The Commons Math random package includes utilities for

• generating random numbers
• generating random strings
• generating cryptographically secure sequences of random numbers or strings
• generating random samples and permuations
• analyzing distributions of values in an input file and generating values "like" the values in the file
• generating data for grouped frequency distributions or histograms

The org.apache.commons.math.RandomData interface defines methods for generating random sequences of numbers. The API contracts of these methods use the following concepts:

Random sequence of numbers from a probability distribution

There is no such thing as a single "random number." What can be generated are sequences of numbers that appear to be random. When using the built-in JDK function Math.random(), sequences of values generated follow the Uniform Distribution, which means that the values are evenly spread over the interval between 0 and 1, with no sub-interval having a greater probability of containing generated values than any other interval of the same length. The mathematical concept of a probability distribution basically amounts to asserting that different ranges in the set of possible values for of a random variable have different probabilities of containing the value. Commons Math supports generating random sequences from the following probability distributions. The javadoc for the nextXxx methods in RandomDataImpl describes the algorithms used to generate random deviates from each of these distributions.

• uniform distribution
• exponential distribution
• poisson distribution
• Gaussian distribution

Cryptographically secure random sequences

It is possible for a sequence of numbers to appear random, but nonetheless to be predictable based on the algorithm used to generate the sequence. If in addition to randomness, strong unpredictability is required, it is best to use a secure random number generator to generate values (or strings). The nextSecureXxx methods in the RandomDataImpl implementation of the RandomData interface use the JDK SecureRandom pseudo-random number generator (PRNG) to generate cryptographically secure sequences. The setSecureAlgorithm method allows you to change the underlying PRNG. These methods are much slower than the corresponding "non-secure" versions, so they should only be used when cryptographic security is required.

Seeding pseudo-random number generators

By default, the implementation provided in RandomDataImpl uses the JDK-provided PRNG. Like other PRNGs, the JDK generator generates sequences of random numbers based on an initial "seed value". For the non-secure methods, starting with the same seed always produces the same sequence of values. Secure sequences started with the same seeds will diverge. When a new RandomDataImpl is created, the underlying random number generators are not intialized. The first call to a data generation method, or to a reSeed() method initializes the appropriate generator. If you do not explicitly seed the generator, it is by default seeded with the current time in milliseconds. Therefore, to generate sequences of random data values, you should always instantiate one RandomDataImpl and use it repeatedly instead of creating new instances for subsequent values in the sequence. For example, the following will generate a random sequence of 50 long integers between 1 and 1,000,000, using the current time in milliseconds as the seed for the JDK PRNG: RandomDataImpl randomData = new RandomDataImpl(); for (int i = 0; i < 1000; i++) { value = randomData.nextLong(1, 1000000); } The following will not in general produce a good random sequence, since the PRNG is reseeded each time through the loop with the current time in milliseconds: for (int i = 0; i < 1000; i++) { RandomDataImpl randomData = new RandomDataImpl(); value = randomData.nextLong(1, 1000000); } The following will produce the same random sequence each time it is executed: RandomDataImpl randomData = new RandomDataImpl(); randomData.reSeed(1000); for (int i = 0; i = 1000; i++) { value = randomData.nextLong(1, 1000000); } The following will produce a different random sequence each time it is executed. RandomDataImpl randomData = new RandomDataImpl(); randomData.reSeedSecure(1000); for (int i = 0; i < 1000; i++) { value = randomData.nextSecureLong(1, 1000000); }

The methods nextHexString and nextSecureHexString can be used to generate random strings of hexadecimal characters. Both of these methods produce sequences of strings with good dispersion properties. The difference between the two methods is that the second is cryptographically secure. Specifically, the implementation of nextHexString(n) in RandomDataImpl uses the following simple algorithm to generate a string of n hex digits:

1. n/2+1 binary bytes are generated using the underlying Random
2. Each binary byte is translated into 2 hex digits

1. 20 random bytes are generated using the underlying SecureRandom.
2. SHA-1 hash is applied to yield a 20-byte binary digest.
3. Each byte of the binary digest is converted to 2 hex digits

To select a random sample of objects in a collection, you can use the nextSample method in the RandomData interface. Specifically, if c is a collection containing at least k objects, and ranomData is a RandomDataImpl instance randomData.nextSample(c, k) will return an object[] array of length k consisting of elements randomly selected from the collection. If c contains duplicate references, there may be duplicate references in the returned array; otherwise returned elements will be unique -- i.e., the sampling is without replacement among the object references in the collection.

If randomData is a RandomDataImpl instance, and n and k are integers with k <= n, then randomData.nextPermutation(n, k) returns an int[] array of length k whose whose entries are selected randomly, without repetition, from the integers 0 through n-1 (inclusive), i.e., randomData.nextPermutation(n, k) returns a random permutation of n taken k at a time.

Using the ValueServer class, you can generate data based on the values in an input file in one of two ways:

Replay Mode

The following code will read data from url (a java.net.URL instance), cycling through the values in the file in sequence, reopening and starting at the beginning again when all values have been read. ValueServer vs = new ValueServer(); vs.setValuesFileURL(url); vs.setMode(ValueServer.REPLAY_MODE); vs.resetReplayFile(); double value = vs.getNext(); // ...Generate and use more values... vs.closeReplayFile(); The values in the file are not stored in memory, so it does not matter how large the file is, but you do need to explicitly close the file as above. The expected file format is \n -delimited (i.e. one per line) strings representing valid floating point numbers.

Digest Mode

When used in Digest Mode, the ValueServer reads the entire input file and estimates a probability density function based on data from the file. The estimation method is essentially the Variable Kernel Method with Gaussian smoothing. Once the density has been estimated, getNext() returns random values whose probability distribution matches the empirical distribution -- i.e., if you generate a large number of such values, their distribution should "look like" the distribution of the values in the input file. The values are not stored in memory in this case either, so there is no limit to the size of the input file. Here is an example: ValueServer vs = new ValueServer(); vs.setValuesFileURL(url); vs.setMode(ValueServer.DIGEST_MODE); vs.computeDistribution(500); //Read file and estimate distribution using 500 bins double value = vs.getNext(); // ...Generate and use more values... See the javadoc for ValueServer and EmpiricalDistribution for more details. Note that computeDistribution() opens and closes the input file by itself.