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websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinatesTest.html
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websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinatesTest.html
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websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinatesTest.html
Sat Apr 6 23:42:01 2013
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+<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.TestUtils;<a
name="line.20"></a>
+<FONT color="green">021</FONT> import
org.apache.commons.math3.analysis.differentiation.DerivativeStructure;<a
name="line.21"></a>
+<FONT color="green">022</FONT> import
org.apache.commons.math3.exception.DimensionMismatchException;<a
name="line.22"></a>
+<FONT color="green">023</FONT> import
org.apache.commons.math3.util.FastMath;<a name="line.23"></a>
+<FONT color="green">024</FONT> import org.junit.Assert;<a
name="line.24"></a>
+<FONT color="green">025</FONT> import org.junit.Test;<a name="line.25"></a>
+<FONT color="green">026</FONT> <a name="line.26"></a>
+<FONT color="green">027</FONT> public class SphericalCoordinatesTest {<a
name="line.27"></a>
+<FONT color="green">028</FONT> <a name="line.28"></a>
+<FONT color="green">029</FONT> @Test<a name="line.29"></a>
+<FONT color="green">030</FONT> public void testCoordinatesStoC() throws
DimensionMismatchException {<a name="line.30"></a>
+<FONT color="green">031</FONT> double piO2 = 0.5 * FastMath.PI;<a
name="line.31"></a>
+<FONT color="green">032</FONT> SphericalCoordinates sc1 = new
SphericalCoordinates(2.0, 0, piO2);<a name="line.32"></a>
+<FONT color="green">033</FONT> Assert.assertEquals(0,
sc1.getCartesian().distance(new Vector3D(2, 0, 0)), 1.0e-10);<a
name="line.33"></a>
+<FONT color="green">034</FONT> SphericalCoordinates sc2 = new
SphericalCoordinates(2.0, piO2, piO2);<a name="line.34"></a>
+<FONT color="green">035</FONT> Assert.assertEquals(0,
sc2.getCartesian().distance(new Vector3D(0, 2, 0)), 1.0e-10);<a
name="line.35"></a>
+<FONT color="green">036</FONT> SphericalCoordinates sc3 = new
SphericalCoordinates(2.0, FastMath.PI, piO2);<a name="line.36"></a>
+<FONT color="green">037</FONT> Assert.assertEquals(0,
sc3.getCartesian().distance(new Vector3D(-2, 0, 0)), 1.0e-10);<a
name="line.37"></a>
+<FONT color="green">038</FONT> SphericalCoordinates sc4 = new
SphericalCoordinates(2.0, -piO2, piO2);<a name="line.38"></a>
+<FONT color="green">039</FONT> Assert.assertEquals(0,
sc4.getCartesian().distance(new Vector3D(0, -2, 0)), 1.0e-10);<a
name="line.39"></a>
+<FONT color="green">040</FONT> SphericalCoordinates sc5 = new
SphericalCoordinates(2.0, 1.23456, 0);<a name="line.40"></a>
+<FONT color="green">041</FONT> Assert.assertEquals(0,
sc5.getCartesian().distance(new Vector3D(0, 0, 2)), 1.0e-10);<a
name="line.41"></a>
+<FONT color="green">042</FONT> SphericalCoordinates sc6 = new
SphericalCoordinates(2.0, 6.54321, FastMath.PI);<a name="line.42"></a>
+<FONT color="green">043</FONT> Assert.assertEquals(0,
sc6.getCartesian().distance(new Vector3D(0, 0, -2)), 1.0e-10);<a
name="line.43"></a>
+<FONT color="green">044</FONT> }<a name="line.44"></a>
+<FONT color="green">045</FONT> <a name="line.45"></a>
+<FONT color="green">046</FONT> @Test<a name="line.46"></a>
+<FONT color="green">047</FONT> public void testCoordinatesCtoS() throws
DimensionMismatchException {<a name="line.47"></a>
+<FONT color="green">048</FONT> double piO2 = 0.5 * FastMath.PI;<a
name="line.48"></a>
+<FONT color="green">049</FONT> SphericalCoordinates sc1 = new
SphericalCoordinates(new Vector3D(2, 0, 0));<a name="line.49"></a>
+<FONT color="green">050</FONT> Assert.assertEquals(2,
sc1.getR(), 1.0e-10);<a name="line.50"></a>
+<FONT color="green">051</FONT> Assert.assertEquals(0,
sc1.getTheta(), 1.0e-10);<a name="line.51"></a>
+<FONT color="green">052</FONT> Assert.assertEquals(piO2,
sc1.getPhi(), 1.0e-10);<a name="line.52"></a>
+<FONT color="green">053</FONT> SphericalCoordinates sc2 = new
SphericalCoordinates(new Vector3D(0, 2, 0));<a name="line.53"></a>
+<FONT color="green">054</FONT> Assert.assertEquals(2,
sc2.getR(), 1.0e-10);<a name="line.54"></a>
+<FONT color="green">055</FONT> Assert.assertEquals(piO2,
sc2.getTheta(), 1.0e-10);<a name="line.55"></a>
+<FONT color="green">056</FONT> Assert.assertEquals(piO2,
sc2.getPhi(), 1.0e-10);<a name="line.56"></a>
+<FONT color="green">057</FONT> SphericalCoordinates sc3 = new
SphericalCoordinates(new Vector3D(-2, 0, 0));<a name="line.57"></a>
+<FONT color="green">058</FONT> Assert.assertEquals(2,
sc3.getR(), 1.0e-10);<a name="line.58"></a>
+<FONT color="green">059</FONT> Assert.assertEquals(FastMath.PI,
sc3.getTheta(), 1.0e-10);<a name="line.59"></a>
+<FONT color="green">060</FONT> Assert.assertEquals(piO2,
sc3.getPhi(), 1.0e-10);<a name="line.60"></a>
+<FONT color="green">061</FONT> SphericalCoordinates sc4 = new
SphericalCoordinates(new Vector3D(0, -2, 0));<a name="line.61"></a>
+<FONT color="green">062</FONT> Assert.assertEquals(2,
sc4.getR(), 1.0e-10);<a name="line.62"></a>
+<FONT color="green">063</FONT> Assert.assertEquals(-piO2,
sc4.getTheta(), 1.0e-10);<a name="line.63"></a>
+<FONT color="green">064</FONT> Assert.assertEquals(piO2,
sc4.getPhi(), 1.0e-10);<a name="line.64"></a>
+<FONT color="green">065</FONT> SphericalCoordinates sc5 = new
SphericalCoordinates(new Vector3D(0, 0, 2));<a name="line.65"></a>
+<FONT color="green">066</FONT> Assert.assertEquals(2,
sc5.getR(), 1.0e-10);<a name="line.66"></a>
+<FONT color="green">067</FONT> // don't check theta on poles, as
it is singular<a name="line.67"></a>
+<FONT color="green">068</FONT> Assert.assertEquals(0,
sc5.getPhi(), 1.0e-10);<a name="line.68"></a>
+<FONT color="green">069</FONT> SphericalCoordinates sc6 = new
SphericalCoordinates(new Vector3D(0, 0, -2));<a name="line.69"></a>
+<FONT color="green">070</FONT> Assert.assertEquals(2,
sc6.getR(), 1.0e-10);<a name="line.70"></a>
+<FONT color="green">071</FONT> // don't check theta on poles, as
it is singular<a name="line.71"></a>
+<FONT color="green">072</FONT> Assert.assertEquals(FastMath.PI,
sc6.getPhi(), 1.0e-10);<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> @Test<a name="line.75"></a>
+<FONT color="green">076</FONT> public void testGradient() {<a
name="line.76"></a>
+<FONT color="green">077</FONT> for (double r = 0.2; r < 10; r +=
0.5) {<a name="line.77"></a>
+<FONT color="green">078</FONT> for (double theta = 0; theta
< 2 * FastMath.PI; theta += 0.1) {<a name="line.78"></a>
+<FONT color="green">079</FONT> for (double phi = 0.1; phi
< FastMath.PI; phi += 0.1) {<a name="line.79"></a>
+<FONT color="green">080</FONT> SphericalCoordinates sc
= new SphericalCoordinates(r, theta, phi);<a name="line.80"></a>
+<FONT color="green">081</FONT> <a name="line.81"></a>
+<FONT color="green">082</FONT> DerivativeStructure
svalue = valueSpherical(new DerivativeStructure(3, 1, 0, r),<a
name="line.82"></a>
+<FONT color="green">083</FONT>
new DerivativeStructure(3, 1, 1, theta),<a
name="line.83"></a>
+<FONT color="green">084</FONT>
new DerivativeStructure(3, 1, 2, phi));<a name="line.84"></a>
+<FONT color="green">085</FONT> double[] sGradient = new
double[] {<a name="line.85"></a>
+<FONT color="green">086</FONT>
svalue.getPartialDerivative(1, 0, 0),<a name="line.86"></a>
+<FONT color="green">087</FONT>
svalue.getPartialDerivative(0, 1, 0),<a name="line.87"></a>
+<FONT color="green">088</FONT>
svalue.getPartialDerivative(0, 0, 1),<a name="line.88"></a>
+<FONT color="green">089</FONT> };<a name="line.89"></a>
+<FONT color="green">090</FONT> <a name="line.90"></a>
+<FONT color="green">091</FONT> DerivativeStructure
cvalue = valueCartesian(new DerivativeStructure(3, 1, 0,
sc.getCartesian().getX()),<a name="line.91"></a>
+<FONT color="green">092</FONT>
new DerivativeStructure(3, 1, 1,
sc.getCartesian().getY()),<a name="line.92"></a>
+<FONT color="green">093</FONT>
new DerivativeStructure(3, 1, 2,
sc.getCartesian().getZ()));<a name="line.93"></a>
+<FONT color="green">094</FONT> Vector3D refCGradient =
new Vector3D(cvalue.getPartialDerivative(1, 0, 0),<a name="line.94"></a>
+<FONT color="green">095</FONT>
cvalue.getPartialDerivative(0, 1, 0),<a name="line.95"></a>
+<FONT color="green">096</FONT>
cvalue.getPartialDerivative(0, 0, 1));<a name="line.96"></a>
+<FONT color="green">097</FONT> <a name="line.97"></a>
+<FONT color="green">098</FONT> Vector3D testCGradient =
new Vector3D(sc.toCartesianGradient(sGradient));<a name="line.98"></a>
+<FONT color="green">099</FONT> <a name="line.99"></a>
+<FONT color="green">100</FONT> Assert.assertEquals(0,
testCGradient.distance(refCGradient) / refCGradient.getNorm(), 5.0e-14);<a
name="line.100"></a>
+<FONT color="green">101</FONT> <a name="line.101"></a>
+<FONT color="green">102</FONT> }<a name="line.102"></a>
+<FONT color="green">103</FONT> }<a name="line.103"></a>
+<FONT color="green">104</FONT> }<a name="line.104"></a>
+<FONT color="green">105</FONT> }<a name="line.105"></a>
+<FONT color="green">106</FONT> <a name="line.106"></a>
+<FONT color="green">107</FONT> @Test<a name="line.107"></a>
+<FONT color="green">108</FONT> public void testHessian() {<a
name="line.108"></a>
+<FONT color="green">109</FONT> for (double r = 0.2; r < 10; r +=
0.5) {<a name="line.109"></a>
+<FONT color="green">110</FONT> for (double theta = 0; theta
< 2 * FastMath.PI; theta += 0.2) {<a name="line.110"></a>
+<FONT color="green">111</FONT> for (double phi = 0.1; phi
< FastMath.PI; phi += 0.2) {<a name="line.111"></a>
+<FONT color="green">112</FONT> SphericalCoordinates sc
= new SphericalCoordinates(r, theta, phi);<a name="line.112"></a>
+<FONT color="green">113</FONT> <a name="line.113"></a>
+<FONT color="green">114</FONT> DerivativeStructure
svalue = valueSpherical(new DerivativeStructure(3, 2, 0, r),<a
name="line.114"></a>
+<FONT color="green">115</FONT>
new DerivativeStructure(3, 2, 1, theta),<a
name="line.115"></a>
+<FONT color="green">116</FONT>
new DerivativeStructure(3, 2, 2, phi));<a
name="line.116"></a>
+<FONT color="green">117</FONT> double[] sGradient = new
double[] {<a name="line.117"></a>
+<FONT color="green">118</FONT>
svalue.getPartialDerivative(1, 0, 0),<a name="line.118"></a>
+<FONT color="green">119</FONT>
svalue.getPartialDerivative(0, 1, 0),<a name="line.119"></a>
+<FONT color="green">120</FONT>
svalue.getPartialDerivative(0, 0, 1),<a name="line.120"></a>
+<FONT color="green">121</FONT> };<a name="line.121"></a>
+<FONT color="green">122</FONT> double[][] sHessian =
new double[3][3];<a name="line.122"></a>
+<FONT color="green">123</FONT> sHessian[0][0] =
svalue.getPartialDerivative(2, 0, 0); // d2F/dR2<a name="line.123"></a>
+<FONT color="green">124</FONT> sHessian[1][0] =
svalue.getPartialDerivative(1, 1, 0); // d2F/dRdTheta<a name="line.124"></a>
+<FONT color="green">125</FONT> sHessian[2][0] =
svalue.getPartialDerivative(1, 0, 1); // d2F/dRdPhi<a name="line.125"></a>
+<FONT color="green">126</FONT> sHessian[0][1] =
Double.NaN; // just to check upper-right part is not used<a name="line.126"></a>
+<FONT color="green">127</FONT> sHessian[1][1] =
svalue.getPartialDerivative(0, 2, 0); // d2F/dTheta2<a name="line.127"></a>
+<FONT color="green">128</FONT> sHessian[2][1] =
svalue.getPartialDerivative(0, 1, 1); // d2F/dThetadPhi<a name="line.128"></a>
+<FONT color="green">129</FONT> sHessian[0][2] =
Double.NaN; // just to check upper-right part is not used<a name="line.129"></a>
+<FONT color="green">130</FONT> sHessian[1][2] =
Double.NaN; // just to check upper-right part is not used<a name="line.130"></a>
+<FONT color="green">131</FONT> sHessian[2][2] =
svalue.getPartialDerivative(0, 0, 2); // d2F/dPhi2<a name="line.131"></a>
+<FONT color="green">132</FONT> <a name="line.132"></a>
+<FONT color="green">133</FONT> DerivativeStructure
cvalue = valueCartesian(new DerivativeStructure(3, 2, 0,
sc.getCartesian().getX()),<a name="line.133"></a>
+<FONT color="green">134</FONT>
new DerivativeStructure(3, 2, 1,
sc.getCartesian().getY()),<a name="line.134"></a>
+<FONT color="green">135</FONT>
new DerivativeStructure(3, 2, 2,
sc.getCartesian().getZ()));<a name="line.135"></a>
+<FONT color="green">136</FONT> double[][] refCHessian =
new double[3][3];<a name="line.136"></a>
+<FONT color="green">137</FONT> refCHessian[0][0] =
cvalue.getPartialDerivative(2, 0, 0); // d2F/dX2<a name="line.137"></a>
+<FONT color="green">138</FONT> refCHessian[1][0] =
cvalue.getPartialDerivative(1, 1, 0); // d2F/dXdY<a name="line.138"></a>
+<FONT color="green">139</FONT> refCHessian[2][0] =
cvalue.getPartialDerivative(1, 0, 1); // d2F/dXdZ<a name="line.139"></a>
+<FONT color="green">140</FONT> refCHessian[0][1] =
refCHessian[1][0];<a name="line.140"></a>
+<FONT color="green">141</FONT> refCHessian[1][1] =
cvalue.getPartialDerivative(0, 2, 0); // d2F/dY2<a name="line.141"></a>
+<FONT color="green">142</FONT> refCHessian[2][1] =
cvalue.getPartialDerivative(0, 1, 1); // d2F/dYdZ<a name="line.142"></a>
+<FONT color="green">143</FONT> refCHessian[0][2] =
refCHessian[2][0];<a name="line.143"></a>
+<FONT color="green">144</FONT> refCHessian[1][2] =
refCHessian[2][1];<a name="line.144"></a>
+<FONT color="green">145</FONT> refCHessian[2][2] =
cvalue.getPartialDerivative(0, 0, 2); // d2F/dZ2<a name="line.145"></a>
+<FONT color="green">146</FONT> double norm = 0;<a
name="line.146"></a>
+<FONT color="green">147</FONT> for (int i = 0; i <
3; ++i) {<a name="line.147"></a>
+<FONT color="green">148</FONT> for (int j = 0; j
< 3; ++j) {<a name="line.148"></a>
+<FONT color="green">149</FONT> norm =
FastMath.max(norm, FastMath.abs(refCHessian[i][j]));<a name="line.149"></a>
+<FONT color="green">150</FONT> }<a
name="line.150"></a>
+<FONT color="green">151</FONT> }<a name="line.151"></a>
+<FONT color="green">152</FONT> <a name="line.152"></a>
+<FONT color="green">153</FONT> double[][] testCHessian
= sc.toCartesianHessian(sHessian, sGradient);<a name="line.153"></a>
+<FONT color="green">154</FONT> for (int i = 0; i <
3; ++i) {<a name="line.154"></a>
+<FONT color="green">155</FONT> for (int j = 0; j
< 3; ++j) {<a name="line.155"></a>
+<FONT color="green">156</FONT>
Assert.assertEquals("" + FastMath.abs((refCHessian[i][j] - testCHessian[i][j])
/ norm),<a name="line.156"></a>
+<FONT color="green">157</FONT>
refCHessian[i][j], testCHessian[i][j], 1.0e-14 * norm);<a
name="line.157"></a>
+<FONT color="green">158</FONT> }<a
name="line.158"></a>
+<FONT color="green">159</FONT> }<a name="line.159"></a>
+<FONT color="green">160</FONT> <a name="line.160"></a>
+<FONT color="green">161</FONT> }<a name="line.161"></a>
+<FONT color="green">162</FONT> }<a name="line.162"></a>
+<FONT color="green">163</FONT> }<a name="line.163"></a>
+<FONT color="green">164</FONT> }<a name="line.164"></a>
+<FONT color="green">165</FONT> <a name="line.165"></a>
+<FONT color="green">166</FONT> public DerivativeStructure
valueCartesian(DerivativeStructure x, DerivativeStructure y,
DerivativeStructure z) {<a name="line.166"></a>
+<FONT color="green">167</FONT> return
x.divide(y.multiply(5).add(10)).multiply(z.pow(3));<a name="line.167"></a>
+<FONT color="green">168</FONT> }<a name="line.168"></a>
+<FONT color="green">169</FONT> <a name="line.169"></a>
+<FONT color="green">170</FONT> public DerivativeStructure
valueSpherical(DerivativeStructure r, DerivativeStructure theta,
DerivativeStructure phi) {<a name="line.170"></a>
+<FONT color="green">171</FONT> return
valueCartesian(r.multiply(theta.cos()).multiply(phi.sin()),<a
name="line.171"></a>
+<FONT color="green">172</FONT>
r.multiply(theta.sin()).multiply(phi.sin()),<a name="line.172"></a>
+<FONT color="green">173</FONT>
r.multiply(phi.cos()));<a name="line.173"></a>
+<FONT color="green">174</FONT> }<a name="line.174"></a>
+<FONT color="green">175</FONT> <a name="line.175"></a>
+<FONT color="green">176</FONT> @Test<a name="line.176"></a>
+<FONT color="green">177</FONT> public void testSerialization() {<a
name="line.177"></a>
+<FONT color="green">178</FONT> SphericalCoordinates a = new
SphericalCoordinates(3, 2, 1);<a name="line.178"></a>
+<FONT color="green">179</FONT> SphericalCoordinates b =
(SphericalCoordinates) TestUtils.serializeAndRecover(a);<a name="line.179"></a>
+<FONT color="green">180</FONT> Assert.assertEquals(0,
a.getCartesian().distance(b.getCartesian()), 1.0e-10);<a name="line.180"></a>
+<FONT color="green">181</FONT> Assert.assertEquals(a.getR(),
b.getR(), 1.0e-10);<a name="line.181"></a>
+<FONT color="green">182</FONT> Assert.assertEquals(a.getTheta(),
b.getTheta(), 1.0e-10);<a name="line.182"></a>
+<FONT color="green">183</FONT> Assert.assertEquals(a.getPhi(),
b.getPhi(), 1.0e-10);<a name="line.183"></a>
+<FONT color="green">184</FONT> }<a name="line.184"></a>
+<FONT color="green">185</FONT> <a name="line.185"></a>
+<FONT color="green">186</FONT> }<a name="line.186"></a>
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