Merged userguide updates from MATH_1_1 release branch.
git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@358646 13f79535-47bb-0310-9956-ffa450edef68
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<?xml version="1.0"?>
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<?xml version="1.0"?>
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<!--
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<!--
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Copyright 2003-2004 The Apache Software Foundation
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Copyright 2003-2005 The Apache Software Foundation
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Licensed under the Apache License, Version 2.0 (the "License");
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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you may not use this file except in compliance with the License.
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<!-- $Revision$ $Date$ -->
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<!-- $Revision$ $Date$ -->
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<document url="stat.html">
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<document url="stat.html">
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<properties>
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<properties>
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<title>The Commons Math User Guide - Statistics</title>
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<title>The Commons Math User Guide - Complex Numbers</title>
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</properties>
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</properties>
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<body>
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<body>
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<section name="7 Complex Numbers">
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<section name="7 Complex Numbers">
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org.apache.commons.math.complex.Complex</a> provides a complex number
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org.apache.commons.math.complex.Complex</a> provides a complex number
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type that forms the basis for the complex functionality found in
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type that forms the basis for the complex functionality found in
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commons-math.
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commons-math.
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</p>
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<p>
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Complex functions and arithmetic operations are implemented in
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commons-math by applying standard computational formulas and
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following the rules for <code>java.lang.Double</code> arithmetic in
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handling infinite and <code>NaN</code> values. No attempt is made
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to comply with ANSII/IEC C99x Annex G or any other standard for
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Complex arithmetic. See the class and method javadocs for the
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<a href="../apidocs/org/apache/commons/math/complex/Complex.html">
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Complex</a> and
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<a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
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ComplexUtils</a> classes for details on computing formulas.
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</p>
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</p>
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<p>
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<p>
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To create a complex number, simply call the constructor passing in two
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To create a complex number, simply call the constructor passing in two
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<source>Complex c = new Complex(1.0, 3.0); // 1 + 3i</source>
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<source>Complex c = new Complex(1.0, 3.0); // 1 + 3i</source>
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</p>
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</p>
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<p>
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<p>
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The <code>Complex</code> class provides many unary and binary
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Complex numbers may also be created from polar representations
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using the <code>polar2Complex</code> method in
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<code>ComplexUtils</code>.
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</p>
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<p>
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The <code>Complex</code> class provides basic unary and binary
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complex number operations. These operations provide the means to add,
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complex number operations. These operations provide the means to add,
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subtract, multiple and, divide complex numbers along with other
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subtract, multiply and divide complex numbers along with other
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complex number functions similar to the real number functions found in
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complex number functions similar to the real number functions found in
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<code>java.math.BigDecimal</code>:
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<code>java.math.BigDecimal</code>:
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<source>Complex lhs = new Complex(1.0, 3.0);
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<source>Complex lhs = new Complex(1.0, 3.0);
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<subsection name="7.3 Complex Transcendental Functions" href="function">
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<subsection name="7.3 Complex Transcendental Functions" href="function">
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<p>
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<p>
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<a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
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<a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
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org.apache.commons.math.complex.ComplexMath</a> provides
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org.apache.commons.math.complex.ComplexUtils</a> provides
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implementations of serveral transcendental functions involving complex
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implementations of serveral transcendental functions involving complex
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number arguments. These operations provide the means to compute the
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number arguments. These operations provide the means to compute the
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log, sine, tangent and, other complex values similar to the real
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log, sine, tangent and, other complex values similar to the real
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// One more with three rows, two columns
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// One more with three rows, two columns
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double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
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double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
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RealMatrix n = new RealMatrixImpl(matrixData2);
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RealMatrix n = new RealMatixImpl(matrixData2);
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// Note: The constructor copies the input double[][] array.
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// Note: constructor makes a
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// Fresh copy of the input double[][] array
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// Now multiply m by n
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// Now multiply m by n
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RealMatrix p = m.multiply(n);
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RealMatrix p = m.multiply(n);
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