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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 [2/39] - 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...
Modified: websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html (original)
+++ websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html Sat Apr 6 23:42:01 2013
@@ -23,1237 +23,1465 @@
<FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a>
<FONT color="green">021</FONT> import java.util.List;<a name="line.21"></a>
<FONT color="green">022</FONT> <a name="line.22"></a>
-<FONT color="green">023</FONT> import org.apache.commons.math3.TestUtils;<a name="line.23"></a>
-<FONT color="green">024</FONT> import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;<a name="line.24"></a>
-<FONT color="green">025</FONT> import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.25"></a>
-<FONT color="green">026</FONT> import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.26"></a>
-<FONT color="green">027</FONT> import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.27"></a>
-<FONT color="green">028</FONT> import org.apache.commons.math3.util.FastMath;<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> * Test for class {@link DerivativeStructure}.<a name="line.33"></a>
-<FONT color="green">034</FONT> */<a name="line.34"></a>
-<FONT color="green">035</FONT> public class DerivativeStructureTest {<a name="line.35"></a>
-<FONT color="green">036</FONT> <a name="line.36"></a>
-<FONT color="green">037</FONT> @Test(expected=NumberIsTooLargeException.class)<a name="line.37"></a>
-<FONT color="green">038</FONT> public void testWrongVariableIndex() {<a name="line.38"></a>
-<FONT color="green">039</FONT> new DerivativeStructure(3, 1, 3, 1.0);<a name="line.39"></a>
-<FONT color="green">040</FONT> }<a name="line.40"></a>
-<FONT color="green">041</FONT> <a name="line.41"></a>
-<FONT color="green">042</FONT> @Test(expected=DimensionMismatchException.class)<a name="line.42"></a>
-<FONT color="green">043</FONT> public void testMissingOrders() {<a name="line.43"></a>
-<FONT color="green">044</FONT> new DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(0, 1);<a name="line.44"></a>
-<FONT color="green">045</FONT> }<a name="line.45"></a>
-<FONT color="green">046</FONT> <a name="line.46"></a>
-<FONT color="green">047</FONT> @Test(expected=NumberIsTooLargeException.class)<a name="line.47"></a>
-<FONT color="green">048</FONT> public void testTooLargeOrder() {<a name="line.48"></a>
-<FONT color="green">049</FONT> new DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(1, 1, 2);<a name="line.49"></a>
-<FONT color="green">050</FONT> }<a name="line.50"></a>
-<FONT color="green">051</FONT> <a name="line.51"></a>
-<FONT color="green">052</FONT> @Test<a name="line.52"></a>
-<FONT color="green">053</FONT> public void testVariableWithoutDerivative0() {<a name="line.53"></a>
-<FONT color="green">054</FONT> DerivativeStructure v = new DerivativeStructure(1, 0, 0, 1.0);<a name="line.54"></a>
-<FONT color="green">055</FONT> Assert.assertEquals(1.0, v.getValue(), 1.0e-15);<a name="line.55"></a>
+<FONT color="green">023</FONT> import org.apache.commons.math3.ExtendedFieldElementAbstractTest;<a name="line.23"></a>
+<FONT color="green">024</FONT> import org.apache.commons.math3.TestUtils;<a name="line.24"></a>
+<FONT color="green">025</FONT> import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;<a name="line.25"></a>
+<FONT color="green">026</FONT> import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.26"></a>
+<FONT color="green">027</FONT> import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.27"></a>
+<FONT color="green">028</FONT> import org.apache.commons.math3.random.Well1024a;<a name="line.28"></a>
+<FONT color="green">029</FONT> import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.29"></a>
+<FONT color="green">030</FONT> import org.apache.commons.math3.util.FastMath;<a name="line.30"></a>
+<FONT color="green">031</FONT> import org.junit.Assert;<a name="line.31"></a>
+<FONT color="green">032</FONT> import org.junit.Test;<a name="line.32"></a>
+<FONT color="green">033</FONT> <a name="line.33"></a>
+<FONT color="green">034</FONT> /**<a name="line.34"></a>
+<FONT color="green">035</FONT> * Test for class {@link DerivativeStructure}.<a name="line.35"></a>
+<FONT color="green">036</FONT> */<a name="line.36"></a>
+<FONT color="green">037</FONT> public class DerivativeStructureTest extends ExtendedFieldElementAbstractTest<DerivativeStructure> {<a name="line.37"></a>
+<FONT color="green">038</FONT> <a name="line.38"></a>
+<FONT color="green">039</FONT> protected DerivativeStructure build(final double x) {<a name="line.39"></a>
+<FONT color="green">040</FONT> return new DerivativeStructure(2, 1, 0, x);<a name="line.40"></a>
+<FONT color="green">041</FONT> }<a name="line.41"></a>
+<FONT color="green">042</FONT> <a name="line.42"></a>
+<FONT color="green">043</FONT> @Test(expected=NumberIsTooLargeException.class)<a name="line.43"></a>
+<FONT color="green">044</FONT> public void testWrongVariableIndex() {<a name="line.44"></a>
+<FONT color="green">045</FONT> new DerivativeStructure(3, 1, 3, 1.0);<a name="line.45"></a>
+<FONT color="green">046</FONT> }<a name="line.46"></a>
+<FONT color="green">047</FONT> <a name="line.47"></a>
+<FONT color="green">048</FONT> @Test(expected=DimensionMismatchException.class)<a name="line.48"></a>
+<FONT color="green">049</FONT> public void testMissingOrders() {<a name="line.49"></a>
+<FONT color="green">050</FONT> new DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(0, 1);<a name="line.50"></a>
+<FONT color="green">051</FONT> }<a name="line.51"></a>
+<FONT color="green">052</FONT> <a name="line.52"></a>
+<FONT color="green">053</FONT> @Test(expected=NumberIsTooLargeException.class)<a name="line.53"></a>
+<FONT color="green">054</FONT> public void testTooLargeOrder() {<a name="line.54"></a>
+<FONT color="green">055</FONT> new DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(1, 1, 2);<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(expected=NumberIsTooLargeException.class)<a name="line.58"></a>
-<FONT color="green">059</FONT> public void testVariableWithoutDerivative1() {<a name="line.59"></a>
+<FONT color="green">058</FONT> @Test<a name="line.58"></a>
+<FONT color="green">059</FONT> public void testVariableWithoutDerivative0() {<a name="line.59"></a>
<FONT color="green">060</FONT> DerivativeStructure v = new DerivativeStructure(1, 0, 0, 1.0);<a name="line.60"></a>
-<FONT color="green">061</FONT> Assert.assertEquals(1.0, v.getPartialDerivative(1), 1.0e-15);<a name="line.61"></a>
+<FONT color="green">061</FONT> Assert.assertEquals(1.0, v.getValue(), 1.0e-15);<a name="line.61"></a>
<FONT color="green">062</FONT> }<a name="line.62"></a>
<FONT color="green">063</FONT> <a name="line.63"></a>
-<FONT color="green">064</FONT> @Test<a name="line.64"></a>
-<FONT color="green">065</FONT> public void testVariable() {<a name="line.65"></a>
-<FONT color="green">066</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.66"></a>
-<FONT color="green">067</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0),<a name="line.67"></a>
-<FONT color="green">068</FONT> 1.0, 1.0, 0.0, 0.0);<a name="line.68"></a>
-<FONT color="green">069</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0),<a name="line.69"></a>
-<FONT color="green">070</FONT> 2.0, 0.0, 1.0, 0.0);<a name="line.70"></a>
-<FONT color="green">071</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0),<a name="line.71"></a>
-<FONT color="green">072</FONT> 3.0, 0.0, 0.0, 1.0);<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> <a name="line.75"></a>
-<FONT color="green">076</FONT> @Test<a name="line.76"></a>
-<FONT color="green">077</FONT> public void testConstant() {<a name="line.77"></a>
-<FONT color="green">078</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.78"></a>
-<FONT color="green">079</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, FastMath.PI),<a name="line.79"></a>
-<FONT color="green">080</FONT> FastMath.PI, 0.0, 0.0, 0.0);<a name="line.80"></a>
-<FONT color="green">081</FONT> }<a name="line.81"></a>
-<FONT color="green">082</FONT> }<a name="line.82"></a>
-<FONT color="green">083</FONT> <a name="line.83"></a>
-<FONT color="green">084</FONT> @Test<a name="line.84"></a>
-<FONT color="green">085</FONT> public void testPrimitiveAdd() {<a name="line.85"></a>
-<FONT color="green">086</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.86"></a>
-<FONT color="green">087</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).add(5), 6.0, 1.0, 0.0, 0.0);<a name="line.87"></a>
-<FONT color="green">088</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).add(5), 7.0, 0.0, 1.0, 0.0);<a name="line.88"></a>
-<FONT color="green">089</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).add(5), 8.0, 0.0, 0.0, 1.0);<a name="line.89"></a>
-<FONT color="green">090</FONT> }<a name="line.90"></a>
-<FONT color="green">091</FONT> }<a name="line.91"></a>
-<FONT color="green">092</FONT> <a name="line.92"></a>
-<FONT color="green">093</FONT> @Test<a name="line.93"></a>
-<FONT color="green">094</FONT> public void testAdd() {<a name="line.94"></a>
-<FONT color="green">095</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.95"></a>
-<FONT color="green">096</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.96"></a>
-<FONT color="green">097</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.97"></a>
-<FONT color="green">098</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.98"></a>
-<FONT color="green">099</FONT> DerivativeStructure xyz = x.add(y.add(z));<a name="line.99"></a>
-<FONT color="green">100</FONT> checkF0F1(xyz, x.getValue() + y.getValue() + z.getValue(), 1.0, 1.0, 1.0);<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> @Test<a name="line.104"></a>
-<FONT color="green">105</FONT> public void testPrimitiveSubtract() {<a name="line.105"></a>
-<FONT color="green">106</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.106"></a>
-<FONT color="green">107</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).subtract(5), -4.0, 1.0, 0.0, 0.0);<a name="line.107"></a>
-<FONT color="green">108</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).subtract(5), -3.0, 0.0, 1.0, 0.0);<a name="line.108"></a>
-<FONT color="green">109</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).subtract(5), -2.0, 0.0, 0.0, 1.0);<a name="line.109"></a>
-<FONT color="green">110</FONT> }<a name="line.110"></a>
-<FONT color="green">111</FONT> }<a name="line.111"></a>
-<FONT color="green">112</FONT> <a name="line.112"></a>
-<FONT color="green">113</FONT> @Test<a name="line.113"></a>
-<FONT color="green">114</FONT> public void testSubtract() {<a name="line.114"></a>
-<FONT color="green">115</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.115"></a>
-<FONT color="green">116</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.116"></a>
-<FONT color="green">117</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.117"></a>
-<FONT color="green">118</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.118"></a>
-<FONT color="green">119</FONT> DerivativeStructure xyz = x.subtract(y.subtract(z));<a name="line.119"></a>
-<FONT color="green">120</FONT> checkF0F1(xyz, x.getValue() - (y.getValue() - z.getValue()), 1.0, -1.0, 1.0);<a name="line.120"></a>
-<FONT color="green">121</FONT> }<a name="line.121"></a>
-<FONT color="green">122</FONT> }<a name="line.122"></a>
-<FONT color="green">123</FONT> <a name="line.123"></a>
-<FONT color="green">124</FONT> @Test<a name="line.124"></a>
-<FONT color="green">125</FONT> public void testPrimitiveMultiply() {<a name="line.125"></a>
-<FONT color="green">126</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.126"></a>
-<FONT color="green">127</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).multiply(5), 5.0, 5.0, 0.0, 0.0);<a name="line.127"></a>
-<FONT color="green">128</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).multiply(5), 10.0, 0.0, 5.0, 0.0);<a name="line.128"></a>
-<FONT color="green">129</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).multiply(5), 15.0, 0.0, 0.0, 5.0);<a name="line.129"></a>
-<FONT color="green">130</FONT> }<a name="line.130"></a>
-<FONT color="green">131</FONT> }<a name="line.131"></a>
-<FONT color="green">132</FONT> <a name="line.132"></a>
-<FONT color="green">133</FONT> @Test<a name="line.133"></a>
-<FONT color="green">134</FONT> public void testMultiply() {<a name="line.134"></a>
-<FONT color="green">135</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.135"></a>
-<FONT color="green">136</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.136"></a>
-<FONT color="green">137</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.137"></a>
-<FONT color="green">138</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.138"></a>
-<FONT color="green">139</FONT> DerivativeStructure xyz = x.multiply(y.multiply(z));<a name="line.139"></a>
-<FONT color="green">140</FONT> for (int i = 0; i <= maxOrder; ++i) {<a name="line.140"></a>
-<FONT color="green">141</FONT> for (int j = 0; j <= maxOrder; ++j) {<a name="line.141"></a>
-<FONT color="green">142</FONT> for (int k = 0; k <= maxOrder; ++k) {<a name="line.142"></a>
-<FONT color="green">143</FONT> if (i + j + k <= maxOrder) {<a name="line.143"></a>
-<FONT color="green">144</FONT> Assert.assertEquals((i == 0 ? x.getValue() : (i == 1 ? 1.0 : 0.0)) *<a name="line.144"></a>
-<FONT color="green">145</FONT> (j == 0 ? y.getValue() : (j == 1 ? 1.0 : 0.0)) *<a name="line.145"></a>
-<FONT color="green">146</FONT> (k == 0 ? z.getValue() : (k == 1 ? 1.0 : 0.0)),<a name="line.146"></a>
-<FONT color="green">147</FONT> xyz.getPartialDerivative(i, j, k),<a name="line.147"></a>
-<FONT color="green">148</FONT> 1.0e-15);<a name="line.148"></a>
-<FONT color="green">149</FONT> }<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> }<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 testNegate() {<a name="line.157"></a>
-<FONT color="green">158</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.158"></a>
-<FONT color="green">159</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).negate(), -1.0, -1.0, 0.0, 0.0);<a name="line.159"></a>
-<FONT color="green">160</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).negate(), -2.0, 0.0, -1.0, 0.0);<a name="line.160"></a>
-<FONT color="green">161</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).negate(), -3.0, 0.0, 0.0, -1.0);<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> @Test<a name="line.165"></a>
-<FONT color="green">166</FONT> public void testReciprocal() {<a name="line.166"></a>
-<FONT color="green">167</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.167"></a>
-<FONT color="green">168</FONT> DerivativeStructure r = new DerivativeStructure(1, 6, 0, x).reciprocal();<a name="line.168"></a>
-<FONT color="green">169</FONT> Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);<a name="line.169"></a>
-<FONT color="green">170</FONT> for (int i = 1; i < r.getOrder(); ++i) {<a name="line.170"></a>
-<FONT color="green">171</FONT> double expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /<a name="line.171"></a>
-<FONT color="green">172</FONT> FastMath.pow(x, i + 1);<a name="line.172"></a>
-<FONT color="green">173</FONT> Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));<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> }<a name="line.176"></a>
-<FONT color="green">177</FONT> <a name="line.177"></a>
-<FONT color="green">178</FONT> @Test<a name="line.178"></a>
-<FONT color="green">179</FONT> public void testPow() {<a name="line.179"></a>
-<FONT color="green">180</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.180"></a>
-<FONT color="green">181</FONT> for (int n = 0; n < 10; ++n) {<a name="line.181"></a>
-<FONT color="green">182</FONT> <a name="line.182"></a>
-<FONT color="green">183</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.183"></a>
-<FONT color="green">184</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.184"></a>
-<FONT color="green">185</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.185"></a>
-<FONT color="green">186</FONT> List<DerivativeStructure> list = Arrays.asList(x, y, z,<a name="line.186"></a>
-<FONT color="green">187</FONT> x.add(y).add(z),<a name="line.187"></a>
-<FONT color="green">188</FONT> x.multiply(y).multiply(z));<a name="line.188"></a>
-<FONT color="green">189</FONT> <a name="line.189"></a>
-<FONT color="green">190</FONT> if (n == 0) {<a name="line.190"></a>
-<FONT color="green">191</FONT> for (DerivativeStructure ds : list) {<a name="line.191"></a>
-<FONT color="green">192</FONT> checkEquals(ds.getField().getOne(), ds.pow(n), 1.0e-15);<a name="line.192"></a>
-<FONT color="green">193</FONT> }<a name="line.193"></a>
-<FONT color="green">194</FONT> } else if (n == 1) {<a name="line.194"></a>
-<FONT color="green">195</FONT> for (DerivativeStructure ds : list) {<a name="line.195"></a>
-<FONT color="green">196</FONT> checkEquals(ds, ds.pow(n), 1.0e-15);<a name="line.196"></a>
-<FONT color="green">197</FONT> }<a name="line.197"></a>
-<FONT color="green">198</FONT> } else {<a name="line.198"></a>
-<FONT color="green">199</FONT> for (DerivativeStructure ds : list) {<a name="line.199"></a>
-<FONT color="green">200</FONT> DerivativeStructure p = ds.getField().getOne();<a name="line.200"></a>
-<FONT color="green">201</FONT> for (int i = 0; i < n; ++i) {<a name="line.201"></a>
-<FONT color="green">202</FONT> p = p.multiply(ds);<a name="line.202"></a>
-<FONT color="green">203</FONT> }<a name="line.203"></a>
-<FONT color="green">204</FONT> checkEquals(p, ds.pow(n), 1.0e-15);<a name="line.204"></a>
-<FONT color="green">205</FONT> }<a name="line.205"></a>
-<FONT color="green">206</FONT> }<a name="line.206"></a>
-<FONT color="green">207</FONT> }<a name="line.207"></a>
-<FONT color="green">208</FONT> }<a name="line.208"></a>
-<FONT color="green">209</FONT> }<a name="line.209"></a>
-<FONT color="green">210</FONT> <a name="line.210"></a>
-<FONT color="green">211</FONT> @Test<a name="line.211"></a>
-<FONT color="green">212</FONT> public void testExpression() {<a name="line.212"></a>
-<FONT color="green">213</FONT> double epsilon = 2.5e-13;<a name="line.213"></a>
-<FONT color="green">214</FONT> for (double x = 0; x < 2; x += 0.2) {<a name="line.214"></a>
-<FONT color="green">215</FONT> DerivativeStructure dsX = new DerivativeStructure(3, 5, 0, x);<a name="line.215"></a>
-<FONT color="green">216</FONT> for (double y = 0; y < 2; y += 0.2) {<a name="line.216"></a>
-<FONT color="green">217</FONT> DerivativeStructure dsY = new DerivativeStructure(3, 5, 1, y);<a name="line.217"></a>
-<FONT color="green">218</FONT> for (double z = 0; z >- 2; z -= 0.2) {<a name="line.218"></a>
-<FONT color="green">219</FONT> DerivativeStructure dsZ = new DerivativeStructure(3, 5, 2, z);<a name="line.219"></a>
-<FONT color="green">220</FONT> <a name="line.220"></a>
-<FONT color="green">221</FONT> // f(x, y, z) = x + 5 x y - 2 z + (8 z x - y)^3<a name="line.221"></a>
-<FONT color="green">222</FONT> DerivativeStructure ds =<a name="line.222"></a>
-<FONT color="green">223</FONT> new DerivativeStructure(1, dsX,<a name="line.223"></a>
-<FONT color="green">224</FONT> 5, dsX.multiply(dsY),<a name="line.224"></a>
-<FONT color="green">225</FONT> -2, dsZ,<a name="line.225"></a>
-<FONT color="green">226</FONT> 1, new DerivativeStructure(8, dsZ.multiply(dsX),<a name="line.226"></a>
-<FONT color="green">227</FONT> -1, dsY).pow(3));<a name="line.227"></a>
-<FONT color="green">228</FONT> DerivativeStructure dsOther =<a name="line.228"></a>
+<FONT color="green">064</FONT> @Test(expected=NumberIsTooLargeException.class)<a name="line.64"></a>
+<FONT color="green">065</FONT> public void testVariableWithoutDerivative1() {<a name="line.65"></a>
+<FONT color="green">066</FONT> DerivativeStructure v = new DerivativeStructure(1, 0, 0, 1.0);<a name="line.66"></a>
+<FONT color="green">067</FONT> Assert.assertEquals(1.0, v.getPartialDerivative(1), 1.0e-15);<a name="line.67"></a>
+<FONT color="green">068</FONT> }<a name="line.68"></a>
+<FONT color="green">069</FONT> <a name="line.69"></a>
+<FONT color="green">070</FONT> @Test<a name="line.70"></a>
+<FONT color="green">071</FONT> public void testVariable() {<a name="line.71"></a>
+<FONT color="green">072</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.72"></a>
+<FONT color="green">073</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0),<a name="line.73"></a>
+<FONT color="green">074</FONT> 1.0, 1.0, 0.0, 0.0);<a name="line.74"></a>
+<FONT color="green">075</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0),<a name="line.75"></a>
+<FONT color="green">076</FONT> 2.0, 0.0, 1.0, 0.0);<a name="line.76"></a>
+<FONT color="green">077</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0),<a name="line.77"></a>
+<FONT color="green">078</FONT> 3.0, 0.0, 0.0, 1.0);<a name="line.78"></a>
+<FONT color="green">079</FONT> }<a name="line.79"></a>
+<FONT color="green">080</FONT> }<a name="line.80"></a>
+<FONT color="green">081</FONT> <a name="line.81"></a>
+<FONT color="green">082</FONT> @Test<a name="line.82"></a>
+<FONT color="green">083</FONT> public void testConstant() {<a name="line.83"></a>
+<FONT color="green">084</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.84"></a>
+<FONT color="green">085</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, FastMath.PI),<a name="line.85"></a>
+<FONT color="green">086</FONT> FastMath.PI, 0.0, 0.0, 0.0);<a name="line.86"></a>
+<FONT color="green">087</FONT> }<a name="line.87"></a>
+<FONT color="green">088</FONT> }<a name="line.88"></a>
+<FONT color="green">089</FONT> <a name="line.89"></a>
+<FONT color="green">090</FONT> @Test<a name="line.90"></a>
+<FONT color="green">091</FONT> public void testPrimitiveAdd() {<a name="line.91"></a>
+<FONT color="green">092</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.92"></a>
+<FONT color="green">093</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).add(5), 6.0, 1.0, 0.0, 0.0);<a name="line.93"></a>
+<FONT color="green">094</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).add(5), 7.0, 0.0, 1.0, 0.0);<a name="line.94"></a>
+<FONT color="green">095</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).add(5), 8.0, 0.0, 0.0, 1.0);<a name="line.95"></a>
+<FONT color="green">096</FONT> }<a name="line.96"></a>
+<FONT color="green">097</FONT> }<a name="line.97"></a>
+<FONT color="green">098</FONT> <a name="line.98"></a>
+<FONT color="green">099</FONT> @Test<a name="line.99"></a>
+<FONT color="green">100</FONT> public void testAdd() {<a name="line.100"></a>
+<FONT color="green">101</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.101"></a>
+<FONT color="green">102</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.102"></a>
+<FONT color="green">103</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.103"></a>
+<FONT color="green">104</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.104"></a>
+<FONT color="green">105</FONT> DerivativeStructure xyz = x.add(y.add(z));<a name="line.105"></a>
+<FONT color="green">106</FONT> checkF0F1(xyz, x.getValue() + y.getValue() + z.getValue(), 1.0, 1.0, 1.0);<a name="line.106"></a>
+<FONT color="green">107</FONT> }<a name="line.107"></a>
+<FONT color="green">108</FONT> }<a name="line.108"></a>
+<FONT color="green">109</FONT> <a name="line.109"></a>
+<FONT color="green">110</FONT> @Test<a name="line.110"></a>
+<FONT color="green">111</FONT> public void testPrimitiveSubtract() {<a name="line.111"></a>
+<FONT color="green">112</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.112"></a>
+<FONT color="green">113</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).subtract(5), -4.0, 1.0, 0.0, 0.0);<a name="line.113"></a>
+<FONT color="green">114</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).subtract(5), -3.0, 0.0, 1.0, 0.0);<a name="line.114"></a>
+<FONT color="green">115</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).subtract(5), -2.0, 0.0, 0.0, 1.0);<a name="line.115"></a>
+<FONT color="green">116</FONT> }<a name="line.116"></a>
+<FONT color="green">117</FONT> }<a name="line.117"></a>
+<FONT color="green">118</FONT> <a name="line.118"></a>
+<FONT color="green">119</FONT> @Test<a name="line.119"></a>
+<FONT color="green">120</FONT> public void testSubtract() {<a name="line.120"></a>
+<FONT color="green">121</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.121"></a>
+<FONT color="green">122</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.122"></a>
+<FONT color="green">123</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.123"></a>
+<FONT color="green">124</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.124"></a>
+<FONT color="green">125</FONT> DerivativeStructure xyz = x.subtract(y.subtract(z));<a name="line.125"></a>
+<FONT color="green">126</FONT> checkF0F1(xyz, x.getValue() - (y.getValue() - z.getValue()), 1.0, -1.0, 1.0);<a name="line.126"></a>
+<FONT color="green">127</FONT> }<a name="line.127"></a>
+<FONT color="green">128</FONT> }<a name="line.128"></a>
+<FONT color="green">129</FONT> <a name="line.129"></a>
+<FONT color="green">130</FONT> @Test<a name="line.130"></a>
+<FONT color="green">131</FONT> public void testPrimitiveMultiply() {<a name="line.131"></a>
+<FONT color="green">132</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.132"></a>
+<FONT color="green">133</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).multiply(5), 5.0, 5.0, 0.0, 0.0);<a name="line.133"></a>
+<FONT color="green">134</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).multiply(5), 10.0, 0.0, 5.0, 0.0);<a name="line.134"></a>
+<FONT color="green">135</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).multiply(5), 15.0, 0.0, 0.0, 5.0);<a name="line.135"></a>
+<FONT color="green">136</FONT> }<a name="line.136"></a>
+<FONT color="green">137</FONT> }<a name="line.137"></a>
+<FONT color="green">138</FONT> <a name="line.138"></a>
+<FONT color="green">139</FONT> @Test<a name="line.139"></a>
+<FONT color="green">140</FONT> public void testMultiply() {<a name="line.140"></a>
+<FONT color="green">141</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.141"></a>
+<FONT color="green">142</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.142"></a>
+<FONT color="green">143</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.143"></a>
+<FONT color="green">144</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.144"></a>
+<FONT color="green">145</FONT> DerivativeStructure xyz = x.multiply(y.multiply(z));<a name="line.145"></a>
+<FONT color="green">146</FONT> for (int i = 0; i <= maxOrder; ++i) {<a name="line.146"></a>
+<FONT color="green">147</FONT> for (int j = 0; j <= maxOrder; ++j) {<a name="line.147"></a>
+<FONT color="green">148</FONT> for (int k = 0; k <= maxOrder; ++k) {<a name="line.148"></a>
+<FONT color="green">149</FONT> if (i + j + k <= maxOrder) {<a name="line.149"></a>
+<FONT color="green">150</FONT> Assert.assertEquals((i == 0 ? x.getValue() : (i == 1 ? 1.0 : 0.0)) *<a name="line.150"></a>
+<FONT color="green">151</FONT> (j == 0 ? y.getValue() : (j == 1 ? 1.0 : 0.0)) *<a name="line.151"></a>
+<FONT color="green">152</FONT> (k == 0 ? z.getValue() : (k == 1 ? 1.0 : 0.0)),<a name="line.152"></a>
+<FONT color="green">153</FONT> xyz.getPartialDerivative(i, j, k),<a name="line.153"></a>
+<FONT color="green">154</FONT> 1.0e-15);<a name="line.154"></a>
+<FONT color="green">155</FONT> }<a name="line.155"></a>
+<FONT color="green">156</FONT> }<a name="line.156"></a>
+<FONT color="green">157</FONT> }<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> @Test<a name="line.162"></a>
+<FONT color="green">163</FONT> public void testNegate() {<a name="line.163"></a>
+<FONT color="green">164</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.164"></a>
+<FONT color="green">165</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 0, 1.0).negate(), -1.0, -1.0, 0.0, 0.0);<a name="line.165"></a>
+<FONT color="green">166</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 1, 2.0).negate(), -2.0, 0.0, -1.0, 0.0);<a name="line.166"></a>
+<FONT color="green">167</FONT> checkF0F1(new DerivativeStructure(3, maxOrder, 2, 3.0).negate(), -3.0, 0.0, 0.0, -1.0);<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> <a name="line.170"></a>
+<FONT color="green">171</FONT> @Test<a name="line.171"></a>
+<FONT color="green">172</FONT> public void testReciprocal() {<a name="line.172"></a>
+<FONT color="green">173</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.173"></a>
+<FONT color="green">174</FONT> DerivativeStructure r = new DerivativeStructure(1, 6, 0, x).reciprocal();<a name="line.174"></a>
+<FONT color="green">175</FONT> Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);<a name="line.175"></a>
+<FONT color="green">176</FONT> for (int i = 1; i < r.getOrder(); ++i) {<a name="line.176"></a>
+<FONT color="green">177</FONT> double expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /<a name="line.177"></a>
+<FONT color="green">178</FONT> FastMath.pow(x, i + 1);<a name="line.178"></a>
+<FONT color="green">179</FONT> Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));<a name="line.179"></a>
+<FONT color="green">180</FONT> }<a name="line.180"></a>
+<FONT color="green">181</FONT> }<a name="line.181"></a>
+<FONT color="green">182</FONT> }<a name="line.182"></a>
+<FONT color="green">183</FONT> <a name="line.183"></a>
+<FONT color="green">184</FONT> @Test<a name="line.184"></a>
+<FONT color="green">185</FONT> public void testPow() {<a name="line.185"></a>
+<FONT color="green">186</FONT> for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {<a name="line.186"></a>
+<FONT color="green">187</FONT> for (int n = 0; n < 10; ++n) {<a name="line.187"></a>
+<FONT color="green">188</FONT> <a name="line.188"></a>
+<FONT color="green">189</FONT> DerivativeStructure x = new DerivativeStructure(3, maxOrder, 0, 1.0);<a name="line.189"></a>
+<FONT color="green">190</FONT> DerivativeStructure y = new DerivativeStructure(3, maxOrder, 1, 2.0);<a name="line.190"></a>
+<FONT color="green">191</FONT> DerivativeStructure z = new DerivativeStructure(3, maxOrder, 2, 3.0);<a name="line.191"></a>
+<FONT color="green">192</FONT> List<DerivativeStructure> list = Arrays.asList(x, y, z,<a name="line.192"></a>
+<FONT color="green">193</FONT> x.add(y).add(z),<a name="line.193"></a>
+<FONT color="green">194</FONT> x.multiply(y).multiply(z));<a name="line.194"></a>
+<FONT color="green">195</FONT> <a name="line.195"></a>
+<FONT color="green">196</FONT> if (n == 0) {<a name="line.196"></a>
+<FONT color="green">197</FONT> for (DerivativeStructure ds : list) {<a name="line.197"></a>
+<FONT color="green">198</FONT> checkEquals(ds.getField().getOne(), ds.pow(n), 1.0e-15);<a name="line.198"></a>
+<FONT color="green">199</FONT> }<a name="line.199"></a>
+<FONT color="green">200</FONT> } else if (n == 1) {<a name="line.200"></a>
+<FONT color="green">201</FONT> for (DerivativeStructure ds : list) {<a name="line.201"></a>
+<FONT color="green">202</FONT> checkEquals(ds, ds.pow(n), 1.0e-15);<a name="line.202"></a>
+<FONT color="green">203</FONT> }<a name="line.203"></a>
+<FONT color="green">204</FONT> } else {<a name="line.204"></a>
+<FONT color="green">205</FONT> for (DerivativeStructure ds : list) {<a name="line.205"></a>
+<FONT color="green">206</FONT> DerivativeStructure p = ds.getField().getOne();<a name="line.206"></a>
+<FONT color="green">207</FONT> for (int i = 0; i < n; ++i) {<a name="line.207"></a>
+<FONT color="green">208</FONT> p = p.multiply(ds);<a name="line.208"></a>
+<FONT color="green">209</FONT> }<a name="line.209"></a>
+<FONT color="green">210</FONT> checkEquals(p, ds.pow(n), 1.0e-15);<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> }<a name="line.215"></a>
+<FONT color="green">216</FONT> <a name="line.216"></a>
+<FONT color="green">217</FONT> @Test<a name="line.217"></a>
+<FONT color="green">218</FONT> public void testExpression() {<a name="line.218"></a>
+<FONT color="green">219</FONT> double epsilon = 2.5e-13;<a name="line.219"></a>
+<FONT color="green">220</FONT> for (double x = 0; x < 2; x += 0.2) {<a name="line.220"></a>
+<FONT color="green">221</FONT> DerivativeStructure dsX = new DerivativeStructure(3, 5, 0, x);<a name="line.221"></a>
+<FONT color="green">222</FONT> for (double y = 0; y < 2; y += 0.2) {<a name="line.222"></a>
+<FONT color="green">223</FONT> DerivativeStructure dsY = new DerivativeStructure(3, 5, 1, y);<a name="line.223"></a>
+<FONT color="green">224</FONT> for (double z = 0; z >- 2; z -= 0.2) {<a name="line.224"></a>
+<FONT color="green">225</FONT> DerivativeStructure dsZ = new DerivativeStructure(3, 5, 2, z);<a name="line.225"></a>
+<FONT color="green">226</FONT> <a name="line.226"></a>
+<FONT color="green">227</FONT> // f(x, y, z) = x + 5 x y - 2 z + (8 z x - y)^3<a name="line.227"></a>
+<FONT color="green">228</FONT> DerivativeStructure ds =<a name="line.228"></a>
<FONT color="green">229</FONT> new DerivativeStructure(1, dsX,<a name="line.229"></a>
<FONT color="green">230</FONT> 5, dsX.multiply(dsY),<a name="line.230"></a>
-<FONT color="green">231</FONT> -2, dsZ).add(new DerivativeStructure(8, dsZ.multiply(dsX),<a name="line.231"></a>
-<FONT color="green">232</FONT> -1, dsY).pow(3));<a name="line.232"></a>
-<FONT color="green">233</FONT> double f = x + 5 * x * y - 2 * z + FastMath.pow(8 * z * x - y, 3);<a name="line.233"></a>
-<FONT color="green">234</FONT> Assert.assertEquals(f, ds.getValue(),<a name="line.234"></a>
-<FONT color="green">235</FONT> FastMath.abs(epsilon * f));<a name="line.235"></a>
-<FONT color="green">236</FONT> Assert.assertEquals(f, dsOther.getValue(),<a name="line.236"></a>
-<FONT color="green">237</FONT> FastMath.abs(epsilon * f));<a name="line.237"></a>
-<FONT color="green">238</FONT> <a name="line.238"></a>
-<FONT color="green">239</FONT> // df/dx = 1 + 5 y + 24 (8 z x - y)^2 z<a name="line.239"></a>
-<FONT color="green">240</FONT> double dfdx = 1 + 5 * y + 24 * z * FastMath.pow(8 * z * x - y, 2);<a name="line.240"></a>
-<FONT color="green">241</FONT> Assert.assertEquals(dfdx, ds.getPartialDerivative(1, 0, 0),<a name="line.241"></a>
-<FONT color="green">242</FONT> FastMath.abs(epsilon * dfdx));<a name="line.242"></a>
-<FONT color="green">243</FONT> Assert.assertEquals(dfdx, dsOther.getPartialDerivative(1, 0, 0),<a name="line.243"></a>
-<FONT color="green">244</FONT> FastMath.abs(epsilon * dfdx));<a name="line.244"></a>
-<FONT color="green">245</FONT> <a name="line.245"></a>
-<FONT color="green">246</FONT> // df/dxdy = 5 + 48 z*(y - 8 z x)<a name="line.246"></a>
-<FONT color="green">247</FONT> double dfdxdy = 5 + 48 * z * (y - 8 * z * x);<a name="line.247"></a>
-<FONT color="green">248</FONT> Assert.assertEquals(dfdxdy, ds.getPartialDerivative(1, 1, 0),<a name="line.248"></a>
-<FONT color="green">249</FONT> FastMath.abs(epsilon * dfdxdy));<a name="line.249"></a>
-<FONT color="green">250</FONT> Assert.assertEquals(dfdxdy, dsOther.getPartialDerivative(1, 1, 0),<a name="line.250"></a>
-<FONT color="green">251</FONT> FastMath.abs(epsilon * dfdxdy));<a name="line.251"></a>
-<FONT color="green">252</FONT> <a name="line.252"></a>
-<FONT color="green">253</FONT> // df/dxdydz = 48 (y - 16 z x)<a name="line.253"></a>
-<FONT color="green">254</FONT> double dfdxdydz = 48 * (y - 16 * z * x);<a name="line.254"></a>
-<FONT color="green">255</FONT> Assert.assertEquals(dfdxdydz, ds.getPartialDerivative(1, 1, 1),<a name="line.255"></a>
-<FONT color="green">256</FONT> FastMath.abs(epsilon * dfdxdydz));<a name="line.256"></a>
-<FONT color="green">257</FONT> Assert.assertEquals(dfdxdydz, dsOther.getPartialDerivative(1, 1, 1),<a name="line.257"></a>
-<FONT color="green">258</FONT> FastMath.abs(epsilon * dfdxdydz));<a name="line.258"></a>
-<FONT color="green">259</FONT> <a name="line.259"></a>
-<FONT color="green">260</FONT> }<a name="line.260"></a>
-<FONT color="green">261</FONT> <a name="line.261"></a>
-<FONT color="green">262</FONT> }<a name="line.262"></a>
-<FONT color="green">263</FONT> }<a name="line.263"></a>
-<FONT color="green">264</FONT> }<a name="line.264"></a>
+<FONT color="green">231</FONT> -2, dsZ,<a name="line.231"></a>
+<FONT color="green">232</FONT> 1, new DerivativeStructure(8, dsZ.multiply(dsX),<a name="line.232"></a>
+<FONT color="green">233</FONT> -1, dsY).pow(3));<a name="line.233"></a>
+<FONT color="green">234</FONT> DerivativeStructure dsOther =<a name="line.234"></a>
+<FONT color="green">235</FONT> new DerivativeStructure(1, dsX,<a name="line.235"></a>
+<FONT color="green">236</FONT> 5, dsX.multiply(dsY),<a name="line.236"></a>
+<FONT color="green">237</FONT> -2, dsZ).add(new DerivativeStructure(8, dsZ.multiply(dsX),<a name="line.237"></a>
+<FONT color="green">238</FONT> -1, dsY).pow(3));<a name="line.238"></a>
+<FONT color="green">239</FONT> double f = x + 5 * x * y - 2 * z + FastMath.pow(8 * z * x - y, 3);<a name="line.239"></a>
+<FONT color="green">240</FONT> Assert.assertEquals(f, ds.getValue(),<a name="line.240"></a>
+<FONT color="green">241</FONT> FastMath.abs(epsilon * f));<a name="line.241"></a>
+<FONT color="green">242</FONT> Assert.assertEquals(f, dsOther.getValue(),<a name="line.242"></a>
+<FONT color="green">243</FONT> FastMath.abs(epsilon * f));<a name="line.243"></a>
+<FONT color="green">244</FONT> <a name="line.244"></a>
+<FONT color="green">245</FONT> // df/dx = 1 + 5 y + 24 (8 z x - y)^2 z<a name="line.245"></a>
+<FONT color="green">246</FONT> double dfdx = 1 + 5 * y + 24 * z * FastMath.pow(8 * z * x - y, 2);<a name="line.246"></a>
+<FONT color="green">247</FONT> Assert.assertEquals(dfdx, ds.getPartialDerivative(1, 0, 0),<a name="line.247"></a>
+<FONT color="green">248</FONT> FastMath.abs(epsilon * dfdx));<a name="line.248"></a>
+<FONT color="green">249</FONT> Assert.assertEquals(dfdx, dsOther.getPartialDerivative(1, 0, 0),<a name="line.249"></a>
+<FONT color="green">250</FONT> FastMath.abs(epsilon * dfdx));<a name="line.250"></a>
+<FONT color="green">251</FONT> <a name="line.251"></a>
+<FONT color="green">252</FONT> // df/dxdy = 5 + 48 z*(y - 8 z x)<a name="line.252"></a>
+<FONT color="green">253</FONT> double dfdxdy = 5 + 48 * z * (y - 8 * z * x);<a name="line.253"></a>
+<FONT color="green">254</FONT> Assert.assertEquals(dfdxdy, ds.getPartialDerivative(1, 1, 0),<a name="line.254"></a>
+<FONT color="green">255</FONT> FastMath.abs(epsilon * dfdxdy));<a name="line.255"></a>
+<FONT color="green">256</FONT> Assert.assertEquals(dfdxdy, dsOther.getPartialDerivative(1, 1, 0),<a name="line.256"></a>
+<FONT color="green">257</FONT> FastMath.abs(epsilon * dfdxdy));<a name="line.257"></a>
+<FONT color="green">258</FONT> <a name="line.258"></a>
+<FONT color="green">259</FONT> // df/dxdydz = 48 (y - 16 z x)<a name="line.259"></a>
+<FONT color="green">260</FONT> double dfdxdydz = 48 * (y - 16 * z * x);<a name="line.260"></a>
+<FONT color="green">261</FONT> Assert.assertEquals(dfdxdydz, ds.getPartialDerivative(1, 1, 1),<a name="line.261"></a>
+<FONT color="green">262</FONT> FastMath.abs(epsilon * dfdxdydz));<a name="line.262"></a>
+<FONT color="green">263</FONT> Assert.assertEquals(dfdxdydz, dsOther.getPartialDerivative(1, 1, 1),<a name="line.263"></a>
+<FONT color="green">264</FONT> FastMath.abs(epsilon * dfdxdydz));<a name="line.264"></a>
<FONT color="green">265</FONT> <a name="line.265"></a>
-<FONT color="green">266</FONT> @Test<a name="line.266"></a>
-<FONT color="green">267</FONT> public void testCompositionOneVariableX() {<a name="line.267"></a>
-<FONT color="green">268</FONT> double epsilon = 1.0e-13;<a name="line.268"></a>
-<FONT color="green">269</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.269"></a>
-<FONT color="green">270</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.270"></a>
-<FONT color="green">271</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.271"></a>
-<FONT color="green">272</FONT> for (double y = 0.1; y < 1.2; y += 0.1) {<a name="line.272"></a>
-<FONT color="green">273</FONT> DerivativeStructure dsY = new DerivativeStructure(1, maxOrder, y);<a name="line.273"></a>
-<FONT color="green">274</FONT> DerivativeStructure f = dsX.divide(dsY).sqrt();<a name="line.274"></a>
-<FONT color="green">275</FONT> double f0 = FastMath.sqrt(x / y);<a name="line.275"></a>
-<FONT color="green">276</FONT> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));<a name="line.276"></a>
-<FONT color="green">277</FONT> if (f.getOrder() > 0) {<a name="line.277"></a>
-<FONT color="green">278</FONT> double f1 = 1 / (2 * FastMath.sqrt(x * y));<a name="line.278"></a>
-<FONT color="green">279</FONT> Assert.assertEquals(f1, f.getPartialDerivative(1), FastMath.abs(epsilon * f1));<a name="line.279"></a>
-<FONT color="green">280</FONT> if (f.getOrder() > 1) {<a name="line.280"></a>
-<FONT color="green">281</FONT> double f2 = -f1 / (2 * x); <a name="line.281"></a>
-<FONT color="green">282</FONT> Assert.assertEquals(f2, f.getPartialDerivative(2), FastMath.abs(epsilon * f2));<a name="line.282"></a>
-<FONT color="green">283</FONT> if (f.getOrder() > 2) {<a name="line.283"></a>
-<FONT color="green">284</FONT> double f3 = (f0 + x / (2 * y * f0)) / (4 * x * x * x); <a name="line.284"></a>
-<FONT color="green">285</FONT> Assert.assertEquals(f3, f.getPartialDerivative(3), FastMath.abs(epsilon * f3));<a name="line.285"></a>
-<FONT color="green">286</FONT> }<a name="line.286"></a>
-<FONT color="green">287</FONT> }<a name="line.287"></a>
-<FONT color="green">288</FONT> }<a name="line.288"></a>
-<FONT color="green">289</FONT> }<a name="line.289"></a>
-<FONT color="green">290</FONT> }<a name="line.290"></a>
-<FONT color="green">291</FONT> } <a name="line.291"></a>
-<FONT color="green">292</FONT> }<a name="line.292"></a>
-<FONT color="green">293</FONT> <a name="line.293"></a>
-<FONT color="green">294</FONT> @Test<a name="line.294"></a>
-<FONT color="green">295</FONT> public void testTrigo() {<a name="line.295"></a>
-<FONT color="green">296</FONT> double epsilon = 2.0e-12;<a name="line.296"></a>
-<FONT color="green">297</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.297"></a>
-<FONT color="green">298</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.298"></a>
-<FONT color="green">299</FONT> DerivativeStructure dsX = new DerivativeStructure(3, maxOrder, 0, x);<a name="line.299"></a>
-<FONT color="green">300</FONT> for (double y = 0.1; y < 1.2; y += 0.1) {<a name="line.300"></a>
-<FONT color="green">301</FONT> DerivativeStructure dsY = new DerivativeStructure(3, maxOrder, 1, y);<a name="line.301"></a>
-<FONT color="green">302</FONT> for (double z = 0.1; z < 1.2; z += 0.1) {<a name="line.302"></a>
-<FONT color="green">303</FONT> DerivativeStructure dsZ = new DerivativeStructure(3, maxOrder, 2, z);<a name="line.303"></a>
-<FONT color="green">304</FONT> DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();<a name="line.304"></a>
-<FONT color="green">305</FONT> double a = FastMath.cos(y) + FastMath.tan(z);<a name="line.305"></a>
-<FONT color="green">306</FONT> double f0 = FastMath.sin(x / a);<a name="line.306"></a>
-<FONT color="green">307</FONT> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));<a name="line.307"></a>
-<FONT color="green">308</FONT> if (f.getOrder() > 0) {<a name="line.308"></a>
-<FONT color="green">309</FONT> double dfdx = FastMath.cos(x / a) / a;<a name="line.309"></a>
-<FONT color="green">310</FONT> Assert.assertEquals(dfdx, f.getPartialDerivative(1, 0, 0), FastMath.abs(epsilon * dfdx));<a name="line.310"></a>
-<FONT color="green">311</FONT> double dfdy = x * FastMath.sin(y) * dfdx / a;<a name="line.311"></a>
-<FONT color="green">312</FONT> Assert.assertEquals(dfdy, f.getPartialDerivative(0, 1, 0), FastMath.abs(epsilon * dfdy));<a name="line.312"></a>
-<FONT color="green">313</FONT> double cz = FastMath.cos(z);<a name="line.313"></a>
-<FONT color="green">314</FONT> double cz2 = cz * cz;<a name="line.314"></a>
-<FONT color="green">315</FONT> double dfdz = -x * dfdx / (a * cz2);<a name="line.315"></a>
-<FONT color="green">316</FONT> Assert.assertEquals(dfdz, f.getPartialDerivative(0, 0, 1), FastMath.abs(epsilon * dfdz));<a name="line.316"></a>
-<FONT color="green">317</FONT> if (f.getOrder() > 1) {<a name="line.317"></a>
-<FONT color="green">318</FONT> double df2dx2 = -(f0 / (a * a));<a name="line.318"></a>
-<FONT color="green">319</FONT> Assert.assertEquals(df2dx2, f.getPartialDerivative(2, 0, 0), FastMath.abs(epsilon * df2dx2));<a name="line.319"></a>
-<FONT color="green">320</FONT> double df2dy2 = x * FastMath.cos(y) * dfdx / a -<a name="line.320"></a>
-<FONT color="green">321</FONT> x * x * FastMath.sin(y) * FastMath.sin(y) * f0 / (a * a * a * a) +<a name="line.321"></a>
-<FONT color="green">322</FONT> 2 * FastMath.sin(y) * dfdy / a;<a name="line.322"></a>
-<FONT color="green">323</FONT> Assert.assertEquals(df2dy2, f.getPartialDerivative(0, 2, 0), FastMath.abs(epsilon * df2dy2));<a name="line.323"></a>
-<FONT color="green">324</FONT> double c4 = cz2 * cz2;<a name="line.324"></a>
-<FONT color="green">325</FONT> double df2dz2 = x * (2 * a * (1 - a * cz * FastMath.sin(z)) * dfdx - x * f0 / a ) / (a * a * a * c4);<a name="line.325"></a>
-<FONT color="green">326</FONT> Assert.assertEquals(df2dz2, f.getPartialDerivative(0, 0, 2), FastMath.abs(epsilon * df2dz2));<a name="line.326"></a>
-<FONT color="green">327</FONT> double df2dxdy = dfdy / x - x * FastMath.sin(y) * f0 / (a * a * a);<a name="line.327"></a>
-<FONT color="green">328</FONT> Assert.assertEquals(df2dxdy, f.getPartialDerivative(1, 1, 0), FastMath.abs(epsilon * df2dxdy));<a name="line.328"></a>
-<FONT color="green">329</FONT> }<a name="line.329"></a>
-<FONT color="green">330</FONT> }<a name="line.330"></a>
-<FONT color="green">331</FONT> }<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> <a name="line.336"></a>
-<FONT color="green">337</FONT> @Test<a name="line.337"></a>
-<FONT color="green">338</FONT> public void testSqrtDefinition() {<a name="line.338"></a>
-<FONT color="green">339</FONT> double[] epsilon = new double[] { 5.0e-16, 5.0e-16, 2.0e-15, 5.0e-14, 2.0e-12 };<a name="line.339"></a>
-<FONT color="green">340</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.340"></a>
-<FONT color="green">341</FONT> for (double x = 0.1; x < 1.2; x += 0.001) {<a name="line.341"></a>
-<FONT color="green">342</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.342"></a>
-<FONT color="green">343</FONT> DerivativeStructure sqrt1 = dsX.pow(0.5);<a name="line.343"></a>
-<FONT color="green">344</FONT> DerivativeStructure sqrt2 = dsX.sqrt();<a name="line.344"></a>
-<FONT color="green">345</FONT> DerivativeStructure zero = sqrt1.subtract(sqrt2);<a name="line.345"></a>
-<FONT color="green">346</FONT> for (int n = 0; n <= maxOrder; ++n) {<a name="line.346"></a>
-<FONT color="green">347</FONT> Assert.assertEquals(0, zero.getPartialDerivative(n), epsilon[n]);<a name="line.347"></a>
-<FONT color="green">348</FONT> }<a name="line.348"></a>
-<FONT color="green">349</FONT> }<a name="line.349"></a>
-<FONT color="green">350</FONT> }<a name="line.350"></a>
-<FONT color="green">351</FONT> }<a name="line.351"></a>
-<FONT color="green">352</FONT> <a name="line.352"></a>
-<FONT color="green">353</FONT> @Test<a name="line.353"></a>
-<FONT color="green">354</FONT> public void testRootNSingularity() {<a name="line.354"></a>
-<FONT color="green">355</FONT> for (int n = 2; n < 10; ++n) {<a name="line.355"></a>
-<FONT color="green">356</FONT> for (int maxOrder = 0; maxOrder < 12; ++maxOrder) {<a name="line.356"></a>
-<FONT color="green">357</FONT> DerivativeStructure dsZero = new DerivativeStructure(1, maxOrder, 0, 0.0);<a name="line.357"></a>
-<FONT color="green">358</FONT> DerivativeStructure rootN = dsZero.rootN(n);<a name="line.358"></a>
-<FONT color="green">359</FONT> Assert.assertEquals(0.0, rootN.getValue(), 1.0e-20);<a name="line.359"></a>
-<FONT color="green">360</FONT> if (maxOrder > 0) {<a name="line.360"></a>
-<FONT color="green">361</FONT> Assert.assertTrue(Double.isInfinite(rootN.getPartialDerivative(1)));<a name="line.361"></a>
-<FONT color="green">362</FONT> Assert.assertTrue(rootN.getPartialDerivative(1) > 0);<a name="line.362"></a>
-<FONT color="green">363</FONT> for (int order = 2; order <= maxOrder; ++order) {<a name="line.363"></a>
-<FONT color="green">364</FONT> // the following checks shows a LIMITATION of the current implementation<a name="line.364"></a>
-<FONT color="green">365</FONT> // we have no way to tell dsZero is a pure linear variable x = 0<a name="line.365"></a>
-<FONT color="green">366</FONT> // we only say: "dsZero is a structure with value = 0.0,<a name="line.366"></a>
-<FONT color="green">367</FONT> // first derivative = 1.0, second and higher derivatives = 0.0".<a name="line.367"></a>
-<FONT color="green">368</FONT> // Function composition rule for second derivatives is:<a name="line.368"></a>
-<FONT color="green">369</FONT> // d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)<a name="line.369"></a>
-<FONT color="green">370</FONT> // when function f is the nth root and x = 0 we have:<a name="line.370"></a>
-<FONT color="green">371</FONT> // f(0) = 0, f'(0) = +infinity, f''(0) = -infinity (and higher<a name="line.371"></a>
-<FONT color="green">372</FONT> // derivatives keep switching between +infinity and -infinity)<a name="line.372"></a>
-<FONT color="green">373</FONT> // so given that in our case dsZero represents g, we have g(x) = 0,<a name="line.373"></a>
-<FONT color="green">374</FONT> // g'(x) = 1 and g''(x) = 0<a name="line.374"></a>
-<FONT color="green">375</FONT> // applying the composition rules gives:<a name="line.375"></a>
-<FONT color="green">376</FONT> // d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)<a name="line.376"></a>
-<FONT color="green">377</FONT> // = -infinity * 1^2 + +infinity * 0<a name="line.377"></a>
-<FONT color="green">378</FONT> // = -infinity + NaN<a name="line.378"></a>
-<FONT color="green">379</FONT> // = NaN<a name="line.379"></a>
-<FONT color="green">380</FONT> // if we knew dsZero is really the x variable and not the identity<a name="line.380"></a>
-<FONT color="green">381</FONT> // function applied to x, we would not have computed f'(g(x)) * g''(x)<a name="line.381"></a>
-<FONT color="green">382</FONT> // and we would have found that the result was -infinity and not NaN<a name="line.382"></a>
-<FONT color="green">383</FONT> Assert.assertTrue(Double.isNaN(rootN.getPartialDerivative(order)));<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> // the following shows that the limitation explained above is NOT a bug...<a name="line.387"></a>
-<FONT color="green">388</FONT> // if we set up the higher order derivatives for g appropriately, we do<a name="line.388"></a>
-<FONT color="green">389</FONT> // compute the higher order derivatives of the composition correctly<a name="line.389"></a>
-<FONT color="green">390</FONT> double[] gDerivatives = new double[ 1 + maxOrder];<a name="line.390"></a>
-<FONT color="green">391</FONT> gDerivatives[0] = 0.0;<a name="line.391"></a>
-<FONT color="green">392</FONT> for (int k = 1; k <= maxOrder; ++k) {<a name="line.392"></a>
-<FONT color="green">393</FONT> gDerivatives[k] = FastMath.pow(-1.0, k + 1);<a name="line.393"></a>
-<FONT color="green">394</FONT> }<a name="line.394"></a>
-<FONT color="green">395</FONT> DerivativeStructure correctRoot = new DerivativeStructure(1, maxOrder, gDerivatives).rootN(n);<a name="line.395"></a>
-<FONT color="green">396</FONT> Assert.assertEquals(0.0, correctRoot.getValue(), 1.0e-20);<a name="line.396"></a>
-<FONT color="green">397</FONT> if (maxOrder > 0) {<a name="line.397"></a>
-<FONT color="green">398</FONT> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(1)));<a name="line.398"></a>
-<FONT color="green">399</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(1) > 0);<a name="line.399"></a>
-<FONT color="green">400</FONT> for (int order = 2; order <= maxOrder; ++order) {<a name="line.400"></a>
-<FONT color="green">401</FONT> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(order)));<a name="line.401"></a>
-<FONT color="green">402</FONT> if ((order % 2) == 0) {<a name="line.402"></a>
-<FONT color="green">403</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(order) < 0);<a name="line.403"></a>
-<FONT color="green">404</FONT> } else {<a name="line.404"></a>
-<FONT color="green">405</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(order) > 0);<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> <a name="line.411"></a>
-<FONT color="green">412</FONT> }<a name="line.412"></a>
-<FONT color="green">413</FONT> <a name="line.413"></a>
-<FONT color="green">414</FONT> }<a name="line.414"></a>
+<FONT color="green">266</FONT> }<a name="line.266"></a>
+<FONT color="green">267</FONT> <a name="line.267"></a>
+<FONT color="green">268</FONT> }<a name="line.268"></a>
+<FONT color="green">269</FONT> }<a name="line.269"></a>
+<FONT color="green">270</FONT> }<a name="line.270"></a>
+<FONT color="green">271</FONT> <a name="line.271"></a>
+<FONT color="green">272</FONT> @Test<a name="line.272"></a>
+<FONT color="green">273</FONT> public void testCompositionOneVariableX() {<a name="line.273"></a>
+<FONT color="green">274</FONT> double epsilon = 1.0e-13;<a name="line.274"></a>
+<FONT color="green">275</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.275"></a>
+<FONT color="green">276</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.276"></a>
+<FONT color="green">277</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.277"></a>
+<FONT color="green">278</FONT> for (double y = 0.1; y < 1.2; y += 0.1) {<a name="line.278"></a>
+<FONT color="green">279</FONT> DerivativeStructure dsY = new DerivativeStructure(1, maxOrder, y);<a name="line.279"></a>
+<FONT color="green">280</FONT> DerivativeStructure f = dsX.divide(dsY).sqrt();<a name="line.280"></a>
+<FONT color="green">281</FONT> double f0 = FastMath.sqrt(x / y);<a name="line.281"></a>
+<FONT color="green">282</FONT> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));<a name="line.282"></a>
+<FONT color="green">283</FONT> if (f.getOrder() > 0) {<a name="line.283"></a>
+<FONT color="green">284</FONT> double f1 = 1 / (2 * FastMath.sqrt(x * y));<a name="line.284"></a>
+<FONT color="green">285</FONT> Assert.assertEquals(f1, f.getPartialDerivative(1), FastMath.abs(epsilon * f1));<a name="line.285"></a>
+<FONT color="green">286</FONT> if (f.getOrder() > 1) {<a name="line.286"></a>
+<FONT color="green">287</FONT> double f2 = -f1 / (2 * x); <a name="line.287"></a>
+<FONT color="green">288</FONT> Assert.assertEquals(f2, f.getPartialDerivative(2), FastMath.abs(epsilon * f2));<a name="line.288"></a>
+<FONT color="green">289</FONT> if (f.getOrder() > 2) {<a name="line.289"></a>
+<FONT color="green">290</FONT> double f3 = (f0 + x / (2 * y * f0)) / (4 * x * x * x); <a name="line.290"></a>
+<FONT color="green">291</FONT> Assert.assertEquals(f3, f.getPartialDerivative(3), FastMath.abs(epsilon * f3));<a name="line.291"></a>
+<FONT color="green">292</FONT> }<a name="line.292"></a>
+<FONT color="green">293</FONT> }<a name="line.293"></a>
+<FONT color="green">294</FONT> }<a name="line.294"></a>
+<FONT color="green">295</FONT> }<a name="line.295"></a>
+<FONT color="green">296</FONT> }<a name="line.296"></a>
+<FONT color="green">297</FONT> } <a name="line.297"></a>
+<FONT color="green">298</FONT> }<a name="line.298"></a>
+<FONT color="green">299</FONT> <a name="line.299"></a>
+<FONT color="green">300</FONT> @Test<a name="line.300"></a>
+<FONT color="green">301</FONT> public void testTrigo() {<a name="line.301"></a>
+<FONT color="green">302</FONT> double epsilon = 2.0e-12;<a name="line.302"></a>
+<FONT color="green">303</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.303"></a>
+<FONT color="green">304</FONT> for (double x = 0.1; x < 1.2; x += 0.1) {<a name="line.304"></a>
+<FONT color="green">305</FONT> DerivativeStructure dsX = new DerivativeStructure(3, maxOrder, 0, x);<a name="line.305"></a>
+<FONT color="green">306</FONT> for (double y = 0.1; y < 1.2; y += 0.1) {<a name="line.306"></a>
+<FONT color="green">307</FONT> DerivativeStructure dsY = new DerivativeStructure(3, maxOrder, 1, y);<a name="line.307"></a>
+<FONT color="green">308</FONT> for (double z = 0.1; z < 1.2; z += 0.1) {<a name="line.308"></a>
+<FONT color="green">309</FONT> DerivativeStructure dsZ = new DerivativeStructure(3, maxOrder, 2, z);<a name="line.309"></a>
+<FONT color="green">310</FONT> DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();<a name="line.310"></a>
+<FONT color="green">311</FONT> double a = FastMath.cos(y) + FastMath.tan(z);<a name="line.311"></a>
+<FONT color="green">312</FONT> double f0 = FastMath.sin(x / a);<a name="line.312"></a>
+<FONT color="green">313</FONT> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));<a name="line.313"></a>
+<FONT color="green">314</FONT> if (f.getOrder() > 0) {<a name="line.314"></a>
+<FONT color="green">315</FONT> double dfdx = FastMath.cos(x / a) / a;<a name="line.315"></a>
+<FONT color="green">316</FONT> Assert.assertEquals(dfdx, f.getPartialDerivative(1, 0, 0), FastMath.abs(epsilon * dfdx));<a name="line.316"></a>
+<FONT color="green">317</FONT> double dfdy = x * FastMath.sin(y) * dfdx / a;<a name="line.317"></a>
+<FONT color="green">318</FONT> Assert.assertEquals(dfdy, f.getPartialDerivative(0, 1, 0), FastMath.abs(epsilon * dfdy));<a name="line.318"></a>
+<FONT color="green">319</FONT> double cz = FastMath.cos(z);<a name="line.319"></a>
+<FONT color="green">320</FONT> double cz2 = cz * cz;<a name="line.320"></a>
+<FONT color="green">321</FONT> double dfdz = -x * dfdx / (a * cz2);<a name="line.321"></a>
+<FONT color="green">322</FONT> Assert.assertEquals(dfdz, f.getPartialDerivative(0, 0, 1), FastMath.abs(epsilon * dfdz));<a name="line.322"></a>
+<FONT color="green">323</FONT> if (f.getOrder() > 1) {<a name="line.323"></a>
+<FONT color="green">324</FONT> double df2dx2 = -(f0 / (a * a));<a name="line.324"></a>
+<FONT color="green">325</FONT> Assert.assertEquals(df2dx2, f.getPartialDerivative(2, 0, 0), FastMath.abs(epsilon * df2dx2));<a name="line.325"></a>
+<FONT color="green">326</FONT> double df2dy2 = x * FastMath.cos(y) * dfdx / a -<a name="line.326"></a>
+<FONT color="green">327</FONT> x * x * FastMath.sin(y) * FastMath.sin(y) * f0 / (a * a * a * a) +<a name="line.327"></a>
+<FONT color="green">328</FONT> 2 * FastMath.sin(y) * dfdy / a;<a name="line.328"></a>
+<FONT color="green">329</FONT> Assert.assertEquals(df2dy2, f.getPartialDerivative(0, 2, 0), FastMath.abs(epsilon * df2dy2));<a name="line.329"></a>
+<FONT color="green">330</FONT> double c4 = cz2 * cz2;<a name="line.330"></a>
+<FONT color="green">331</FONT> double df2dz2 = x * (2 * a * (1 - a * cz * FastMath.sin(z)) * dfdx - x * f0 / a ) / (a * a * a * c4);<a name="line.331"></a>
+<FONT color="green">332</FONT> Assert.assertEquals(df2dz2, f.getPartialDerivative(0, 0, 2), FastMath.abs(epsilon * df2dz2));<a name="line.332"></a>
+<FONT color="green">333</FONT> double df2dxdy = dfdy / x - x * FastMath.sin(y) * f0 / (a * a * a);<a name="line.333"></a>
+<FONT color="green">334</FONT> Assert.assertEquals(df2dxdy, f.getPartialDerivative(1, 1, 0), FastMath.abs(epsilon * df2dxdy));<a name="line.334"></a>
+<FONT color="green">335</FONT> }<a name="line.335"></a>
+<FONT color="green">336</FONT> }<a name="line.336"></a>
+<FONT color="green">337</FONT> }<a name="line.337"></a>
+<FONT color="green">338</FONT> }<a name="line.338"></a>
+<FONT color="green">339</FONT> } <a name="line.339"></a>
+<FONT color="green">340</FONT> }<a name="line.340"></a>
+<FONT color="green">341</FONT> }<a name="line.341"></a>
+<FONT color="green">342</FONT> <a name="line.342"></a>
+<FONT color="green">343</FONT> @Test<a name="line.343"></a>
+<FONT color="green">344</FONT> public void testSqrtDefinition() {<a name="line.344"></a>
+<FONT color="green">345</FONT> double[] epsilon = new double[] { 5.0e-16, 5.0e-16, 2.0e-15, 5.0e-14, 2.0e-12 };<a name="line.345"></a>
+<FONT color="green">346</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.346"></a>
+<FONT color="green">347</FONT> for (double x = 0.1; x < 1.2; x += 0.001) {<a name="line.347"></a>
+<FONT color="green">348</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.348"></a>
+<FONT color="green">349</FONT> DerivativeStructure sqrt1 = dsX.pow(0.5);<a name="line.349"></a>
+<FONT color="green">350</FONT> DerivativeStructure sqrt2 = dsX.sqrt();<a name="line.350"></a>
+<FONT color="green">351</FONT> DerivativeStructure zero = sqrt1.subtract(sqrt2);<a name="line.351"></a>
+<FONT color="green">352</FONT> for (int n = 0; n <= maxOrder; ++n) {<a name="line.352"></a>
+<FONT color="green">353</FONT> Assert.assertEquals(0, zero.getPartialDerivative(n), epsilon[n]);<a name="line.353"></a>
+<FONT color="green">354</FONT> }<a name="line.354"></a>
+<FONT color="green">355</FONT> }<a name="line.355"></a>
+<FONT color="green">356</FONT> }<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> @Test<a name="line.359"></a>
+<FONT color="green">360</FONT> public void testRootNSingularity() {<a name="line.360"></a>
+<FONT color="green">361</FONT> for (int n = 2; n < 10; ++n) {<a name="line.361"></a>
+<FONT color="green">362</FONT> for (int maxOrder = 0; maxOrder < 12; ++maxOrder) {<a name="line.362"></a>
+<FONT color="green">363</FONT> DerivativeStructure dsZero = new DerivativeStructure(1, maxOrder, 0, 0.0);<a name="line.363"></a>
+<FONT color="green">364</FONT> DerivativeStructure rootN = dsZero.rootN(n);<a name="line.364"></a>
+<FONT color="green">365</FONT> Assert.assertEquals(0.0, rootN.getValue(), 1.0e-20);<a name="line.365"></a>
+<FONT color="green">366</FONT> if (maxOrder > 0) {<a name="line.366"></a>
+<FONT color="green">367</FONT> Assert.assertTrue(Double.isInfinite(rootN.getPartialDerivative(1)));<a name="line.367"></a>
+<FONT color="green">368</FONT> Assert.assertTrue(rootN.getPartialDerivative(1) > 0);<a name="line.368"></a>
+<FONT color="green">369</FONT> for (int order = 2; order <= maxOrder; ++order) {<a name="line.369"></a>
+<FONT color="green">370</FONT> // the following checks shows a LIMITATION of the current implementation<a name="line.370"></a>
+<FONT color="green">371</FONT> // we have no way to tell dsZero is a pure linear variable x = 0<a name="line.371"></a>
+<FONT color="green">372</FONT> // we only say: "dsZero is a structure with value = 0.0,<a name="line.372"></a>
+<FONT color="green">373</FONT> // first derivative = 1.0, second and higher derivatives = 0.0".<a name="line.373"></a>
+<FONT color="green">374</FONT> // Function composition rule for second derivatives is:<a name="line.374"></a>
+<FONT color="green">375</FONT> // d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)<a name="line.375"></a>
+<FONT color="green">376</FONT> // when function f is the nth root and x = 0 we have:<a name="line.376"></a>
+<FONT color="green">377</FONT> // f(0) = 0, f'(0) = +infinity, f''(0) = -infinity (and higher<a name="line.377"></a>
+<FONT color="green">378</FONT> // derivatives keep switching between +infinity and -infinity)<a name="line.378"></a>
+<FONT color="green">379</FONT> // so given that in our case dsZero represents g, we have g(x) = 0,<a name="line.379"></a>
+<FONT color="green">380</FONT> // g'(x) = 1 and g''(x) = 0<a name="line.380"></a>
+<FONT color="green">381</FONT> // applying the composition rules gives:<a name="line.381"></a>
+<FONT color="green">382</FONT> // d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)<a name="line.382"></a>
+<FONT color="green">383</FONT> // = -infinity * 1^2 + +infinity * 0<a name="line.383"></a>
+<FONT color="green">384</FONT> // = -infinity + NaN<a name="line.384"></a>
+<FONT color="green">385</FONT> // = NaN<a name="line.385"></a>
+<FONT color="green">386</FONT> // if we knew dsZero is really the x variable and not the identity<a name="line.386"></a>
+<FONT color="green">387</FONT> // function applied to x, we would not have computed f'(g(x)) * g''(x)<a name="line.387"></a>
+<FONT color="green">388</FONT> // and we would have found that the result was -infinity and not NaN<a name="line.388"></a>
+<FONT color="green">389</FONT> Assert.assertTrue(Double.isNaN(rootN.getPartialDerivative(order)));<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> <a name="line.392"></a>
+<FONT color="green">393</FONT> // the following shows that the limitation explained above is NOT a bug...<a name="line.393"></a>
+<FONT color="green">394</FONT> // if we set up the higher order derivatives for g appropriately, we do<a name="line.394"></a>
+<FONT color="green">395</FONT> // compute the higher order derivatives of the composition correctly<a name="line.395"></a>
+<FONT color="green">396</FONT> double[] gDerivatives = new double[ 1 + maxOrder];<a name="line.396"></a>
+<FONT color="green">397</FONT> gDerivatives[0] = 0.0;<a name="line.397"></a>
+<FONT color="green">398</FONT> for (int k = 1; k <= maxOrder; ++k) {<a name="line.398"></a>
+<FONT color="green">399</FONT> gDerivatives[k] = FastMath.pow(-1.0, k + 1);<a name="line.399"></a>
+<FONT color="green">400</FONT> }<a name="line.400"></a>
+<FONT color="green">401</FONT> DerivativeStructure correctRoot = new DerivativeStructure(1, maxOrder, gDerivatives).rootN(n);<a name="line.401"></a>
+<FONT color="green">402</FONT> Assert.assertEquals(0.0, correctRoot.getValue(), 1.0e-20);<a name="line.402"></a>
+<FONT color="green">403</FONT> if (maxOrder > 0) {<a name="line.403"></a>
+<FONT color="green">404</FONT> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(1)));<a name="line.404"></a>
+<FONT color="green">405</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(1) > 0);<a name="line.405"></a>
+<FONT color="green">406</FONT> for (int order = 2; order <= maxOrder; ++order) {<a name="line.406"></a>
+<FONT color="green">407</FONT> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(order)));<a name="line.407"></a>
+<FONT color="green">408</FONT> if ((order % 2) == 0) {<a name="line.408"></a>
+<FONT color="green">409</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(order) < 0);<a name="line.409"></a>
+<FONT color="green">410</FONT> } else {<a name="line.410"></a>
+<FONT color="green">411</FONT> Assert.assertTrue(correctRoot.getPartialDerivative(order) > 0);<a name="line.411"></a>
+<FONT color="green">412</FONT> }<a name="line.412"></a>
+<FONT color="green">413</FONT> }<a name="line.413"></a>
+<FONT color="green">414</FONT> }<a name="line.414"></a>
<FONT color="green">415</FONT> <a name="line.415"></a>
-<FONT color="green">416</FONT> @Test<a name="line.416"></a>
-<FONT color="green">417</FONT> public void testSqrtPow2() {<a name="line.417"></a>
-<FONT color="green">418</FONT> double[] epsilon = new double[] { 1.0e-16, 3.0e-16, 2.0e-15, 6.0e-14, 6.0e-12 };<a name="line.418"></a>
-<FONT color="green">419</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.419"></a>
-<FONT color="green">420</FONT> for (double x = 0.1; x < 1.2; x += 0.001) {<a name="line.420"></a>
-<FONT color="green">421</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.421"></a>
-<FONT color="green">422</FONT> DerivativeStructure rebuiltX = dsX.multiply(dsX).sqrt();<a name="line.422"></a>
-<FONT color="green">423</FONT> DerivativeStructure zero = rebuiltX.subtract(dsX);<a name="line.423"></a>
-<FONT color="green">424</FONT> for (int n = 0; n <= maxOrder; ++n) {<a name="line.424"></a>
-<FONT color="green">425</FONT> Assert.assertEquals(0.0, zero.getPartialDerivative(n), epsilon[n]);<a name="line.425"></a>
-<FONT color="green">426</FONT> }<a name="line.426"></a>
-<FONT color="green">427</FONT> }<a name="line.427"></a>
-<FONT color="green">428</FONT> }<a name="line.428"></a>
-<FONT color="green">429</FONT> }<a name="line.429"></a>
-<FONT color="green">430</FONT> <a name="line.430"></a>
-<FONT color="green">431</FONT> @Test<a name="line.431"></a>
-<FONT color="green">432</FONT> public void testCbrtDefinition() {<a name="line.432"></a>
-<FONT color="green">433</FONT> double[] epsilon = new double[] { 4.0e-16, 9.0e-16, 6.0e-15, 2.0e-13, 4.0e-12 };<a name="line.433"></a>
-<FONT color="green">434</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.434"></a>
-<FONT color="green">435</FONT> for (double x = 0.1; x < 1.2; x += 0.001) {<a name="line.435"></a>
-<FONT color="green">436</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.436"></a>
-<FONT color="green">437</FONT> DerivativeStructure cbrt1 = dsX.pow(1.0 / 3.0);<a name="line.437"></a>
-<FONT color="green">438</FONT> DerivativeStructure cbrt2 = dsX.cbrt();<a name="line.438"></a>
-<FONT color="green">439</FONT> DerivativeStructure zero = cbrt1.subtract(cbrt2);<a name="line.439"></a>
-<FONT color="green">440</FONT> for (int n = 0; n <= maxOrder; ++n) {<a name="line.440"></a>
-<FONT color="green">441</FONT> Assert.assertEquals(0, zero.getPartialDerivative(n), epsilon[n]);<a name="line.441"></a>
-<FONT color="green">442</FONT> }<a name="line.442"></a>
-<FONT color="green">443</FONT> }<a name="line.443"></a>
-<FONT color="green">444</FONT> }<a name="line.444"></a>
-<FONT color="green">445</FONT> }<a name="line.445"></a>
-<FONT color="green">446</FONT> <a name="line.446"></a>
-<FONT color="green">447</FONT> @Test<a name="line.447"></a>
-<FONT color="green">448</FONT> public void testCbrtPow3() {<a name="line.448"></a>
-<FONT color="green">449</FONT> double[] epsilon = new double[] { 1.0e-16, 5.0e-16, 8.0e-15, 3.0e-13, 4.0e-11 };<a name="line.449"></a>
-<FONT color="green">450</FONT> for (int maxOrder = 0; maxOrder < 5; ++maxOrder) {<a name="line.450"></a>
-<FONT color="green">451</FONT> for (double x = 0.1; x < 1.2; x += 0.001) {<a name="line.451"></a>
-<FONT color="green">452</FONT> DerivativeStructure dsX = new DerivativeStructure(1, maxOrder, 0, x);<a name="line.452"></a>
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