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From l..@apache.org
Subject svn commit: r857590 [9/48] - 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/fun...
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/FieldRotationDSTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html (added)
+++ websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html Sun Apr  7 07:52:05 2013
@@ -0,0 +1,859 @@
+<!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>FieldRotationDSTest 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/FieldRotationDSTest.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> org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+<a class="jxr_linenumber" name="21" href="#21">21</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.MathArithmeticException;
+<a class="jxr_linenumber" name="22" href="#22">22</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.MathIllegalArgumentException;
+<a class="jxr_linenumber" name="23" href="#23">23</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.linear.MatrixUtils;
+<a class="jxr_linenumber" name="24" href="#24">24</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.linear.RealMatrix;
+<a class="jxr_linenumber" name="25" href="#25">25</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;
+<a class="jxr_linenumber" name="26" href="#26">26</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.random.Well1024a;
+<a class="jxr_linenumber" name="27" href="#27">27</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
+<a class="jxr_linenumber" name="28" href="#28">28</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.MathUtils;
+<a class="jxr_linenumber" name="29" href="#29">29</a>  <strong class="jxr_keyword">import</strong> org.junit.Assert;
+<a class="jxr_linenumber" name="30" href="#30">30</a>  <strong class="jxr_keyword">import</strong> org.junit.Test;
+<a class="jxr_linenumber" name="31" href="#31">31</a>  
+<a class="jxr_linenumber" name="32" href="#32">32</a>  
+<a class="jxr_linenumber" name="33" href="#33">33</a>  <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html">FieldRotationDSTest</a> {
+<a class="jxr_linenumber" name="34" href="#34">34</a>  
+<a class="jxr_linenumber" name="35" href="#35">35</a>      @Test
+<a class="jxr_linenumber" name="36" href="#36">36</a>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testIdentity() {
+<a class="jxr_linenumber" name="37" href="#37">37</a>  
+<a class="jxr_linenumber" name="38" href="#38">38</a>          FieldRotation&lt;DerivativeStructure&gt; r = createRotation(1, 0, 0, 0, false);
+<a class="jxr_linenumber" name="39" href="#39">39</a>          checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="40" href="#40">40</a>          checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="41" href="#41">41</a>          checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="42" href="#42">42</a>          checkAngle(r.getAngle(), 0);
+<a class="jxr_linenumber" name="43" href="#43">43</a>  
+<a class="jxr_linenumber" name="44" href="#44">44</a>          r = createRotation(-1, 0, 0, 0, false);
+<a class="jxr_linenumber" name="45" href="#45">45</a>          checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="46" href="#46">46</a>          checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="47" href="#47">47</a>          checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="48" href="#48">48</a>          checkAngle(r.getAngle(), 0);
+<a class="jxr_linenumber" name="49" href="#49">49</a>  
+<a class="jxr_linenumber" name="50" href="#50">50</a>          r = createRotation(42, 0, 0, 0, <strong class="jxr_keyword">true</strong>);
+<a class="jxr_linenumber" name="51" href="#51">51</a>          checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="52" href="#52">52</a>          checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="53" href="#53">53</a>          checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="54" href="#54">54</a>          checkAngle(r.getAngle(), 0);
+<a class="jxr_linenumber" name="55" href="#55">55</a>  
+<a class="jxr_linenumber" name="56" href="#56">56</a>      }
+<a class="jxr_linenumber" name="57" href="#57">57</a>  
+<a class="jxr_linenumber" name="58" href="#58">58</a>      @Test
+<a class="jxr_linenumber" name="59" href="#59">59</a>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAxisAngle() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="60" href="#60">60</a>  
+<a class="jxr_linenumber" name="61" href="#61">61</a>          FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(10, 10, 10), createAngle(2 * FastMath.PI / 3));
+<a class="jxr_linenumber" name="62" href="#62">62</a>          checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="63" href="#63">63</a>          checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="64" href="#64">64</a>          checkVector(r.applyTo(createVector(0, 0, 1)), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="65" href="#65">65</a>          <strong class="jxr_keyword">double</strong> s = 1 / FastMath.sqrt(3);
+<a class="jxr_linenumber" name="66" href="#66">66</a>          checkVector(r.getAxis(), createVector(s, s, s));
+<a class="jxr_linenumber" name="67" href="#67">67</a>          checkAngle(r.getAngle(), 2 * FastMath.PI / 3);
+<a class="jxr_linenumber" name="68" href="#68">68</a>  
+<a class="jxr_linenumber" name="69" href="#69">69</a>          <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="70" href="#70">70</a>              <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(0, 0, 0), createAngle(2 * FastMath.PI / 3));
+<a class="jxr_linenumber" name="71" href="#71">71</a>              Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="72" href="#72">72</a>          } <strong class="jxr_keyword">catch</strong> (MathIllegalArgumentException e) {
+<a class="jxr_linenumber" name="73" href="#73">73</a>          }
+<a class="jxr_linenumber" name="74" href="#74">74</a>  
+<a class="jxr_linenumber" name="75" href="#75">75</a>          r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(0, 0, 1), createAngle(1.5 * FastMath.PI));
+<a class="jxr_linenumber" name="76" href="#76">76</a>          checkVector(r.getAxis(), createVector(0, 0, -1));
+<a class="jxr_linenumber" name="77" href="#77">77</a>          checkAngle(r.getAngle(), 0.5 * FastMath.PI);
+<a class="jxr_linenumber" name="78" href="#78">78</a>  
+<a class="jxr_linenumber" name="79" href="#79">79</a>          r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(0, 1, 0), createAngle(FastMath.PI));
+<a class="jxr_linenumber" name="80" href="#80">80</a>          checkVector(r.getAxis(), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="81" href="#81">81</a>          checkAngle(r.getAngle(), FastMath.PI);
+<a class="jxr_linenumber" name="82" href="#82">82</a>  
+<a class="jxr_linenumber" name="83" href="#83">83</a>          checkVector(createRotation(1, 0, 0, 0, false).getAxis(), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="84" href="#84">84</a>  
+<a class="jxr_linenumber" name="85" href="#85">85</a>      }
+<a class="jxr_linenumber" name="86" href="#86">86</a>  
+<a class="jxr_linenumber" name="87" href="#87">87</a>      @Test
+<a class="jxr_linenumber" name="88" href="#88">88</a>      <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testRevert() {
+<a class="jxr_linenumber" name="89" href="#89">89</a>          <strong class="jxr_keyword">double</strong> a = 0.001;
+<a class="jxr_linenumber" name="90" href="#90">90</a>          <strong class="jxr_keyword">double</strong> b = 0.36;
+<a class="jxr_linenumber" name="91" href="#91">91</a>          <strong class="jxr_keyword">double</strong> c = 0.48;
+<a class="jxr_linenumber" name="92" href="#92">92</a>          <strong class="jxr_keyword">double</strong> d = 0.8;
+<a class="jxr_linenumber" name="93" href="#93">93</a>          FieldRotation&lt;DerivativeStructure&gt; r = createRotation(a, b, c, d, <strong class="jxr_keyword">true</strong>);
+<a class="jxr_linenumber" name="94" href="#94">94</a>          <strong class="jxr_keyword">double</strong> a2 = a * a;
+<a class="jxr_linenumber" name="95" href="#95">95</a>          <strong class="jxr_keyword">double</strong> b2 = b * b;
+<a class="jxr_linenumber" name="96" href="#96">96</a>          <strong class="jxr_keyword">double</strong> c2 = c * c;
+<a class="jxr_linenumber" name="97" href="#97">97</a>          <strong class="jxr_keyword">double</strong> d2 = d * d;
+<a class="jxr_linenumber" name="98" href="#98">98</a>          <strong class="jxr_keyword">double</strong> den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);
+<a class="jxr_linenumber" name="99" href="#99">99</a>          Assert.assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="100" href="#100">100</a>         Assert.assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="101" href="#101">101</a>         Assert.assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="102" href="#102">102</a>         Assert.assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="103" href="#103">103</a>         Assert.assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="104" href="#104">104</a>         Assert.assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="105" href="#105">105</a>         Assert.assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="106" href="#106">106</a>         Assert.assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="107" href="#107">107</a>         Assert.assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="108" href="#108">108</a>         Assert.assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="109" href="#109">109</a>         Assert.assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="110" href="#110">110</a>         Assert.assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="111" href="#111">111</a>         Assert.assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="112" href="#112">112</a>         Assert.assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="113" href="#113">113</a>         Assert.assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="114" href="#114">114</a>         Assert.assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="115" href="#115">115</a>         FieldRotation&lt;DerivativeStructure&gt; reverted = r.revert();
+<a class="jxr_linenumber" name="116" href="#116">116</a>         FieldRotation&lt;DerivativeStructure&gt; rrT = r.applyTo(reverted);
+<a class="jxr_linenumber" name="117" href="#117">117</a>         checkRotationDS(rrT, 1, 0, 0, 0);
+<a class="jxr_linenumber" name="118" href="#118">118</a>         Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="119" href="#119">119</a>         Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="120" href="#120">120</a>         Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="121" href="#121">121</a>         Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="122" href="#122">122</a>         Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="123" href="#123">123</a>         Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="124" href="#124">124</a>         Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="125" href="#125">125</a>         Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="126" href="#126">126</a>         Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="127" href="#127">127</a>         Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="128" href="#128">128</a>         Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="129" href="#129">129</a>         Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="130" href="#130">130</a>         Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="131" href="#131">131</a>         Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="132" href="#132">132</a>         Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="133" href="#133">133</a>         Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="134" href="#134">134</a>         FieldRotation&lt;DerivativeStructure&gt; rTr = reverted.applyTo(r);
+<a class="jxr_linenumber" name="135" href="#135">135</a>         checkRotationDS(rTr, 1, 0, 0, 0);
+<a class="jxr_linenumber" name="136" href="#136">136</a>         Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="137" href="#137">137</a>         Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="138" href="#138">138</a>         Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="139" href="#139">139</a>         Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="140" href="#140">140</a>         Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="141" href="#141">141</a>         Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="142" href="#142">142</a>         Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="143" href="#143">143</a>         Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="144" href="#144">144</a>         Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="145" href="#145">145</a>         Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="146" href="#146">146</a>         Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="147" href="#147">147</a>         Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="148" href="#148">148</a>         Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="149" href="#149">149</a>         Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);
+<a class="jxr_linenumber" name="150" href="#150">150</a>         Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);
+<a class="jxr_linenumber" name="151" href="#151">151</a>         Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);
+<a class="jxr_linenumber" name="152" href="#152">152</a>         Assert.assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);
+<a class="jxr_linenumber" name="153" href="#153">153</a>         Assert.assertEquals(-1, FieldVector3D.dotProduct(r.getAxis(), reverted.getAxis()).getReal(), 1.0e-15);
+<a class="jxr_linenumber" name="154" href="#154">154</a>     }
+<a class="jxr_linenumber" name="155" href="#155">155</a> 
+<a class="jxr_linenumber" name="156" href="#156">156</a>     @Test
+<a class="jxr_linenumber" name="157" href="#157">157</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVectorOnePair() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="158" href="#158">158</a> 
+<a class="jxr_linenumber" name="159" href="#159">159</a>         FieldVector3D&lt;DerivativeStructure&gt; u = createVector(3, 2, 1);
+<a class="jxr_linenumber" name="160" href="#160">160</a>         FieldVector3D&lt;DerivativeStructure&gt; v = createVector(-4, 2, 2);
+<a class="jxr_linenumber" name="161" href="#161">161</a>         FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u, v);
+<a class="jxr_linenumber" name="162" href="#162">162</a>         checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));
+<a class="jxr_linenumber" name="163" href="#163">163</a> 
+<a class="jxr_linenumber" name="164" href="#164">164</a>         checkAngle(<strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u, u.negate()).getAngle(), FastMath.PI);
+<a class="jxr_linenumber" name="165" href="#165">165</a> 
+<a class="jxr_linenumber" name="166" href="#166">166</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="167" href="#167">167</a>             <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u, createVector(0, 0, 0));
+<a class="jxr_linenumber" name="168" href="#168">168</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="169" href="#169">169</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException e) {
+<a class="jxr_linenumber" name="170" href="#170">170</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="171" href="#171">171</a>         }
+<a class="jxr_linenumber" name="172" href="#172">172</a> 
+<a class="jxr_linenumber" name="173" href="#173">173</a>     }
+<a class="jxr_linenumber" name="174" href="#174">174</a> 
+<a class="jxr_linenumber" name="175" href="#175">175</a>     @Test
+<a class="jxr_linenumber" name="176" href="#176">176</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVectorTwoPairs() <strong class="jxr_keyword">throws</strong> MathArithmeticException {
+<a class="jxr_linenumber" name="177" href="#177">177</a> 
+<a class="jxr_linenumber" name="178" href="#178">178</a>         FieldVector3D&lt;DerivativeStructure&gt; u1 = createVector(3, 0, 0);
+<a class="jxr_linenumber" name="179" href="#179">179</a>         FieldVector3D&lt;DerivativeStructure&gt; u2 = createVector(0, 5, 0);
+<a class="jxr_linenumber" name="180" href="#180">180</a>         FieldVector3D&lt;DerivativeStructure&gt; v1 = createVector(0, 0, 2);
+<a class="jxr_linenumber" name="181" href="#181">181</a>         FieldVector3D&lt;DerivativeStructure&gt; v2 = createVector(-2, 0, 2);
+<a class="jxr_linenumber" name="182" href="#182">182</a>         FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u1, u2, v1, v2);
+<a class="jxr_linenumber" name="183" href="#183">183</a>         checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="184" href="#184">184</a>         checkVector(r.applyTo(createVector(0, 1, 0)), createVector(-1, 0, 0));
+<a class="jxr_linenumber" name="185" href="#185">185</a> 
+<a class="jxr_linenumber" name="186" href="#186">186</a>         r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u1, u2, u1.negate(), u2.negate());
+<a class="jxr_linenumber" name="187" href="#187">187</a>         FieldVector3D&lt;DerivativeStructure&gt; axis = r.getAxis();
+<a class="jxr_linenumber" name="188" href="#188">188</a>         <strong class="jxr_keyword">if</strong> (FieldVector3D.dotProduct(axis, createVector(0, 0, 1)).getReal() &gt; 0) {
+<a class="jxr_linenumber" name="189" href="#189">189</a>             checkVector(axis, createVector(0, 0, 1));
+<a class="jxr_linenumber" name="190" href="#190">190</a>         } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="191" href="#191">191</a>             checkVector(axis, createVector(0, 0, -1));
+<a class="jxr_linenumber" name="192" href="#192">192</a>         }
+<a class="jxr_linenumber" name="193" href="#193">193</a>         checkAngle(r.getAngle(), FastMath.PI);
+<a class="jxr_linenumber" name="194" href="#194">194</a> 
+<a class="jxr_linenumber" name="195" href="#195">195</a>         <strong class="jxr_keyword">double</strong> sqrt = FastMath.sqrt(2) / 2;
+<a class="jxr_linenumber" name="196" href="#196">196</a>         r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(1, 0, 0),  createVector(0, 1, 0),
+<a class="jxr_linenumber" name="197" href="#197">197</a>                            createVector(0.5, 0.5,  sqrt),
+<a class="jxr_linenumber" name="198" href="#198">198</a>                            createVector(0.5, 0.5, -sqrt));
+<a class="jxr_linenumber" name="199" href="#199">199</a>         checkRotationDS(r, sqrt, 0.5, 0.5, 0);
+<a class="jxr_linenumber" name="200" href="#200">200</a> 
+<a class="jxr_linenumber" name="201" href="#201">201</a>         r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u1, u2, u1, FieldVector3D.crossProduct(u1, u2));
+<a class="jxr_linenumber" name="202" href="#202">202</a>         checkRotationDS(r, sqrt, -sqrt, 0, 0);
+<a class="jxr_linenumber" name="203" href="#203">203</a> 
+<a class="jxr_linenumber" name="204" href="#204">204</a>         checkRotationDS(<strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u1, u2, u1, u2), 1, 0, 0, 0);
+<a class="jxr_linenumber" name="205" href="#205">205</a> 
+<a class="jxr_linenumber" name="206" href="#206">206</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="207" href="#207">207</a>             <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(u1, u2, createVector(0, 0, 0), v2);
+<a class="jxr_linenumber" name="208" href="#208">208</a>             Assert.fail(<span class="jxr_string">"an exception should have been thrown"</span>);
+<a class="jxr_linenumber" name="209" href="#209">209</a>         } <strong class="jxr_keyword">catch</strong> (MathArithmeticException e) {
+<a class="jxr_linenumber" name="210" href="#210">210</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="211" href="#211">211</a>         }
+<a class="jxr_linenumber" name="212" href="#212">212</a> 
+<a class="jxr_linenumber" name="213" href="#213">213</a>     }
+<a class="jxr_linenumber" name="214" href="#214">214</a> 
+<a class="jxr_linenumber" name="215" href="#215">215</a>     @Test
+<a class="jxr_linenumber" name="216" href="#216">216</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMatrix()
+<a class="jxr_linenumber" name="217" href="#217">217</a>             <strong class="jxr_keyword">throws</strong> NotARotationMatrixException {
+<a class="jxr_linenumber" name="218" href="#218">218</a> 
+<a class="jxr_linenumber" name="219" href="#219">219</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="220" href="#220">220</a>             createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="221" href="#221">221</a>                 { 0.0, 1.0, 0.0 },
+<a class="jxr_linenumber" name="222" href="#222">222</a>                 { 1.0, 0.0, 0.0 }
+<a class="jxr_linenumber" name="223" href="#223">223</a>             }, 1.0e-7);
+<a class="jxr_linenumber" name="224" href="#224">224</a>             Assert.fail(<span class="jxr_string">"Expecting NotARotationMatrixException"</span>);
+<a class="jxr_linenumber" name="225" href="#225">225</a>         } <strong class="jxr_keyword">catch</strong> (NotARotationMatrixException nrme) {
+<a class="jxr_linenumber" name="226" href="#226">226</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="227" href="#227">227</a>         }
+<a class="jxr_linenumber" name="228" href="#228">228</a> 
+<a class="jxr_linenumber" name="229" href="#229">229</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="230" href="#230">230</a>             createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="231" href="#231">231</a>                 {  0.445888,  0.797184, -0.407040 },
+<a class="jxr_linenumber" name="232" href="#232">232</a>                 {  0.821760, -0.184320,  0.539200 },
+<a class="jxr_linenumber" name="233" href="#233">233</a>                 { -0.354816,  0.574912,  0.737280 }
+<a class="jxr_linenumber" name="234" href="#234">234</a>             }, 1.0e-7);
+<a class="jxr_linenumber" name="235" href="#235">235</a>             Assert.fail(<span class="jxr_string">"Expecting NotARotationMatrixException"</span>);
+<a class="jxr_linenumber" name="236" href="#236">236</a>         } <strong class="jxr_keyword">catch</strong> (NotARotationMatrixException nrme) {
+<a class="jxr_linenumber" name="237" href="#237">237</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="238" href="#238">238</a>         }
+<a class="jxr_linenumber" name="239" href="#239">239</a> 
+<a class="jxr_linenumber" name="240" href="#240">240</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="241" href="#241">241</a>             createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="242" href="#242">242</a>                 {  0.4,  0.8, -0.4 },
+<a class="jxr_linenumber" name="243" href="#243">243</a>                 { -0.4,  0.6,  0.7 },
+<a class="jxr_linenumber" name="244" href="#244">244</a>                 {  0.8, -0.2,  0.5 }
+<a class="jxr_linenumber" name="245" href="#245">245</a>             }, 1.0e-15);
+<a class="jxr_linenumber" name="246" href="#246">246</a>             Assert.fail(<span class="jxr_string">"Expecting NotARotationMatrixException"</span>);
+<a class="jxr_linenumber" name="247" href="#247">247</a>         } <strong class="jxr_keyword">catch</strong> (NotARotationMatrixException nrme) {
+<a class="jxr_linenumber" name="248" href="#248">248</a>             <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="249" href="#249">249</a>         }
+<a class="jxr_linenumber" name="250" href="#250">250</a> 
+<a class="jxr_linenumber" name="251" href="#251">251</a>         checkRotationDS(createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="252" href="#252">252</a>             {  0.445888,  0.797184, -0.407040 },
+<a class="jxr_linenumber" name="253" href="#253">253</a>             { -0.354816,  0.574912,  0.737280 },
+<a class="jxr_linenumber" name="254" href="#254">254</a>             {  0.821760, -0.184320,  0.539200 }
+<a class="jxr_linenumber" name="255" href="#255">255</a>         }, 1.0e-10),
+<a class="jxr_linenumber" name="256" href="#256">256</a>         0.8, 0.288, 0.384, 0.36);
+<a class="jxr_linenumber" name="257" href="#257">257</a> 
+<a class="jxr_linenumber" name="258" href="#258">258</a>         checkRotationDS(createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="259" href="#259">259</a>             {  0.539200,  0.737280,  0.407040 },
+<a class="jxr_linenumber" name="260" href="#260">260</a>             {  0.184320, -0.574912,  0.797184 },
+<a class="jxr_linenumber" name="261" href="#261">261</a>             {  0.821760, -0.354816, -0.445888 }
+<a class="jxr_linenumber" name="262" href="#262">262</a>         }, 1.0e-10),
+<a class="jxr_linenumber" name="263" href="#263">263</a>         0.36, 0.8, 0.288, 0.384);
+<a class="jxr_linenumber" name="264" href="#264">264</a> 
+<a class="jxr_linenumber" name="265" href="#265">265</a>         checkRotationDS(createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="266" href="#266">266</a>             { -0.445888,  0.797184, -0.407040 },
+<a class="jxr_linenumber" name="267" href="#267">267</a>             {  0.354816,  0.574912,  0.737280 },
+<a class="jxr_linenumber" name="268" href="#268">268</a>             {  0.821760,  0.184320, -0.539200 }
+<a class="jxr_linenumber" name="269" href="#269">269</a>         }, 1.0e-10),
+<a class="jxr_linenumber" name="270" href="#270">270</a>         0.384, 0.36, 0.8, 0.288);
+<a class="jxr_linenumber" name="271" href="#271">271</a> 
+<a class="jxr_linenumber" name="272" href="#272">272</a>         checkRotationDS(createRotation(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="273" href="#273">273</a>             { -0.539200,  0.737280,  0.407040 },
+<a class="jxr_linenumber" name="274" href="#274">274</a>             { -0.184320, -0.574912,  0.797184 },
+<a class="jxr_linenumber" name="275" href="#275">275</a>             {  0.821760,  0.354816,  0.445888 }
+<a class="jxr_linenumber" name="276" href="#276">276</a>         }, 1.0e-10),
+<a class="jxr_linenumber" name="277" href="#277">277</a>         0.288, 0.384, 0.36, 0.8);
+<a class="jxr_linenumber" name="278" href="#278">278</a> 
+<a class="jxr_linenumber" name="279" href="#279">279</a>         <strong class="jxr_keyword">double</strong>[][] m1 = { { 0.0, 1.0, 0.0 },
+<a class="jxr_linenumber" name="280" href="#280">280</a>             { 0.0, 0.0, 1.0 },
+<a class="jxr_linenumber" name="281" href="#281">281</a>             { 1.0, 0.0, 0.0 } };
+<a class="jxr_linenumber" name="282" href="#282">282</a>         FieldRotation&lt;DerivativeStructure&gt; r = createRotation(m1, 1.0e-7);
+<a class="jxr_linenumber" name="283" href="#283">283</a>         checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));
+<a class="jxr_linenumber" name="284" href="#284">284</a>         checkVector(r.applyTo(createVector(0, 1, 0)), createVector(1, 0, 0));
+<a class="jxr_linenumber" name="285" href="#285">285</a>         checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 1, 0));
+<a class="jxr_linenumber" name="286" href="#286">286</a> 
+<a class="jxr_linenumber" name="287" href="#287">287</a>         <strong class="jxr_keyword">double</strong>[][] m2 = { { 0.83203, -0.55012, -0.07139 },
+<a class="jxr_linenumber" name="288" href="#288">288</a>             { 0.48293,  0.78164, -0.39474 },
+<a class="jxr_linenumber" name="289" href="#289">289</a>             { 0.27296,  0.29396,  0.91602 } };
+<a class="jxr_linenumber" name="290" href="#290">290</a>         r = createRotation(m2, 1.0e-12);
+<a class="jxr_linenumber" name="291" href="#291">291</a> 
+<a class="jxr_linenumber" name="292" href="#292">292</a>         DerivativeStructure[][] m3 = r.getMatrix();
+<a class="jxr_linenumber" name="293" href="#293">293</a>         <strong class="jxr_keyword">double</strong> d00 = m2[0][0] - m3[0][0].getReal();
+<a class="jxr_linenumber" name="294" href="#294">294</a>         <strong class="jxr_keyword">double</strong> d01 = m2[0][1] - m3[0][1].getReal();
+<a class="jxr_linenumber" name="295" href="#295">295</a>         <strong class="jxr_keyword">double</strong> d02 = m2[0][2] - m3[0][2].getReal();
+<a class="jxr_linenumber" name="296" href="#296">296</a>         <strong class="jxr_keyword">double</strong> d10 = m2[1][0] - m3[1][0].getReal();
+<a class="jxr_linenumber" name="297" href="#297">297</a>         <strong class="jxr_keyword">double</strong> d11 = m2[1][1] - m3[1][1].getReal();
+<a class="jxr_linenumber" name="298" href="#298">298</a>         <strong class="jxr_keyword">double</strong> d12 = m2[1][2] - m3[1][2].getReal();
+<a class="jxr_linenumber" name="299" href="#299">299</a>         <strong class="jxr_keyword">double</strong> d20 = m2[2][0] - m3[2][0].getReal();
+<a class="jxr_linenumber" name="300" href="#300">300</a>         <strong class="jxr_keyword">double</strong> d21 = m2[2][1] - m3[2][1].getReal();
+<a class="jxr_linenumber" name="301" href="#301">301</a>         <strong class="jxr_keyword">double</strong> d22 = m2[2][2] - m3[2][2].getReal();
+<a class="jxr_linenumber" name="302" href="#302">302</a> 
+<a class="jxr_linenumber" name="303" href="#303">303</a>         Assert.assertTrue(FastMath.abs(d00) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="304" href="#304">304</a>         Assert.assertTrue(FastMath.abs(d01) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="305" href="#305">305</a>         Assert.assertTrue(FastMath.abs(d02) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="306" href="#306">306</a>         Assert.assertTrue(FastMath.abs(d10) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="307" href="#307">307</a>         Assert.assertTrue(FastMath.abs(d11) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="308" href="#308">308</a>         Assert.assertTrue(FastMath.abs(d12) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="309" href="#309">309</a>         Assert.assertTrue(FastMath.abs(d20) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="310" href="#310">310</a>         Assert.assertTrue(FastMath.abs(d21) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="311" href="#311">311</a>         Assert.assertTrue(FastMath.abs(d22) &lt; 6.0e-6);
+<a class="jxr_linenumber" name="312" href="#312">312</a> 
+<a class="jxr_linenumber" name="313" href="#313">313</a>         Assert.assertTrue(FastMath.abs(d00) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="314" href="#314">314</a>         Assert.assertTrue(FastMath.abs(d01) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="315" href="#315">315</a>         Assert.assertTrue(FastMath.abs(d02) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="316" href="#316">316</a>         Assert.assertTrue(FastMath.abs(d10) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="317" href="#317">317</a>         Assert.assertTrue(FastMath.abs(d11) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="318" href="#318">318</a>         Assert.assertTrue(FastMath.abs(d12) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="319" href="#319">319</a>         Assert.assertTrue(FastMath.abs(d20) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="320" href="#320">320</a>         Assert.assertTrue(FastMath.abs(d21) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="321" href="#321">321</a>         Assert.assertTrue(FastMath.abs(d22) &gt; 4.0e-7);
+<a class="jxr_linenumber" name="322" href="#322">322</a> 
+<a class="jxr_linenumber" name="323" href="#323">323</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; 3; ++i) {
+<a class="jxr_linenumber" name="324" href="#324">324</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j &lt; 3; ++j) {
+<a class="jxr_linenumber" name="325" href="#325">325</a>                 <strong class="jxr_keyword">double</strong> m3tm3 = m3[i][0].getReal() * m3[j][0].getReal() +
+<a class="jxr_linenumber" name="326" href="#326">326</a>                                m3[i][1].getReal() * m3[j][1].getReal() +
+<a class="jxr_linenumber" name="327" href="#327">327</a>                                m3[i][2].getReal() * m3[j][2].getReal();
+<a class="jxr_linenumber" name="328" href="#328">328</a>                 <strong class="jxr_keyword">if</strong> (i == j) {
+<a class="jxr_linenumber" name="329" href="#329">329</a>                     Assert.assertTrue(FastMath.abs(m3tm3 - 1.0) &lt; 1.0e-10);
+<a class="jxr_linenumber" name="330" href="#330">330</a>                 } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="331" href="#331">331</a>                     Assert.assertTrue(FastMath.abs(m3tm3) &lt; 1.0e-10);
+<a class="jxr_linenumber" name="332" href="#332">332</a>                 }
+<a class="jxr_linenumber" name="333" href="#333">333</a>             }
+<a class="jxr_linenumber" name="334" href="#334">334</a>         }
+<a class="jxr_linenumber" name="335" href="#335">335</a> 
+<a class="jxr_linenumber" name="336" href="#336">336</a>         checkVector(r.applyTo(createVector(1, 0, 0)),
+<a class="jxr_linenumber" name="337" href="#337">337</a>                     <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(m3[0][0], m3[1][0], m3[2][0]));
+<a class="jxr_linenumber" name="338" href="#338">338</a>         checkVector(r.applyTo(createVector(0, 1, 0)),
+<a class="jxr_linenumber" name="339" href="#339">339</a>                     <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(m3[0][1], m3[1][1], m3[2][1]));
+<a class="jxr_linenumber" name="340" href="#340">340</a>         checkVector(r.applyTo(createVector(0, 0, 1)),
+<a class="jxr_linenumber" name="341" href="#341">341</a>                     <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(m3[0][2], m3[1][2], m3[2][2]));
+<a class="jxr_linenumber" name="342" href="#342">342</a> 
+<a class="jxr_linenumber" name="343" href="#343">343</a>         <strong class="jxr_keyword">double</strong>[][] m4 = { { 1.0,  0.0,  0.0 },
+<a class="jxr_linenumber" name="344" href="#344">344</a>             { 0.0, -1.0,  0.0 },
+<a class="jxr_linenumber" name="345" href="#345">345</a>             { 0.0,  0.0, -1.0 } };
+<a class="jxr_linenumber" name="346" href="#346">346</a>         r = createRotation(m4, 1.0e-7);
+<a class="jxr_linenumber" name="347" href="#347">347</a>         checkAngle(r.getAngle(), FastMath.PI);
+<a class="jxr_linenumber" name="348" href="#348">348</a> 
+<a class="jxr_linenumber" name="349" href="#349">349</a>         <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="350" href="#350">350</a>             <strong class="jxr_keyword">double</strong>[][] m5 = { { 0.0, 0.0, 1.0 },
+<a class="jxr_linenumber" name="351" href="#351">351</a>                 { 0.0, 1.0, 0.0 },
+<a class="jxr_linenumber" name="352" href="#352">352</a>                 { 1.0, 0.0, 0.0 } };
+<a class="jxr_linenumber" name="353" href="#353">353</a>             r = createRotation(m5, 1.0e-7);
+<a class="jxr_linenumber" name="354" href="#354">354</a>             Assert.fail(<span class="jxr_string">"got "</span> + r + <span class="jxr_string">", should have caught an exception"</span>);
+<a class="jxr_linenumber" name="355" href="#355">355</a>         } <strong class="jxr_keyword">catch</strong> (NotARotationMatrixException e) {
+<a class="jxr_linenumber" name="356" href="#356">356</a>             <em class="jxr_comment">// expected</em>
+<a class="jxr_linenumber" name="357" href="#357">357</a>         }
+<a class="jxr_linenumber" name="358" href="#358">358</a> 
+<a class="jxr_linenumber" name="359" href="#359">359</a>     }
+<a class="jxr_linenumber" name="360" href="#360">360</a> 
+<a class="jxr_linenumber" name="361" href="#361">361</a>     @Test
+<a class="jxr_linenumber" name="362" href="#362">362</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAngles()
+<a class="jxr_linenumber" name="363" href="#363">363</a>             <strong class="jxr_keyword">throws</strong> CardanEulerSingularityException {
+<a class="jxr_linenumber" name="364" href="#364">364</a> 
+<a class="jxr_linenumber" name="365" href="#365">365</a>         RotationOrder[] CardanOrders = {
+<a class="jxr_linenumber" name="366" href="#366">366</a>             RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
+<a class="jxr_linenumber" name="367" href="#367">367</a>             RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
+<a class="jxr_linenumber" name="368" href="#368">368</a>         };
+<a class="jxr_linenumber" name="369" href="#369">369</a> 
+<a class="jxr_linenumber" name="370" href="#370">370</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; CardanOrders.length; ++i) {
+<a class="jxr_linenumber" name="371" href="#371">371</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha1 = 0.1; alpha1 &lt; 6.2; alpha1 += 0.3) {
+<a class="jxr_linenumber" name="372" href="#372">372</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha2 = -1.55; alpha2 &lt; 1.55; alpha2 += 0.3) {
+<a class="jxr_linenumber" name="373" href="#373">373</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha3 = 0.1; alpha3 &lt; 6.2; alpha3 += 0.3) {
+<a class="jxr_linenumber" name="374" href="#374">374</a>                         FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(CardanOrders[i],
+<a class="jxr_linenumber" name="375" href="#375">375</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, alpha1),
+<a class="jxr_linenumber" name="376" href="#376">376</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, alpha2),
+<a class="jxr_linenumber" name="377" href="#377">377</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, alpha3));
+<a class="jxr_linenumber" name="378" href="#378">378</a>                         DerivativeStructure[] angles = r.getAngles(CardanOrders[i]);
+<a class="jxr_linenumber" name="379" href="#379">379</a>                         checkAngle(angles[0], alpha1);
+<a class="jxr_linenumber" name="380" href="#380">380</a>                         checkAngle(angles[1], alpha2);
+<a class="jxr_linenumber" name="381" href="#381">381</a>                         checkAngle(angles[2], alpha3);
+<a class="jxr_linenumber" name="382" href="#382">382</a>                     }
+<a class="jxr_linenumber" name="383" href="#383">383</a>                 }
+<a class="jxr_linenumber" name="384" href="#384">384</a>             }
+<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>         RotationOrder[] EulerOrders = {
+<a class="jxr_linenumber" name="388" href="#388">388</a>             RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
+<a class="jxr_linenumber" name="389" href="#389">389</a>             RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
+<a class="jxr_linenumber" name="390" href="#390">390</a>         };
+<a class="jxr_linenumber" name="391" href="#391">391</a> 
+<a class="jxr_linenumber" name="392" href="#392">392</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; EulerOrders.length; ++i) {
+<a class="jxr_linenumber" name="393" href="#393">393</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha1 = 0.1; alpha1 &lt; 6.2; alpha1 += 0.3) {
+<a class="jxr_linenumber" name="394" href="#394">394</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha2 = 0.05; alpha2 &lt; 3.1; alpha2 += 0.3) {
+<a class="jxr_linenumber" name="395" href="#395">395</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> alpha3 = 0.1; alpha3 &lt; 6.2; alpha3 += 0.3) {
+<a class="jxr_linenumber" name="396" href="#396">396</a>                         FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(EulerOrders[i],
+<a class="jxr_linenumber" name="397" href="#397">397</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, alpha1),
+<a class="jxr_linenumber" name="398" href="#398">398</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, alpha2),
+<a class="jxr_linenumber" name="399" href="#399">399</a>                                                       <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, alpha3));
+<a class="jxr_linenumber" name="400" href="#400">400</a>                         DerivativeStructure[] angles = r.getAngles(EulerOrders[i]);
+<a class="jxr_linenumber" name="401" href="#401">401</a>                         checkAngle(angles[0], alpha1);
+<a class="jxr_linenumber" name="402" href="#402">402</a>                         checkAngle(angles[1], alpha2);
+<a class="jxr_linenumber" name="403" href="#403">403</a>                         checkAngle(angles[2], alpha3);
+<a class="jxr_linenumber" name="404" href="#404">404</a>                     }
+<a class="jxr_linenumber" name="405" href="#405">405</a>                 }
+<a class="jxr_linenumber" name="406" href="#406">406</a>             }
+<a class="jxr_linenumber" name="407" href="#407">407</a>         }
+<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> testSingularities() {
+<a class="jxr_linenumber" name="413" href="#413">413</a> 
+<a class="jxr_linenumber" name="414" href="#414">414</a>         RotationOrder[] CardanOrders = {
+<a class="jxr_linenumber" name="415" href="#415">415</a>             RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,
+<a class="jxr_linenumber" name="416" href="#416">416</a>             RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX
+<a class="jxr_linenumber" name="417" href="#417">417</a>         };
+<a class="jxr_linenumber" name="418" href="#418">418</a> 
+<a class="jxr_linenumber" name="419" href="#419">419</a>         <strong class="jxr_keyword">double</strong>[] singularCardanAngle = { FastMath.PI / 2, -FastMath.PI / 2 };
+<a class="jxr_linenumber" name="420" href="#420">420</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; CardanOrders.length; ++i) {
+<a class="jxr_linenumber" name="421" href="#421">421</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j &lt; singularCardanAngle.length; ++j) {
+<a class="jxr_linenumber" name="422" href="#422">422</a>                 FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(CardanOrders[i],
+<a class="jxr_linenumber" name="423" href="#423">423</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 0.1),
+<a class="jxr_linenumber" name="424" href="#424">424</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, singularCardanAngle[j]),
+<a class="jxr_linenumber" name="425" href="#425">425</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 0.3));
+<a class="jxr_linenumber" name="426" href="#426">426</a>                 <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="427" href="#427">427</a>                     r.getAngles(CardanOrders[i]);
+<a class="jxr_linenumber" name="428" href="#428">428</a>                     Assert.fail(<span class="jxr_string">"an exception should have been caught"</span>);
+<a class="jxr_linenumber" name="429" href="#429">429</a>                 } <strong class="jxr_keyword">catch</strong> (CardanEulerSingularityException cese) {
+<a class="jxr_linenumber" name="430" href="#430">430</a>                     <em class="jxr_comment">// expected behavior</em>
+<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> 
+<a class="jxr_linenumber" name="435" href="#435">435</a>         RotationOrder[] EulerOrders = {
+<a class="jxr_linenumber" name="436" href="#436">436</a>             RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,
+<a class="jxr_linenumber" name="437" href="#437">437</a>             RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ
+<a class="jxr_linenumber" name="438" href="#438">438</a>         };
+<a class="jxr_linenumber" name="439" href="#439">439</a> 
+<a class="jxr_linenumber" name="440" href="#440">440</a>         <strong class="jxr_keyword">double</strong>[] singularEulerAngle = { 0, FastMath.PI };
+<a class="jxr_linenumber" name="441" href="#441">441</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; EulerOrders.length; ++i) {
+<a class="jxr_linenumber" name="442" href="#442">442</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j &lt; singularEulerAngle.length; ++j) {
+<a class="jxr_linenumber" name="443" href="#443">443</a>                 FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(EulerOrders[i],
+<a class="jxr_linenumber" name="444" href="#444">444</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 0.1),
+<a class="jxr_linenumber" name="445" href="#445">445</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 1, singularEulerAngle[j]),
+<a class="jxr_linenumber" name="446" href="#446">446</a>                                               <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 2, 0.3));
+<a class="jxr_linenumber" name="447" href="#447">447</a>                 <strong class="jxr_keyword">try</strong> {
+<a class="jxr_linenumber" name="448" href="#448">448</a>                     r.getAngles(EulerOrders[i]);
+<a class="jxr_linenumber" name="449" href="#449">449</a>                     Assert.fail(<span class="jxr_string">"an exception should have been caught"</span>);
+<a class="jxr_linenumber" name="450" href="#450">450</a>                 } <strong class="jxr_keyword">catch</strong> (CardanEulerSingularityException cese) {
+<a class="jxr_linenumber" name="451" href="#451">451</a>                     <em class="jxr_comment">// expected behavior</em>
+<a class="jxr_linenumber" name="452" href="#452">452</a>                 }
+<a class="jxr_linenumber" name="453" href="#453">453</a>             }
+<a class="jxr_linenumber" name="454" href="#454">454</a>         }
+<a class="jxr_linenumber" name="455" href="#455">455</a> 
+<a class="jxr_linenumber" name="456" href="#456">456</a> 
+<a class="jxr_linenumber" name="457" href="#457">457</a>     }
+<a class="jxr_linenumber" name="458" href="#458">458</a> 
+<a class="jxr_linenumber" name="459" href="#459">459</a>     @Test
+<a class="jxr_linenumber" name="460" href="#460">460</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testQuaternion() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="461" href="#461">461</a> 
+<a class="jxr_linenumber" name="462" href="#462">462</a>         FieldRotation&lt;DerivativeStructure&gt; r1 = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(2, -3, 5), createAngle(1.7));
+<a class="jxr_linenumber" name="463" href="#463">463</a>         <strong class="jxr_keyword">double</strong> n = 23.5;
+<a class="jxr_linenumber" name="464" href="#464">464</a>         FieldRotation&lt;DerivativeStructure&gt; r2 = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(r1.getQ0().multiply(n), r1.getQ1().multiply(n),
+<a class="jxr_linenumber" name="465" href="#465">465</a>                                        r1.getQ2().multiply(n), r1.getQ3().multiply(n),
+<a class="jxr_linenumber" name="466" href="#466">466</a>                                        <strong class="jxr_keyword">true</strong>);
+<a class="jxr_linenumber" name="467" href="#467">467</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="468" href="#468">468</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="469" href="#469">469</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="470" href="#470">470</a>                     FieldVector3D&lt;DerivativeStructure&gt; u = createVector(x, y, z);
+<a class="jxr_linenumber" name="471" href="#471">471</a>                     checkVector(r2.applyTo(u), r1.applyTo(u));
+<a class="jxr_linenumber" name="472" href="#472">472</a>                 }
+<a class="jxr_linenumber" name="473" href="#473">473</a>             }
+<a class="jxr_linenumber" name="474" href="#474">474</a>         }
+<a class="jxr_linenumber" name="475" href="#475">475</a> 
+<a class="jxr_linenumber" name="476" href="#476">476</a>         r1 = createRotation(0.288,  0.384,  0.36,  0.8, false);
+<a class="jxr_linenumber" name="477" href="#477">477</a>         checkRotationDS(r1,
+<a class="jxr_linenumber" name="478" href="#478">478</a>                         -r1.getQ0().getReal(), -r1.getQ1().getReal(),
+<a class="jxr_linenumber" name="479" href="#479">479</a>                         -r1.getQ2().getReal(), -r1.getQ3().getReal());
+<a class="jxr_linenumber" name="480" href="#480">480</a>         Assert.assertEquals(0.288, r1.toRotation().getQ0(), 1.0e-15);
+<a class="jxr_linenumber" name="481" href="#481">481</a>         Assert.assertEquals(0.384, r1.toRotation().getQ1(), 1.0e-15);
+<a class="jxr_linenumber" name="482" href="#482">482</a>         Assert.assertEquals(0.36,  r1.toRotation().getQ2(), 1.0e-15);
+<a class="jxr_linenumber" name="483" href="#483">483</a>         Assert.assertEquals(0.8,   r1.toRotation().getQ3(), 1.0e-15);
+<a class="jxr_linenumber" name="484" href="#484">484</a> 
+<a class="jxr_linenumber" name="485" href="#485">485</a>     }
+<a class="jxr_linenumber" name="486" href="#486">486</a> 
+<a class="jxr_linenumber" name="487" href="#487">487</a>     @Test
+<a class="jxr_linenumber" name="488" href="#488">488</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCompose() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="489" href="#489">489</a> 
+<a class="jxr_linenumber" name="490" href="#490">490</a>         FieldRotation&lt;DerivativeStructure&gt; r1       = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(2, -3, 5), createAngle(1.7));
+<a class="jxr_linenumber" name="491" href="#491">491</a>         FieldRotation&lt;DerivativeStructure&gt; r2       = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(-1, 3, 2), createAngle(0.3));
+<a class="jxr_linenumber" name="492" href="#492">492</a>         FieldRotation&lt;DerivativeStructure&gt; r3       = r2.applyTo(r1);
+<a class="jxr_linenumber" name="493" href="#493">493</a>         FieldRotation&lt;DerivativeStructure&gt; r3Double = r2.applyTo(<strong class="jxr_keyword">new</strong> Rotation(r1.getQ0().getReal(),
+<a class="jxr_linenumber" name="494" href="#494">494</a>                                                       r1.getQ1().getReal(),
+<a class="jxr_linenumber" name="495" href="#495">495</a>                                                       r1.getQ2().getReal(),
+<a class="jxr_linenumber" name="496" href="#496">496</a>                                                       r1.getQ3().getReal(),
+<a class="jxr_linenumber" name="497" href="#497">497</a>                                                       false));
+<a class="jxr_linenumber" name="498" href="#498">498</a> 
+<a class="jxr_linenumber" name="499" href="#499">499</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="500" href="#500">500</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="501" href="#501">501</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="502" href="#502">502</a>                     FieldVector3D&lt;DerivativeStructure&gt; u = createVector(x, y, z);
+<a class="jxr_linenumber" name="503" href="#503">503</a>                     checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
+<a class="jxr_linenumber" name="504" href="#504">504</a>                     checkVector(r2.applyTo(r1.applyTo(u)), r3Double.applyTo(u));
+<a class="jxr_linenumber" name="505" href="#505">505</a>                 }
+<a class="jxr_linenumber" name="506" href="#506">506</a>             }
+<a class="jxr_linenumber" name="507" href="#507">507</a>         }
+<a class="jxr_linenumber" name="508" href="#508">508</a> 
+<a class="jxr_linenumber" name="509" href="#509">509</a>     }
+<a class="jxr_linenumber" name="510" href="#510">510</a> 
+<a class="jxr_linenumber" name="511" href="#511">511</a>     @Test
+<a class="jxr_linenumber" name="512" href="#512">512</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testComposeInverse() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="513" href="#513">513</a> 
+<a class="jxr_linenumber" name="514" href="#514">514</a>         FieldRotation&lt;DerivativeStructure&gt; r1 = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(2, -3, 5), createAngle(1.7));
+<a class="jxr_linenumber" name="515" href="#515">515</a>         FieldRotation&lt;DerivativeStructure&gt; r2 = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(-1, 3, 2), createAngle(0.3));
+<a class="jxr_linenumber" name="516" href="#516">516</a>         FieldRotation&lt;DerivativeStructure&gt; r3 = r2.applyInverseTo(r1);
+<a class="jxr_linenumber" name="517" href="#517">517</a>         FieldRotation&lt;DerivativeStructure&gt; r3Double = r2.applyInverseTo(<strong class="jxr_keyword">new</strong> Rotation(r1.getQ0().getReal(),
+<a class="jxr_linenumber" name="518" href="#518">518</a>                                                              r1.getQ1().getReal(),
+<a class="jxr_linenumber" name="519" href="#519">519</a>                                                              r1.getQ2().getReal(),
+<a class="jxr_linenumber" name="520" href="#520">520</a>                                                              r1.getQ3().getReal(),
+<a class="jxr_linenumber" name="521" href="#521">521</a>                                                              false));
+<a class="jxr_linenumber" name="522" href="#522">522</a> 
+<a class="jxr_linenumber" name="523" href="#523">523</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="524" href="#524">524</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="525" href="#525">525</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="526" href="#526">526</a>                     FieldVector3D&lt;DerivativeStructure&gt; u = createVector(x, y, z);
+<a class="jxr_linenumber" name="527" href="#527">527</a>                     checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
+<a class="jxr_linenumber" name="528" href="#528">528</a>                     checkVector(r2.applyInverseTo(r1.applyTo(u)), r3Double.applyTo(u));
+<a class="jxr_linenumber" name="529" href="#529">529</a>                 }
+<a class="jxr_linenumber" name="530" href="#530">530</a>             }
+<a class="jxr_linenumber" name="531" href="#531">531</a>         }
+<a class="jxr_linenumber" name="532" href="#532">532</a> 
+<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> testDoubleVectors() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="537" href="#537">537</a> 
+<a class="jxr_linenumber" name="538" href="#538">538</a>         Well1024a random = <strong class="jxr_keyword">new</strong> Well1024a(0x180b41cfeeffaf67l);
+<a class="jxr_linenumber" name="539" href="#539">539</a>         UnitSphereRandomVectorGenerator g = <strong class="jxr_keyword">new</strong> UnitSphereRandomVectorGenerator(3, random);
+<a class="jxr_linenumber" name="540" href="#540">540</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; 10; ++i) {
+<a class="jxr_linenumber" name="541" href="#541">541</a>             <strong class="jxr_keyword">double</strong>[] unit = g.nextVector();
+<a class="jxr_linenumber" name="542" href="#542">542</a>             FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(unit[0], unit[1], unit[2]),
+<a class="jxr_linenumber" name="543" href="#543">543</a>                                           createAngle(random.nextDouble()));
+<a class="jxr_linenumber" name="544" href="#544">544</a> 
+<a class="jxr_linenumber" name="545" href="#545">545</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="546" href="#546">546</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="547" href="#547">547</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="548" href="#548">548</a>                         FieldVector3D&lt;DerivativeStructure&gt; uds   = createVector(x, y, z);
+<a class="jxr_linenumber" name="549" href="#549">549</a>                         FieldVector3D&lt;DerivativeStructure&gt; ruds  = r.applyTo(uds);
+<a class="jxr_linenumber" name="550" href="#550">550</a>                         FieldVector3D&lt;DerivativeStructure&gt; rIuds = r.applyInverseTo(uds);
+<a class="jxr_linenumber" name="551" href="#551">551</a>                         Vector3D   u     = <strong class="jxr_keyword">new</strong> Vector3D(x, y, z);
+<a class="jxr_linenumber" name="552" href="#552">552</a>                         FieldVector3D&lt;DerivativeStructure&gt; ru    = r.applyTo(u);
+<a class="jxr_linenumber" name="553" href="#553">553</a>                         FieldVector3D&lt;DerivativeStructure&gt; rIu   = r.applyInverseTo(u);
+<a class="jxr_linenumber" name="554" href="#554">554</a>                         DerivativeStructure[] ruArray = <strong class="jxr_keyword">new</strong> DerivativeStructure[3];
+<a class="jxr_linenumber" name="555" href="#555">555</a>                         r.applyTo(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { x, y, z}, ruArray);
+<a class="jxr_linenumber" name="556" href="#556">556</a>                         DerivativeStructure[] rIuArray = <strong class="jxr_keyword">new</strong> DerivativeStructure[3];
+<a class="jxr_linenumber" name="557" href="#557">557</a>                         r.applyInverseTo(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { x, y, z}, rIuArray);
+<a class="jxr_linenumber" name="558" href="#558">558</a>                         checkVector(ruds, ru);
+<a class="jxr_linenumber" name="559" href="#559">559</a>                         checkVector(ruds, <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(ruArray));
+<a class="jxr_linenumber" name="560" href="#560">560</a>                         checkVector(rIuds, rIu);
+<a class="jxr_linenumber" name="561" href="#561">561</a>                         checkVector(rIuds, <strong class="jxr_keyword">new</strong> FieldVector3D&lt;DerivativeStructure&gt;(rIuArray));
+<a class="jxr_linenumber" name="562" href="#562">562</a>                     }
+<a class="jxr_linenumber" name="563" href="#563">563</a>                 }
+<a class="jxr_linenumber" name="564" href="#564">564</a>             }
+<a class="jxr_linenumber" name="565" href="#565">565</a>         }
+<a class="jxr_linenumber" name="566" href="#566">566</a> 
+<a class="jxr_linenumber" name="567" href="#567">567</a>     }
+<a class="jxr_linenumber" name="568" href="#568">568</a> 
+<a class="jxr_linenumber" name="569" href="#569">569</a>     @Test
+<a class="jxr_linenumber" name="570" href="#570">570</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDoubleRotations() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="571" href="#571">571</a> 
+<a class="jxr_linenumber" name="572" href="#572">572</a>         Well1024a random = <strong class="jxr_keyword">new</strong> Well1024a(0x180b41cfeeffaf67l);
+<a class="jxr_linenumber" name="573" href="#573">573</a>         UnitSphereRandomVectorGenerator g = <strong class="jxr_keyword">new</strong> UnitSphereRandomVectorGenerator(3, random);
+<a class="jxr_linenumber" name="574" href="#574">574</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; 10; ++i) {
+<a class="jxr_linenumber" name="575" href="#575">575</a>             <strong class="jxr_keyword">double</strong>[] unit1 = g.nextVector();
+<a class="jxr_linenumber" name="576" href="#576">576</a>             Rotation r1 = <strong class="jxr_keyword">new</strong> Rotation(<strong class="jxr_keyword">new</strong> Vector3D(unit1[0], unit1[1], unit1[2]),
+<a class="jxr_linenumber" name="577" href="#577">577</a>                                       random.nextDouble());
+<a class="jxr_linenumber" name="578" href="#578">578</a>             FieldRotation&lt;DerivativeStructure&gt; r1Prime = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(<strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 0, r1.getQ0()),
+<a class="jxr_linenumber" name="579" href="#579">579</a>                                                 <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 1, r1.getQ1()),
+<a class="jxr_linenumber" name="580" href="#580">580</a>                                                 <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 2, r1.getQ2()),
+<a class="jxr_linenumber" name="581" href="#581">581</a>                                                 <strong class="jxr_keyword">new</strong> DerivativeStructure(4, 1, 3, r1.getQ3()),
+<a class="jxr_linenumber" name="582" href="#582">582</a>                                                 false);
+<a class="jxr_linenumber" name="583" href="#583">583</a>             <strong class="jxr_keyword">double</strong>[] unit2 = g.nextVector();
+<a class="jxr_linenumber" name="584" href="#584">584</a>             FieldRotation&lt;DerivativeStructure&gt; r2 = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createVector(unit2[0], unit2[1], unit2[2]),
+<a class="jxr_linenumber" name="585" href="#585">585</a>                                            createAngle(random.nextDouble()));
+<a class="jxr_linenumber" name="586" href="#586">586</a> 
+<a class="jxr_linenumber" name="587" href="#587">587</a>             FieldRotation&lt;DerivativeStructure&gt; rA = FieldRotation.applyTo(r1, r2);
+<a class="jxr_linenumber" name="588" href="#588">588</a>             FieldRotation&lt;DerivativeStructure&gt; rB = r1Prime.applyTo(r2);
+<a class="jxr_linenumber" name="589" href="#589">589</a>             FieldRotation&lt;DerivativeStructure&gt; rC = FieldRotation.applyInverseTo(r1, r2);
+<a class="jxr_linenumber" name="590" href="#590">590</a>             FieldRotation&lt;DerivativeStructure&gt; rD = r1Prime.applyInverseTo(r2);
+<a class="jxr_linenumber" name="591" href="#591">591</a> 
+<a class="jxr_linenumber" name="592" href="#592">592</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="593" href="#593">593</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="594" href="#594">594</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="595" href="#595">595</a> 
+<a class="jxr_linenumber" name="596" href="#596">596</a>                         FieldVector3D&lt;DerivativeStructure&gt; uds   = createVector(x, y, z);
+<a class="jxr_linenumber" name="597" href="#597">597</a>                         checkVector(r1Prime.applyTo(uds), FieldRotation.applyTo(r1, uds));
+<a class="jxr_linenumber" name="598" href="#598">598</a>                         checkVector(r1Prime.applyInverseTo(uds), FieldRotation.applyInverseTo(r1, uds));
+<a class="jxr_linenumber" name="599" href="#599">599</a>                         checkVector(rA.applyTo(uds), rB.applyTo(uds));
+<a class="jxr_linenumber" name="600" href="#600">600</a>                         checkVector(rA.applyInverseTo(uds), rB.applyInverseTo(uds));
+<a class="jxr_linenumber" name="601" href="#601">601</a>                         checkVector(rC.applyTo(uds), rD.applyTo(uds));
+<a class="jxr_linenumber" name="602" href="#602">602</a>                         checkVector(rC.applyInverseTo(uds), rD.applyInverseTo(uds));
+<a class="jxr_linenumber" name="603" href="#603">603</a> 
+<a class="jxr_linenumber" name="604" href="#604">604</a>                     }
+<a class="jxr_linenumber" name="605" href="#605">605</a>                 }
+<a class="jxr_linenumber" name="606" href="#606">606</a>             }
+<a class="jxr_linenumber" name="607" href="#607">607</a>         }
+<a class="jxr_linenumber" name="608" href="#608">608</a> 
+<a class="jxr_linenumber" name="609" href="#609">609</a>     }
+<a class="jxr_linenumber" name="610" href="#610">610</a> 
+<a class="jxr_linenumber" name="611" href="#611">611</a>     @Test
+<a class="jxr_linenumber" name="612" href="#612">612</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDerivatives() {
+<a class="jxr_linenumber" name="613" href="#613">613</a> 
+<a class="jxr_linenumber" name="614" href="#614">614</a>         <strong class="jxr_keyword">double</strong> eps      = 5.0e-16;
+<a class="jxr_linenumber" name="615" href="#615">615</a>         <strong class="jxr_keyword">double</strong> kx       = 2;
+<a class="jxr_linenumber" name="616" href="#616">616</a>         <strong class="jxr_keyword">double</strong> ky       = -3;
+<a class="jxr_linenumber" name="617" href="#617">617</a>         <strong class="jxr_keyword">double</strong> kz       = 5;
+<a class="jxr_linenumber" name="618" href="#618">618</a>         <strong class="jxr_keyword">double</strong> n2       = kx * kx + ky * ky + kz * kz;
+<a class="jxr_linenumber" name="619" href="#619">619</a>         <strong class="jxr_keyword">double</strong> n        = FastMath.sqrt(n2);
+<a class="jxr_linenumber" name="620" href="#620">620</a>         <strong class="jxr_keyword">double</strong> theta    = 1.7;
+<a class="jxr_linenumber" name="621" href="#621">621</a>         <strong class="jxr_keyword">double</strong> cosTheta = FastMath.cos(theta);
+<a class="jxr_linenumber" name="622" href="#622">622</a>         <strong class="jxr_keyword">double</strong> sinTheta = FastMath.sin(theta);
+<a class="jxr_linenumber" name="623" href="#623">623</a>         FieldRotation&lt;DerivativeStructure&gt; r    = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(kx, ky, kz), createAngle(theta));
+<a class="jxr_linenumber" name="624" href="#624">624</a>         Vector3D a      = <strong class="jxr_keyword">new</strong> Vector3D(kx / n, ky / n, kz / n);
+<a class="jxr_linenumber" name="625" href="#625">625</a> 
+<a class="jxr_linenumber" name="626" href="#626">626</a>         <em class="jxr_comment">// Jacobian of the normalized rotation axis a with respect to the Cartesian vector k</em>
+<a class="jxr_linenumber" name="627" href="#627">627</a>         RealMatrix dadk = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="628" href="#628">628</a>             { (ky * ky + kz * kz) / ( n * n2),            -kx * ky / ( n * n2),            -kx * kz / ( n * n2) },
+<a class="jxr_linenumber" name="629" href="#629">629</a>             {            -kx * ky / ( n * n2), (kx * kx + kz * kz) / ( n * n2),            -ky * kz / ( n * n2) },
+<a class="jxr_linenumber" name="630" href="#630">630</a>             {            -kx * kz / ( n * n2),            -ky * kz / ( n * n2), (kx * kx + ky * ky) / ( n * n2) }
+<a class="jxr_linenumber" name="631" href="#631">631</a>         });
+<a class="jxr_linenumber" name="632" href="#632">632</a> 
+<a class="jxr_linenumber" name="633" href="#633">633</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="634" href="#634">634</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="635" href="#635">635</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="636" href="#636">636</a>                     Vector3D   u = <strong class="jxr_keyword">new</strong> Vector3D(x, y, z);
+<a class="jxr_linenumber" name="637" href="#637">637</a>                     FieldVector3D&lt;DerivativeStructure&gt; v = r.applyTo(createVector(x, y, z));
+<a class="jxr_linenumber" name="638" href="#638">638</a> 
+<a class="jxr_linenumber" name="639" href="#639">639</a>                     <em class="jxr_comment">// explicit formula for rotation of vector u around axis a with angle theta</em>
+<a class="jxr_linenumber" name="640" href="#640">640</a>                     <strong class="jxr_keyword">double</strong> dot     = Vector3D.dotProduct(u, a);
+<a class="jxr_linenumber" name="641" href="#641">641</a>                     Vector3D cross = Vector3D.crossProduct(a, u);
+<a class="jxr_linenumber" name="642" href="#642">642</a>                     <strong class="jxr_keyword">double</strong> c1      = 1 - cosTheta;
+<a class="jxr_linenumber" name="643" href="#643">643</a>                     <strong class="jxr_keyword">double</strong> c2      = c1 * dot;
+<a class="jxr_linenumber" name="644" href="#644">644</a>                     Vector3D rt    = <strong class="jxr_keyword">new</strong> Vector3D(cosTheta, u, c2, a, sinTheta, cross);
+<a class="jxr_linenumber" name="645" href="#645">645</a>                     Assert.assertEquals(rt.getX(), v.getX().getReal(), eps);
+<a class="jxr_linenumber" name="646" href="#646">646</a>                     Assert.assertEquals(rt.getY(), v.getY().getReal(), eps);
+<a class="jxr_linenumber" name="647" href="#647">647</a>                     Assert.assertEquals(rt.getZ(), v.getZ().getReal(), eps);
+<a class="jxr_linenumber" name="648" href="#648">648</a> 
+<a class="jxr_linenumber" name="649" href="#649">649</a>                     <em class="jxr_comment">// Jacobian of the image v = r(u) with respect to rotation axis a</em>
+<a class="jxr_linenumber" name="650" href="#650">650</a>                     <em class="jxr_comment">// (analytical differentiation of the explicit formula)</em>
+<a class="jxr_linenumber" name="651" href="#651">651</a>                     RealMatrix dvda = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] {
+<a class="jxr_linenumber" name="652" href="#652">652</a>                         { c1 * x * a.getX() + c2,           c1 * y * a.getX() + sinTheta * z, c1 * z * a.getX() - sinTheta * y },
+<a class="jxr_linenumber" name="653" href="#653">653</a>                         { c1 * x * a.getY() - sinTheta * z, c1 * y * a.getY() + c2,           c1 * z * a.getY() + sinTheta * x },
+<a class="jxr_linenumber" name="654" href="#654">654</a>                         { c1 * x * a.getZ() + sinTheta * y, c1 * y * a.getZ() - sinTheta * x, c1 * z * a.getZ() + c2           }
+<a class="jxr_linenumber" name="655" href="#655">655</a>                     });
+<a class="jxr_linenumber" name="656" href="#656">656</a> 
+<a class="jxr_linenumber" name="657" href="#657">657</a>                     <em class="jxr_comment">// compose Jacobians</em>
+<a class="jxr_linenumber" name="658" href="#658">658</a>                     RealMatrix dvdk = dvda.multiply(dadk);
+<a class="jxr_linenumber" name="659" href="#659">659</a> 
+<a class="jxr_linenumber" name="660" href="#660">660</a>                     <em class="jxr_comment">// derivatives with respect to un-normalized axis</em>
+<a class="jxr_linenumber" name="661" href="#661">661</a>                     Assert.assertEquals(dvdk.getEntry(0, 0), v.getX().getPartialDerivative(1, 0, 0, 0), eps);
+<a class="jxr_linenumber" name="662" href="#662">662</a>                     Assert.assertEquals(dvdk.getEntry(0, 1), v.getX().getPartialDerivative(0, 1, 0, 0), eps);
+<a class="jxr_linenumber" name="663" href="#663">663</a>                     Assert.assertEquals(dvdk.getEntry(0, 2), v.getX().getPartialDerivative(0, 0, 1, 0), eps);
+<a class="jxr_linenumber" name="664" href="#664">664</a>                     Assert.assertEquals(dvdk.getEntry(1, 0), v.getY().getPartialDerivative(1, 0, 0, 0), eps);
+<a class="jxr_linenumber" name="665" href="#665">665</a>                     Assert.assertEquals(dvdk.getEntry(1, 1), v.getY().getPartialDerivative(0, 1, 0, 0), eps);
+<a class="jxr_linenumber" name="666" href="#666">666</a>                     Assert.assertEquals(dvdk.getEntry(1, 2), v.getY().getPartialDerivative(0, 0, 1, 0), eps);
+<a class="jxr_linenumber" name="667" href="#667">667</a>                     Assert.assertEquals(dvdk.getEntry(2, 0), v.getZ().getPartialDerivative(1, 0, 0, 0), eps);
+<a class="jxr_linenumber" name="668" href="#668">668</a>                     Assert.assertEquals(dvdk.getEntry(2, 1), v.getZ().getPartialDerivative(0, 1, 0, 0), eps);
+<a class="jxr_linenumber" name="669" href="#669">669</a>                     Assert.assertEquals(dvdk.getEntry(2, 2), v.getZ().getPartialDerivative(0, 0, 1, 0), eps);
+<a class="jxr_linenumber" name="670" href="#670">670</a> 
+<a class="jxr_linenumber" name="671" href="#671">671</a>                     <em class="jxr_comment">// derivative with respect to rotation angle</em>
+<a class="jxr_linenumber" name="672" href="#672">672</a>                     <em class="jxr_comment">// (analytical differentiation of the explicit formula)</em>
+<a class="jxr_linenumber" name="673" href="#673">673</a>                     Vector3D dvdTheta =
+<a class="jxr_linenumber" name="674" href="#674">674</a>                             <strong class="jxr_keyword">new</strong> Vector3D(-sinTheta, u, sinTheta * dot, a, cosTheta, cross);
+<a class="jxr_linenumber" name="675" href="#675">675</a>                     Assert.assertEquals(dvdTheta.getX(), v.getX().getPartialDerivative(0, 0, 0, 1), eps);
+<a class="jxr_linenumber" name="676" href="#676">676</a>                     Assert.assertEquals(dvdTheta.getY(), v.getY().getPartialDerivative(0, 0, 0, 1), eps);
+<a class="jxr_linenumber" name="677" href="#677">677</a>                     Assert.assertEquals(dvdTheta.getZ(), v.getZ().getPartialDerivative(0, 0, 0, 1), eps);
+<a class="jxr_linenumber" name="678" href="#678">678</a> 
+<a class="jxr_linenumber" name="679" href="#679">679</a>                 }
+<a class="jxr_linenumber" name="680" href="#680">680</a>             }
+<a class="jxr_linenumber" name="681" href="#681">681</a>         }
+<a class="jxr_linenumber" name="682" href="#682">682</a>      }
+<a class="jxr_linenumber" name="683" href="#683">683</a> 
+<a class="jxr_linenumber" name="684" href="#684">684</a>     @Test
+<a class="jxr_linenumber" name="685" href="#685">685</a>     <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testArray() <strong class="jxr_keyword">throws</strong> MathIllegalArgumentException {
+<a class="jxr_linenumber" name="686" href="#686">686</a> 
+<a class="jxr_linenumber" name="687" href="#687">687</a>         FieldRotation&lt;DerivativeStructure&gt; r = <strong class="jxr_keyword">new</strong> FieldRotation&lt;DerivativeStructure&gt;(createAxis(2, -3, 5), createAngle(1.7));
+<a class="jxr_linenumber" name="688" href="#688">688</a> 
+<a class="jxr_linenumber" name="689" href="#689">689</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = -0.9; x &lt; 0.9; x += 0.2) {
+<a class="jxr_linenumber" name="690" href="#690">690</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = -0.9; y &lt; 0.9; y += 0.2) {
+<a class="jxr_linenumber" name="691" href="#691">691</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = -0.9; z &lt; 0.9; z += 0.2) {
+<a class="jxr_linenumber" name="692" href="#692">692</a>                     FieldVector3D&lt;DerivativeStructure&gt; u = createVector(x, y, z);
+<a class="jxr_linenumber" name="693" href="#693">693</a>                     FieldVector3D&lt;DerivativeStructure&gt; v = r.applyTo(u);
+<a class="jxr_linenumber" name="694" href="#694">694</a>                     DerivativeStructure[] out = <strong class="jxr_keyword">new</strong> DerivativeStructure[3];
+<a class="jxr_linenumber" name="695" href="#695">695</a>                     r.applyTo(<strong class="jxr_keyword">new</strong> DerivativeStructure[] { u.getX(), u.getY(), u.getZ() }, out);
+<a class="jxr_linenumber" name="696" href="#696">696</a>                     Assert.assertEquals(v.getX().getReal(), out[0].getReal(), 1.0e-10);
+<a class="jxr_linenumber" name="697" href="#697">697</a>                     Assert.assertEquals(v.getY().getReal(), out[1].getReal(), 1.0e-10);

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