <= a</tt>
* @throws IllegalArgumentException if <tt>b - a >= Integer.MAX_VALUE</tt>
*/
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).
* @throws IllegalArgumentException unless <tt>a < b</tt>
*/
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.
* @throws IllegalArgumentException unless <tt>p >= 0.0</tt> and <tt>p <= 1.0</tt>
*/
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.
*/
public static boolean bernoulli() {
return bernoulli(0.5);
} /**
* Returns a real number with a standard Gaussian distribution.
*/
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
*/
public static double gaussian(double mean, double stddev) {
return mean + stddev * gaussian();
} /**
* Returns an integer with a geometric distribution with mean 1/p.
* @throws IllegalArgumentException unless <tt>p >= 0.0</tt> and <tt>p <= 1.0</tt>
*/
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.
* @throws IllegalArgumentException unless <tt>lambda > 0.0</tt> and not infinite
*/
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.
* @throws IllegalArgumentException unless <tt>alpha > 0.0</tt>
*/
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.
*/
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 <tt>1.0</tt>
* throws IllegalArgumentException unless <tt>a[i] >= 0.0</tt> for each index <tt>i</tt>
*/
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.
* @throws IllegalArgumentException unless <tt>lambda > 0.0</tt>
*/
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.
*/
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.
*/
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.
*/
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.
*/
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.
*/
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.
*/
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();
} }