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Removed obsolete documentation.
Project: http://gitwipus.apache.org/repos/asf/commonsmath/repo
Commit: http://gitwipus.apache.org/repos/asf/commonsmath/commit/34b96986
Tree: http://gitwipus.apache.org/repos/asf/commonsmath/tree/34b96986
Diff: http://gitwipus.apache.org/repos/asf/commonsmath/diff/34b96986
Branch: refs/heads/taskMATH1366
Commit: 34b96986624a87da2f0f2b3d2878c7be4d0eb25c
Parents: 156dfa6
Author: Gilles <gilles@harfang.homelinux.org>
Authored: Sun May 29 18:08:41 2016 +0200
Committer: Gilles <gilles@harfang.homelinux.org>
Committed: Sun May 29 18:08:41 2016 +0200

.../commons/math4/random/packageinfo.java  127 ++
1 file changed, 14 insertions(+), 113 deletions()

http://gitwipus.apache.org/repos/asf/commonsmath/blob/34b96986/src/main/java/org/apache/commons/math4/random/packageinfo.java

diff git a/src/main/java/org/apache/commons/math4/random/packageinfo.java b/src/main/java/org/apache/commons/math4/random/packageinfo.java
index 4d42815..45d810a 100644
 a/src/main/java/org/apache/commons/math4/random/packageinfo.java
+++ b/src/main/java/org/apache/commons/math4/random/packageinfo.java
@@ 15,118 +15,19 @@
* limitations under the License.
*/
/**
 *
 * <p>Random number and random data generators.</p>
 * <p>Commonsmath 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.math4.random.JDKRandomGenerator JDKRandomGenerator}
 * that extends the JDK provided generator</li>
 * <li>AbstractRandomGenerator as a helper for users generators</li>
 * <li>BitStreamGenerator which is an abstract class for several generators
and
 * which in turn is extended by:
 * <ul>
 * <li>{@link org.apache.commons.math4.random.MersenneTwister MersenneTwister}</li>
 * <li>{@link org.apache.commons.math4.random.Well512a Well512a}</li>
 * <li>{@link org.apache.commons.math4.random.Well1024a Well1024a}</li>
 * <li>{@link org.apache.commons.math4.random.Well19937a Well19937a}</li>
 * <li>{@link org.apache.commons.math4.random.Well19937c Well19937c}</li>
 * <li>{@link org.apache.commons.math4.random.Well44497a Well44497a}</li>
 * <li>{@link org.apache.commons.math4.random.Well44497b Well44497b}</li>
 * </ul>
 * </li>
 * </ul>
 * </p>
 *
 * <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
 * MonteCarlo 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.hiroshimau.ac.jp/~mmat/MT/ARTICLES/mt.pdf">Mersenne
Twister:
 * A 623Dimensionally Equidistributed Uniform PseudoRandom Number Generator</a>,
ACM
 * Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp
330.
 * 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
LongPeriod
 * 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/wellrngerrata.txt">wellrngerrata.txt</a>.
 * </p>
 *
 * <p>
 * For simple sampling, any of these generators is sufficient. For MonteCarlo 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 MonteCarlo
 * 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 MonteCarlo 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>
 *
 * <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>
 *
 * <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>
 *
 * <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>
 *
 * <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.math4.random.MersenneTwister MersenneTwister}</td><td>1</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.JDKRandomGenerator
JDKRandomGenerator}</td><td>between 0.96 and 1.16</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well512a Well512a}</td><td>between
0.85 and 0.88</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well1024a Well1024a}</td><td>between
0.63 and 0.73</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well19937a Well19937a}</td><td>between
0.70 and 0.71</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well19937c Well19937c}</td><td>between
0.57 and 0.71</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well44497a Well44497a}</td><td>between
0.69 and 0.71</td></tr>
 * <tr><td>{@link org.apache.commons.math4.random.Well44497b Well44497b}</td><td>between
0.65 and 0.71</td></tr>
 * </table>
 * </p>
 *
 * <p>
 * So for most simulation problems, the better generators like {@link
 * org.apache.commons.math4.random.Well19937c Well19937c} and {@link
 * org.apache.commons.math4.random.Well44497b Well44497b} are probably very good choices.
 * </p>
 *
 * <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.
 * </p>
 *
 *
+ * <p>Random Data Generation</p>
+ *
+ * <p>
+ * Some of the utilities in this package use the pseudorandom number
+ * generators defined in package {@link org.apache.commons.math4.rng}
+ * to provide higher level functionality (such as random strings) based
+ * on an underlying source of randomness that provides sequences of
+ * uniformly distributed integers.
+ * </p>
+ * <p>
+ * Others are sources of pseudorandomness that directly produce "compound"
+ * types such as {@link org.apache.commons.math4.random.RandomVectorGenerator
+ * random vectors}.
+ * </p>
*/
package org.apache.commons.math4.random;
