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From l..@apache.org
Subject svn commit: r857590 [11/48] - in /websites/production/commons/content/proper/commons-math/xref-test: ./ org/apache/commons/math3/ org/apache/commons/math3/analysis/ org/apache/commons/math3/analysis/differentiation/ org/apache/commons/math3/analysis/fu...
Date Sun, 07 Apr 2013 07:52:13 GMT
Added: websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3DTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3DTest.html (added)
+++ websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3DTest.html Sun Apr  7 07:52:05 2013
@@ -0,0 +1,744 @@
+<!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" xml:lang="en" lang="en">
+<head>
+<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<title>FieldVector3DTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../../../testapidocs/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3DTest.html">View Javadoc</a></div><pre>
+
+<a class="jxr_linenumber" name="1" href="#1">1</a>   <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="2" href="#2">2</a>   <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em>
+<a class="jxr_linenumber" name="3" href="#3">3</a>   <em class="jxr_comment"> * contributor license agreements.  See the NOTICE file distributed with</em>
+<a class="jxr_linenumber" name="4" href="#4">4</a>   <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em>
+<a class="jxr_linenumber" name="5" href="#5">5</a>   <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em>
+<a class="jxr_linenumber" name="6" href="#6">6</a>   <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em>
+<a class="jxr_linenumber" name="7" href="#7">7</a>   <em class="jxr_comment"> * the License.  You may obtain a copy of the License at</em>
+<a class="jxr_linenumber" name="8" href="#8">8</a>   <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="9" href="#9">9</a>   <em class="jxr_comment"> *      <a href="http://www.apache.org/licenses/LICENSE-2.0" target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em>
+<a class="jxr_linenumber" name="10" href="#10">10</a>  <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="11" href="#11">11</a>  <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em>
+<a class="jxr_linenumber" name="12" href="#12">12</a>  <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em>
+<a class="jxr_linenumber" name="13" href="#13">13</a>  <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em>
+<a class="jxr_linenumber" name="14" href="#14">14</a>  <em class="jxr_comment"> * See the License for the specific language governing permissions and</em>
+<a class="jxr_linenumber" name="15" href="#15">15</a>  <em class="jxr_comment"> * limitations under the License.</em>
+<a class="jxr_linenumber" name="16" href="#16">16</a>  <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="17" href="#17">17</a>  
+<a class="jxr_linenumber" name="18" href="#18">18</a>  <strong class="jxr_keyword">package</strong> org.apache.commons.math3.geometry.euclidean.threed;
+<a class="jxr_linenumber" name="19" href="#19">19</a>  
+<a class="jxr_linenumber" name="20" href="#20">20</a>  <strong class="jxr_keyword">import</strong> java.text.DecimalFormat;
+<a class="jxr_linenumber" name="21" href="#21">21</a>  <strong class="jxr_keyword">import</strong> java.text.DecimalFormatSymbols;
+<a class="jxr_linenumber" name="22" href="#22">22</a>  <strong class="jxr_keyword">import</strong> java.text.NumberFormat;
+<a class="jxr_linenumber" name="23" href="#23">23</a>  <strong class="jxr_keyword">import</strong> java.util.Locale;
+<a class="jxr_linenumber" name="24" href="#24">24</a>  
+<a class="jxr_linenumber" name="25" href="#25">25</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+<a class="jxr_linenumber" name="26" href="#26">26</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.DimensionMismatchException;
+<a class="jxr_linenumber" name="27" href="#27">27</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.MathArithmeticException;
+<a class="jxr_linenumber" name="28" href="#28">28</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.random.Well1024a;
+<a class="jxr_linenumber" name="29" href="#29">29</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
+<a class="jxr_linenumber" name="30" href="#30">30</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.Precision;
+<a class="jxr_linenumber" name="31" href="#31">31</a>  <strong class="jxr_keyword">import</strong> org.junit.Assert;
+<a class="jxr_linenumber" name="32" href="#32">32</a>  <strong class="jxr_keyword">import</strong> org.junit.Test;
+<a class="jxr_linenumber" name="33" href="#33">33</a>  
+<a class="jxr_linenumber" name="34" href="#34">34</a>  <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/FieldVector3DTest.html">FieldVector3DTest</a> {
+<a class="jxr_linenumber" name="35" href="#35">35</a>  
+<a class="jxr_linenumber" name="36" href="#36">36</a>      @Test
+<a class="jxr_linenumber" name="37" href="#37">37</a>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testConstructors() <strong class="jxr_keyword">throws</strong> DimensionMismatchException {
+<a class="jxr_linenumber" name="38" href="#38">38</a>          <strong class="jxr_keyword">double</strong> cosAlpha = 1 / 2.0;
+<a class="jxr_linenumber" name="39" href="#39">39</a>          <strong class="jxr_keyword">double</strong> sinAlpha = FastMath.sqrt(3) / 2.0;
+<a class="jxr_linenumber" name="40" href="#40">40</a>          <strong class="jxr_keyword">double</strong> cosDelta = FastMath.sqrt(2) / 2.0;
+<a class="jxr_linenumber" name="41" href="#41">41</a>          <strong class="jxr_keyword">double</strong> sinDelta = -FastMath.sqrt(2) / 2.0;
+<a class="jxr_linenumber" name="42" href="#42">42</a>          FieldVector3D&lt;DerivativeStructure&gt; u = <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(2,
+<a class="jxr_linenumber" name="43" href="#43">43</a>                  <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(2, 1, 0,  FastMath.PI / 3),
+<a class="jxr_linenumber" name="44" href="#44">44</a>                          <strong class="jxr_keyword">new</strong> DerivativeStructure(2, 1, 1, -FastMath.PI / 4)));
+<a class="jxr_linenumber" name="45" href="#45">45</a>          checkVector(u, 2 * cosAlpha * cosDelta, 2 * sinAlpha * cosDelta, 2 * sinDelta);
+<a class="jxr_linenumber" name="46" href="#46">46</a>          Assert.assertEquals(-2 * sinAlpha * cosDelta, u.getX().getPartialDerivative(1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="47" href="#47">47</a>          Assert.assertEquals(+2 * cosAlpha * cosDelta, u.getY().getPartialDerivative(1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="48" href="#48">48</a>          Assert.assertEquals(0,                        u.getZ().getPartialDerivative(1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="49" href="#49">49</a>          Assert.assertEquals(-2 * cosAlpha * sinDelta, u.getX().getPartialDerivative(0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="50" href="#50">50</a>          Assert.assertEquals(-2 * sinAlpha * sinDelta, u.getY().getPartialDerivative(0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="51" href="#51">51</a>          Assert.assertEquals(2 * cosDelta,             u.getZ().getPartialDerivative(0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="52" href="#52">52</a>  
+<a class="jxr_linenumber" name="53" href="#53">53</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(2, createVector(1, 0,  0, 3)),
+<a class="jxr_linenumber" name="54" href="#54">54</a>                                     2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2);
+<a class="jxr_linenumber" name="55" href="#55">55</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="56" href="#56">56</a>                                     createVector(1, 0,  0, 4)),
+<a class="jxr_linenumber" name="57" href="#57">57</a>                                     2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0);
+<a class="jxr_linenumber" name="58" href="#58">58</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="59" href="#59">59</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(1, 0,  0)),
+<a class="jxr_linenumber" name="60" href="#60">60</a>                                     2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0);
+<a class="jxr_linenumber" name="61" href="#61">61</a>  
+<a class="jxr_linenumber" name="62" href="#62">62</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(2, createVector(1, 0,  0, 3),
+<a class="jxr_linenumber" name="63" href="#63">63</a>                                     -3, createVector(0, 0, -1, 3)),
+<a class="jxr_linenumber" name="64" href="#64">64</a>                                     2, 0, 3, -1, 0, 0, 0, -1, 0, 0, 0, -1);
+<a class="jxr_linenumber" name="65" href="#65">65</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="66" href="#66">66</a>                                     createVector(1, 0,  0, 4),
+<a class="jxr_linenumber" name="67" href="#67">67</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="68" href="#68">68</a>                                     createVector(0, 0, -1, 4)),
+<a class="jxr_linenumber" name="69" href="#69">69</a>                                     2, 0, 3, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1);
+<a class="jxr_linenumber" name="70" href="#70">70</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="71" href="#71">71</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(1, 0,  0),
+<a class="jxr_linenumber" name="72" href="#72">72</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="73" href="#73">73</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(0, 0, -1)),
+<a class="jxr_linenumber" name="74" href="#74">74</a>                                     2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1);
+<a class="jxr_linenumber" name="75" href="#75">75</a>  
+<a class="jxr_linenumber" name="76" href="#76">76</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(2, createVector(1, 0, 0, 3),
+<a class="jxr_linenumber" name="77" href="#77">77</a>                                     5, createVector(0, 1, 0, 3),
+<a class="jxr_linenumber" name="78" href="#78">78</a>                                     -3, createVector(0, 0, -1, 3)),
+<a class="jxr_linenumber" name="79" href="#79">79</a>                                     2, 5, 3, 4, 0, 0, 0, 4, 0, 0, 0, 4);
+<a class="jxr_linenumber" name="80" href="#80">80</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="81" href="#81">81</a>                                     createVector(1, 0,  0, 4),
+<a class="jxr_linenumber" name="82" href="#82">82</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="83" href="#83">83</a>                                     createVector(0, 1,  0, 4),
+<a class="jxr_linenumber" name="84" href="#84">84</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="85" href="#85">85</a>                                     createVector(0, 0, -1, 4)),
+<a class="jxr_linenumber" name="86" href="#86">86</a>                                     2, 5, 3, 4, 0, 0, 1, 0, 4, 0, 1, 0, 0, 4, -1);
+<a class="jxr_linenumber" name="87" href="#87">87</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="88" href="#88">88</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(1, 0,  0),
+<a class="jxr_linenumber" name="89" href="#89">89</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="90" href="#90">90</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(0, 1,  0),
+<a class="jxr_linenumber" name="91" href="#91">91</a>                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="92" href="#92">92</a>                                     <strong class="jxr_keyword">new</strong> Vector3D(0, 0, -1)),
+<a class="jxr_linenumber" name="93" href="#93">93</a>                                     2, 5, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1);
+<a class="jxr_linenumber" name="94" href="#94">94</a>  
+<a class="jxr_linenumber" name="95" href="#95">95</a>          checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(2, createVector(1, 0, 0, 3),
+<a class="jxr_linenumber" name="96" href="#96">96</a>                                     5, createVector(0, 1, 0, 3),
+<a class="jxr_linenumber" name="97" href="#97">97</a>                                     5, createVector(0, -1, 0, 3),
+<a class="jxr_linenumber" name="98" href="#98">98</a>                                     -3, createVector(0, 0, -1, 3)),
+<a class="jxr_linenumber" name="99" href="#99">99</a>                                     2, 0, 3, 9, 0, 0, 0, 9, 0, 0, 0, 9);
+<a class="jxr_linenumber" name="100" href="#100">100</a>         checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="101" href="#101">101</a>                                    createVector(1, 0,  0, 4),
+<a class="jxr_linenumber" name="102" href="#102">102</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="103" href="#103">103</a>                                    createVector(0, 1,  0, 4),
+<a class="jxr_linenumber" name="104" href="#104">104</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="105" href="#105">105</a>                                    createVector(0, -1,  0, 4),
+<a class="jxr_linenumber" name="106" href="#106">106</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="107" href="#107">107</a>                                    createVector(0, 0, -1, 4)),
+<a class="jxr_linenumber" name="108" href="#108">108</a>                                    2, 0, 3, 9, 0, 0, 1, 0, 9, 0, 0, 0, 0, 9, -1);
+<a class="jxr_linenumber" name="109" href="#109">109</a>         checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  2.0),
+<a class="jxr_linenumber" name="110" href="#110">110</a>                                    <strong class="jxr_keyword">new</strong> Vector3D(1, 0,  0),
+<a class="jxr_linenumber" name="111" href="#111">111</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="112" href="#112">112</a>                                    <strong class="jxr_keyword">new</strong> Vector3D(0, 1,  0),
+<a class="jxr_linenumber" name="113" href="#113">113</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3,  5.0),
+<a class="jxr_linenumber" name="114" href="#114">114</a>                                    <strong class="jxr_keyword">new</strong> Vector3D(0, -1,  0),
+<a class="jxr_linenumber" name="115" href="#115">115</a>                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, -3.0),
+<a class="jxr_linenumber" name="116" href="#116">116</a>                                    <strong class="jxr_keyword">new</strong> Vector3D(0, 0, -1)),
+<a class="jxr_linenumber" name="117" href="#117">117</a>                                    2, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1);
+<a class="jxr_linenumber" name="118" href="#118">118</a> 
+<a class="jxr_linenumber" name="119" href="#119">119</a>         checkVector(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure[] {
+<a class="jxr_linenumber" name="120" href="#120">120</a>             <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2,  2),
+<a class="jxr_linenumber" name="121" href="#121">121</a>             <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1,  5),
+<a class="jxr_linenumber" name="122" href="#122">122</a>             <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, -3)
+<a class="jxr_linenumber" name="123" href="#123">123</a>         }),
+<a class="jxr_linenumber" name="124" href="#124">124</a>         2, 5, -3, 0, 0, 1, 0, 1, 0, 1, 0, 0);
+<a class="jxr_linenumber" name="125" href="#125">125</a> 
+<a class="jxr_linenumber" name="126" href="#126">126</a>     }
+<a class="jxr_linenumber" name="127" href="#127">127</a> 
+<a class="jxr_linenumber" name="128" href="#128">128</a>     @Test
+<a class="jxr_linenumber" name="129" href="#129">129</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testEquals() {
+<a class="jxr_linenumber" name="130" href="#130">130</a>         FieldVector3D&lt;DerivativeStructure&gt; u1 = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="131" href="#131">131</a>         FieldVector3D&lt;DerivativeStructure&gt; v  = createVector(1, 2, 3 + 10 * Precision.EPSILON, 3);
+<a class="jxr_linenumber" name="132" href="#132">132</a>         Assert.assertTrue(u1.equals(u1));
+<a class="jxr_linenumber" name="133" href="#133">133</a>         Assert.assertTrue(u1.equals(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0),
+<a class="jxr_linenumber" name="134" href="#134">134</a>                                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, 2.0),
+<a class="jxr_linenumber" name="135" href="#135">135</a>                                                    <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 3.0))));
+<a class="jxr_linenumber" name="136" href="#136">136</a>         Assert.assertFalse(u1.equals(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1.0),
+<a class="jxr_linenumber" name="137" href="#137">137</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, 2.0),
+<a class="jxr_linenumber" name="138" href="#138">138</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 3.0))));
+<a class="jxr_linenumber" name="139" href="#139">139</a>         Assert.assertFalse(u1.equals(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0),
+<a class="jxr_linenumber" name="140" href="#140">140</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2.0),
+<a class="jxr_linenumber" name="141" href="#141">141</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 3.0))));
+<a class="jxr_linenumber" name="142" href="#142">142</a>         Assert.assertFalse(u1.equals(<strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0),
+<a class="jxr_linenumber" name="143" href="#143">143</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, 2.0),
+<a class="jxr_linenumber" name="144" href="#144">144</a>                                                     <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 3.0))));
+<a class="jxr_linenumber" name="145" href="#145">145</a>         Assert.assertFalse(u1.equals(v));
+<a class="jxr_linenumber" name="146" href="#146">146</a>         Assert.assertFalse(u1.equals(u1.toVector3D()));
+<a class="jxr_linenumber" name="147" href="#147">147</a>         Assert.assertTrue(createVector(0, Double.NaN, 0, 3).equals(createVector(0, 0, Double.NaN, 3)));
+<a class="jxr_linenumber" name="148" href="#148">148</a>     }
+<a class="jxr_linenumber" name="149" href="#149">149</a> 
+<a class="jxr_linenumber" name="150" href="#150">150</a>     @Test
+<a class="jxr_linenumber" name="151" href="#151">151</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testHash() {
+<a class="jxr_linenumber" name="152" href="#152">152</a>         Assert.assertEquals(createVector(0, Double.NaN, 0, 3).hashCode(), createVector(0, 0, Double.NaN, 3).hashCode());
+<a class="jxr_linenumber" name="153" href="#153">153</a>         FieldVector3D&lt;DerivativeStructure&gt; u = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="154" href="#154">154</a>         FieldVector3D&lt;DerivativeStructure&gt; v = createVector(1, 2, 3 + 10 * Precision.EPSILON, 3);
+<a class="jxr_linenumber" name="155" href="#155">155</a>         Assert.assertTrue(u.hashCode() != v.hashCode());
+<a class="jxr_linenumber" name="156" href="#156">156</a>     }
+<a class="jxr_linenumber" name="157" href="#157">157</a> 
+<a class="jxr_linenumber" name="158" href="#158">158</a>     @Test
+<a class="jxr_linenumber" name="159" href="#159">159</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testInfinite() {
+<a class="jxr_linenumber" name="160" href="#160">160</a>         Assert.assertTrue(createVector(1, 1, Double.NEGATIVE_INFINITY, 3).isInfinite());
+<a class="jxr_linenumber" name="161" href="#161">161</a>         Assert.assertTrue(createVector(1, Double.NEGATIVE_INFINITY, 1, 3).isInfinite());
+<a class="jxr_linenumber" name="162" href="#162">162</a>         Assert.assertTrue(createVector(Double.NEGATIVE_INFINITY, 1, 1, 3).isInfinite());
+<a class="jxr_linenumber" name="163" href="#163">163</a>         Assert.assertFalse(createVector(1, 1, 2, 3).isInfinite());
+<a class="jxr_linenumber" name="164" href="#164">164</a>         Assert.assertFalse(createVector(1, Double.NaN, Double.NEGATIVE_INFINITY, 3).isInfinite());
+<a class="jxr_linenumber" name="165" href="#165">165</a>     }
+<a class="jxr_linenumber" name="166" href="#166">166</a> 
+<a class="jxr_linenumber" name="167" href="#167">167</a>     @Test
+<a class="jxr_linenumber" name="168" href="#168">168</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNaN() {
+<a class="jxr_linenumber" name="169" href="#169">169</a>         Assert.assertTrue(createVector(1, 1, Double.NaN, 3).isNaN());
+<a class="jxr_linenumber" name="170" href="#170">170</a>         Assert.assertTrue(createVector(1, Double.NaN, 1, 3).isNaN());
+<a class="jxr_linenumber" name="171" href="#171">171</a>         Assert.assertTrue(createVector(Double.NaN, 1, 1, 3).isNaN());
+<a class="jxr_linenumber" name="172" href="#172">172</a>         Assert.assertFalse(createVector(1, 1, 2, 3).isNaN());
+<a class="jxr_linenumber" name="173" href="#173">173</a>         Assert.assertFalse(createVector(1, 1, Double.NEGATIVE_INFINITY, 3).isNaN());
+<a class="jxr_linenumber" name="174" href="#174">174</a>     }
+<a class="jxr_linenumber" name="175" href="#175">175</a> 
+<a class="jxr_linenumber" name="176" href="#176">176</a>     @Test
+<a class="jxr_linenumber" name="177" href="#177">177</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testToString() {
+<a class="jxr_linenumber" name="178" href="#178">178</a>         Assert.assertEquals(<span class="jxr_string">"{3; 2; 1}"</span>, createVector(3, 2, 1, 3).toString());
+<a class="jxr_linenumber" name="179" href="#179">179</a>         NumberFormat format = <strong class="jxr_keyword">new</strong> DecimalFormat(<span class="jxr_string">"0.000"</span>, <strong class="jxr_keyword">new</strong> DecimalFormatSymbols(Locale.US));
+<a class="jxr_linenumber" name="180" href="#180">180</a>         Assert.assertEquals(<span class="jxr_string">"{3.000; 2.000; 1.000}"</span>, createVector(3, 2, 1, 3).toString(format));
+<a class="jxr_linenumber" name="181" href="#181">181</a>     }
+<a class="jxr_linenumber" name="182" href="#182">182</a> 
+<a class="jxr_linenumber" name="183" href="#183">183</a>     @Test(expected=DimensionMismatchException.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="184" href="#184">184</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testWrongDimension() <strong class="jxr_keyword">throws</strong> DimensionMismatchException {
+<a class="jxr_linenumber" name="185" href="#185">185</a>         <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure[] {
+<a class="jxr_linenumber" name="186" href="#186">186</a>             <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 2),
+<a class="jxr_linenumber" name="187" href="#187">187</a>             <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 5)
+<a class="jxr_linenumber" name="188" href="#188">188</a>         });
+<a class="jxr_linenumber" name="189" href="#189">189</a>     }
+<a class="jxr_linenumber" name="190" href="#190">190</a> 
+<a class="jxr_linenumber" name="191" href="#191">191</a>     @Test
+<a class="jxr_linenumber" name="192" href="#192">192</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCoordinates() {
+<a class="jxr_linenumber" name="193" href="#193">193</a>         FieldVector3D&lt;DerivativeStructure&gt; v = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="194" href="#194">194</a>         Assert.assertTrue(FastMath.abs(v.getX().getReal() - 1) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="195" href="#195">195</a>         Assert.assertTrue(FastMath.abs(v.getY().getReal() - 2) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="196" href="#196">196</a>         Assert.assertTrue(FastMath.abs(v.getZ().getReal() - 3) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="197" href="#197">197</a>         DerivativeStructure[] coordinates = v.toArray();
+<a class="jxr_linenumber" name="198" href="#198">198</a>         Assert.assertTrue(FastMath.abs(coordinates[0].getReal() - 1) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="199" href="#199">199</a>         Assert.assertTrue(FastMath.abs(coordinates[1].getReal() - 2) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="200" href="#200">200</a>         Assert.assertTrue(FastMath.abs(coordinates[2].getReal() - 3) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="201" href="#201">201</a>     }
+<a class="jxr_linenumber" name="202" href="#202">202</a> 
+<a class="jxr_linenumber" name="203" href="#203">203</a>     @Test
+<a class="jxr_linenumber" name="204" href="#204">204</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNorm1() {
+<a class="jxr_linenumber" name="205" href="#205">205</a>         Assert.assertEquals( 0.0, createVector(0, 0, 0, 3).getNorm1().getReal(), 0);
+<a class="jxr_linenumber" name="206" href="#206">206</a>         Assert.assertEquals( 6.0, createVector(1, -2, 3, 3).getNorm1().getReal(), 0);
+<a class="jxr_linenumber" name="207" href="#207">207</a>         Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="208" href="#208">208</a>         Assert.assertEquals(-1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="209" href="#209">209</a>         Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNorm1().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="210" href="#210">210</a>     }
+<a class="jxr_linenumber" name="211" href="#211">211</a> 
+<a class="jxr_linenumber" name="212" href="#212">212</a>     @Test
+<a class="jxr_linenumber" name="213" href="#213">213</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNorm() {
+<a class="jxr_linenumber" name="214" href="#214">214</a>         <strong class="jxr_keyword">double</strong> r = FastMath.sqrt(14);
+<a class="jxr_linenumber" name="215" href="#215">215</a>         Assert.assertEquals(0.0, createVector(0, 0, 0, 3).getNorm().getReal(), 0);
+<a class="jxr_linenumber" name="216" href="#216">216</a>         Assert.assertEquals(r, createVector(1, 2, 3, 3).getNorm().getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="217" href="#217">217</a>         Assert.assertEquals( 1.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="218" href="#218">218</a>         Assert.assertEquals( 2.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="219" href="#219">219</a>         Assert.assertEquals( 3.0 / r, createVector(1, 2, 3, 3).getNorm().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="220" href="#220">220</a>     }
+<a class="jxr_linenumber" name="221" href="#221">221</a> 
+<a class="jxr_linenumber" name="222" href="#222">222</a>     @Test
+<a class="jxr_linenumber" name="223" href="#223">223</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNormSq() {
+<a class="jxr_linenumber" name="224" href="#224">224</a>         Assert.assertEquals(0.0, createVector(0, 0, 0, 3).getNormSq().getReal(), 0);
+<a class="jxr_linenumber" name="225" href="#225">225</a>         Assert.assertEquals(14, createVector(1, 2, 3, 3).getNormSq().getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="226" href="#226">226</a>         Assert.assertEquals( 2, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="227" href="#227">227</a>         Assert.assertEquals( 4, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="228" href="#228">228</a>         Assert.assertEquals( 6, createVector(1, 2, 3, 3).getNormSq().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="229" href="#229">229</a>     }
+<a class="jxr_linenumber" name="230" href="#230">230</a> 
+<a class="jxr_linenumber" name="231" href="#231">231</a>     @Test
+<a class="jxr_linenumber" name="232" href="#232">232</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNormInf() {
+<a class="jxr_linenumber" name="233" href="#233">233</a>         Assert.assertEquals( 0.0, createVector(0, 0, 0, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="234" href="#234">234</a>         Assert.assertEquals( 3.0, createVector(1, -2, 3, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="235" href="#235">235</a>         Assert.assertEquals( 0.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="236" href="#236">236</a>         Assert.assertEquals( 0.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="237" href="#237">237</a>         Assert.assertEquals( 1.0, createVector(1, -2, 3, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="238" href="#238">238</a>         Assert.assertEquals( 3.0, createVector(2, -1, 3, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="239" href="#239">239</a>         Assert.assertEquals( 0.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="240" href="#240">240</a>         Assert.assertEquals( 0.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="241" href="#241">241</a>         Assert.assertEquals( 1.0, createVector(2, -1, 3, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="242" href="#242">242</a>         Assert.assertEquals( 3.0, createVector(1, -3, 2, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="243" href="#243">243</a>         Assert.assertEquals( 0.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="244" href="#244">244</a>         Assert.assertEquals(-1.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="245" href="#245">245</a>         Assert.assertEquals( 0.0, createVector(1, -3, 2, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="246" href="#246">246</a>         Assert.assertEquals( 3.0, createVector(2, -3, 1, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="247" href="#247">247</a>         Assert.assertEquals( 0.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="248" href="#248">248</a>         Assert.assertEquals(-1.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="249" href="#249">249</a>         Assert.assertEquals( 0.0, createVector(2, -3, 1, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="250" href="#250">250</a>         Assert.assertEquals( 3.0, createVector(3, -1, 2, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="251" href="#251">251</a>         Assert.assertEquals( 1.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="252" href="#252">252</a>         Assert.assertEquals( 0.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="253" href="#253">253</a>         Assert.assertEquals( 0.0, createVector(3, -1, 2, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="254" href="#254">254</a>         Assert.assertEquals( 3.0, createVector(3, -2, 1, 3).getNormInf().getReal(), 0);
+<a class="jxr_linenumber" name="255" href="#255">255</a>         Assert.assertEquals( 1.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(1, 0, 0), 0);
+<a class="jxr_linenumber" name="256" href="#256">256</a>         Assert.assertEquals( 0.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(0, 1, 0), 0);
+<a class="jxr_linenumber" name="257" href="#257">257</a>         Assert.assertEquals( 0.0, createVector(3, -2, 1, 3).getNormInf().getPartialDerivative(0, 0, 1), 0);
+<a class="jxr_linenumber" name="258" href="#258">258</a>     }
+<a class="jxr_linenumber" name="259" href="#259">259</a> 
+<a class="jxr_linenumber" name="260" href="#260">260</a>     @Test
+<a class="jxr_linenumber" name="261" href="#261">261</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDistance1() {
+<a class="jxr_linenumber" name="262" href="#262">262</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, -2, 3, 3);
+<a class="jxr_linenumber" name="263" href="#263">263</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-4, 2, 0, 3);
+<a class="jxr_linenumber" name="264" href="#264">264</a>         Assert.assertEquals(0.0, FieldVector3D.distance1(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
+<a class="jxr_linenumber" name="265" href="#265">265</a>         DerivativeStructure distance = FieldVector3D.distance1(v1, v2);
+<a class="jxr_linenumber" name="266" href="#266">266</a>         Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="267" href="#267">267</a>         Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="268" href="#268">268</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="269" href="#269">269</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="270" href="#270">270</a>         distance = FieldVector3D.distance1(v1, <strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0));
+<a class="jxr_linenumber" name="271" href="#271">271</a>         Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="272" href="#272">272</a>         Assert.assertEquals( 1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="273" href="#273">273</a>         Assert.assertEquals(-1, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="274" href="#274">274</a>         Assert.assertEquals( 1, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="275" href="#275">275</a>         distance = FieldVector3D.distance1(<strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0), v1);
+<a class="jxr_linenumber" name="276" href="#276">276</a>         Assert.assertEquals(12.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="277" href="#277">277</a>         Assert.assertEquals( 1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="278" href="#278">278</a>         Assert.assertEquals(-1, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="279" href="#279">279</a>         Assert.assertEquals( 1, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="280" href="#280">280</a>     }
+<a class="jxr_linenumber" name="281" href="#281">281</a> 
+<a class="jxr_linenumber" name="282" href="#282">282</a>     @Test
+<a class="jxr_linenumber" name="283" href="#283">283</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDistance() {
+<a class="jxr_linenumber" name="284" href="#284">284</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, -2, 3, 3);
+<a class="jxr_linenumber" name="285" href="#285">285</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-4, 2, 0, 3);
+<a class="jxr_linenumber" name="286" href="#286">286</a>         Assert.assertEquals(0.0, FieldVector3D.distance(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
+<a class="jxr_linenumber" name="287" href="#287">287</a>         DerivativeStructure distance = FieldVector3D.distance(v1, v2);
+<a class="jxr_linenumber" name="288" href="#288">288</a>         Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="289" href="#289">289</a>         Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="290" href="#290">290</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="291" href="#291">291</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="292" href="#292">292</a>         distance = FieldVector3D.distance(v1, <strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0));
+<a class="jxr_linenumber" name="293" href="#293">293</a>         Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="294" href="#294">294</a>         Assert.assertEquals( 5 / FastMath.sqrt(50), distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="295" href="#295">295</a>         Assert.assertEquals(-4 / FastMath.sqrt(50), distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="296" href="#296">296</a>         Assert.assertEquals( 3 / FastMath.sqrt(50), distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="297" href="#297">297</a>         distance = FieldVector3D.distance(<strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0), v1);
+<a class="jxr_linenumber" name="298" href="#298">298</a>         Assert.assertEquals(FastMath.sqrt(50), distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="299" href="#299">299</a>         Assert.assertEquals( 5 / FastMath.sqrt(50), distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="300" href="#300">300</a>         Assert.assertEquals(-4 / FastMath.sqrt(50), distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="301" href="#301">301</a>         Assert.assertEquals( 3 / FastMath.sqrt(50), distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="302" href="#302">302</a>     }
+<a class="jxr_linenumber" name="303" href="#303">303</a> 
+<a class="jxr_linenumber" name="304" href="#304">304</a>     @Test
+<a class="jxr_linenumber" name="305" href="#305">305</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDistanceSq() {
+<a class="jxr_linenumber" name="306" href="#306">306</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, -2, 3, 3);
+<a class="jxr_linenumber" name="307" href="#307">307</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-4, 2, 0, 3);
+<a class="jxr_linenumber" name="308" href="#308">308</a>         Assert.assertEquals(0.0, FieldVector3D.distanceSq(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
+<a class="jxr_linenumber" name="309" href="#309">309</a>         DerivativeStructure distanceSq = FieldVector3D.distanceSq(v1, v2);
+<a class="jxr_linenumber" name="310" href="#310">310</a>         Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="311" href="#311">311</a>         Assert.assertEquals(0, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="312" href="#312">312</a>         Assert.assertEquals(0, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="313" href="#313">313</a>         Assert.assertEquals(0, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="314" href="#314">314</a>         distanceSq = FieldVector3D.distanceSq(v1, <strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0));
+<a class="jxr_linenumber" name="315" href="#315">315</a>         Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="316" href="#316">316</a>         Assert.assertEquals(10, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="317" href="#317">317</a>         Assert.assertEquals(-8, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="318" href="#318">318</a>         Assert.assertEquals( 6, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="319" href="#319">319</a>         distanceSq = FieldVector3D.distanceSq(<strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0), v1);
+<a class="jxr_linenumber" name="320" href="#320">320</a>         Assert.assertEquals(50.0, distanceSq.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="321" href="#321">321</a>         Assert.assertEquals(10, distanceSq.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="322" href="#322">322</a>         Assert.assertEquals(-8, distanceSq.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="323" href="#323">323</a>         Assert.assertEquals( 6, distanceSq.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="324" href="#324">324</a>   }
+<a class="jxr_linenumber" name="325" href="#325">325</a> 
+<a class="jxr_linenumber" name="326" href="#326">326</a>     @Test
+<a class="jxr_linenumber" name="327" href="#327">327</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDistanceInf() {
+<a class="jxr_linenumber" name="328" href="#328">328</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, -2, 3, 3);
+<a class="jxr_linenumber" name="329" href="#329">329</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-4, 2, 0, 3);
+<a class="jxr_linenumber" name="330" href="#330">330</a>         Assert.assertEquals(0.0, FieldVector3D.distanceInf(createVector(-1, 0, 0, 3), createVector(-1, 0, 0, 3)).getReal(), 0);
+<a class="jxr_linenumber" name="331" href="#331">331</a>         DerivativeStructure distance = FieldVector3D.distanceInf(v1, v2);
+<a class="jxr_linenumber" name="332" href="#332">332</a>         Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="333" href="#333">333</a>         Assert.assertEquals(0, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="334" href="#334">334</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="335" href="#335">335</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="336" href="#336">336</a>         distance = FieldVector3D.distanceInf(v1, <strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0));
+<a class="jxr_linenumber" name="337" href="#337">337</a>         Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="338" href="#338">338</a>         Assert.assertEquals(1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="339" href="#339">339</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="340" href="#340">340</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="341" href="#341">341</a>         distance = FieldVector3D.distanceInf(<strong class="jxr_keyword">new</strong> Vector3D(-4, 2, 0), v1);
+<a class="jxr_linenumber" name="342" href="#342">342</a>         Assert.assertEquals(5.0, distance.getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="343" href="#343">343</a>         Assert.assertEquals(1, distance.getPartialDerivative(1, 0, 0), 1.0e-12);
+<a class="jxr_linenumber" name="344" href="#344">344</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 1, 0), 1.0e-12);
+<a class="jxr_linenumber" name="345" href="#345">345</a>         Assert.assertEquals(0, distance.getPartialDerivative(0, 0, 1), 1.0e-12);
+<a class="jxr_linenumber" name="346" href="#346">346</a>         Assert.assertEquals(v1.subtract(v2).getNormInf().getReal(), FieldVector3D.distanceInf(v1, v2).getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="347" href="#347">347</a> 
+<a class="jxr_linenumber" name="348" href="#348">348</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="349" href="#349">349</a>                             FieldVector3D.distanceInf(createVector( 1, -2, 3, 3), createVector(-4,  2, 0, 3)).getReal(),
+<a class="jxr_linenumber" name="350" href="#350">350</a>                             1.0e-12);
+<a class="jxr_linenumber" name="351" href="#351">351</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="352" href="#352">352</a>                             FieldVector3D.distanceInf(createVector( 1, 3, -2, 3), createVector(-4, 0,  2, 3)).getReal(),
+<a class="jxr_linenumber" name="353" href="#353">353</a>                             1.0e-12);
+<a class="jxr_linenumber" name="354" href="#354">354</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="355" href="#355">355</a>                             FieldVector3D.distanceInf(createVector(-2,  1, 3, 3), createVector( 2, -4, 0, 3)).getReal(),
+<a class="jxr_linenumber" name="356" href="#356">356</a>                             1.0e-12);
+<a class="jxr_linenumber" name="357" href="#357">357</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="358" href="#358">358</a>                             FieldVector3D.distanceInf(createVector(-2, 3,  1, 3), createVector( 2, 0, -4, 3)).getReal(),
+<a class="jxr_linenumber" name="359" href="#359">359</a>                             1.0e-12);
+<a class="jxr_linenumber" name="360" href="#360">360</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="361" href="#361">361</a>                             FieldVector3D.distanceInf(createVector(3, -2,  1, 3), createVector(0,  2, -4, 3)).getReal(),
+<a class="jxr_linenumber" name="362" href="#362">362</a>                             1.0e-12);
+<a class="jxr_linenumber" name="363" href="#363">363</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="364" href="#364">364</a>                             FieldVector3D.distanceInf(createVector(3,  1, -2, 3), createVector(0, -4,  2, 3)).getReal(),
+<a class="jxr_linenumber" name="365" href="#365">365</a>                             1.0e-12);
+<a class="jxr_linenumber" name="366" href="#366">366</a> 
+<a class="jxr_linenumber" name="367" href="#367">367</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="368" href="#368">368</a>                             FieldVector3D.distanceInf(createVector( 1, -2, 3, 3), <strong class="jxr_keyword">new</strong> Vector3D(-4,  2, 0)).getReal(),
+<a class="jxr_linenumber" name="369" href="#369">369</a>                             1.0e-12);
+<a class="jxr_linenumber" name="370" href="#370">370</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="371" href="#371">371</a>                             FieldVector3D.distanceInf(createVector( 1, 3, -2, 3), <strong class="jxr_keyword">new</strong> Vector3D(-4, 0,  2)).getReal(),
+<a class="jxr_linenumber" name="372" href="#372">372</a>                             1.0e-12);
+<a class="jxr_linenumber" name="373" href="#373">373</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="374" href="#374">374</a>                             FieldVector3D.distanceInf(createVector(-2,  1, 3, 3), <strong class="jxr_keyword">new</strong> Vector3D( 2, -4, 0)).getReal(),
+<a class="jxr_linenumber" name="375" href="#375">375</a>                             1.0e-12);
+<a class="jxr_linenumber" name="376" href="#376">376</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="377" href="#377">377</a>                             FieldVector3D.distanceInf(createVector(-2, 3,  1, 3), <strong class="jxr_keyword">new</strong> Vector3D( 2, 0, -4)).getReal(),
+<a class="jxr_linenumber" name="378" href="#378">378</a>                             1.0e-12);
+<a class="jxr_linenumber" name="379" href="#379">379</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="380" href="#380">380</a>                             FieldVector3D.distanceInf(createVector(3, -2,  1, 3), <strong class="jxr_keyword">new</strong> Vector3D(0,  2, -4)).getReal(),
+<a class="jxr_linenumber" name="381" href="#381">381</a>                             1.0e-12);
+<a class="jxr_linenumber" name="382" href="#382">382</a>         Assert.assertEquals(5.0,
+<a class="jxr_linenumber" name="383" href="#383">383</a>                             FieldVector3D.distanceInf(createVector(3,  1, -2, 3), <strong class="jxr_keyword">new</strong> Vector3D(0, -4,  2)).getReal(),
+<a class="jxr_linenumber" name="384" href="#384">384</a>                             1.0e-12);
+<a class="jxr_linenumber" name="385" href="#385">385</a> 
+<a class="jxr_linenumber" name="386" href="#386">386</a>     }
+<a class="jxr_linenumber" name="387" href="#387">387</a> 
+<a class="jxr_linenumber" name="388" href="#388">388</a>     @Test
+<a class="jxr_linenumber" name="389" href="#389">389</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSubtract() {
+<a class="jxr_linenumber" name="390" href="#390">390</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="391" href="#391">391</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-3, -2, -1, 3);
+<a class="jxr_linenumber" name="392" href="#392">392</a>         v1 = v1.subtract(v2);
+<a class="jxr_linenumber" name="393" href="#393">393</a>         checkVector(v1, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0);
+<a class="jxr_linenumber" name="394" href="#394">394</a> 
+<a class="jxr_linenumber" name="395" href="#395">395</a>         checkVector(v2.subtract(v1), -7, -6, -5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="396" href="#396">396</a>         checkVector(v2.subtract(<strong class="jxr_keyword">new</strong> Vector3D(4, 4, 4)), -7, -6, -5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="397" href="#397">397</a>         checkVector(v2.subtract(3, v1), -15, -14, -13, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="398" href="#398">398</a>         checkVector(v2.subtract(3, <strong class="jxr_keyword">new</strong> Vector3D(4, 4, 4)), -15, -14, -13, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="399" href="#399">399</a>         checkVector(v2.subtract(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 3), <strong class="jxr_keyword">new</strong> Vector3D(4, 4, 4)),
+<a class="jxr_linenumber" name="400" href="#400">400</a>                     -15, -14, -13, 1, 0, -4, 0, 1, -4, 0, 0, -3);
+<a class="jxr_linenumber" name="401" href="#401">401</a> 
+<a class="jxr_linenumber" name="402" href="#402">402</a>         checkVector(createVector(1, 2, 3, 4).subtract(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, 5.0),
+<a class="jxr_linenumber" name="403" href="#403">403</a>                                                       createVector(3, -2, 1, 4)),
+<a class="jxr_linenumber" name="404" href="#404">404</a>                     -14, 12, -2,
+<a class="jxr_linenumber" name="405" href="#405">405</a>                      -4,  0,  0, -3,
+<a class="jxr_linenumber" name="406" href="#406">406</a>                       0, -4,  0,  2,
+<a class="jxr_linenumber" name="407" href="#407">407</a>                       0,  0, -4, -1);
+<a class="jxr_linenumber" name="408" href="#408">408</a> 
+<a class="jxr_linenumber" name="409" href="#409">409</a>     }
+<a class="jxr_linenumber" name="410" href="#410">410</a> 
+<a class="jxr_linenumber" name="411" href="#411">411</a>     @Test
+<a class="jxr_linenumber" name="412" href="#412">412</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAdd() {
+<a class="jxr_linenumber" name="413" href="#413">413</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="414" href="#414">414</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-3, -2, -1, 3);
+<a class="jxr_linenumber" name="415" href="#415">415</a>         v1 = v1.add(v2);
+<a class="jxr_linenumber" name="416" href="#416">416</a>         checkVector(v1, -2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2);
+<a class="jxr_linenumber" name="417" href="#417">417</a> 
+<a class="jxr_linenumber" name="418" href="#418">418</a>         checkVector(v2.add(v1), -5, -2, 1, 3, 0, 0, 0, 3, 0, 0, 0, 3);
+<a class="jxr_linenumber" name="419" href="#419">419</a>         checkVector(v2.add(<strong class="jxr_keyword">new</strong> Vector3D(-2, 0, 2)), -5, -2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="420" href="#420">420</a>         checkVector(v2.add(3, v1), -9, -2, 5, 7, 0, 0, 0, 7, 0, 0, 0, 7);
+<a class="jxr_linenumber" name="421" href="#421">421</a>         checkVector(v2.add(3, <strong class="jxr_keyword">new</strong> Vector3D(-2, 0, 2)), -9, -2, 5, 1, 0, 0, 0, 1, 0, 0, 0, 1);
+<a class="jxr_linenumber" name="422" href="#422">422</a>         checkVector(v2.add(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 3), <strong class="jxr_keyword">new</strong> Vector3D(-2, 0, 2)),
+<a class="jxr_linenumber" name="423" href="#423">423</a>                     -9, -2, 5, 1, 0, -2, 0, 1, 0, 0, 0, 3);
+<a class="jxr_linenumber" name="424" href="#424">424</a> 
+<a class="jxr_linenumber" name="425" href="#425">425</a>         checkVector(createVector(1, 2, 3, 4).add(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, 5.0),
+<a class="jxr_linenumber" name="426" href="#426">426</a>                                                  createVector(3, -2, 1, 4)),
+<a class="jxr_linenumber" name="427" href="#427">427</a>                     16, -8,  8,
+<a class="jxr_linenumber" name="428" href="#428">428</a>                      6,  0,  0,  3,
+<a class="jxr_linenumber" name="429" href="#429">429</a>                      0,  6,  0, -2,
+<a class="jxr_linenumber" name="430" href="#430">430</a>                      0,  0,  6,  1);
+<a class="jxr_linenumber" name="431" href="#431">431</a> 
+<a class="jxr_linenumber" name="432" href="#432">432</a>     }
+<a class="jxr_linenumber" name="433" href="#433">433</a> 
+<a class="jxr_linenumber" name="434" href="#434">434</a>     @Test
+<a class="jxr_linenumber" name="435" href="#435">435</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testScalarProduct() {
+<a class="jxr_linenumber" name="436" href="#436">436</a>         FieldVector3D&lt;DerivativeStructure&gt; v = createVector(1, 2, 3, 3);
+<a class="jxr_linenumber" name="437" href="#437">437</a>         v = v.scalarMultiply(3);
+<a class="jxr_linenumber" name="438" href="#438">438</a>         checkVector(v, 3, 6, 9);
+<a class="jxr_linenumber" name="439" href="#439">439</a> 
+<a class="jxr_linenumber" name="440" href="#440">440</a>         checkVector(v.scalarMultiply(0.5), 1.5, 3, 4.5);
+<a class="jxr_linenumber" name="441" href="#441">441</a>     }
+<a class="jxr_linenumber" name="442" href="#442">442</a> 
+<a class="jxr_linenumber" name="443" href="#443">443</a>     @Test
+<a class="jxr_linenumber" name="444" href="#444">444</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVectorialProducts() {
+<a class="jxr_linenumber" name="445" href="#445">445</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(2, 1, -4, 3);
+<a class="jxr_linenumber" name="446" href="#446">446</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(3, 1, -1, 3);
+<a class="jxr_linenumber" name="447" href="#447">447</a> 
+<a class="jxr_linenumber" name="448" href="#448">448</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v2).getReal() - 11) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="449" href="#449">449</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v2.toVector3D()).getReal() - 11) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="450" href="#450">450</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1.toVector3D(), v2).getReal() - 11) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="451" href="#451">451</a> 
+<a class="jxr_linenumber" name="452" href="#452">452</a>         FieldVector3D&lt;DerivativeStructure&gt; v3 = FieldVector3D.crossProduct(v1, v2);
+<a class="jxr_linenumber" name="453" href="#453">453</a>         checkVector(v3, 3, -10, -1);
+<a class="jxr_linenumber" name="454" href="#454">454</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="455" href="#455">455</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="456" href="#456">456</a> 
+<a class="jxr_linenumber" name="457" href="#457">457</a>         v3 = FieldVector3D.crossProduct(v1, v2.toVector3D());
+<a class="jxr_linenumber" name="458" href="#458">458</a>         checkVector(v3, 3, -10, -1);
+<a class="jxr_linenumber" name="459" href="#459">459</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="460" href="#460">460</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="461" href="#461">461</a> 
+<a class="jxr_linenumber" name="462" href="#462">462</a>         v3 = FieldVector3D.crossProduct(v1.toVector3D(), v2);
+<a class="jxr_linenumber" name="463" href="#463">463</a>         checkVector(v3, 3, -10, -1);
+<a class="jxr_linenumber" name="464" href="#464">464</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v1, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="465" href="#465">465</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.dotProduct(v2, v3).getReal()) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="466" href="#466">466</a> 
+<a class="jxr_linenumber" name="467" href="#467">467</a>     }
+<a class="jxr_linenumber" name="468" href="#468">468</a> 
+<a class="jxr_linenumber" name="469" href="#469">469</a>     @Test
+<a class="jxr_linenumber" name="470" href="#470">470</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCrossProductCancellation() {
+<a class="jxr_linenumber" name="471" href="#471">471</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(9070467121.0, 4535233560.0, 1, 3);
+<a class="jxr_linenumber" name="472" href="#472">472</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(9070467123.0, 4535233561.0, 1, 3);
+<a class="jxr_linenumber" name="473" href="#473">473</a>         checkVector(FieldVector3D.crossProduct(v1, v2), -1, 2, 1);
+<a class="jxr_linenumber" name="474" href="#474">474</a> 
+<a class="jxr_linenumber" name="475" href="#475">475</a>         <strong class="jxr_keyword">double</strong> scale    = FastMath.scalb(1.0, 100);
+<a class="jxr_linenumber" name="476" href="#476">476</a>         FieldVector3D&lt;DerivativeStructure&gt; big1   = <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(scale, v1);
+<a class="jxr_linenumber" name="477" href="#477">477</a>         FieldVector3D&lt;DerivativeStructure&gt; small2 = <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(1 / scale, v2);
+<a class="jxr_linenumber" name="478" href="#478">478</a>         checkVector(FieldVector3D.crossProduct(big1, small2), -1, 2, 1);
+<a class="jxr_linenumber" name="479" href="#479">479</a> 
+<a class="jxr_linenumber" name="480" href="#480">480</a>     }
+<a class="jxr_linenumber" name="481" href="#481">481</a> 
+<a class="jxr_linenumber" name="482" href="#482">482</a>     @Test
+<a class="jxr_linenumber" name="483" href="#483">483</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAngular() {
+<a class="jxr_linenumber" name="484" href="#484">484</a>         Assert.assertEquals(0,           createVector(1, 0, 0, 3).getAlpha().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="485" href="#485">485</a>         Assert.assertEquals(0,           createVector(1, 0, 0, 3).getDelta().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="486" href="#486">486</a>         Assert.assertEquals(FastMath.PI / 2, createVector(0, 1, 0, 3).getAlpha().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="487" href="#487">487</a>         Assert.assertEquals(0,           createVector(0, 1, 0, 3).getDelta().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="488" href="#488">488</a>         Assert.assertEquals(FastMath.PI / 2, createVector(0, 0, 1, 3).getDelta().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="489" href="#489">489</a>       
+<a class="jxr_linenumber" name="490" href="#490">490</a>         FieldVector3D&lt;DerivativeStructure&gt; u = createVector(-1, 1, -1, 3);
+<a class="jxr_linenumber" name="491" href="#491">491</a>         Assert.assertEquals(3 * FastMath.PI /4, u.getAlpha().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="492" href="#492">492</a>         Assert.assertEquals(-1.0 / FastMath.sqrt(3), u.getDelta().sin().getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="493" href="#493">493</a>     }
+<a class="jxr_linenumber" name="494" href="#494">494</a> 
+<a class="jxr_linenumber" name="495" href="#495">495</a>     @Test
+<a class="jxr_linenumber" name="496" href="#496">496</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAngularSeparation() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="497" href="#497">497</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(2, -1, 4, 3);
+<a class="jxr_linenumber" name="498" href="#498">498</a> 
+<a class="jxr_linenumber" name="499" href="#499">499</a>         FieldVector3D&lt;DerivativeStructure&gt;  k = v1.normalize();
+<a class="jxr_linenumber" name="500" href="#500">500</a>         FieldVector3D&lt;DerivativeStructure&gt;  i = k.orthogonal();
+<a class="jxr_linenumber" name="501" href="#501">501</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = k.scalarMultiply(FastMath.cos(1.2)).add(i.scalarMultiply(FastMath.sin(1.2)));
+<a class="jxr_linenumber" name="502" href="#502">502</a> 
+<a class="jxr_linenumber" name="503" href="#503">503</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1, v2).getReal() - 1.2) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="504" href="#504">504</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1, v2.toVector3D()).getReal() - 1.2) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="505" href="#505">505</a>         Assert.assertTrue(FastMath.abs(FieldVector3D.angle(v1.toVector3D(), v2).getReal() - 1.2) &lt; 1.0e-12);
+<a class="jxr_linenumber" name="506" href="#506">506</a> 
+<a class="jxr_linenumber" name="507" href="#507">507</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="508" href="#508">508</a>             FieldVector3D.angle(v1, Vector3D.ZERO);
+<a class="jxr_linenumber" name="509" href="#509">509</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="510" href="#510">510</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException mae) {
+<a class="jxr_linenumber" name="511" href="#511">511</a>             <em class="jxr_comment">// expected</em>
+<a class="jxr_linenumber" name="512" href="#512">512</a>         }
+<a class="jxr_linenumber" name="513" href="#513">513</a>         Assert.assertEquals(0.0, FieldVector3D.angle(v1, v1.toVector3D()).getReal(), 1.0e-15);
+<a class="jxr_linenumber" name="514" href="#514">514</a>         Assert.assertEquals(FastMath.PI, FieldVector3D.angle(v1, v1.negate().toVector3D()).getReal(), 1.0e-15);
+<a class="jxr_linenumber" name="515" href="#515">515</a> 
+<a class="jxr_linenumber" name="516" href="#516">516</a>     }
+<a class="jxr_linenumber" name="517" href="#517">517</a> 
+<a class="jxr_linenumber" name="518" href="#518">518</a>     @Test
+<a class="jxr_linenumber" name="519" href="#519">519</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNormalize() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="520" href="#520">520</a>         Assert.assertEquals(1.0, createVector(5, -4, 2, 3).normalize().getNorm().getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="521" href="#521">521</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="522" href="#522">522</a>             createVector(0, 0, 0, 3).normalize();
+<a class="jxr_linenumber" name="523" href="#523">523</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="524" href="#524">524</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException ae) {
+<a class="jxr_linenumber" name="525" href="#525">525</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="526" href="#526">526</a>         }
+<a class="jxr_linenumber" name="527" href="#527">527</a>     }
+<a class="jxr_linenumber" name="528" href="#528">528</a> 
+<a class="jxr_linenumber" name="529" href="#529">529</a>     @Test
+<a class="jxr_linenumber" name="530" href="#530">530</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNegate() {
+<a class="jxr_linenumber" name="531" href="#531">531</a>         checkVector(createVector(0.1, 2.5, 1.3, 3).negate(),
+<a class="jxr_linenumber" name="532" href="#532">532</a>                     -0.1, -2.5, -1.3, -1, 0, 0, 0, -1, 0, 0, 0, -1);
+<a class="jxr_linenumber" name="533" href="#533">533</a>     }
+<a class="jxr_linenumber" name="534" href="#534">534</a> 
+<a class="jxr_linenumber" name="535" href="#535">535</a>     @Test
+<a class="jxr_linenumber" name="536" href="#536">536</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testOrthogonal() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="537" href="#537">537</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(0.1, 2.5, 1.3, 3);
+<a class="jxr_linenumber" name="538" href="#538">538</a>         Assert.assertEquals(0.0, FieldVector3D.dotProduct(v1, v1.orthogonal()).getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="539" href="#539">539</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(2.3, -0.003, 7.6, 3);
+<a class="jxr_linenumber" name="540" href="#540">540</a>         Assert.assertEquals(0.0, FieldVector3D.dotProduct(v2, v2.orthogonal()).getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="541" href="#541">541</a>         FieldVector3D&lt;DerivativeStructure&gt; v3 = createVector(-1.7, 1.4, 0.2, 3);
+<a class="jxr_linenumber" name="542" href="#542">542</a>         Assert.assertEquals(0.0, FieldVector3D.dotProduct(v3, v3.orthogonal()).getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="543" href="#543">543</a>         FieldVector3D&lt;DerivativeStructure&gt; v4 = createVector(4.2, 0.1, -1.8, 3);
+<a class="jxr_linenumber" name="544" href="#544">544</a>         Assert.assertEquals(0.0, FieldVector3D.dotProduct(v4, v4.orthogonal()).getReal(), 1.0e-12);
+<a class="jxr_linenumber" name="545" href="#545">545</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="546" href="#546">546</a>             createVector(0, 0, 0, 3).orthogonal();
+<a class="jxr_linenumber" name="547" href="#547">547</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="548" href="#548">548</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException ae) {
+<a class="jxr_linenumber" name="549" href="#549">549</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="550" href="#550">550</a>         }
+<a class="jxr_linenumber" name="551" href="#551">551</a>     }
+<a class="jxr_linenumber" name="552" href="#552">552</a> 
+<a class="jxr_linenumber" name="553" href="#553">553</a>     @Test
+<a class="jxr_linenumber" name="554" href="#554">554</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAngle() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="555" href="#555">555</a>         Assert.assertEquals(0.22572612855273393616,
+<a class="jxr_linenumber" name="556" href="#556">556</a>                             FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(4, 5, 6, 3)).getReal(),
+<a class="jxr_linenumber" name="557" href="#557">557</a>                             1.0e-12);
+<a class="jxr_linenumber" name="558" href="#558">558</a>         Assert.assertEquals(7.98595620686106654517199e-8,
+<a class="jxr_linenumber" name="559" href="#559">559</a>                             FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(2, 4, 6.000001, 3)).getReal(),
+<a class="jxr_linenumber" name="560" href="#560">560</a>                             1.0e-12);
+<a class="jxr_linenumber" name="561" href="#561">561</a>         Assert.assertEquals(3.14159257373023116985197793156,
+<a class="jxr_linenumber" name="562" href="#562">562</a>                             FieldVector3D.angle(createVector(1, 2, 3, 3), createVector(-2, -4, -6.000001, 3)).getReal(),
+<a class="jxr_linenumber" name="563" href="#563">563</a>                             1.0e-12);
+<a class="jxr_linenumber" name="564" href="#564">564</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="565" href="#565">565</a>             FieldVector3D.angle(createVector(0, 0, 0, 3), createVector(1, 0, 0, 3));
+<a class="jxr_linenumber" name="566" href="#566">566</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="567" href="#567">567</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException ae) {
+<a class="jxr_linenumber" name="568" href="#568">568</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="569" href="#569">569</a>         }
+<a class="jxr_linenumber" name="570" href="#570">570</a>     }
+<a class="jxr_linenumber" name="571" href="#571">571</a> 
+<a class="jxr_linenumber" name="572" href="#572">572</a>     @Test
+<a class="jxr_linenumber" name="573" href="#573">573</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAccurateDotProduct() {
+<a class="jxr_linenumber" name="574" href="#574">574</a>         <em class="jxr_comment">// the following two vectors are nearly but not exactly orthogonal</em>
+<a class="jxr_linenumber" name="575" href="#575">575</a>         <em class="jxr_comment">// naive dot product (i.e. computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z</em>
+<a class="jxr_linenumber" name="576" href="#576">576</a>         <em class="jxr_comment">// leads to a result of 0.0, instead of the correct -1.855129...</em>
+<a class="jxr_linenumber" name="577" href="#577">577</a>         FieldVector3D&lt;DerivativeStructure&gt; u1 = createVector(-1321008684645961.0 /  268435456.0,
+<a class="jxr_linenumber" name="578" href="#578">578</a>                                    -5774608829631843.0 /  268435456.0,
+<a class="jxr_linenumber" name="579" href="#579">579</a>                                    -7645843051051357.0 / 8589934592.0, 3);
+<a class="jxr_linenumber" name="580" href="#580">580</a>         FieldVector3D&lt;DerivativeStructure&gt; u2 = createVector(-5712344449280879.0 /    2097152.0,
+<a class="jxr_linenumber" name="581" href="#581">581</a>                                    -4550117129121957.0 /    2097152.0,
+<a class="jxr_linenumber" name="582" href="#582">582</a>                                     8846951984510141.0 /     131072.0, 3);
+<a class="jxr_linenumber" name="583" href="#583">583</a>         DerivativeStructure sNaive = u1.getX().multiply(u2.getX()).add(u1.getY().multiply(u2.getY())).add(u1.getZ().multiply(u2.getZ()));
+<a class="jxr_linenumber" name="584" href="#584">584</a>         DerivativeStructure sAccurate = FieldVector3D.dotProduct(u1, u2);
+<a class="jxr_linenumber" name="585" href="#585">585</a>         Assert.assertEquals(0.0, sNaive.getReal(), 1.0e-30);
+<a class="jxr_linenumber" name="586" href="#586">586</a>         Assert.assertEquals(-2088690039198397.0 / 1125899906842624.0, sAccurate.getReal(), 1.0e-16);
+<a class="jxr_linenumber" name="587" href="#587">587</a>     }
+<a class="jxr_linenumber" name="588" href="#588">588</a> 
+<a class="jxr_linenumber" name="589" href="#589">589</a>     @Test
+<a class="jxr_linenumber" name="590" href="#590">590</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDotProduct() {
+<a class="jxr_linenumber" name="591" href="#591">591</a>         <em class="jxr_comment">// we compare accurate versus naive dot product implementations</em>
+<a class="jxr_linenumber" name="592" href="#592">592</a>         <em class="jxr_comment">// on regular vectors (i.e. not extreme cases like in the previous test)</em>
+<a class="jxr_linenumber" name="593" href="#593">593</a>         Well1024a random = <strong class="jxr_keyword">new</strong> Well1024a(553267312521321234l);
+<a class="jxr_linenumber" name="594" href="#594">594</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; 10000; ++i) {
+<a class="jxr_linenumber" name="595" href="#595">595</a>             <strong class="jxr_keyword">double</strong> ux = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="596" href="#596">596</a>             <strong class="jxr_keyword">double</strong> uy = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="597" href="#597">597</a>             <strong class="jxr_keyword">double</strong> uz = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="598" href="#598">598</a>             <strong class="jxr_keyword">double</strong> vx = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="599" href="#599">599</a>             <strong class="jxr_keyword">double</strong> vy = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="600" href="#600">600</a>             <strong class="jxr_keyword">double</strong> vz = 10000 * random.nextDouble();
+<a class="jxr_linenumber" name="601" href="#601">601</a>             <strong class="jxr_keyword">double</strong> sNaive = ux * vx + uy * vy + uz * vz;
+<a class="jxr_linenumber" name="602" href="#602">602</a> 
+<a class="jxr_linenumber" name="603" href="#603">603</a>             FieldVector3D&lt;DerivativeStructure&gt; uds = createVector(ux, uy, uz, 3);
+<a class="jxr_linenumber" name="604" href="#604">604</a>             FieldVector3D&lt;DerivativeStructure&gt; vds = createVector(vx, vy, vz, 3);
+<a class="jxr_linenumber" name="605" href="#605">605</a>             Vector3D v = <strong class="jxr_keyword">new</strong> Vector3D(vx, vy, vz);
+<a class="jxr_linenumber" name="606" href="#606">606</a> 
+<a class="jxr_linenumber" name="607" href="#607">607</a>             DerivativeStructure sAccurate = FieldVector3D.dotProduct(uds, vds);
+<a class="jxr_linenumber" name="608" href="#608">608</a>             Assert.assertEquals(sNaive, sAccurate.getReal(), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="609" href="#609">609</a>             Assert.assertEquals(ux + vx, sAccurate.getPartialDerivative(1, 0, 0), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="610" href="#610">610</a>             Assert.assertEquals(uy + vy, sAccurate.getPartialDerivative(0, 1, 0), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="611" href="#611">611</a>             Assert.assertEquals(uz + vz, sAccurate.getPartialDerivative(0, 0, 1), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="612" href="#612">612</a> 
+<a class="jxr_linenumber" name="613" href="#613">613</a>             sAccurate = FieldVector3D.dotProduct(uds, v);
+<a class="jxr_linenumber" name="614" href="#614">614</a>             Assert.assertEquals(sNaive, sAccurate.getReal(), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="615" href="#615">615</a>             Assert.assertEquals(vx, sAccurate.getPartialDerivative(1, 0, 0), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="616" href="#616">616</a>             Assert.assertEquals(vy, sAccurate.getPartialDerivative(0, 1, 0), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="617" href="#617">617</a>             Assert.assertEquals(vz, sAccurate.getPartialDerivative(0, 0, 1), 2.5e-16 * sNaive);
+<a class="jxr_linenumber" name="618" href="#618">618</a> 
+<a class="jxr_linenumber" name="619" href="#619">619</a>         }
+<a class="jxr_linenumber" name="620" href="#620">620</a>     }
+<a class="jxr_linenumber" name="621" href="#621">621</a> 
+<a class="jxr_linenumber" name="622" href="#622">622</a>     @Test
+<a class="jxr_linenumber" name="623" href="#623">623</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAccurateCrossProduct() {
+<a class="jxr_linenumber" name="624" href="#624">624</a>         <em class="jxr_comment">// the vectors u1 and u2 are nearly but not exactly anti-parallel</em>
+<a class="jxr_linenumber" name="625" href="#625">625</a>         <em class="jxr_comment">// (7.31e-16 degrees from 180 degrees) naive cross product (i.e.</em>
+<a class="jxr_linenumber" name="626" href="#626">626</a>         <em class="jxr_comment">// computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z</em>
+<a class="jxr_linenumber" name="627" href="#627">627</a>         <em class="jxr_comment">// leads to a result of   [0.0009765, -0.0001220, -0.0039062],</em>
+<a class="jxr_linenumber" name="628" href="#628">628</a>         <em class="jxr_comment">// instead of the correct [0.0006913, -0.0001254, -0.0007909]</em>
+<a class="jxr_linenumber" name="629" href="#629">629</a>         <strong class="jxr_keyword">final</strong> FieldVector3D&lt;DerivativeStructure&gt; u1 = createVector(-1321008684645961.0 /   268435456.0,
+<a class="jxr_linenumber" name="630" href="#630">630</a>                                          -5774608829631843.0 /   268435456.0,
+<a class="jxr_linenumber" name="631" href="#631">631</a>                                          -7645843051051357.0 /  8589934592.0, 3);
+<a class="jxr_linenumber" name="632" href="#632">632</a>         <strong class="jxr_keyword">final</strong> FieldVector3D&lt;DerivativeStructure&gt; u2 = createVector( 1796571811118507.0 /  2147483648.0,
+<a class="jxr_linenumber" name="633" href="#633">633</a>                                           7853468008299307.0 /  2147483648.0,
+<a class="jxr_linenumber" name="634" href="#634">634</a>                                           2599586637357461.0 / 17179869184.0, 3);
+<a class="jxr_linenumber" name="635" href="#635">635</a>         <strong class="jxr_keyword">final</strong> FieldVector3D&lt;DerivativeStructure&gt; u3 = createVector(12753243807587107.0 / 18446744073709551616.0, 
+<a class="jxr_linenumber" name="636" href="#636">636</a>                                          -2313766922703915.0 / 18446744073709551616.0, 
+<a class="jxr_linenumber" name="637" href="#637">637</a>                                           -227970081415313.0 /   288230376151711744.0, 3);
+<a class="jxr_linenumber" name="638" href="#638">638</a>         FieldVector3D&lt;DerivativeStructure&gt; cNaive = <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(u1.getY().multiply(u2.getZ()).subtract(u1.getZ().multiply(u2.getY())),
+<a class="jxr_linenumber" name="639" href="#639">639</a>                                        u1.getZ().multiply(u2.getX()).subtract(u1.getX().multiply(u2.getZ())),
+<a class="jxr_linenumber" name="640" href="#640">640</a>                                        u1.getX().multiply(u2.getY()).subtract(u1.getY().multiply(u2.getX())));
+<a class="jxr_linenumber" name="641" href="#641">641</a>         FieldVector3D&lt;DerivativeStructure&gt; cAccurate = FieldVector3D.crossProduct(u1, u2);
+<a class="jxr_linenumber" name="642" href="#642">642</a>         Assert.assertTrue(FieldVector3D.distance(u3, cNaive).getReal() &gt; 2.9 * u3.getNorm().getReal());
+<a class="jxr_linenumber" name="643" href="#643">643</a>         Assert.assertEquals(0.0, FieldVector3D.distance(u3, cAccurate).getReal(), 1.0e-30 * cAccurate.getNorm().getReal());
+<a class="jxr_linenumber" name="644" href="#644">644</a>     }
+<a class="jxr_linenumber" name="645" href="#645">645</a> 
+<a class="jxr_linenumber" name="646" href="#646">646</a>     @Test
+<a class="jxr_linenumber" name="647" href="#647">647</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCrossProduct() {
+<a class="jxr_linenumber" name="648" href="#648">648</a>         <em class="jxr_comment">// we compare accurate versus naive cross product implementations</em>
+<a class="jxr_linenumber" name="649" href="#649">649</a>         <em class="jxr_comment">// on regular vectors (i.e. not extreme cases like in the previous test)</em>
+<a class="jxr_linenumber" name="650" href="#650">650</a>         Well1024a random = <strong class="jxr_keyword">new</strong> Well1024a(885362227452043214l);
+<a class="jxr_linenumber" name="651" href="#651">651</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; 10000; ++i) {
+<a class="jxr_linenumber" name="652" href="#652">652</a>             <strong class="jxr_keyword">double</strong> ux = random.nextDouble();
+<a class="jxr_linenumber" name="653" href="#653">653</a>             <strong class="jxr_keyword">double</strong> uy = random.nextDouble();
+<a class="jxr_linenumber" name="654" href="#654">654</a>             <strong class="jxr_keyword">double</strong> uz = random.nextDouble();
+<a class="jxr_linenumber" name="655" href="#655">655</a>             <strong class="jxr_keyword">double</strong> vx = random.nextDouble();
+<a class="jxr_linenumber" name="656" href="#656">656</a>             <strong class="jxr_keyword">double</strong> vy = random.nextDouble();
+<a class="jxr_linenumber" name="657" href="#657">657</a>             <strong class="jxr_keyword">double</strong> vz = random.nextDouble();
+<a class="jxr_linenumber" name="658" href="#658">658</a>             Vector3D cNaive = <strong class="jxr_keyword">new</strong> Vector3D(uy * vz - uz * vy, uz * vx - ux * vz, ux * vy - uy * vx);
+<a class="jxr_linenumber" name="659" href="#659">659</a> 
+<a class="jxr_linenumber" name="660" href="#660">660</a>             FieldVector3D&lt;DerivativeStructure&gt; uds = createVector(ux, uy, uz, 3);
+<a class="jxr_linenumber" name="661" href="#661">661</a>             FieldVector3D&lt;DerivativeStructure&gt; vds = createVector(vx, vy, vz, 3);
+<a class="jxr_linenumber" name="662" href="#662">662</a>             Vector3D v = <strong class="jxr_keyword">new</strong> Vector3D(vx, vy, vz);
+<a class="jxr_linenumber" name="663" href="#663">663</a> 
+<a class="jxr_linenumber" name="664" href="#664">664</a>             checkVector(FieldVector3D.crossProduct(uds, vds),
+<a class="jxr_linenumber" name="665" href="#665">665</a>                         cNaive.getX(), cNaive.getY(), cNaive.getZ(),
+<a class="jxr_linenumber" name="666" href="#666">666</a>                         0, vz - uz, uy - vy,
+<a class="jxr_linenumber" name="667" href="#667">667</a>                         uz - vz, 0, vx - ux,
+<a class="jxr_linenumber" name="668" href="#668">668</a>                         vy - uy, ux - vx, 0);
+<a class="jxr_linenumber" name="669" href="#669">669</a> 
+<a class="jxr_linenumber" name="670" href="#670">670</a>             checkVector(FieldVector3D.crossProduct(uds, v),
+<a class="jxr_linenumber" name="671" href="#671">671</a>                         cNaive.getX(), cNaive.getY(), cNaive.getZ(),
+<a class="jxr_linenumber" name="672" href="#672">672</a>                           0,  vz, -vy,
+<a class="jxr_linenumber" name="673" href="#673">673</a>                         -vz,   0,  vx,

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