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Posted to commits@commons.apache.org by lu...@apache.org on 2013/04/07 01:42:02 UTC
svn commit: r857558 [7/39] - in
/websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3:
./ analysis/ analysis/differentiation/ analysis/interpolation/ complex/
dfp/ distribution/ distribution/fitting/ exc...
Added: websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html
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--- websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html (added)
+++ websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/FieldRotationDSTest.html Sat Apr 6 23:42:01 2013
@@ -0,0 +1,911 @@
+<HTML>
+<BODY BGCOLOR="white">
+<PRE>
+<FONT color="green">001</FONT> /*<a name="line.1"></a>
+<FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
+<FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
+<FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
+<FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
+<FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
+<FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
+<FONT color="green">008</FONT> *<a name="line.8"></a>
+<FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
+<FONT color="green">010</FONT> *<a name="line.10"></a>
+<FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
+<FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
+<FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
+<FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
+<FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
+<FONT color="green">016</FONT> */<a name="line.16"></a>
+<FONT color="green">017</FONT> <a name="line.17"></a>
+<FONT color="green">018</FONT> package org.apache.commons.math3.geometry.euclidean.threed;<a name="line.18"></a>
+<FONT color="green">019</FONT> <a name="line.19"></a>
+<FONT color="green">020</FONT> import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;<a name="line.20"></a>
+<FONT color="green">021</FONT> import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.21"></a>
+<FONT color="green">022</FONT> import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.22"></a>
+<FONT color="green">023</FONT> import org.apache.commons.math3.linear.MatrixUtils;<a name="line.23"></a>
+<FONT color="green">024</FONT> import org.apache.commons.math3.linear.RealMatrix;<a name="line.24"></a>
+<FONT color="green">025</FONT> import org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;<a name="line.25"></a>
+<FONT color="green">026</FONT> import org.apache.commons.math3.random.Well1024a;<a name="line.26"></a>
+<FONT color="green">027</FONT> import org.apache.commons.math3.util.FastMath;<a name="line.27"></a>
+<FONT color="green">028</FONT> import org.apache.commons.math3.util.MathUtils;<a name="line.28"></a>
+<FONT color="green">029</FONT> import org.junit.Assert;<a name="line.29"></a>
+<FONT color="green">030</FONT> import org.junit.Test;<a name="line.30"></a>
+<FONT color="green">031</FONT> <a name="line.31"></a>
+<FONT color="green">032</FONT> <a name="line.32"></a>
+<FONT color="green">033</FONT> public class FieldRotationDSTest {<a name="line.33"></a>
+<FONT color="green">034</FONT> <a name="line.34"></a>
+<FONT color="green">035</FONT> @Test<a name="line.35"></a>
+<FONT color="green">036</FONT> public void testIdentity() {<a name="line.36"></a>
+<FONT color="green">037</FONT> <a name="line.37"></a>
+<FONT color="green">038</FONT> FieldRotation<DerivativeStructure> r = createRotation(1, 0, 0, 0, false);<a name="line.38"></a>
+<FONT color="green">039</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));<a name="line.39"></a>
+<FONT color="green">040</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));<a name="line.40"></a>
+<FONT color="green">041</FONT> checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));<a name="line.41"></a>
+<FONT color="green">042</FONT> checkAngle(r.getAngle(), 0);<a name="line.42"></a>
+<FONT color="green">043</FONT> <a name="line.43"></a>
+<FONT color="green">044</FONT> r = createRotation(-1, 0, 0, 0, false);<a name="line.44"></a>
+<FONT color="green">045</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));<a name="line.45"></a>
+<FONT color="green">046</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));<a name="line.46"></a>
+<FONT color="green">047</FONT> checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));<a name="line.47"></a>
+<FONT color="green">048</FONT> checkAngle(r.getAngle(), 0);<a name="line.48"></a>
+<FONT color="green">049</FONT> <a name="line.49"></a>
+<FONT color="green">050</FONT> r = createRotation(42, 0, 0, 0, true);<a name="line.50"></a>
+<FONT color="green">051</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(1, 0, 0));<a name="line.51"></a>
+<FONT color="green">052</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 1, 0));<a name="line.52"></a>
+<FONT color="green">053</FONT> checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 0, 1));<a name="line.53"></a>
+<FONT color="green">054</FONT> checkAngle(r.getAngle(), 0);<a name="line.54"></a>
+<FONT color="green">055</FONT> <a name="line.55"></a>
+<FONT color="green">056</FONT> }<a name="line.56"></a>
+<FONT color="green">057</FONT> <a name="line.57"></a>
+<FONT color="green">058</FONT> @Test<a name="line.58"></a>
+<FONT color="green">059</FONT> public void testAxisAngle() throws MathIllegalArgumentException {<a name="line.59"></a>
+<FONT color="green">060</FONT> <a name="line.60"></a>
+<FONT color="green">061</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(10, 10, 10), createAngle(2 * FastMath.PI / 3));<a name="line.61"></a>
+<FONT color="green">062</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 1, 0));<a name="line.62"></a>
+<FONT color="green">063</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(0, 0, 1));<a name="line.63"></a>
+<FONT color="green">064</FONT> checkVector(r.applyTo(createVector(0, 0, 1)), createVector(1, 0, 0));<a name="line.64"></a>
+<FONT color="green">065</FONT> double s = 1 / FastMath.sqrt(3);<a name="line.65"></a>
+<FONT color="green">066</FONT> checkVector(r.getAxis(), createVector(s, s, s));<a name="line.66"></a>
+<FONT color="green">067</FONT> checkAngle(r.getAngle(), 2 * FastMath.PI / 3);<a name="line.67"></a>
+<FONT color="green">068</FONT> <a name="line.68"></a>
+<FONT color="green">069</FONT> try {<a name="line.69"></a>
+<FONT color="green">070</FONT> new FieldRotation<DerivativeStructure>(createAxis(0, 0, 0), createAngle(2 * FastMath.PI / 3));<a name="line.70"></a>
+<FONT color="green">071</FONT> Assert.fail("an exception should have been thrown");<a name="line.71"></a>
+<FONT color="green">072</FONT> } catch (MathIllegalArgumentException e) {<a name="line.72"></a>
+<FONT color="green">073</FONT> }<a name="line.73"></a>
+<FONT color="green">074</FONT> <a name="line.74"></a>
+<FONT color="green">075</FONT> r = new FieldRotation<DerivativeStructure>(createAxis(0, 0, 1), createAngle(1.5 * FastMath.PI));<a name="line.75"></a>
+<FONT color="green">076</FONT> checkVector(r.getAxis(), createVector(0, 0, -1));<a name="line.76"></a>
+<FONT color="green">077</FONT> checkAngle(r.getAngle(), 0.5 * FastMath.PI);<a name="line.77"></a>
+<FONT color="green">078</FONT> <a name="line.78"></a>
+<FONT color="green">079</FONT> r = new FieldRotation<DerivativeStructure>(createAxis(0, 1, 0), createAngle(FastMath.PI));<a name="line.79"></a>
+<FONT color="green">080</FONT> checkVector(r.getAxis(), createVector(0, 1, 0));<a name="line.80"></a>
+<FONT color="green">081</FONT> checkAngle(r.getAngle(), FastMath.PI);<a name="line.81"></a>
+<FONT color="green">082</FONT> <a name="line.82"></a>
+<FONT color="green">083</FONT> checkVector(createRotation(1, 0, 0, 0, false).getAxis(), createVector(1, 0, 0));<a name="line.83"></a>
+<FONT color="green">084</FONT> <a name="line.84"></a>
+<FONT color="green">085</FONT> }<a name="line.85"></a>
+<FONT color="green">086</FONT> <a name="line.86"></a>
+<FONT color="green">087</FONT> @Test<a name="line.87"></a>
+<FONT color="green">088</FONT> public void testRevert() {<a name="line.88"></a>
+<FONT color="green">089</FONT> double a = 0.001;<a name="line.89"></a>
+<FONT color="green">090</FONT> double b = 0.36;<a name="line.90"></a>
+<FONT color="green">091</FONT> double c = 0.48;<a name="line.91"></a>
+<FONT color="green">092</FONT> double d = 0.8;<a name="line.92"></a>
+<FONT color="green">093</FONT> FieldRotation<DerivativeStructure> r = createRotation(a, b, c, d, true);<a name="line.93"></a>
+<FONT color="green">094</FONT> double a2 = a * a;<a name="line.94"></a>
+<FONT color="green">095</FONT> double b2 = b * b;<a name="line.95"></a>
+<FONT color="green">096</FONT> double c2 = c * c;<a name="line.96"></a>
+<FONT color="green">097</FONT> double d2 = d * d;<a name="line.97"></a>
+<FONT color="green">098</FONT> double den = (a2 + b2 + c2 + d2) * FastMath.sqrt(a2 + b2 + c2 + d2);<a name="line.98"></a>
+<FONT color="green">099</FONT> Assert.assertEquals((b2 + c2 + d2) / den, r.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.99"></a>
+<FONT color="green">100</FONT> Assert.assertEquals(-a * b / den, r.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.100"></a>
+<FONT color="green">101</FONT> Assert.assertEquals(-a * c / den, r.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.101"></a>
+<FONT color="green">102</FONT> Assert.assertEquals(-a * d / den, r.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.102"></a>
+<FONT color="green">103</FONT> Assert.assertEquals(-b * a / den, r.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.103"></a>
+<FONT color="green">104</FONT> Assert.assertEquals((a2 + c2 + d2) / den, r.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.104"></a>
+<FONT color="green">105</FONT> Assert.assertEquals(-b * c / den, r.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.105"></a>
+<FONT color="green">106</FONT> Assert.assertEquals(-b * d / den, r.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.106"></a>
+<FONT color="green">107</FONT> Assert.assertEquals(-c * a / den, r.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.107"></a>
+<FONT color="green">108</FONT> Assert.assertEquals(-c * b / den, r.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.108"></a>
+<FONT color="green">109</FONT> Assert.assertEquals((a2 + b2 + d2) / den, r.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.109"></a>
+<FONT color="green">110</FONT> Assert.assertEquals(-c * d / den, r.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.110"></a>
+<FONT color="green">111</FONT> Assert.assertEquals(-d * a / den, r.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.111"></a>
+<FONT color="green">112</FONT> Assert.assertEquals(-d * b / den, r.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.112"></a>
+<FONT color="green">113</FONT> Assert.assertEquals(-d * c / den, r.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.113"></a>
+<FONT color="green">114</FONT> Assert.assertEquals((a2 + b2 + c2) / den, r.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.114"></a>
+<FONT color="green">115</FONT> FieldRotation<DerivativeStructure> reverted = r.revert();<a name="line.115"></a>
+<FONT color="green">116</FONT> FieldRotation<DerivativeStructure> rrT = r.applyTo(reverted);<a name="line.116"></a>
+<FONT color="green">117</FONT> checkRotationDS(rrT, 1, 0, 0, 0);<a name="line.117"></a>
+<FONT color="green">118</FONT> Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.118"></a>
+<FONT color="green">119</FONT> Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.119"></a>
+<FONT color="green">120</FONT> Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.120"></a>
+<FONT color="green">121</FONT> Assert.assertEquals(0, rrT.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.121"></a>
+<FONT color="green">122</FONT> Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.122"></a>
+<FONT color="green">123</FONT> Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.123"></a>
+<FONT color="green">124</FONT> Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.124"></a>
+<FONT color="green">125</FONT> Assert.assertEquals(0, rrT.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.125"></a>
+<FONT color="green">126</FONT> Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.126"></a>
+<FONT color="green">127</FONT> Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.127"></a>
+<FONT color="green">128</FONT> Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.128"></a>
+<FONT color="green">129</FONT> Assert.assertEquals(0, rrT.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.129"></a>
+<FONT color="green">130</FONT> Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.130"></a>
+<FONT color="green">131</FONT> Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.131"></a>
+<FONT color="green">132</FONT> Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.132"></a>
+<FONT color="green">133</FONT> Assert.assertEquals(0, rrT.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.133"></a>
+<FONT color="green">134</FONT> FieldRotation<DerivativeStructure> rTr = reverted.applyTo(r);<a name="line.134"></a>
+<FONT color="green">135</FONT> checkRotationDS(rTr, 1, 0, 0, 0);<a name="line.135"></a>
+<FONT color="green">136</FONT> Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.136"></a>
+<FONT color="green">137</FONT> Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.137"></a>
+<FONT color="green">138</FONT> Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.138"></a>
+<FONT color="green">139</FONT> Assert.assertEquals(0, rTr.getQ0().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.139"></a>
+<FONT color="green">140</FONT> Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.140"></a>
+<FONT color="green">141</FONT> Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.141"></a>
+<FONT color="green">142</FONT> Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.142"></a>
+<FONT color="green">143</FONT> Assert.assertEquals(0, rTr.getQ1().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.143"></a>
+<FONT color="green">144</FONT> Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.144"></a>
+<FONT color="green">145</FONT> Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.145"></a>
+<FONT color="green">146</FONT> Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.146"></a>
+<FONT color="green">147</FONT> Assert.assertEquals(0, rTr.getQ2().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.147"></a>
+<FONT color="green">148</FONT> Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(1, 0, 0, 0), 1.0e-15);<a name="line.148"></a>
+<FONT color="green">149</FONT> Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 1, 0, 0), 1.0e-15);<a name="line.149"></a>
+<FONT color="green">150</FONT> Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 1, 0), 1.0e-15);<a name="line.150"></a>
+<FONT color="green">151</FONT> Assert.assertEquals(0, rTr.getQ3().getPartialDerivative(0, 0, 0, 1), 1.0e-15);<a name="line.151"></a>
+<FONT color="green">152</FONT> Assert.assertEquals(r.getAngle().getReal(), reverted.getAngle().getReal(), 1.0e-15);<a name="line.152"></a>
+<FONT color="green">153</FONT> Assert.assertEquals(-1, FieldVector3D.dotProduct(r.getAxis(), reverted.getAxis()).getReal(), 1.0e-15);<a name="line.153"></a>
+<FONT color="green">154</FONT> }<a name="line.154"></a>
+<FONT color="green">155</FONT> <a name="line.155"></a>
+<FONT color="green">156</FONT> @Test<a name="line.156"></a>
+<FONT color="green">157</FONT> public void testVectorOnePair() throws MathArithmeticException {<a name="line.157"></a>
+<FONT color="green">158</FONT> <a name="line.158"></a>
+<FONT color="green">159</FONT> FieldVector3D<DerivativeStructure> u = createVector(3, 2, 1);<a name="line.159"></a>
+<FONT color="green">160</FONT> FieldVector3D<DerivativeStructure> v = createVector(-4, 2, 2);<a name="line.160"></a>
+<FONT color="green">161</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(u, v);<a name="line.161"></a>
+<FONT color="green">162</FONT> checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));<a name="line.162"></a>
+<FONT color="green">163</FONT> <a name="line.163"></a>
+<FONT color="green">164</FONT> checkAngle(new FieldRotation<DerivativeStructure>(u, u.negate()).getAngle(), FastMath.PI);<a name="line.164"></a>
+<FONT color="green">165</FONT> <a name="line.165"></a>
+<FONT color="green">166</FONT> try {<a name="line.166"></a>
+<FONT color="green">167</FONT> new FieldRotation<DerivativeStructure>(u, createVector(0, 0, 0));<a name="line.167"></a>
+<FONT color="green">168</FONT> Assert.fail("an exception should have been thrown");<a name="line.168"></a>
+<FONT color="green">169</FONT> } catch (MathArithmeticException e) {<a name="line.169"></a>
+<FONT color="green">170</FONT> // expected behavior<a name="line.170"></a>
+<FONT color="green">171</FONT> }<a name="line.171"></a>
+<FONT color="green">172</FONT> <a name="line.172"></a>
+<FONT color="green">173</FONT> }<a name="line.173"></a>
+<FONT color="green">174</FONT> <a name="line.174"></a>
+<FONT color="green">175</FONT> @Test<a name="line.175"></a>
+<FONT color="green">176</FONT> public void testVectorTwoPairs() throws MathArithmeticException {<a name="line.176"></a>
+<FONT color="green">177</FONT> <a name="line.177"></a>
+<FONT color="green">178</FONT> FieldVector3D<DerivativeStructure> u1 = createVector(3, 0, 0);<a name="line.178"></a>
+<FONT color="green">179</FONT> FieldVector3D<DerivativeStructure> u2 = createVector(0, 5, 0);<a name="line.179"></a>
+<FONT color="green">180</FONT> FieldVector3D<DerivativeStructure> v1 = createVector(0, 0, 2);<a name="line.180"></a>
+<FONT color="green">181</FONT> FieldVector3D<DerivativeStructure> v2 = createVector(-2, 0, 2);<a name="line.181"></a>
+<FONT color="green">182</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(u1, u2, v1, v2);<a name="line.182"></a>
+<FONT color="green">183</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));<a name="line.183"></a>
+<FONT color="green">184</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(-1, 0, 0));<a name="line.184"></a>
+<FONT color="green">185</FONT> <a name="line.185"></a>
+<FONT color="green">186</FONT> r = new FieldRotation<DerivativeStructure>(u1, u2, u1.negate(), u2.negate());<a name="line.186"></a>
+<FONT color="green">187</FONT> FieldVector3D<DerivativeStructure> axis = r.getAxis();<a name="line.187"></a>
+<FONT color="green">188</FONT> if (FieldVector3D.dotProduct(axis, createVector(0, 0, 1)).getReal() > 0) {<a name="line.188"></a>
+<FONT color="green">189</FONT> checkVector(axis, createVector(0, 0, 1));<a name="line.189"></a>
+<FONT color="green">190</FONT> } else {<a name="line.190"></a>
+<FONT color="green">191</FONT> checkVector(axis, createVector(0, 0, -1));<a name="line.191"></a>
+<FONT color="green">192</FONT> }<a name="line.192"></a>
+<FONT color="green">193</FONT> checkAngle(r.getAngle(), FastMath.PI);<a name="line.193"></a>
+<FONT color="green">194</FONT> <a name="line.194"></a>
+<FONT color="green">195</FONT> double sqrt = FastMath.sqrt(2) / 2;<a name="line.195"></a>
+<FONT color="green">196</FONT> r = new FieldRotation<DerivativeStructure>(createVector(1, 0, 0), createVector(0, 1, 0),<a name="line.196"></a>
+<FONT color="green">197</FONT> createVector(0.5, 0.5, sqrt),<a name="line.197"></a>
+<FONT color="green">198</FONT> createVector(0.5, 0.5, -sqrt));<a name="line.198"></a>
+<FONT color="green">199</FONT> checkRotationDS(r, sqrt, 0.5, 0.5, 0);<a name="line.199"></a>
+<FONT color="green">200</FONT> <a name="line.200"></a>
+<FONT color="green">201</FONT> r = new FieldRotation<DerivativeStructure>(u1, u2, u1, FieldVector3D.crossProduct(u1, u2));<a name="line.201"></a>
+<FONT color="green">202</FONT> checkRotationDS(r, sqrt, -sqrt, 0, 0);<a name="line.202"></a>
+<FONT color="green">203</FONT> <a name="line.203"></a>
+<FONT color="green">204</FONT> checkRotationDS(new FieldRotation<DerivativeStructure>(u1, u2, u1, u2), 1, 0, 0, 0);<a name="line.204"></a>
+<FONT color="green">205</FONT> <a name="line.205"></a>
+<FONT color="green">206</FONT> try {<a name="line.206"></a>
+<FONT color="green">207</FONT> new FieldRotation<DerivativeStructure>(u1, u2, createVector(0, 0, 0), v2);<a name="line.207"></a>
+<FONT color="green">208</FONT> Assert.fail("an exception should have been thrown");<a name="line.208"></a>
+<FONT color="green">209</FONT> } catch (MathArithmeticException e) {<a name="line.209"></a>
+<FONT color="green">210</FONT> // expected behavior<a name="line.210"></a>
+<FONT color="green">211</FONT> }<a name="line.211"></a>
+<FONT color="green">212</FONT> <a name="line.212"></a>
+<FONT color="green">213</FONT> }<a name="line.213"></a>
+<FONT color="green">214</FONT> <a name="line.214"></a>
+<FONT color="green">215</FONT> @Test<a name="line.215"></a>
+<FONT color="green">216</FONT> public void testMatrix()<a name="line.216"></a>
+<FONT color="green">217</FONT> throws NotARotationMatrixException {<a name="line.217"></a>
+<FONT color="green">218</FONT> <a name="line.218"></a>
+<FONT color="green">219</FONT> try {<a name="line.219"></a>
+<FONT color="green">220</FONT> createRotation(new double[][] {<a name="line.220"></a>
+<FONT color="green">221</FONT> { 0.0, 1.0, 0.0 },<a name="line.221"></a>
+<FONT color="green">222</FONT> { 1.0, 0.0, 0.0 }<a name="line.222"></a>
+<FONT color="green">223</FONT> }, 1.0e-7);<a name="line.223"></a>
+<FONT color="green">224</FONT> Assert.fail("Expecting NotARotationMatrixException");<a name="line.224"></a>
+<FONT color="green">225</FONT> } catch (NotARotationMatrixException nrme) {<a name="line.225"></a>
+<FONT color="green">226</FONT> // expected behavior<a name="line.226"></a>
+<FONT color="green">227</FONT> }<a name="line.227"></a>
+<FONT color="green">228</FONT> <a name="line.228"></a>
+<FONT color="green">229</FONT> try {<a name="line.229"></a>
+<FONT color="green">230</FONT> createRotation(new double[][] {<a name="line.230"></a>
+<FONT color="green">231</FONT> { 0.445888, 0.797184, -0.407040 },<a name="line.231"></a>
+<FONT color="green">232</FONT> { 0.821760, -0.184320, 0.539200 },<a name="line.232"></a>
+<FONT color="green">233</FONT> { -0.354816, 0.574912, 0.737280 }<a name="line.233"></a>
+<FONT color="green">234</FONT> }, 1.0e-7);<a name="line.234"></a>
+<FONT color="green">235</FONT> Assert.fail("Expecting NotARotationMatrixException");<a name="line.235"></a>
+<FONT color="green">236</FONT> } catch (NotARotationMatrixException nrme) {<a name="line.236"></a>
+<FONT color="green">237</FONT> // expected behavior<a name="line.237"></a>
+<FONT color="green">238</FONT> }<a name="line.238"></a>
+<FONT color="green">239</FONT> <a name="line.239"></a>
+<FONT color="green">240</FONT> try {<a name="line.240"></a>
+<FONT color="green">241</FONT> createRotation(new double[][] {<a name="line.241"></a>
+<FONT color="green">242</FONT> { 0.4, 0.8, -0.4 },<a name="line.242"></a>
+<FONT color="green">243</FONT> { -0.4, 0.6, 0.7 },<a name="line.243"></a>
+<FONT color="green">244</FONT> { 0.8, -0.2, 0.5 }<a name="line.244"></a>
+<FONT color="green">245</FONT> }, 1.0e-15);<a name="line.245"></a>
+<FONT color="green">246</FONT> Assert.fail("Expecting NotARotationMatrixException");<a name="line.246"></a>
+<FONT color="green">247</FONT> } catch (NotARotationMatrixException nrme) {<a name="line.247"></a>
+<FONT color="green">248</FONT> // expected behavior<a name="line.248"></a>
+<FONT color="green">249</FONT> }<a name="line.249"></a>
+<FONT color="green">250</FONT> <a name="line.250"></a>
+<FONT color="green">251</FONT> checkRotationDS(createRotation(new double[][] {<a name="line.251"></a>
+<FONT color="green">252</FONT> { 0.445888, 0.797184, -0.407040 },<a name="line.252"></a>
+<FONT color="green">253</FONT> { -0.354816, 0.574912, 0.737280 },<a name="line.253"></a>
+<FONT color="green">254</FONT> { 0.821760, -0.184320, 0.539200 }<a name="line.254"></a>
+<FONT color="green">255</FONT> }, 1.0e-10),<a name="line.255"></a>
+<FONT color="green">256</FONT> 0.8, 0.288, 0.384, 0.36);<a name="line.256"></a>
+<FONT color="green">257</FONT> <a name="line.257"></a>
+<FONT color="green">258</FONT> checkRotationDS(createRotation(new double[][] {<a name="line.258"></a>
+<FONT color="green">259</FONT> { 0.539200, 0.737280, 0.407040 },<a name="line.259"></a>
+<FONT color="green">260</FONT> { 0.184320, -0.574912, 0.797184 },<a name="line.260"></a>
+<FONT color="green">261</FONT> { 0.821760, -0.354816, -0.445888 }<a name="line.261"></a>
+<FONT color="green">262</FONT> }, 1.0e-10),<a name="line.262"></a>
+<FONT color="green">263</FONT> 0.36, 0.8, 0.288, 0.384);<a name="line.263"></a>
+<FONT color="green">264</FONT> <a name="line.264"></a>
+<FONT color="green">265</FONT> checkRotationDS(createRotation(new double[][] {<a name="line.265"></a>
+<FONT color="green">266</FONT> { -0.445888, 0.797184, -0.407040 },<a name="line.266"></a>
+<FONT color="green">267</FONT> { 0.354816, 0.574912, 0.737280 },<a name="line.267"></a>
+<FONT color="green">268</FONT> { 0.821760, 0.184320, -0.539200 }<a name="line.268"></a>
+<FONT color="green">269</FONT> }, 1.0e-10),<a name="line.269"></a>
+<FONT color="green">270</FONT> 0.384, 0.36, 0.8, 0.288);<a name="line.270"></a>
+<FONT color="green">271</FONT> <a name="line.271"></a>
+<FONT color="green">272</FONT> checkRotationDS(createRotation(new double[][] {<a name="line.272"></a>
+<FONT color="green">273</FONT> { -0.539200, 0.737280, 0.407040 },<a name="line.273"></a>
+<FONT color="green">274</FONT> { -0.184320, -0.574912, 0.797184 },<a name="line.274"></a>
+<FONT color="green">275</FONT> { 0.821760, 0.354816, 0.445888 }<a name="line.275"></a>
+<FONT color="green">276</FONT> }, 1.0e-10),<a name="line.276"></a>
+<FONT color="green">277</FONT> 0.288, 0.384, 0.36, 0.8);<a name="line.277"></a>
+<FONT color="green">278</FONT> <a name="line.278"></a>
+<FONT color="green">279</FONT> double[][] m1 = { { 0.0, 1.0, 0.0 },<a name="line.279"></a>
+<FONT color="green">280</FONT> { 0.0, 0.0, 1.0 },<a name="line.280"></a>
+<FONT color="green">281</FONT> { 1.0, 0.0, 0.0 } };<a name="line.281"></a>
+<FONT color="green">282</FONT> FieldRotation<DerivativeStructure> r = createRotation(m1, 1.0e-7);<a name="line.282"></a>
+<FONT color="green">283</FONT> checkVector(r.applyTo(createVector(1, 0, 0)), createVector(0, 0, 1));<a name="line.283"></a>
+<FONT color="green">284</FONT> checkVector(r.applyTo(createVector(0, 1, 0)), createVector(1, 0, 0));<a name="line.284"></a>
+<FONT color="green">285</FONT> checkVector(r.applyTo(createVector(0, 0, 1)), createVector(0, 1, 0));<a name="line.285"></a>
+<FONT color="green">286</FONT> <a name="line.286"></a>
+<FONT color="green">287</FONT> double[][] m2 = { { 0.83203, -0.55012, -0.07139 },<a name="line.287"></a>
+<FONT color="green">288</FONT> { 0.48293, 0.78164, -0.39474 },<a name="line.288"></a>
+<FONT color="green">289</FONT> { 0.27296, 0.29396, 0.91602 } };<a name="line.289"></a>
+<FONT color="green">290</FONT> r = createRotation(m2, 1.0e-12);<a name="line.290"></a>
+<FONT color="green">291</FONT> <a name="line.291"></a>
+<FONT color="green">292</FONT> DerivativeStructure[][] m3 = r.getMatrix();<a name="line.292"></a>
+<FONT color="green">293</FONT> double d00 = m2[0][0] - m3[0][0].getReal();<a name="line.293"></a>
+<FONT color="green">294</FONT> double d01 = m2[0][1] - m3[0][1].getReal();<a name="line.294"></a>
+<FONT color="green">295</FONT> double d02 = m2[0][2] - m3[0][2].getReal();<a name="line.295"></a>
+<FONT color="green">296</FONT> double d10 = m2[1][0] - m3[1][0].getReal();<a name="line.296"></a>
+<FONT color="green">297</FONT> double d11 = m2[1][1] - m3[1][1].getReal();<a name="line.297"></a>
+<FONT color="green">298</FONT> double d12 = m2[1][2] - m3[1][2].getReal();<a name="line.298"></a>
+<FONT color="green">299</FONT> double d20 = m2[2][0] - m3[2][0].getReal();<a name="line.299"></a>
+<FONT color="green">300</FONT> double d21 = m2[2][1] - m3[2][1].getReal();<a name="line.300"></a>
+<FONT color="green">301</FONT> double d22 = m2[2][2] - m3[2][2].getReal();<a name="line.301"></a>
+<FONT color="green">302</FONT> <a name="line.302"></a>
+<FONT color="green">303</FONT> Assert.assertTrue(FastMath.abs(d00) < 6.0e-6);<a name="line.303"></a>
+<FONT color="green">304</FONT> Assert.assertTrue(FastMath.abs(d01) < 6.0e-6);<a name="line.304"></a>
+<FONT color="green">305</FONT> Assert.assertTrue(FastMath.abs(d02) < 6.0e-6);<a name="line.305"></a>
+<FONT color="green">306</FONT> Assert.assertTrue(FastMath.abs(d10) < 6.0e-6);<a name="line.306"></a>
+<FONT color="green">307</FONT> Assert.assertTrue(FastMath.abs(d11) < 6.0e-6);<a name="line.307"></a>
+<FONT color="green">308</FONT> Assert.assertTrue(FastMath.abs(d12) < 6.0e-6);<a name="line.308"></a>
+<FONT color="green">309</FONT> Assert.assertTrue(FastMath.abs(d20) < 6.0e-6);<a name="line.309"></a>
+<FONT color="green">310</FONT> Assert.assertTrue(FastMath.abs(d21) < 6.0e-6);<a name="line.310"></a>
+<FONT color="green">311</FONT> Assert.assertTrue(FastMath.abs(d22) < 6.0e-6);<a name="line.311"></a>
+<FONT color="green">312</FONT> <a name="line.312"></a>
+<FONT color="green">313</FONT> Assert.assertTrue(FastMath.abs(d00) > 4.0e-7);<a name="line.313"></a>
+<FONT color="green">314</FONT> Assert.assertTrue(FastMath.abs(d01) > 4.0e-7);<a name="line.314"></a>
+<FONT color="green">315</FONT> Assert.assertTrue(FastMath.abs(d02) > 4.0e-7);<a name="line.315"></a>
+<FONT color="green">316</FONT> Assert.assertTrue(FastMath.abs(d10) > 4.0e-7);<a name="line.316"></a>
+<FONT color="green">317</FONT> Assert.assertTrue(FastMath.abs(d11) > 4.0e-7);<a name="line.317"></a>
+<FONT color="green">318</FONT> Assert.assertTrue(FastMath.abs(d12) > 4.0e-7);<a name="line.318"></a>
+<FONT color="green">319</FONT> Assert.assertTrue(FastMath.abs(d20) > 4.0e-7);<a name="line.319"></a>
+<FONT color="green">320</FONT> Assert.assertTrue(FastMath.abs(d21) > 4.0e-7);<a name="line.320"></a>
+<FONT color="green">321</FONT> Assert.assertTrue(FastMath.abs(d22) > 4.0e-7);<a name="line.321"></a>
+<FONT color="green">322</FONT> <a name="line.322"></a>
+<FONT color="green">323</FONT> for (int i = 0; i < 3; ++i) {<a name="line.323"></a>
+<FONT color="green">324</FONT> for (int j = 0; j < 3; ++j) {<a name="line.324"></a>
+<FONT color="green">325</FONT> double m3tm3 = m3[i][0].getReal() * m3[j][0].getReal() +<a name="line.325"></a>
+<FONT color="green">326</FONT> m3[i][1].getReal() * m3[j][1].getReal() +<a name="line.326"></a>
+<FONT color="green">327</FONT> m3[i][2].getReal() * m3[j][2].getReal();<a name="line.327"></a>
+<FONT color="green">328</FONT> if (i == j) {<a name="line.328"></a>
+<FONT color="green">329</FONT> Assert.assertTrue(FastMath.abs(m3tm3 - 1.0) < 1.0e-10);<a name="line.329"></a>
+<FONT color="green">330</FONT> } else {<a name="line.330"></a>
+<FONT color="green">331</FONT> Assert.assertTrue(FastMath.abs(m3tm3) < 1.0e-10);<a name="line.331"></a>
+<FONT color="green">332</FONT> }<a name="line.332"></a>
+<FONT color="green">333</FONT> }<a name="line.333"></a>
+<FONT color="green">334</FONT> }<a name="line.334"></a>
+<FONT color="green">335</FONT> <a name="line.335"></a>
+<FONT color="green">336</FONT> checkVector(r.applyTo(createVector(1, 0, 0)),<a name="line.336"></a>
+<FONT color="green">337</FONT> new FieldVector3D<DerivativeStructure>(m3[0][0], m3[1][0], m3[2][0]));<a name="line.337"></a>
+<FONT color="green">338</FONT> checkVector(r.applyTo(createVector(0, 1, 0)),<a name="line.338"></a>
+<FONT color="green">339</FONT> new FieldVector3D<DerivativeStructure>(m3[0][1], m3[1][1], m3[2][1]));<a name="line.339"></a>
+<FONT color="green">340</FONT> checkVector(r.applyTo(createVector(0, 0, 1)),<a name="line.340"></a>
+<FONT color="green">341</FONT> new FieldVector3D<DerivativeStructure>(m3[0][2], m3[1][2], m3[2][2]));<a name="line.341"></a>
+<FONT color="green">342</FONT> <a name="line.342"></a>
+<FONT color="green">343</FONT> double[][] m4 = { { 1.0, 0.0, 0.0 },<a name="line.343"></a>
+<FONT color="green">344</FONT> { 0.0, -1.0, 0.0 },<a name="line.344"></a>
+<FONT color="green">345</FONT> { 0.0, 0.0, -1.0 } };<a name="line.345"></a>
+<FONT color="green">346</FONT> r = createRotation(m4, 1.0e-7);<a name="line.346"></a>
+<FONT color="green">347</FONT> checkAngle(r.getAngle(), FastMath.PI);<a name="line.347"></a>
+<FONT color="green">348</FONT> <a name="line.348"></a>
+<FONT color="green">349</FONT> try {<a name="line.349"></a>
+<FONT color="green">350</FONT> double[][] m5 = { { 0.0, 0.0, 1.0 },<a name="line.350"></a>
+<FONT color="green">351</FONT> { 0.0, 1.0, 0.0 },<a name="line.351"></a>
+<FONT color="green">352</FONT> { 1.0, 0.0, 0.0 } };<a name="line.352"></a>
+<FONT color="green">353</FONT> r = createRotation(m5, 1.0e-7);<a name="line.353"></a>
+<FONT color="green">354</FONT> Assert.fail("got " + r + ", should have caught an exception");<a name="line.354"></a>
+<FONT color="green">355</FONT> } catch (NotARotationMatrixException e) {<a name="line.355"></a>
+<FONT color="green">356</FONT> // expected<a name="line.356"></a>
+<FONT color="green">357</FONT> }<a name="line.357"></a>
+<FONT color="green">358</FONT> <a name="line.358"></a>
+<FONT color="green">359</FONT> }<a name="line.359"></a>
+<FONT color="green">360</FONT> <a name="line.360"></a>
+<FONT color="green">361</FONT> @Test<a name="line.361"></a>
+<FONT color="green">362</FONT> public void testAngles()<a name="line.362"></a>
+<FONT color="green">363</FONT> throws CardanEulerSingularityException {<a name="line.363"></a>
+<FONT color="green">364</FONT> <a name="line.364"></a>
+<FONT color="green">365</FONT> RotationOrder[] CardanOrders = {<a name="line.365"></a>
+<FONT color="green">366</FONT> RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,<a name="line.366"></a>
+<FONT color="green">367</FONT> RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX<a name="line.367"></a>
+<FONT color="green">368</FONT> };<a name="line.368"></a>
+<FONT color="green">369</FONT> <a name="line.369"></a>
+<FONT color="green">370</FONT> for (int i = 0; i < CardanOrders.length; ++i) {<a name="line.370"></a>
+<FONT color="green">371</FONT> for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {<a name="line.371"></a>
+<FONT color="green">372</FONT> for (double alpha2 = -1.55; alpha2 < 1.55; alpha2 += 0.3) {<a name="line.372"></a>
+<FONT color="green">373</FONT> for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {<a name="line.373"></a>
+<FONT color="green">374</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(CardanOrders[i],<a name="line.374"></a>
+<FONT color="green">375</FONT> new DerivativeStructure(3, 1, 0, alpha1),<a name="line.375"></a>
+<FONT color="green">376</FONT> new DerivativeStructure(3, 1, 1, alpha2),<a name="line.376"></a>
+<FONT color="green">377</FONT> new DerivativeStructure(3, 1, 2, alpha3));<a name="line.377"></a>
+<FONT color="green">378</FONT> DerivativeStructure[] angles = r.getAngles(CardanOrders[i]);<a name="line.378"></a>
+<FONT color="green">379</FONT> checkAngle(angles[0], alpha1);<a name="line.379"></a>
+<FONT color="green">380</FONT> checkAngle(angles[1], alpha2);<a name="line.380"></a>
+<FONT color="green">381</FONT> checkAngle(angles[2], alpha3);<a name="line.381"></a>
+<FONT color="green">382</FONT> }<a name="line.382"></a>
+<FONT color="green">383</FONT> }<a name="line.383"></a>
+<FONT color="green">384</FONT> }<a name="line.384"></a>
+<FONT color="green">385</FONT> }<a name="line.385"></a>
+<FONT color="green">386</FONT> <a name="line.386"></a>
+<FONT color="green">387</FONT> RotationOrder[] EulerOrders = {<a name="line.387"></a>
+<FONT color="green">388</FONT> RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,<a name="line.388"></a>
+<FONT color="green">389</FONT> RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ<a name="line.389"></a>
+<FONT color="green">390</FONT> };<a name="line.390"></a>
+<FONT color="green">391</FONT> <a name="line.391"></a>
+<FONT color="green">392</FONT> for (int i = 0; i < EulerOrders.length; ++i) {<a name="line.392"></a>
+<FONT color="green">393</FONT> for (double alpha1 = 0.1; alpha1 < 6.2; alpha1 += 0.3) {<a name="line.393"></a>
+<FONT color="green">394</FONT> for (double alpha2 = 0.05; alpha2 < 3.1; alpha2 += 0.3) {<a name="line.394"></a>
+<FONT color="green">395</FONT> for (double alpha3 = 0.1; alpha3 < 6.2; alpha3 += 0.3) {<a name="line.395"></a>
+<FONT color="green">396</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(EulerOrders[i],<a name="line.396"></a>
+<FONT color="green">397</FONT> new DerivativeStructure(3, 1, 0, alpha1),<a name="line.397"></a>
+<FONT color="green">398</FONT> new DerivativeStructure(3, 1, 1, alpha2),<a name="line.398"></a>
+<FONT color="green">399</FONT> new DerivativeStructure(3, 1, 2, alpha3));<a name="line.399"></a>
+<FONT color="green">400</FONT> DerivativeStructure[] angles = r.getAngles(EulerOrders[i]);<a name="line.400"></a>
+<FONT color="green">401</FONT> checkAngle(angles[0], alpha1);<a name="line.401"></a>
+<FONT color="green">402</FONT> checkAngle(angles[1], alpha2);<a name="line.402"></a>
+<FONT color="green">403</FONT> checkAngle(angles[2], alpha3);<a name="line.403"></a>
+<FONT color="green">404</FONT> }<a name="line.404"></a>
+<FONT color="green">405</FONT> }<a name="line.405"></a>
+<FONT color="green">406</FONT> }<a name="line.406"></a>
+<FONT color="green">407</FONT> }<a name="line.407"></a>
+<FONT color="green">408</FONT> <a name="line.408"></a>
+<FONT color="green">409</FONT> }<a name="line.409"></a>
+<FONT color="green">410</FONT> <a name="line.410"></a>
+<FONT color="green">411</FONT> @Test<a name="line.411"></a>
+<FONT color="green">412</FONT> public void testSingularities() {<a name="line.412"></a>
+<FONT color="green">413</FONT> <a name="line.413"></a>
+<FONT color="green">414</FONT> RotationOrder[] CardanOrders = {<a name="line.414"></a>
+<FONT color="green">415</FONT> RotationOrder.XYZ, RotationOrder.XZY, RotationOrder.YXZ,<a name="line.415"></a>
+<FONT color="green">416</FONT> RotationOrder.YZX, RotationOrder.ZXY, RotationOrder.ZYX<a name="line.416"></a>
+<FONT color="green">417</FONT> };<a name="line.417"></a>
+<FONT color="green">418</FONT> <a name="line.418"></a>
+<FONT color="green">419</FONT> double[] singularCardanAngle = { FastMath.PI / 2, -FastMath.PI / 2 };<a name="line.419"></a>
+<FONT color="green">420</FONT> for (int i = 0; i < CardanOrders.length; ++i) {<a name="line.420"></a>
+<FONT color="green">421</FONT> for (int j = 0; j < singularCardanAngle.length; ++j) {<a name="line.421"></a>
+<FONT color="green">422</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(CardanOrders[i],<a name="line.422"></a>
+<FONT color="green">423</FONT> new DerivativeStructure(3, 1, 0, 0.1),<a name="line.423"></a>
+<FONT color="green">424</FONT> new DerivativeStructure(3, 1, 1, singularCardanAngle[j]),<a name="line.424"></a>
+<FONT color="green">425</FONT> new DerivativeStructure(3, 1, 2, 0.3));<a name="line.425"></a>
+<FONT color="green">426</FONT> try {<a name="line.426"></a>
+<FONT color="green">427</FONT> r.getAngles(CardanOrders[i]);<a name="line.427"></a>
+<FONT color="green">428</FONT> Assert.fail("an exception should have been caught");<a name="line.428"></a>
+<FONT color="green">429</FONT> } catch (CardanEulerSingularityException cese) {<a name="line.429"></a>
+<FONT color="green">430</FONT> // expected behavior<a name="line.430"></a>
+<FONT color="green">431</FONT> }<a name="line.431"></a>
+<FONT color="green">432</FONT> }<a name="line.432"></a>
+<FONT color="green">433</FONT> }<a name="line.433"></a>
+<FONT color="green">434</FONT> <a name="line.434"></a>
+<FONT color="green">435</FONT> RotationOrder[] EulerOrders = {<a name="line.435"></a>
+<FONT color="green">436</FONT> RotationOrder.XYX, RotationOrder.XZX, RotationOrder.YXY,<a name="line.436"></a>
+<FONT color="green">437</FONT> RotationOrder.YZY, RotationOrder.ZXZ, RotationOrder.ZYZ<a name="line.437"></a>
+<FONT color="green">438</FONT> };<a name="line.438"></a>
+<FONT color="green">439</FONT> <a name="line.439"></a>
+<FONT color="green">440</FONT> double[] singularEulerAngle = { 0, FastMath.PI };<a name="line.440"></a>
+<FONT color="green">441</FONT> for (int i = 0; i < EulerOrders.length; ++i) {<a name="line.441"></a>
+<FONT color="green">442</FONT> for (int j = 0; j < singularEulerAngle.length; ++j) {<a name="line.442"></a>
+<FONT color="green">443</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(EulerOrders[i],<a name="line.443"></a>
+<FONT color="green">444</FONT> new DerivativeStructure(3, 1, 0, 0.1),<a name="line.444"></a>
+<FONT color="green">445</FONT> new DerivativeStructure(3, 1, 1, singularEulerAngle[j]),<a name="line.445"></a>
+<FONT color="green">446</FONT> new DerivativeStructure(3, 1, 2, 0.3));<a name="line.446"></a>
+<FONT color="green">447</FONT> try {<a name="line.447"></a>
+<FONT color="green">448</FONT> r.getAngles(EulerOrders[i]);<a name="line.448"></a>
+<FONT color="green">449</FONT> Assert.fail("an exception should have been caught");<a name="line.449"></a>
+<FONT color="green">450</FONT> } catch (CardanEulerSingularityException cese) {<a name="line.450"></a>
+<FONT color="green">451</FONT> // expected behavior<a name="line.451"></a>
+<FONT color="green">452</FONT> }<a name="line.452"></a>
+<FONT color="green">453</FONT> }<a name="line.453"></a>
+<FONT color="green">454</FONT> }<a name="line.454"></a>
+<FONT color="green">455</FONT> <a name="line.455"></a>
+<FONT color="green">456</FONT> <a name="line.456"></a>
+<FONT color="green">457</FONT> }<a name="line.457"></a>
+<FONT color="green">458</FONT> <a name="line.458"></a>
+<FONT color="green">459</FONT> @Test<a name="line.459"></a>
+<FONT color="green">460</FONT> public void testQuaternion() throws MathIllegalArgumentException {<a name="line.460"></a>
+<FONT color="green">461</FONT> <a name="line.461"></a>
+<FONT color="green">462</FONT> FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));<a name="line.462"></a>
+<FONT color="green">463</FONT> double n = 23.5;<a name="line.463"></a>
+<FONT color="green">464</FONT> FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(r1.getQ0().multiply(n), r1.getQ1().multiply(n),<a name="line.464"></a>
+<FONT color="green">465</FONT> r1.getQ2().multiply(n), r1.getQ3().multiply(n),<a name="line.465"></a>
+<FONT color="green">466</FONT> true);<a name="line.466"></a>
+<FONT color="green">467</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.467"></a>
+<FONT color="green">468</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.468"></a>
+<FONT color="green">469</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.469"></a>
+<FONT color="green">470</FONT> FieldVector3D<DerivativeStructure> u = createVector(x, y, z);<a name="line.470"></a>
+<FONT color="green">471</FONT> checkVector(r2.applyTo(u), r1.applyTo(u));<a name="line.471"></a>
+<FONT color="green">472</FONT> }<a name="line.472"></a>
+<FONT color="green">473</FONT> }<a name="line.473"></a>
+<FONT color="green">474</FONT> }<a name="line.474"></a>
+<FONT color="green">475</FONT> <a name="line.475"></a>
+<FONT color="green">476</FONT> r1 = createRotation(0.288, 0.384, 0.36, 0.8, false);<a name="line.476"></a>
+<FONT color="green">477</FONT> checkRotationDS(r1,<a name="line.477"></a>
+<FONT color="green">478</FONT> -r1.getQ0().getReal(), -r1.getQ1().getReal(),<a name="line.478"></a>
+<FONT color="green">479</FONT> -r1.getQ2().getReal(), -r1.getQ3().getReal());<a name="line.479"></a>
+<FONT color="green">480</FONT> Assert.assertEquals(0.288, r1.toRotation().getQ0(), 1.0e-15);<a name="line.480"></a>
+<FONT color="green">481</FONT> Assert.assertEquals(0.384, r1.toRotation().getQ1(), 1.0e-15);<a name="line.481"></a>
+<FONT color="green">482</FONT> Assert.assertEquals(0.36, r1.toRotation().getQ2(), 1.0e-15);<a name="line.482"></a>
+<FONT color="green">483</FONT> Assert.assertEquals(0.8, r1.toRotation().getQ3(), 1.0e-15);<a name="line.483"></a>
+<FONT color="green">484</FONT> <a name="line.484"></a>
+<FONT color="green">485</FONT> }<a name="line.485"></a>
+<FONT color="green">486</FONT> <a name="line.486"></a>
+<FONT color="green">487</FONT> @Test<a name="line.487"></a>
+<FONT color="green">488</FONT> public void testCompose() throws MathIllegalArgumentException {<a name="line.488"></a>
+<FONT color="green">489</FONT> <a name="line.489"></a>
+<FONT color="green">490</FONT> FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));<a name="line.490"></a>
+<FONT color="green">491</FONT> FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(-1, 3, 2), createAngle(0.3));<a name="line.491"></a>
+<FONT color="green">492</FONT> FieldRotation<DerivativeStructure> r3 = r2.applyTo(r1);<a name="line.492"></a>
+<FONT color="green">493</FONT> FieldRotation<DerivativeStructure> r3Double = r2.applyTo(new Rotation(r1.getQ0().getReal(),<a name="line.493"></a>
+<FONT color="green">494</FONT> r1.getQ1().getReal(),<a name="line.494"></a>
+<FONT color="green">495</FONT> r1.getQ2().getReal(),<a name="line.495"></a>
+<FONT color="green">496</FONT> r1.getQ3().getReal(),<a name="line.496"></a>
+<FONT color="green">497</FONT> false));<a name="line.497"></a>
+<FONT color="green">498</FONT> <a name="line.498"></a>
+<FONT color="green">499</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.499"></a>
+<FONT color="green">500</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.500"></a>
+<FONT color="green">501</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.501"></a>
+<FONT color="green">502</FONT> FieldVector3D<DerivativeStructure> u = createVector(x, y, z);<a name="line.502"></a>
+<FONT color="green">503</FONT> checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));<a name="line.503"></a>
+<FONT color="green">504</FONT> checkVector(r2.applyTo(r1.applyTo(u)), r3Double.applyTo(u));<a name="line.504"></a>
+<FONT color="green">505</FONT> }<a name="line.505"></a>
+<FONT color="green">506</FONT> }<a name="line.506"></a>
+<FONT color="green">507</FONT> }<a name="line.507"></a>
+<FONT color="green">508</FONT> <a name="line.508"></a>
+<FONT color="green">509</FONT> }<a name="line.509"></a>
+<FONT color="green">510</FONT> <a name="line.510"></a>
+<FONT color="green">511</FONT> @Test<a name="line.511"></a>
+<FONT color="green">512</FONT> public void testComposeInverse() throws MathIllegalArgumentException {<a name="line.512"></a>
+<FONT color="green">513</FONT> <a name="line.513"></a>
+<FONT color="green">514</FONT> FieldRotation<DerivativeStructure> r1 = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));<a name="line.514"></a>
+<FONT color="green">515</FONT> FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(-1, 3, 2), createAngle(0.3));<a name="line.515"></a>
+<FONT color="green">516</FONT> FieldRotation<DerivativeStructure> r3 = r2.applyInverseTo(r1);<a name="line.516"></a>
+<FONT color="green">517</FONT> FieldRotation<DerivativeStructure> r3Double = r2.applyInverseTo(new Rotation(r1.getQ0().getReal(),<a name="line.517"></a>
+<FONT color="green">518</FONT> r1.getQ1().getReal(),<a name="line.518"></a>
+<FONT color="green">519</FONT> r1.getQ2().getReal(),<a name="line.519"></a>
+<FONT color="green">520</FONT> r1.getQ3().getReal(),<a name="line.520"></a>
+<FONT color="green">521</FONT> false));<a name="line.521"></a>
+<FONT color="green">522</FONT> <a name="line.522"></a>
+<FONT color="green">523</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.523"></a>
+<FONT color="green">524</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.524"></a>
+<FONT color="green">525</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.525"></a>
+<FONT color="green">526</FONT> FieldVector3D<DerivativeStructure> u = createVector(x, y, z);<a name="line.526"></a>
+<FONT color="green">527</FONT> checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));<a name="line.527"></a>
+<FONT color="green">528</FONT> checkVector(r2.applyInverseTo(r1.applyTo(u)), r3Double.applyTo(u));<a name="line.528"></a>
+<FONT color="green">529</FONT> }<a name="line.529"></a>
+<FONT color="green">530</FONT> }<a name="line.530"></a>
+<FONT color="green">531</FONT> }<a name="line.531"></a>
+<FONT color="green">532</FONT> <a name="line.532"></a>
+<FONT color="green">533</FONT> }<a name="line.533"></a>
+<FONT color="green">534</FONT> <a name="line.534"></a>
+<FONT color="green">535</FONT> @Test<a name="line.535"></a>
+<FONT color="green">536</FONT> public void testDoubleVectors() throws MathIllegalArgumentException {<a name="line.536"></a>
+<FONT color="green">537</FONT> <a name="line.537"></a>
+<FONT color="green">538</FONT> Well1024a random = new Well1024a(0x180b41cfeeffaf67l);<a name="line.538"></a>
+<FONT color="green">539</FONT> UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);<a name="line.539"></a>
+<FONT color="green">540</FONT> for (int i = 0; i < 10; ++i) {<a name="line.540"></a>
+<FONT color="green">541</FONT> double[] unit = g.nextVector();<a name="line.541"></a>
+<FONT color="green">542</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createVector(unit[0], unit[1], unit[2]),<a name="line.542"></a>
+<FONT color="green">543</FONT> createAngle(random.nextDouble()));<a name="line.543"></a>
+<FONT color="green">544</FONT> <a name="line.544"></a>
+<FONT color="green">545</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.545"></a>
+<FONT color="green">546</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.546"></a>
+<FONT color="green">547</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.547"></a>
+<FONT color="green">548</FONT> FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);<a name="line.548"></a>
+<FONT color="green">549</FONT> FieldVector3D<DerivativeStructure> ruds = r.applyTo(uds);<a name="line.549"></a>
+<FONT color="green">550</FONT> FieldVector3D<DerivativeStructure> rIuds = r.applyInverseTo(uds);<a name="line.550"></a>
+<FONT color="green">551</FONT> Vector3D u = new Vector3D(x, y, z);<a name="line.551"></a>
+<FONT color="green">552</FONT> FieldVector3D<DerivativeStructure> ru = r.applyTo(u);<a name="line.552"></a>
+<FONT color="green">553</FONT> FieldVector3D<DerivativeStructure> rIu = r.applyInverseTo(u);<a name="line.553"></a>
+<FONT color="green">554</FONT> DerivativeStructure[] ruArray = new DerivativeStructure[3];<a name="line.554"></a>
+<FONT color="green">555</FONT> r.applyTo(new double[] { x, y, z}, ruArray);<a name="line.555"></a>
+<FONT color="green">556</FONT> DerivativeStructure[] rIuArray = new DerivativeStructure[3];<a name="line.556"></a>
+<FONT color="green">557</FONT> r.applyInverseTo(new double[] { x, y, z}, rIuArray);<a name="line.557"></a>
+<FONT color="green">558</FONT> checkVector(ruds, ru);<a name="line.558"></a>
+<FONT color="green">559</FONT> checkVector(ruds, new FieldVector3D<DerivativeStructure>(ruArray));<a name="line.559"></a>
+<FONT color="green">560</FONT> checkVector(rIuds, rIu);<a name="line.560"></a>
+<FONT color="green">561</FONT> checkVector(rIuds, new FieldVector3D<DerivativeStructure>(rIuArray));<a name="line.561"></a>
+<FONT color="green">562</FONT> }<a name="line.562"></a>
+<FONT color="green">563</FONT> }<a name="line.563"></a>
+<FONT color="green">564</FONT> }<a name="line.564"></a>
+<FONT color="green">565</FONT> }<a name="line.565"></a>
+<FONT color="green">566</FONT> <a name="line.566"></a>
+<FONT color="green">567</FONT> }<a name="line.567"></a>
+<FONT color="green">568</FONT> <a name="line.568"></a>
+<FONT color="green">569</FONT> @Test<a name="line.569"></a>
+<FONT color="green">570</FONT> public void testDoubleRotations() throws MathIllegalArgumentException {<a name="line.570"></a>
+<FONT color="green">571</FONT> <a name="line.571"></a>
+<FONT color="green">572</FONT> Well1024a random = new Well1024a(0x180b41cfeeffaf67l);<a name="line.572"></a>
+<FONT color="green">573</FONT> UnitSphereRandomVectorGenerator g = new UnitSphereRandomVectorGenerator(3, random);<a name="line.573"></a>
+<FONT color="green">574</FONT> for (int i = 0; i < 10; ++i) {<a name="line.574"></a>
+<FONT color="green">575</FONT> double[] unit1 = g.nextVector();<a name="line.575"></a>
+<FONT color="green">576</FONT> Rotation r1 = new Rotation(new Vector3D(unit1[0], unit1[1], unit1[2]),<a name="line.576"></a>
+<FONT color="green">577</FONT> random.nextDouble());<a name="line.577"></a>
+<FONT color="green">578</FONT> FieldRotation<DerivativeStructure> r1Prime = new FieldRotation<DerivativeStructure>(new DerivativeStructure(4, 1, 0, r1.getQ0()),<a name="line.578"></a>
+<FONT color="green">579</FONT> new DerivativeStructure(4, 1, 1, r1.getQ1()),<a name="line.579"></a>
+<FONT color="green">580</FONT> new DerivativeStructure(4, 1, 2, r1.getQ2()),<a name="line.580"></a>
+<FONT color="green">581</FONT> new DerivativeStructure(4, 1, 3, r1.getQ3()),<a name="line.581"></a>
+<FONT color="green">582</FONT> false);<a name="line.582"></a>
+<FONT color="green">583</FONT> double[] unit2 = g.nextVector();<a name="line.583"></a>
+<FONT color="green">584</FONT> FieldRotation<DerivativeStructure> r2 = new FieldRotation<DerivativeStructure>(createVector(unit2[0], unit2[1], unit2[2]),<a name="line.584"></a>
+<FONT color="green">585</FONT> createAngle(random.nextDouble()));<a name="line.585"></a>
+<FONT color="green">586</FONT> <a name="line.586"></a>
+<FONT color="green">587</FONT> FieldRotation<DerivativeStructure> rA = FieldRotation.applyTo(r1, r2);<a name="line.587"></a>
+<FONT color="green">588</FONT> FieldRotation<DerivativeStructure> rB = r1Prime.applyTo(r2);<a name="line.588"></a>
+<FONT color="green">589</FONT> FieldRotation<DerivativeStructure> rC = FieldRotation.applyInverseTo(r1, r2);<a name="line.589"></a>
+<FONT color="green">590</FONT> FieldRotation<DerivativeStructure> rD = r1Prime.applyInverseTo(r2);<a name="line.590"></a>
+<FONT color="green">591</FONT> <a name="line.591"></a>
+<FONT color="green">592</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.592"></a>
+<FONT color="green">593</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.593"></a>
+<FONT color="green">594</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.594"></a>
+<FONT color="green">595</FONT> <a name="line.595"></a>
+<FONT color="green">596</FONT> FieldVector3D<DerivativeStructure> uds = createVector(x, y, z);<a name="line.596"></a>
+<FONT color="green">597</FONT> checkVector(r1Prime.applyTo(uds), FieldRotation.applyTo(r1, uds));<a name="line.597"></a>
+<FONT color="green">598</FONT> checkVector(r1Prime.applyInverseTo(uds), FieldRotation.applyInverseTo(r1, uds));<a name="line.598"></a>
+<FONT color="green">599</FONT> checkVector(rA.applyTo(uds), rB.applyTo(uds));<a name="line.599"></a>
+<FONT color="green">600</FONT> checkVector(rA.applyInverseTo(uds), rB.applyInverseTo(uds));<a name="line.600"></a>
+<FONT color="green">601</FONT> checkVector(rC.applyTo(uds), rD.applyTo(uds));<a name="line.601"></a>
+<FONT color="green">602</FONT> checkVector(rC.applyInverseTo(uds), rD.applyInverseTo(uds));<a name="line.602"></a>
+<FONT color="green">603</FONT> <a name="line.603"></a>
+<FONT color="green">604</FONT> }<a name="line.604"></a>
+<FONT color="green">605</FONT> }<a name="line.605"></a>
+<FONT color="green">606</FONT> }<a name="line.606"></a>
+<FONT color="green">607</FONT> }<a name="line.607"></a>
+<FONT color="green">608</FONT> <a name="line.608"></a>
+<FONT color="green">609</FONT> }<a name="line.609"></a>
+<FONT color="green">610</FONT> <a name="line.610"></a>
+<FONT color="green">611</FONT> @Test<a name="line.611"></a>
+<FONT color="green">612</FONT> public void testDerivatives() {<a name="line.612"></a>
+<FONT color="green">613</FONT> <a name="line.613"></a>
+<FONT color="green">614</FONT> double eps = 5.0e-16;<a name="line.614"></a>
+<FONT color="green">615</FONT> double kx = 2;<a name="line.615"></a>
+<FONT color="green">616</FONT> double ky = -3;<a name="line.616"></a>
+<FONT color="green">617</FONT> double kz = 5;<a name="line.617"></a>
+<FONT color="green">618</FONT> double n2 = kx * kx + ky * ky + kz * kz;<a name="line.618"></a>
+<FONT color="green">619</FONT> double n = FastMath.sqrt(n2);<a name="line.619"></a>
+<FONT color="green">620</FONT> double theta = 1.7;<a name="line.620"></a>
+<FONT color="green">621</FONT> double cosTheta = FastMath.cos(theta);<a name="line.621"></a>
+<FONT color="green">622</FONT> double sinTheta = FastMath.sin(theta);<a name="line.622"></a>
+<FONT color="green">623</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(kx, ky, kz), createAngle(theta));<a name="line.623"></a>
+<FONT color="green">624</FONT> Vector3D a = new Vector3D(kx / n, ky / n, kz / n);<a name="line.624"></a>
+<FONT color="green">625</FONT> <a name="line.625"></a>
+<FONT color="green">626</FONT> // Jacobian of the normalized rotation axis a with respect to the Cartesian vector k<a name="line.626"></a>
+<FONT color="green">627</FONT> RealMatrix dadk = MatrixUtils.createRealMatrix(new double[][] {<a name="line.627"></a>
+<FONT color="green">628</FONT> { (ky * ky + kz * kz) / ( n * n2), -kx * ky / ( n * n2), -kx * kz / ( n * n2) },<a name="line.628"></a>
+<FONT color="green">629</FONT> { -kx * ky / ( n * n2), (kx * kx + kz * kz) / ( n * n2), -ky * kz / ( n * n2) },<a name="line.629"></a>
+<FONT color="green">630</FONT> { -kx * kz / ( n * n2), -ky * kz / ( n * n2), (kx * kx + ky * ky) / ( n * n2) }<a name="line.630"></a>
+<FONT color="green">631</FONT> });<a name="line.631"></a>
+<FONT color="green">632</FONT> <a name="line.632"></a>
+<FONT color="green">633</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.633"></a>
+<FONT color="green">634</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.634"></a>
+<FONT color="green">635</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.635"></a>
+<FONT color="green">636</FONT> Vector3D u = new Vector3D(x, y, z);<a name="line.636"></a>
+<FONT color="green">637</FONT> FieldVector3D<DerivativeStructure> v = r.applyTo(createVector(x, y, z));<a name="line.637"></a>
+<FONT color="green">638</FONT> <a name="line.638"></a>
+<FONT color="green">639</FONT> // explicit formula for rotation of vector u around axis a with angle theta<a name="line.639"></a>
+<FONT color="green">640</FONT> double dot = Vector3D.dotProduct(u, a);<a name="line.640"></a>
+<FONT color="green">641</FONT> Vector3D cross = Vector3D.crossProduct(a, u);<a name="line.641"></a>
+<FONT color="green">642</FONT> double c1 = 1 - cosTheta;<a name="line.642"></a>
+<FONT color="green">643</FONT> double c2 = c1 * dot;<a name="line.643"></a>
+<FONT color="green">644</FONT> Vector3D rt = new Vector3D(cosTheta, u, c2, a, sinTheta, cross);<a name="line.644"></a>
+<FONT color="green">645</FONT> Assert.assertEquals(rt.getX(), v.getX().getReal(), eps);<a name="line.645"></a>
+<FONT color="green">646</FONT> Assert.assertEquals(rt.getY(), v.getY().getReal(), eps);<a name="line.646"></a>
+<FONT color="green">647</FONT> Assert.assertEquals(rt.getZ(), v.getZ().getReal(), eps);<a name="line.647"></a>
+<FONT color="green">648</FONT> <a name="line.648"></a>
+<FONT color="green">649</FONT> // Jacobian of the image v = r(u) with respect to rotation axis a<a name="line.649"></a>
+<FONT color="green">650</FONT> // (analytical differentiation of the explicit formula)<a name="line.650"></a>
+<FONT color="green">651</FONT> RealMatrix dvda = MatrixUtils.createRealMatrix(new double[][] {<a name="line.651"></a>
+<FONT color="green">652</FONT> { c1 * x * a.getX() + c2, c1 * y * a.getX() + sinTheta * z, c1 * z * a.getX() - sinTheta * y },<a name="line.652"></a>
+<FONT color="green">653</FONT> { c1 * x * a.getY() - sinTheta * z, c1 * y * a.getY() + c2, c1 * z * a.getY() + sinTheta * x },<a name="line.653"></a>
+<FONT color="green">654</FONT> { c1 * x * a.getZ() + sinTheta * y, c1 * y * a.getZ() - sinTheta * x, c1 * z * a.getZ() + c2 }<a name="line.654"></a>
+<FONT color="green">655</FONT> });<a name="line.655"></a>
+<FONT color="green">656</FONT> <a name="line.656"></a>
+<FONT color="green">657</FONT> // compose Jacobians<a name="line.657"></a>
+<FONT color="green">658</FONT> RealMatrix dvdk = dvda.multiply(dadk);<a name="line.658"></a>
+<FONT color="green">659</FONT> <a name="line.659"></a>
+<FONT color="green">660</FONT> // derivatives with respect to un-normalized axis<a name="line.660"></a>
+<FONT color="green">661</FONT> Assert.assertEquals(dvdk.getEntry(0, 0), v.getX().getPartialDerivative(1, 0, 0, 0), eps);<a name="line.661"></a>
+<FONT color="green">662</FONT> Assert.assertEquals(dvdk.getEntry(0, 1), v.getX().getPartialDerivative(0, 1, 0, 0), eps);<a name="line.662"></a>
+<FONT color="green">663</FONT> Assert.assertEquals(dvdk.getEntry(0, 2), v.getX().getPartialDerivative(0, 0, 1, 0), eps);<a name="line.663"></a>
+<FONT color="green">664</FONT> Assert.assertEquals(dvdk.getEntry(1, 0), v.getY().getPartialDerivative(1, 0, 0, 0), eps);<a name="line.664"></a>
+<FONT color="green">665</FONT> Assert.assertEquals(dvdk.getEntry(1, 1), v.getY().getPartialDerivative(0, 1, 0, 0), eps);<a name="line.665"></a>
+<FONT color="green">666</FONT> Assert.assertEquals(dvdk.getEntry(1, 2), v.getY().getPartialDerivative(0, 0, 1, 0), eps);<a name="line.666"></a>
+<FONT color="green">667</FONT> Assert.assertEquals(dvdk.getEntry(2, 0), v.getZ().getPartialDerivative(1, 0, 0, 0), eps);<a name="line.667"></a>
+<FONT color="green">668</FONT> Assert.assertEquals(dvdk.getEntry(2, 1), v.getZ().getPartialDerivative(0, 1, 0, 0), eps);<a name="line.668"></a>
+<FONT color="green">669</FONT> Assert.assertEquals(dvdk.getEntry(2, 2), v.getZ().getPartialDerivative(0, 0, 1, 0), eps);<a name="line.669"></a>
+<FONT color="green">670</FONT> <a name="line.670"></a>
+<FONT color="green">671</FONT> // derivative with respect to rotation angle<a name="line.671"></a>
+<FONT color="green">672</FONT> // (analytical differentiation of the explicit formula)<a name="line.672"></a>
+<FONT color="green">673</FONT> Vector3D dvdTheta =<a name="line.673"></a>
+<FONT color="green">674</FONT> new Vector3D(-sinTheta, u, sinTheta * dot, a, cosTheta, cross);<a name="line.674"></a>
+<FONT color="green">675</FONT> Assert.assertEquals(dvdTheta.getX(), v.getX().getPartialDerivative(0, 0, 0, 1), eps);<a name="line.675"></a>
+<FONT color="green">676</FONT> Assert.assertEquals(dvdTheta.getY(), v.getY().getPartialDerivative(0, 0, 0, 1), eps);<a name="line.676"></a>
+<FONT color="green">677</FONT> Assert.assertEquals(dvdTheta.getZ(), v.getZ().getPartialDerivative(0, 0, 0, 1), eps);<a name="line.677"></a>
+<FONT color="green">678</FONT> <a name="line.678"></a>
+<FONT color="green">679</FONT> }<a name="line.679"></a>
+<FONT color="green">680</FONT> }<a name="line.680"></a>
+<FONT color="green">681</FONT> }<a name="line.681"></a>
+<FONT color="green">682</FONT> }<a name="line.682"></a>
+<FONT color="green">683</FONT> <a name="line.683"></a>
+<FONT color="green">684</FONT> @Test<a name="line.684"></a>
+<FONT color="green">685</FONT> public void testArray() throws MathIllegalArgumentException {<a name="line.685"></a>
+<FONT color="green">686</FONT> <a name="line.686"></a>
+<FONT color="green">687</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createAxis(2, -3, 5), createAngle(1.7));<a name="line.687"></a>
+<FONT color="green">688</FONT> <a name="line.688"></a>
+<FONT color="green">689</FONT> for (double x = -0.9; x < 0.9; x += 0.2) {<a name="line.689"></a>
+<FONT color="green">690</FONT> for (double y = -0.9; y < 0.9; y += 0.2) {<a name="line.690"></a>
+<FONT color="green">691</FONT> for (double z = -0.9; z < 0.9; z += 0.2) {<a name="line.691"></a>
+<FONT color="green">692</FONT> FieldVector3D<DerivativeStructure> u = createVector(x, y, z);<a name="line.692"></a>
+<FONT color="green">693</FONT> FieldVector3D<DerivativeStructure> v = r.applyTo(u);<a name="line.693"></a>
+<FONT color="green">694</FONT> DerivativeStructure[] out = new DerivativeStructure[3];<a name="line.694"></a>
+<FONT color="green">695</FONT> r.applyTo(new DerivativeStructure[] { u.getX(), u.getY(), u.getZ() }, out);<a name="line.695"></a>
+<FONT color="green">696</FONT> Assert.assertEquals(v.getX().getReal(), out[0].getReal(), 1.0e-10);<a name="line.696"></a>
+<FONT color="green">697</FONT> Assert.assertEquals(v.getY().getReal(), out[1].getReal(), 1.0e-10);<a name="line.697"></a>
+<FONT color="green">698</FONT> Assert.assertEquals(v.getZ().getReal(), out[2].getReal(), 1.0e-10);<a name="line.698"></a>
+<FONT color="green">699</FONT> r.applyInverseTo(out, out);<a name="line.699"></a>
+<FONT color="green">700</FONT> Assert.assertEquals(u.getX().getReal(), out[0].getReal(), 1.0e-10);<a name="line.700"></a>
+<FONT color="green">701</FONT> Assert.assertEquals(u.getY().getReal(), out[1].getReal(), 1.0e-10);<a name="line.701"></a>
+<FONT color="green">702</FONT> Assert.assertEquals(u.getZ().getReal(), out[2].getReal(), 1.0e-10);<a name="line.702"></a>
+<FONT color="green">703</FONT> }<a name="line.703"></a>
+<FONT color="green">704</FONT> }<a name="line.704"></a>
+<FONT color="green">705</FONT> }<a name="line.705"></a>
+<FONT color="green">706</FONT> <a name="line.706"></a>
+<FONT color="green">707</FONT> }<a name="line.707"></a>
+<FONT color="green">708</FONT> <a name="line.708"></a>
+<FONT color="green">709</FONT> @Test<a name="line.709"></a>
+<FONT color="green">710</FONT> public void testApplyInverseTo() throws MathIllegalArgumentException {<a name="line.710"></a>
+<FONT color="green">711</FONT> <a name="line.711"></a>
+<FONT color="green">712</FONT> DerivativeStructure[] in = new DerivativeStructure[3];<a name="line.712"></a>
+<FONT color="green">713</FONT> DerivativeStructure[] out = new DerivativeStructure[3];<a name="line.713"></a>
+<FONT color="green">714</FONT> DerivativeStructure[] rebuilt = new DerivativeStructure[3];<a name="line.714"></a>
+<FONT color="green">715</FONT> FieldRotation<DerivativeStructure> r = new FieldRotation<DerivativeStructure>(createVector(2, -3, 5), createAngle(1.7));<a name="line.715"></a>
+<FONT color="green">716</FONT> for (double lambda = 0; lambda < 6.2; lambda += 0.2) {<a name="line.716"></a>
+<FONT color="green">717</FONT> for (double phi = -1.55; phi < 1.55; phi += 0.2) {<a name="line.717"></a>
+<FONT color="green">718</FONT> FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),<a name="line.718"></a>
+<FONT color="green">719</FONT> FastMath.sin(lambda) * FastMath.cos(phi),<a name="line.719"></a>
+<FONT color="green">720</FONT> FastMath.sin(phi));<a name="line.720"></a>
+<FONT color="green">721</FONT> r.applyInverseTo(r.applyTo(u));<a name="line.721"></a>
+<FONT color="green">722</FONT> checkVector(u, r.applyInverseTo(r.applyTo(u)));<a name="line.722"></a>
+<FONT color="green">723</FONT> checkVector(u, r.applyTo(r.applyInverseTo(u)));<a name="line.723"></a>
+<FONT color="green">724</FONT> in[0] = u.getX();<a name="line.724"></a>
+<FONT color="green">725</FONT> in[1] = u.getY();<a name="line.725"></a>
+<FONT color="green">726</FONT> in[2] = u.getZ();<a name="line.726"></a>
+<FONT color="green">727</FONT> r.applyTo(in, out);<a name="line.727"></a>
+<FONT color="green">728</FONT> r.applyInverseTo(out, rebuilt);<a name="line.728"></a>
+<FONT color="green">729</FONT> Assert.assertEquals(in[0].getReal(), rebuilt[0].getReal(), 1.0e-12);<a name="line.729"></a>
+<FONT color="green">730</FONT> Assert.assertEquals(in[1].getReal(), rebuilt[1].getReal(), 1.0e-12);<a name="line.730"></a>
+<FONT color="green">731</FONT> Assert.assertEquals(in[2].getReal(), rebuilt[2].getReal(), 1.0e-12);<a name="line.731"></a>
+<FONT color="green">732</FONT> }<a name="line.732"></a>
+<FONT color="green">733</FONT> }<a name="line.733"></a>
+<FONT color="green">734</FONT> <a name="line.734"></a>
+<FONT color="green">735</FONT> r = createRotation(1, 0, 0, 0, false);<a name="line.735"></a>
+<FONT color="green">736</FONT> for (double lambda = 0; lambda < 6.2; lambda += 0.2) {<a name="line.736"></a>
+<FONT color="green">737</FONT> for (double phi = -1.55; phi < 1.55; phi += 0.2) {<a name="line.737"></a>
+<FONT color="green">738</FONT> FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),<a name="line.738"></a>
+<FONT color="green">739</FONT> FastMath.sin(lambda) * FastMath.cos(phi),<a name="line.739"></a>
+<FONT color="green">740</FONT> FastMath.sin(phi));<a name="line.740"></a>
+<FONT color="green">741</FONT> checkVector(u, r.applyInverseTo(r.applyTo(u)));<a name="line.741"></a>
+<FONT color="green">742</FONT> checkVector(u, r.applyTo(r.applyInverseTo(u)));<a name="line.742"></a>
+<FONT color="green">743</FONT> }<a name="line.743"></a>
+<FONT color="green">744</FONT> }<a name="line.744"></a>
+<FONT color="green">745</FONT> <a name="line.745"></a>
+<FONT color="green">746</FONT> r = new FieldRotation<DerivativeStructure>(createVector(0, 0, 1), createAngle(FastMath.PI));<a name="line.746"></a>
+<FONT color="green">747</FONT> for (double lambda = 0; lambda < 6.2; lambda += 0.2) {<a name="line.747"></a>
+<FONT color="green">748</FONT> for (double phi = -1.55; phi < 1.55; phi += 0.2) {<a name="line.748"></a>
+<FONT color="green">749</FONT> FieldVector3D<DerivativeStructure> u = createVector(FastMath.cos(lambda) * FastMath.cos(phi),<a name="line.749"></a>
+<FONT color="green">750</FONT> FastMath.sin(lambda) * FastMath.cos(phi),<a name="line.750"></a>
+<FONT color="green">751</FONT> FastMath.sin(phi));<a name="line.751"></a>
+<FONT color="green">752</FONT> checkVector(u, r.applyInverseTo(r.applyTo(u)));<a name="line.752"></a>
+<FONT color="green">753</FONT> checkVector(u, r.applyTo(r.applyInverseTo(u)));<a name="line.753"></a>
+<FONT color="green">754</FONT> }<a name="line.754"></a>
+<FONT color="green">755</FONT> }<a name="line.755"></a>
+<FONT color="green">756</FONT> <a name="line.756"></a>
+<FONT color="green">757</FONT> }<a name="line.757"></a>
+<FONT color="green">758</FONT> <a name="line.758"></a>
+<FONT color="green">759</FONT> @Test<a name="line.759"></a>
+<FONT color="green">760</FONT> public void testIssue639() throws MathArithmeticException{<a name="line.760"></a>
+<FONT color="green">761</FONT> FieldVector3D<DerivativeStructure> u1 = createVector(-1321008684645961.0 / 268435456.0,<a name="line.761"></a>
+<FONT color="green">762</FONT> -5774608829631843.0 / 268435456.0,<a name="line.762"></a>
+<FONT color="green">763</FONT> -3822921525525679.0 / 4294967296.0);<a name="line.763"></a>
+<FONT color="green">764</FONT> FieldVector3D<DerivativeStructure> u2 =createVector( -5712344449280879.0 / 2097152.0,<a name="line.764"></a>
+<FONT color="green">765</FONT> -2275058564560979.0 / 1048576.0,<a name="line.765"></a>
+<FONT color="green">766</FONT> 4423475992255071.0 / 65536.0);<a name="line.766"></a>
+<FONT color="green">767</FONT> FieldRotation<DerivativeStructure> rot = new FieldRotation<DerivativeStructure>(u1, u2, createVector(1, 0, 0),createVector(0, 0, 1));<a name="line.767"></a>
+<FONT color="green">768</FONT> Assert.assertEquals( 0.6228370359608200639829222, rot.getQ0().getReal(), 1.0e-15);<a name="line.768"></a>
+<FONT color="green">769</FONT> Assert.assertEquals( 0.0257707621456498790029987, rot.getQ1().getReal(), 1.0e-15);<a name="line.769"></a>
+<FONT color="green">770</FONT> Assert.assertEquals(-0.0000000002503012255839931, rot.getQ2().getReal(), 1.0e-15);<a name="line.770"></a>
+<FONT color="green">771</FONT> Assert.assertEquals(-0.7819270390861109450724902, rot.getQ3().getReal(), 1.0e-15);<a name="line.771"></a>
+<FONT color="green">772</FONT> }<a name="line.772"></a>
+<FONT color="green">773</FONT> <a name="line.773"></a>
+<FONT color="green">774</FONT> @Test<a name="line.774"></a>
+<FONT color="green">775</FONT> public void testIssue801() throws MathArithmeticException {<a name="line.775"></a>
+<FONT color="green">776</FONT> FieldVector3D<DerivativeStructure> u1 = createVector(0.9999988431610581, -0.0015210774290851095, 0.0);<a name="line.776"></a>
+<FONT color="green">777</FONT> FieldVector3D<DerivativeStructure> u2 = createVector(0.0, 0.0, 1.0);<a name="line.777"></a>
+<FONT color="green">778</FONT> <a name="line.778"></a>
+<FONT color="green">779</FONT> FieldVector3D<DerivativeStructure> v1 = createVector(0.9999999999999999, 0.0, 0.0);<a name="line.779"></a>
+<FONT color="green">780</FONT> FieldVector3D<DerivativeStructure> v2 = createVector(0.0, 0.0, -1.0);<a name="line.780"></a>
+<FONT color="green">781</FONT> <a name="line.781"></a>
+<FONT color="green">782</FONT> FieldRotation<DerivativeStructure> quat = new FieldRotation<DerivativeStructure>(u1, u2, v1, v2);<a name="line.782"></a>
+<FONT color="green">783</FONT> double q2 = quat.getQ0().getReal() * quat.getQ0().getReal() +<a name="line.783"></a>
+<FONT color="green">784</FONT> quat.getQ1().getReal() * quat.getQ1().getReal() +<a name="line.784"></a>
+<FONT color="green">785</FONT> quat.getQ2().getReal() * quat.getQ2().getReal() +<a name="line.785"></a>
+<FONT color="green">786</FONT> quat.getQ3().getReal() * quat.getQ3().getReal();<a name="line.786"></a>
+<FONT color="green">787</FONT> Assert.assertEquals(1.0, q2, 1.0e-14);<a name="line.787"></a>
+<FONT color="green">788</FONT> Assert.assertEquals(0.0, FieldVector3D.angle(v1, quat.applyTo(u1)).getReal(), 1.0e-14);<a name="line.788"></a>
+<FONT color="green">789</FONT> Assert.assertEquals(0.0, FieldVector3D.angle(v2, quat.applyTo(u2)).getReal(), 1.0e-14);<a name="line.789"></a>
+<FONT color="green">790</FONT> <a name="line.790"></a>
+<FONT color="green">791</FONT> }<a name="line.791"></a>
+<FONT color="green">792</FONT> <a name="line.792"></a>
+<FONT color="green">793</FONT> private void checkAngle(DerivativeStructure a1, double a2) {<a name="line.793"></a>
+<FONT color="green">794</FONT> Assert.assertEquals(a1.getReal(), MathUtils.normalizeAngle(a2, a1.getReal()), 1.0e-10);<a name="line.794"></a>
+<FONT color="green">795</FONT> }<a name="line.795"></a>
+<FONT color="green">796</FONT> <a name="line.796"></a>
+<FONT color="green">797</FONT> private void checkRotationDS(FieldRotation<DerivativeStructure> r, double q0, double q1, double q2, double q3) {<a name="line.797"></a>
+<FONT color="green">798</FONT> FieldRotation<DerivativeStructure> rPrime = createRotation(q0, q1, q2, q3, false);<a name="line.798"></a>
+<FONT color="green">799</FONT> Assert.assertEquals(0, FieldRotation.distance(r, rPrime).getReal(), 1.0e-12);<a name="line.799"></a>
+<FONT color="green">800</FONT> }<a name="line.800"></a>
+<FONT color="green">801</FONT> <a name="line.801"></a>
+<FONT color="green">802</FONT> private FieldRotation<DerivativeStructure> createRotation(double q0, double q1, double q2, double q3,<a name="line.802"></a>
+<FONT color="green">803</FONT> boolean needsNormalization) {<a name="line.803"></a>
+<FONT color="green">804</FONT> return new FieldRotation<DerivativeStructure>(new DerivativeStructure(4, 1, 0, q0),<a name="line.804"></a>
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