Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
diff libs/commons-math-2.1/docs/userguide/utilities.html @ 10:5f2c5fb36e93
commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:00:53 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libs/commons-math-2.1/docs/userguide/utilities.html Tue Jan 04 10:00:53 2011 +0100 @@ -0,0 +1,329 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> + + + + + + + + + + + +<html xmlns="http://www.w3.org/1999/xhtml"> + <head> + <title>Math - The Commons Math User Guide - Utilites</title> + <style type="text/css" media="all"> + @import url("../css/maven-base.css"); + @import url("../css/maven-theme.css"); + @import url("../css/site.css"); + </style> + <link rel="stylesheet" href="../css/print.css" type="text/css" media="print" /> + <meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1" /> + </head> + <body class="composite"> + <div id="banner"> + <span id="bannerLeft"> + + Commons Math User Guide + + </span> + <div class="clear"> + <hr/> + </div> + </div> + <div id="breadcrumbs"> + + + + + + + + + <div class="xright"> + + + + + + + + </div> + <div class="clear"> + <hr/> + </div> + </div> + <div id="leftColumn"> + <div id="navcolumn"> + + + + + + + + + <h5>User Guide</h5> + <ul> + + <li class="none"> + <a href="../userguide/index.html">Contents</a> + </li> + + <li class="none"> + <a href="../userguide/overview.html">Overview</a> + </li> + + <li class="none"> + <a href="../userguide/stat.html">Statistics</a> + </li> + + <li class="none"> + <a href="../userguide/random.html">Data Generation</a> + </li> + + <li class="none"> + <a href="../userguide/linear.html">Linear Algebra</a> + </li> + + <li class="none"> + <a href="../userguide/analysis.html">Numerical Analysis</a> + </li> + + <li class="none"> + <a href="../userguide/special.html">Special Functions</a> + </li> + + <li class="none"> + <strong>Utilities</strong> + </li> + + <li class="none"> + <a href="../userguide/complex.html">Complex Numbers</a> + </li> + + <li class="none"> + <a href="../userguide/distribution.html">Distributions</a> + </li> + + <li class="none"> + <a href="../userguide/fraction.html">Fractions</a> + </li> + + <li class="none"> + <a href="../userguide/transform.html">Transform Methods</a> + </li> + + <li class="none"> + <a href="../userguide/geometry.html">3D Geometry</a> + </li> + + <li class="none"> + <a href="../userguide/optimization.html">Optimization</a> + </li> + + <li class="none"> + <a href="../userguide/ode.html">Ordinary Differential Equations</a> + </li> + + <li class="none"> + <a href="../userguide/genetics.html">Genetic Algorithms</a> + </li> + </ul> + <a href="http://maven.apache.org/" title="Built by Maven" class="poweredBy"> + <img alt="Built by Maven" src="../images/logos/maven-feather.png"></img> + </a> + + + + + + + + + </div> + </div> + <div id="bodyColumn"> + <div id="contentBox"> + <div class="section"><h2><a name="a6_Utilities"></a>6 Utilities</h2> +<div class="section"><h3><a name="a6.1_Overview"></a>6.1 Overview</h3> +<p> + The <a href="../apidocs/org/apache/commons/math/util/package-summary.html"> + org.apache.commons.math.util</a> package collects a group of array utilities, + value transformers, and numerical routines used by implementation classes in + commons-math. + </p> +</div> +<div class="section"><h3><a name="a6.2_Double_array_utilities"></a>6.2 Double array utilities</h3> +<p> + To maintain statistics based on a "rolling" window of values, a resizable + array implementation was developed and is provided for reuse in the + <code>util</code> package. The core functionality provided is described in + the documentation for the interface, + <a href="../apidocs/org/apache/commons/math/util/DoubleArray.html"> + org.apache.commons.math.util.DoubleArray.</a> This interface adds one + method, <code>addElementRolling(double)</code> to basic list accessors. + The <code>addElementRolling</code> method adds an element + (the actual parameter) to the end of the list and removes the first element + in the list. + </p> +<p> + The <a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html"> + org.apache.commons.math.util.ResizableDoubleArray</a> class provides a + configurable, array-backed implementation of the <code>DoubleArray</code> + interface. When <code>addElementRolling</code> is invoked, the underlying + array is expanded if necessary, the new element is added to the end of the + array and the "usable window" of the array is moved forward, so that + the first element is effectively discarded, what was the second becomes the + first, and so on. To efficiently manage storage, two maintenance + operations need to be periodically performed -- orphaned elements at the + beginning of the array need to be reclaimed and space for new elements at + the end needs to be created. Both of these operations are handled + automatically, with frequency / effect driven by the configuration + properties <code>expansionMode</code>, <code>expansionFactor</code> and + <code>contractionCriteria.</code> See + <a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html"> + ResizableDoubleArray</a> + for details. + </p> +</div> +<div class="section"><h3><a name="a6.3_intdouble_hash_map"></a>6.3 int/double hash map</h3> +<p> + The <a href="../apidocs/org/apache/commons/math/util/OpenIntToDoubleHashMap.html"> + org.apache.commons.math.util.OpenIntToDoubleHashMap</a> class provides a specialized + hash map implementation for int/double. This implementation has a much smaller memory + overhead than standard <code>java.util.HashMap</code> class. It uses open addressing + and primitive arrays, which greatly reduces the number of intermediate objects and + improve data locality. + </p> +</div> +<div class="section"><h3><a name="a6.4_Continued_Fractions"></a>6.4 Continued Fractions</h3> +<p> + The <a href="../apidocs/org/apache/commons/math/util/ContinuedFraction.html"> + org.apache.commons.math.util.ContinuedFraction</a> class provides a generic + way to create and evaluate continued fractions. The easiest way to create a + continued fraction is to subclass <code>ContinuedFraction</code> and + override the <code>getA</code> and <code>getB</code> methods which return + the continued fraction terms. The precise definition of these terms is + explained in <a href="http://mathworld.wolfram.com/ContinuedFraction.html" class="externalLink"> + Continued Fraction, equation (1)</a> from MathWorld. + </p> +<p> + As an example, the constant Pi could be computed using the continued fraction + defined at <a href="http://functions.wolfram.com/Constants/Pi/10/0002/" class="externalLink"> + http://functions.wolfram.com/Constants/Pi/10/0002/</a>. The following + anonymous class provides the implementation: + <div class="source"><pre>ContinuedFraction c = new ContinuedFraction() { + public double getA(int n, double x) { + switch(n) { + case 0: return 3.0; + default: return 6.0; + } + } + + public double getB(int n, double x) { + double y = (2.0 * n) - 1.0; + return y * y; + } +}</pre> +</div> +</p> +<p> + Then, to evalute Pi, simply call any of the <code>evalute</code> methods + (Note, the point of evalution in this example is meaningless since Pi is a + constant). + </p> +<p> + For a more practical use of continued fractions, consider the exponential + function with the continued fraction definition of + <a href="http://functions.wolfram.com/ElementaryFunctions/Exp/10/" class="externalLink"> + http://functions.wolfram.com/ElementaryFunctions/Exp/10/</a>. The + following anonymous class provides its implementation: + <div class="source"><pre>ContinuedFraction c = new ContinuedFraction() { + public double getA(int n, double x) { + if (n % 2 == 0) { + switch(n) { + case 0: return 1.0; + default: return 2.0; + } + } else { + return n; + } + } + + public double getB(int n, double x) { + if (n % 2 == 0) { + return -x; + } else { + return x; + } + } +}</pre> +</div> +</p> +<p> + Then, to evalute <i>e</i><sup>x</sup> for any value x, simply call any of the + <code>evalute</code> methods. + </p> +</div> +<div class="section"><h3><a name="a6.5_binomial_coefficients_factorials_and_other_common_math_functions"></a>6.5 binomial coefficients, factorials and other common math functions</h3> +<p> + A collection of reusable math functions is provided in the + <a href="../apidocs/org/apache/commons/math/util/MathUtils.html">MathUtils</a> + utility class. MathUtils currently includes methods to compute the following: <ul><li> + Binomial coeffiecients -- "n choose k" available as an (exact) long value, + <code>binomialCoefficient(int, int)</code> for small n, k; as a double, + <code>binomialCoefficientDouble(int, int)</code> for larger values; and in + a "super-sized" version, <code>binomialCoefficientLog(int, int)</code> + that returns the natural logarithm of the value.</li> +<li> + Factorials -- like binomial coefficients, these are available as exact long + values, <code>factorial(int)</code>; doubles, + <code>factorialDouble(int)</code>; or logs, <code>factorialLog(int)</code>. </li> +<li> + Hyperbolic sine and cosine functions -- + <code>cosh(double), sinh(double)</code></li> +<li> + sign (+1 if argument > 0, 0 if x = 0, and -1 if x < 0) and + indicator (+1.0 if argument >= 0 and -1.0 if argument < 0) functions + for variables of all primitive numeric types.</li> +<li> + a hash function, <code>hash(double),</code> returning a long-valued + hash code for a double value. + </li> +<li> + Convience methods to round floating-point number to arbitrary precision. + </li> +<li> + Least common multiple and greatest common denominator functions. + </li> +</ul> +</p> +</div> +</div> + + </div> + </div> + <div class="clear"> + <hr/> + </div> + <div id="footer"> + <div class="xright">© + 2003-2010 + + + + + + + + + + </div> + <div class="clear"> + <hr/> + </div> + </div> + </body> +</html>