  About Us Home Contributors License Components Sandbox Dormant Math Overview Proposal Developers Guide Javadoc (1.0 release) Javadoc (1.1 release) Source Repository (current) Wiki (Wish List) User Guide Contents Overview Statistics Data Generation Linear Algebra Numerical Analysis Special Functions Utilities Complex Numbers Distributions Fractions Project Documentation About Math Project Info Project Reports Development Process General Information Charter Volunteering Contributing Patches Building Components Releasing Components Wiki Jakarta Community Get Involved Mailing Lists Related DB Commons XML Commons | ### 2 Data Generation #### 2.1 Overview 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 source of random data used by the data generation utilities is pluggable. By default, the JDK-supplied PseudoRandom Number Generator (PRNG) is used, but alternative generators can be "plugged in" using an adaptor framework, which provides a generic facility for replacing `java.util.Random` with an alternative PRNG. Sections 2.2-2.5 below show how to use the commons math API to generate different kinds of random data. The examples all use the default JDK-supplied PRNG. PRNG pluggability is covered in 2.6. The only modification required to the examples to use alternative PRNGs is to replace the argumentless constructor calls with invocations including a `RandomGenerator` instance as a parameter. #### 2.2 Random numbers 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 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` 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 most 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:
      RandomData 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:
      RandomData 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.
      RandomData randomData = new RandomDataImpl();
      randomData.reSeedSecure(1000);
      for (int i = 0; i < 1000; i++) {
          value = randomData.nextSecureLong(1, 1000000);
      }
  #### 2.3 Random Strings 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: n/2+1 binary bytes are generated using the underlying Random Each binary byte is translated into 2 hex digits The `RandomDataImpl` implementation of the "secure" version, `nextSecureHexString` generates hex characters in 40-byte "chunks" using a 3-step process: 20 random bytes are generated using the underlying `SecureRandom.` SHA-1 hash is applied to yield a 20-byte binary digest. Each byte of the binary digest is converted to 2 hex digits Similarly to the secure random number generation methods, `nextSecureHexString` is much slower than the non-secure version. It should be used only for applications such as generating unique session or transaction ids where predictability of subsequent ids based on observation of previous values is a security concern. If all that is needed is an even distribution of hex characters in the generated strings, the non-secure method should be used. #### 2.4 Random permutations, combinations, sampling 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 `RandomData` 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 `RandomData` 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. #### 2.5 Generating data 'like' an input file 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. #### 2.6 PRNG Pluggability To enable alternative PRNGs to be "plugged in" to the commons-math data generation utilities and to provide a generic means to replace `java.util.Random` in applications, a random generator adaptor framework has been added to commons-math. The org.apache.commons.math.RandomGenerator interface abstracts the public interface of `java.util.Random` and any implementation of this interface can be used as the source of random data for the commons-math data generation classes. An abstract base class, org.apache.commons.math.AbstractRandomGenerator is provided to make implementation easier. This class provides default implementations of "derived" data generation methods based on the primitive, `nextDouble().` To support generic replacement of `java.util.Random`, the org.apache.commons.math.RandomAdaptor class is provided, which extends `java.util.Random` and wraps and delegates calls to a `RandomGenerator` instance. Examples: Create a RandomGenerator based on RngPack's Mersenne Twister To create a RandomGenerator using the RngPack Mersenne Twister PRNG as the source of randomness, extend `AbstractRandomGenerator` overriding the derived methods that the RngPack implementation provides:
      import edu.cornell.lassp.houle.RngPack.RanMT;
      /**
       * AbstractRandomGenerator based on RngPack RanMT generator.
       */
      public class RngPackGenerator extends AbstractRandomGenerator {

          private RanMT random = new RanMT();

          public void setSeed(long seed) {
             random = new RanMT(seed);
          }

          public double nextDouble() {
              return random.raw();
          }

          public double nextGaussian() {
              return random.gaussian();
          }

          public int nextInt(int n) {
              return random.choose(n);
          }

          public boolean nextBoolean() {
              return random.coin();
          }
      }
  Use the Mersenne Twister RandomGenerator in place of `java.util.Random` in `RandomData`
      RandomData randomData = new RandomDataImpl(new RngPackGenerator());
  Create an adaptor instance based on the Mersenne Twister generator that can be used in place of a `Random`
       RandomGenerator generator = new RngPackGenerator();
       Random random = RandomAdaptor.createAdaptor(generator);
       // random can now be used in place of a Random instance, data generation
       // calls will be delegated to the wrapped Mersenne Twister