Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
diff libs/commons-math-2.1/docs/userguide/complex.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/complex.html Tue Jan 04 10:00:53 2011 +0100 @@ -0,0 +1,299 @@ +<!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 - Complex Numbers</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"> + <a href="../userguide/utilities.html">Utilities</a> + </li> + + <li class="none"> + <strong>Complex Numbers</strong> + </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="a7_Complex_Numbers"></a>7 Complex Numbers</h2> +<div class="section"><h3><a name="a7.1_Overview"></a>7.1 Overview</h3> +<p> + The complex packages provides a complex number type as well as complex + versions of common transcendental functions and complex number + formatting. + </p> +</div> +<div class="section"><h3><a name="a7.2_Complex_Numbers"></a>7.2 Complex Numbers</h3> +<p><a href="../apidocs/org/apache/commons/math/complex/Complex.html"> + org.apache.commons.math.complex.Complex</a> provides a complex number + type that forms the basis for the complex functionality found in + commons-math. + </p> +<p> + Complex functions and arithmetic operations are implemented in + commons-math by applying standard computational formulas and + following the rules for <code>java.lang.Double</code> arithmetic in + handling infinite and <code>NaN</code> values. No attempt is made + to comply with ANSII/IEC C99x Annex G or any other standard for + Complex arithmetic. See the class and method javadocs for the + <a href="../apidocs/org/apache/commons/math/complex/Complex.html"> + Complex</a> and + <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html"> + ComplexUtils</a> classes for details on computing formulas. + </p> +<p> + To create a complex number, simply call the constructor passing in two + floating-point arguments, the first being the real part of the + complex number and the second being the imaginary part: + <div class="source"><pre>Complex c = new Complex(1.0, 3.0); // 1 + 3i</pre> +</div> +</p> +<p> + Complex numbers may also be created from polar representations + using the <code>polar2Complex</code> method in + <code>ComplexUtils</code>. + </p> +<p> + The <code>Complex</code> class provides basic unary and binary + complex number operations. These operations provide the means to add, + subtract, multiply and divide complex numbers along with other + complex number functions similar to the real number functions found in + <code>java.math.BigDecimal</code>: + <div class="source"><pre>Complex lhs = new Complex(1.0, 3.0); +Complex rhs = new Complex(2.0, 5.0); + +Complex answer = lhs.add(rhs); // add two complex numbers + answer = lhs.subtract(rhs); // subtract two complex numbers + answer = lhs.abs(); // absolute value + answer = lhs.conjugate(rhs); // complex conjugate</pre> +</div> +</p> +</div> +<div class="section"><h3><a name="a7.3_Complex_Transcendental_Functions"></a>7.3 Complex Transcendental Functions</h3> +<p><a href="../apidocs/org/apache/commons/math/complex/Complex.html"> + org.apache.commons.math.complex.Complex</a> also provides + implementations of serveral transcendental functions involving complex + number arguments. Prior to version 1.2, these functions were provided + by <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html"> + org.apache.commons.math.complex.ComplexUtils</a> in a way similar to the real + number functions found in <code>java.lang.Math</code>, but this has been + deprecated. These operations provide the means to compute the log, sine, + tangent, and other complex values : + <div class="source"><pre>Complex first = new Complex(1.0, 3.0); +Complex second = new Complex(2.0, 5.0); + +Complex answer = first.log(); // natural logarithm. + answer = first.cos(); // cosine + answer = first.pow(second); // first raised to the power of second</pre> +</div> +</p> +</div> +<div class="section"><h3><a name="a7.4_Complex_Formatting_and_Parsing"></a>7.4 Complex Formatting and Parsing</h3> +<p><code>Complex</code> instances can be converted to and from strings + using the<a href="../apidocs/org/apache/commons/math/complex/ComplexFormat.html"> + org.apache.commons.math.complex.ComplexFormat</a> class. + <code>ComplexFormat</code> is a <code>java.text.Format</code> + extension and, as such, is used like other formatting objects (e.g. + <code>java.text.SimpleDateFormat</code>): + <div class="source"><pre>ComplexFormat format = new ComplexFormat(); // default format +Complex c = new Complex(1.1111, 2.2222); +String s = format.format(c); // s contains "1.11 + 2.22i"</pre> +</div> +</p> +<p> + To customize the formatting output, one or two + <code>java.text.NumberFormat</code> instances can be used to construct + a <code>ComplexFormat</code>. These number formats control the + formatting of the real and imaginary values of the complex number: + <div class="source"><pre>NumberFormat nf = NumberFormat.getInstance(); +nf.setMinimumFractionDigits(3); +nf.setMaximumFractionDigits(3); + +// create complex format with custom number format +// when one number format is used, both real and +// imaginary parts are formatted the same +ComplexFormat cf = new ComplexFormat(nf); +Complex c = new Complex(1.11, 2.2222); +String s = format.format(c); // s contains "1.110 + 2.222i" + +NumberFormat nf2 = NumberFormat.getInstance(); +nf.setMinimumFractionDigits(1); +nf.setMaximumFractionDigits(1); + +// create complex format with custom number formats +cf = new ComplexFormat(nf, nf2); +s = format.format(c); // s contains "1.110 + 2.2i"</pre> +</div> +</p> +<p> + Another formatting customization provided by + <code>ComplexFormat</code> is the text used for the imaginary + designation. By default, the imaginary notation is "i" but, it can be + manipulated using the <code>setImaginaryCharacter</code> method. + </p> +<p> + Formatting inverse operation, parsing, can also be performed by + <code>ComplexFormat</code>. Parse a complex number from a string, + simply call the <code>parse</code> method: + <div class="source"><pre>ComplexFormat cf = new ComplexFormat(); +Complex c = cf.parse("1.110 + 2.222i");</pre> +</div> +</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>