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diff --git a/src/main/java/org/apache/commons/math3/random/package-info.java b/src/main/java/org/apache/commons/math3/random/package-info.java new file mode 100644 index 0000000..212b018 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/random/package-info.java @@ -0,0 +1,115 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +/** + * Random number and random data generators. + * + * <p>Commons-math provides a few pseudo random number generators. The top level interface is + * RandomGenerator. It is implemented by three classes: + * + * <ul> + * <li>{@link org.apache.commons.math3.random.JDKRandomGenerator JDKRandomGenerator} that extends + * the JDK provided generator + * <li>AbstractRandomGenerator as a helper for users generators + * <li>BitStreamGenerator which is an abstract class for several generators and which in turn is + * extended by: + * <ul> + * <li>{@link org.apache.commons.math3.random.MersenneTwister MersenneTwister} + * <li>{@link org.apache.commons.math3.random.Well512a Well512a} + * <li>{@link org.apache.commons.math3.random.Well1024a Well1024a} + * <li>{@link org.apache.commons.math3.random.Well19937a Well19937a} + * <li>{@link org.apache.commons.math3.random.Well19937c Well19937c} + * <li>{@link org.apache.commons.math3.random.Well44497a Well44497a} + * <li>{@link org.apache.commons.math3.random.Well44497b Well44497b} + * </ul> + * </ul> + * + * <p>The JDK provided generator is a simple one that can be used only for very simple needs. The + * Mersenne Twister is a fast generator with very good properties well suited for Monte-Carlo + * simulation. It is equidistributed for generating vectors up to dimension 623 and has a huge + * period: 2<sup>19937</sup> - 1 (which is a Mersenne prime). This generator is described in a paper + * by Makoto Matsumoto and Takuji Nishimura in 1998: <a + * href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf">Mersenne Twister: A + * 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator</a>, ACM Transactions on + * Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30. The WELL generators are + * a family of generators with period ranging from 2<sup>512</sup> - 1 to 2<sup>44497</sup> - 1 + * (this last one is also a Mersenne prime) with even better properties than Mersenne Twister. These + * generators are described in a paper by François Panneton, Pierre L'Ecuyer and Makoto + * Matsumoto <a href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved + * Long-Period Generators Based on Linear Recurrences Modulo 2</a> ACM Transactions on Mathematical + * Software, 32, 1 (2006). The errata for the paper are in <a + * href="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng-errata.txt">wellrng-errata.txt</a>. + * + * <p>For simple sampling, any of these generators is sufficient. For Monte-Carlo simulations the + * JDK generator does not have any of the good mathematical properties of the other generators, so + * it should be avoided. The Mersenne twister and WELL generators have equidistribution properties + * proven according to their bits pool size which is directly linked to their period (all of them + * have maximal period, i.e. a generator with size n pool has a period 2<sup>n</sup>-1). They also + * have equidistribution properties for 32 bits blocks up to s/32 dimension where s is their pool + * size. So WELL19937c for exemple is equidistributed up to dimension 623 (19937/32). This means a + * Monte-Carlo simulation generating a vector of n variables at each iteration has some guarantees + * on the properties of the vector as long as its dimension does not exceed the limit. However, + * since we use bits from two successive 32 bits generated integers to create one double, this limit + * is smaller when the variables are of type double. so for Monte-Carlo simulation where less the 16 + * doubles are generated at each round, WELL1024 may be sufficient. If a larger number of doubles + * are needed a generator with a larger pool would be useful. + * + * <p>The WELL generators are more modern then MersenneTwister (the paper describing than has been + * published in 2006 instead of 1998) and fix some of its (few) drawbacks. If initialization array + * contains many zero bits, MersenneTwister may take a very long time (several hundreds of thousands + * of iterations to reach a steady state with a balanced number of zero and one in its bits pool). + * So the WELL generators are better to <i>escape zeroland</i> as explained by the WELL generators + * creators. The Well19937a and Well44497a generator are not maximally equidistributed (i.e. there + * are some dimensions or bits blocks size for which they are not equidistributed). The Well512a, + * Well1024a, Well19937c and Well44497b are maximally equidistributed for blocks size up to 32 bits + * (they should behave correctly also for double based on more than 32 bits blocks, but + * equidistribution is not proven at these blocks sizes). + * + * <p>The MersenneTwister generator uses a 624 elements integer array, so it consumes less than 2.5 + * kilobytes. The WELL generators use 6 integer arrays with a size equal to the pool size, so for + * example the WELL44497b generator uses about 33 kilobytes. This may be important if a very large + * number of generator instances were used at the same time. + * + * <p>All generators are quite fast. As an example, here are some comparisons, obtained on a 64 bits + * JVM on a linux computer with a 2008 processor (AMD phenom Quad 9550 at 2.2 GHz). The generation + * rate for MersenneTwister was about 27 millions doubles per second (remember we generate two 32 + * bits integers for each double). Generation rates for other PRNG, relative to MersenneTwister: + * + * <p> + * + * <table border="1" align="center"> + * <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example of performances</font></td></tr> + * <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation rate (relative to MersenneTwister)</td></font></tr> + * <tr><td>{@link org.apache.commons.math3.random.MersenneTwister MersenneTwister}</td><td>1</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.JDKRandomGenerator JDKRandomGenerator}</td><td>between 0.96 and 1.16</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well512a Well512a}</td><td>between 0.85 and 0.88</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well1024a Well1024a}</td><td>between 0.63 and 0.73</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well19937a Well19937a}</td><td>between 0.70 and 0.71</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well19937c Well19937c}</td><td>between 0.57 and 0.71</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well44497a Well44497a}</td><td>between 0.69 and 0.71</td></tr> + * <tr><td>{@link org.apache.commons.math3.random.Well44497b Well44497b}</td><td>between 0.65 and 0.71</td></tr> + * </table> + * + * <p>So for most simulation problems, the better generators like {@link + * org.apache.commons.math3.random.Well19937c Well19937c} and {@link + * org.apache.commons.math3.random.Well44497b Well44497b} are probably very good choices. + * + * <p>Note that <em>none</em> of these generators are suitable for cryptography. They are devoted to + * simulation, and to generate very long series with strong properties on the series as a whole + * (equidistribution, no correlation ...). They do not attempt to create small series but with very + * strong properties of unpredictability as needed in cryptography. + */ +package org.apache.commons.math3.random; |