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Posted to commits@commons.apache.org by lu...@apache.org on 2013/04/07 09:52:13 UTC
svn commit: r857590 [3/48] - in
/websites/production/commons/content/proper/commons-math/xref-test: ./
org/apache/commons/math3/ org/apache/commons/math3/analysis/
org/apache/commons/math3/analysis/differentiation/
org/apache/commons/math3/analysis/fun...
Modified: websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html (original)
+++ websites/production/commons/content/proper/commons-math/xref-test/org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html Sun Apr 7 07:52:05 2013
@@ -30,1237 +30,1465 @@
<a class="jxr_linenumber" name="20" href="#20">20</a> <strong class="jxr_keyword">import</strong> java.util.Arrays;
<a class="jxr_linenumber" name="21" href="#21">21</a> <strong class="jxr_keyword">import</strong> java.util.List;
<a class="jxr_linenumber" name="22" href="#22">22</a>
-<a class="jxr_linenumber" name="23" href="#23">23</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.TestUtils;
-<a class="jxr_linenumber" name="24" href="#24">24</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
-<a class="jxr_linenumber" name="25" href="#25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.DimensionMismatchException;
-<a class="jxr_linenumber" name="26" href="#26">26</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.NumberIsTooLargeException;
-<a class="jxr_linenumber" name="27" href="#27">27</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.ArithmeticUtils;
-<a class="jxr_linenumber" name="28" href="#28">28</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
-<a class="jxr_linenumber" name="29" href="#29">29</a> <strong class="jxr_keyword">import</strong> org.junit.Assert;
-<a class="jxr_linenumber" name="30" href="#30">30</a> <strong class="jxr_keyword">import</strong> org.junit.Test;
-<a class="jxr_linenumber" name="31" href="#31">31</a>
-<a class="jxr_linenumber" name="32" href="#32">32</a> <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="33" href="#33">33</a> <em class="jxr_javadoccomment"> * Test for class {@link DerivativeStructure}.</em>
-<a class="jxr_linenumber" name="34" href="#34">34</a> <em class="jxr_javadoccomment"> */</em>
-<a class="jxr_linenumber" name="35" href="#35">35</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html">DerivativeStructureTest</a> {
-<a class="jxr_linenumber" name="36" href="#36">36</a>
-<a class="jxr_linenumber" name="37" href="#37">37</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
-<a class="jxr_linenumber" name="38" href="#38">38</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testWrongVariableIndex() {
-<a class="jxr_linenumber" name="39" href="#39">39</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 3, 1.0);
-<a class="jxr_linenumber" name="40" href="#40">40</a> }
-<a class="jxr_linenumber" name="41" href="#41">41</a>
-<a class="jxr_linenumber" name="42" href="#42">42</a> @Test(expected=DimensionMismatchException.<strong class="jxr_keyword">class</strong>)
-<a class="jxr_linenumber" name="43" href="#43">43</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMissingOrders() {
-<a class="jxr_linenumber" name="44" href="#44">44</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(0, 1);
-<a class="jxr_linenumber" name="45" href="#45">45</a> }
-<a class="jxr_linenumber" name="46" href="#46">46</a>
-<a class="jxr_linenumber" name="47" href="#47">47</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
-<a class="jxr_linenumber" name="48" href="#48">48</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTooLargeOrder() {
-<a class="jxr_linenumber" name="49" href="#49">49</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(1, 1, 2);
-<a class="jxr_linenumber" name="50" href="#50">50</a> }
-<a class="jxr_linenumber" name="51" href="#51">51</a>
-<a class="jxr_linenumber" name="52" href="#52">52</a> @Test
-<a class="jxr_linenumber" name="53" href="#53">53</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariableWithoutDerivative0() {
-<a class="jxr_linenumber" name="54" href="#54">54</a> DerivativeStructure v = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, 0, 0, 1.0);
-<a class="jxr_linenumber" name="55" href="#55">55</a> Assert.assertEquals(1.0, v.getValue(), 1.0e-15);
+<a class="jxr_linenumber" name="23" href="#23">23</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.ExtendedFieldElementAbstractTest;
+<a class="jxr_linenumber" name="24" href="#24">24</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.TestUtils;
+<a class="jxr_linenumber" name="25" href="#25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
+<a class="jxr_linenumber" name="26" href="#26">26</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.DimensionMismatchException;
+<a class="jxr_linenumber" name="27" href="#27">27</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.NumberIsTooLargeException;
+<a class="jxr_linenumber" name="28" href="#28">28</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.random.Well1024a;
+<a class="jxr_linenumber" name="29" href="#29">29</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.ArithmeticUtils;
+<a class="jxr_linenumber" name="30" href="#30">30</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
+<a class="jxr_linenumber" name="31" href="#31">31</a> <strong class="jxr_keyword">import</strong> org.junit.Assert;
+<a class="jxr_linenumber" name="32" href="#32">32</a> <strong class="jxr_keyword">import</strong> org.junit.Test;
+<a class="jxr_linenumber" name="33" href="#33">33</a>
+<a class="jxr_linenumber" name="34" href="#34">34</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="35" href="#35">35</a> <em class="jxr_javadoccomment"> * Test for class {@link DerivativeStructure}.</em>
+<a class="jxr_linenumber" name="36" href="#36">36</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="37" href="#37">37</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructureTest.html">DerivativeStructureTest</a> <strong class="jxr_keyword">extends</strong> ExtendedFieldElementAbstractTest<DerivativeStructure> {
+<a class="jxr_linenumber" name="38" href="#38">38</a>
+<a class="jxr_linenumber" name="39" href="#39">39</a> <strong class="jxr_keyword">protected</strong> DerivativeStructure build(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="40" href="#40">40</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> DerivativeStructure(2, 1, 0, x);
+<a class="jxr_linenumber" name="41" href="#41">41</a> }
+<a class="jxr_linenumber" name="42" href="#42">42</a>
+<a class="jxr_linenumber" name="43" href="#43">43</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="44" href="#44">44</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testWrongVariableIndex() {
+<a class="jxr_linenumber" name="45" href="#45">45</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 3, 1.0);
+<a class="jxr_linenumber" name="46" href="#46">46</a> }
+<a class="jxr_linenumber" name="47" href="#47">47</a>
+<a class="jxr_linenumber" name="48" href="#48">48</a> @Test(expected=DimensionMismatchException.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="49" href="#49">49</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMissingOrders() {
+<a class="jxr_linenumber" name="50" href="#50">50</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(0, 1);
+<a class="jxr_linenumber" name="51" href="#51">51</a> }
+<a class="jxr_linenumber" name="52" href="#52">52</a>
+<a class="jxr_linenumber" name="53" href="#53">53</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="54" href="#54">54</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTooLargeOrder() {
+<a class="jxr_linenumber" name="55" href="#55">55</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 1, 0, 1.0).getPartialDerivative(1, 1, 2);
<a class="jxr_linenumber" name="56" href="#56">56</a> }
<a class="jxr_linenumber" name="57" href="#57">57</a>
-<a class="jxr_linenumber" name="58" href="#58">58</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
-<a class="jxr_linenumber" name="59" href="#59">59</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariableWithoutDerivative1() {
+<a class="jxr_linenumber" name="58" href="#58">58</a> @Test
+<a class="jxr_linenumber" name="59" href="#59">59</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariableWithoutDerivative0() {
<a class="jxr_linenumber" name="60" href="#60">60</a> DerivativeStructure v = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, 0, 0, 1.0);
-<a class="jxr_linenumber" name="61" href="#61">61</a> Assert.assertEquals(1.0, v.getPartialDerivative(1), 1.0e-15);
+<a class="jxr_linenumber" name="61" href="#61">61</a> Assert.assertEquals(1.0, v.getValue(), 1.0e-15);
<a class="jxr_linenumber" name="62" href="#62">62</a> }
<a class="jxr_linenumber" name="63" href="#63">63</a>
-<a class="jxr_linenumber" name="64" href="#64">64</a> @Test
-<a class="jxr_linenumber" name="65" href="#65">65</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariable() {
-<a class="jxr_linenumber" name="66" href="#66">66</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="67" href="#67">67</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0),
-<a class="jxr_linenumber" name="68" href="#68">68</a> 1.0, 1.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="69" href="#69">69</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0),
-<a class="jxr_linenumber" name="70" href="#70">70</a> 2.0, 0.0, 1.0, 0.0);
-<a class="jxr_linenumber" name="71" href="#71">71</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0),
-<a class="jxr_linenumber" name="72" href="#72">72</a> 3.0, 0.0, 0.0, 1.0);
-<a class="jxr_linenumber" name="73" href="#73">73</a> }
-<a class="jxr_linenumber" name="74" href="#74">74</a> }
-<a class="jxr_linenumber" name="75" href="#75">75</a>
-<a class="jxr_linenumber" name="76" href="#76">76</a> @Test
-<a class="jxr_linenumber" name="77" href="#77">77</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testConstant() {
-<a class="jxr_linenumber" name="78" href="#78">78</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="79" href="#79">79</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, FastMath.PI),
-<a class="jxr_linenumber" name="80" href="#80">80</a> FastMath.PI, 0.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="81" href="#81">81</a> }
-<a class="jxr_linenumber" name="82" href="#82">82</a> }
-<a class="jxr_linenumber" name="83" href="#83">83</a>
-<a class="jxr_linenumber" name="84" href="#84">84</a> @Test
-<a class="jxr_linenumber" name="85" href="#85">85</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveAdd() {
-<a class="jxr_linenumber" name="86" href="#86">86</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="87" href="#87">87</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).add(5), 6.0, 1.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="88" href="#88">88</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).add(5), 7.0, 0.0, 1.0, 0.0);
-<a class="jxr_linenumber" name="89" href="#89">89</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).add(5), 8.0, 0.0, 0.0, 1.0);
-<a class="jxr_linenumber" name="90" href="#90">90</a> }
-<a class="jxr_linenumber" name="91" href="#91">91</a> }
-<a class="jxr_linenumber" name="92" href="#92">92</a>
-<a class="jxr_linenumber" name="93" href="#93">93</a> @Test
-<a class="jxr_linenumber" name="94" href="#94">94</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAdd() {
-<a class="jxr_linenumber" name="95" href="#95">95</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="96" href="#96">96</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
-<a class="jxr_linenumber" name="97" href="#97">97</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
-<a class="jxr_linenumber" name="98" href="#98">98</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
-<a class="jxr_linenumber" name="99" href="#99">99</a> DerivativeStructure xyz = x.add(y.add(z));
-<a class="jxr_linenumber" name="100" href="#100">100</a> checkF0F1(xyz, x.getValue() + y.getValue() + z.getValue(), 1.0, 1.0, 1.0);
-<a class="jxr_linenumber" name="101" href="#101">101</a> }
-<a class="jxr_linenumber" name="102" href="#102">102</a> }
-<a class="jxr_linenumber" name="103" href="#103">103</a>
-<a class="jxr_linenumber" name="104" href="#104">104</a> @Test
-<a class="jxr_linenumber" name="105" href="#105">105</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveSubtract() {
-<a class="jxr_linenumber" name="106" href="#106">106</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="107" href="#107">107</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).subtract(5), -4.0, 1.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="108" href="#108">108</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).subtract(5), -3.0, 0.0, 1.0, 0.0);
-<a class="jxr_linenumber" name="109" href="#109">109</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).subtract(5), -2.0, 0.0, 0.0, 1.0);
-<a class="jxr_linenumber" name="110" href="#110">110</a> }
-<a class="jxr_linenumber" name="111" href="#111">111</a> }
-<a class="jxr_linenumber" name="112" href="#112">112</a>
-<a class="jxr_linenumber" name="113" href="#113">113</a> @Test
-<a class="jxr_linenumber" name="114" href="#114">114</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSubtract() {
-<a class="jxr_linenumber" name="115" href="#115">115</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="116" href="#116">116</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
-<a class="jxr_linenumber" name="117" href="#117">117</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
-<a class="jxr_linenumber" name="118" href="#118">118</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
-<a class="jxr_linenumber" name="119" href="#119">119</a> DerivativeStructure xyz = x.subtract(y.subtract(z));
-<a class="jxr_linenumber" name="120" href="#120">120</a> checkF0F1(xyz, x.getValue() - (y.getValue() - z.getValue()), 1.0, -1.0, 1.0);
-<a class="jxr_linenumber" name="121" href="#121">121</a> }
-<a class="jxr_linenumber" name="122" href="#122">122</a> }
-<a class="jxr_linenumber" name="123" href="#123">123</a>
-<a class="jxr_linenumber" name="124" href="#124">124</a> @Test
-<a class="jxr_linenumber" name="125" href="#125">125</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveMultiply() {
-<a class="jxr_linenumber" name="126" href="#126">126</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="127" href="#127">127</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).multiply(5), 5.0, 5.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="128" href="#128">128</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).multiply(5), 10.0, 0.0, 5.0, 0.0);
-<a class="jxr_linenumber" name="129" href="#129">129</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).multiply(5), 15.0, 0.0, 0.0, 5.0);
-<a class="jxr_linenumber" name="130" href="#130">130</a> }
-<a class="jxr_linenumber" name="131" href="#131">131</a> }
-<a class="jxr_linenumber" name="132" href="#132">132</a>
-<a class="jxr_linenumber" name="133" href="#133">133</a> @Test
-<a class="jxr_linenumber" name="134" href="#134">134</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMultiply() {
-<a class="jxr_linenumber" name="135" href="#135">135</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="136" href="#136">136</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
-<a class="jxr_linenumber" name="137" href="#137">137</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
-<a class="jxr_linenumber" name="138" href="#138">138</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
-<a class="jxr_linenumber" name="139" href="#139">139</a> DerivativeStructure xyz = x.multiply(y.multiply(z));
-<a class="jxr_linenumber" name="140" href="#140">140</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i <= maxOrder; ++i) {
-<a class="jxr_linenumber" name="141" href="#141">141</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j <= maxOrder; ++j) {
-<a class="jxr_linenumber" name="142" href="#142">142</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 0; k <= maxOrder; ++k) {
-<a class="jxr_linenumber" name="143" href="#143">143</a> <strong class="jxr_keyword">if</strong> (i + j + k <= maxOrder) {
-<a class="jxr_linenumber" name="144" href="#144">144</a> Assert.assertEquals((i == 0 ? x.getValue() : (i == 1 ? 1.0 : 0.0)) *
-<a class="jxr_linenumber" name="145" href="#145">145</a> (j == 0 ? y.getValue() : (j == 1 ? 1.0 : 0.0)) *
-<a class="jxr_linenumber" name="146" href="#146">146</a> (k == 0 ? z.getValue() : (k == 1 ? 1.0 : 0.0)),
-<a class="jxr_linenumber" name="147" href="#147">147</a> xyz.getPartialDerivative(i, j, k),
-<a class="jxr_linenumber" name="148" href="#148">148</a> 1.0e-15);
-<a class="jxr_linenumber" name="149" href="#149">149</a> }
-<a class="jxr_linenumber" name="150" href="#150">150</a> }
-<a class="jxr_linenumber" name="151" href="#151">151</a> }
-<a class="jxr_linenumber" name="152" href="#152">152</a> }
-<a class="jxr_linenumber" name="153" href="#153">153</a> }
-<a class="jxr_linenumber" name="154" href="#154">154</a> }
-<a class="jxr_linenumber" name="155" href="#155">155</a>
-<a class="jxr_linenumber" name="156" href="#156">156</a> @Test
-<a class="jxr_linenumber" name="157" href="#157">157</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNegate() {
-<a class="jxr_linenumber" name="158" href="#158">158</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="159" href="#159">159</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).negate(), -1.0, -1.0, 0.0, 0.0);
-<a class="jxr_linenumber" name="160" href="#160">160</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).negate(), -2.0, 0.0, -1.0, 0.0);
-<a class="jxr_linenumber" name="161" href="#161">161</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).negate(), -3.0, 0.0, 0.0, -1.0);
-<a class="jxr_linenumber" name="162" href="#162">162</a> }
-<a class="jxr_linenumber" name="163" href="#163">163</a> }
-<a class="jxr_linenumber" name="164" href="#164">164</a>
-<a class="jxr_linenumber" name="165" href="#165">165</a> @Test
-<a class="jxr_linenumber" name="166" href="#166">166</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testReciprocal() {
-<a class="jxr_linenumber" name="167" href="#167">167</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
-<a class="jxr_linenumber" name="168" href="#168">168</a> DerivativeStructure r = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, 6, 0, x).reciprocal();
-<a class="jxr_linenumber" name="169" href="#169">169</a> Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
-<a class="jxr_linenumber" name="170" href="#170">170</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 1; i < r.getOrder(); ++i) {
-<a class="jxr_linenumber" name="171" href="#171">171</a> <strong class="jxr_keyword">double</strong> expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /
-<a class="jxr_linenumber" name="172" href="#172">172</a> FastMath.pow(x, i + 1);
-<a class="jxr_linenumber" name="173" href="#173">173</a> Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));
-<a class="jxr_linenumber" name="174" href="#174">174</a> }
-<a class="jxr_linenumber" name="175" href="#175">175</a> }
-<a class="jxr_linenumber" name="176" href="#176">176</a> }
-<a class="jxr_linenumber" name="177" href="#177">177</a>
-<a class="jxr_linenumber" name="178" href="#178">178</a> @Test
-<a class="jxr_linenumber" name="179" href="#179">179</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPow() {
-<a class="jxr_linenumber" name="180" href="#180">180</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="181" href="#181">181</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> n = 0; n < 10; ++n) {
-<a class="jxr_linenumber" name="182" href="#182">182</a>
-<a class="jxr_linenumber" name="183" href="#183">183</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
-<a class="jxr_linenumber" name="184" href="#184">184</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
-<a class="jxr_linenumber" name="185" href="#185">185</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
-<a class="jxr_linenumber" name="186" href="#186">186</a> List<DerivativeStructure> list = Arrays.asList(x, y, z,
-<a class="jxr_linenumber" name="187" href="#187">187</a> x.add(y).add(z),
-<a class="jxr_linenumber" name="188" href="#188">188</a> x.multiply(y).multiply(z));
-<a class="jxr_linenumber" name="189" href="#189">189</a>
-<a class="jxr_linenumber" name="190" href="#190">190</a> <strong class="jxr_keyword">if</strong> (n == 0) {
-<a class="jxr_linenumber" name="191" href="#191">191</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
-<a class="jxr_linenumber" name="192" href="#192">192</a> checkEquals(ds.getField().getOne(), ds.pow(n), 1.0e-15);
-<a class="jxr_linenumber" name="193" href="#193">193</a> }
-<a class="jxr_linenumber" name="194" href="#194">194</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (n == 1) {
-<a class="jxr_linenumber" name="195" href="#195">195</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
-<a class="jxr_linenumber" name="196" href="#196">196</a> checkEquals(ds, ds.pow(n), 1.0e-15);
-<a class="jxr_linenumber" name="197" href="#197">197</a> }
-<a class="jxr_linenumber" name="198" href="#198">198</a> } <strong class="jxr_keyword">else</strong> {
-<a class="jxr_linenumber" name="199" href="#199">199</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
-<a class="jxr_linenumber" name="200" href="#200">200</a> DerivativeStructure p = ds.getField().getOne();
-<a class="jxr_linenumber" name="201" href="#201">201</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < n; ++i) {
-<a class="jxr_linenumber" name="202" href="#202">202</a> p = p.multiply(ds);
-<a class="jxr_linenumber" name="203" href="#203">203</a> }
-<a class="jxr_linenumber" name="204" href="#204">204</a> checkEquals(p, ds.pow(n), 1.0e-15);
-<a class="jxr_linenumber" name="205" href="#205">205</a> }
-<a class="jxr_linenumber" name="206" href="#206">206</a> }
-<a class="jxr_linenumber" name="207" href="#207">207</a> }
-<a class="jxr_linenumber" name="208" href="#208">208</a> }
-<a class="jxr_linenumber" name="209" href="#209">209</a> }
-<a class="jxr_linenumber" name="210" href="#210">210</a>
-<a class="jxr_linenumber" name="211" href="#211">211</a> @Test
-<a class="jxr_linenumber" name="212" href="#212">212</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testExpression() {
-<a class="jxr_linenumber" name="213" href="#213">213</a> <strong class="jxr_keyword">double</strong> epsilon = 2.5e-13;
-<a class="jxr_linenumber" name="214" href="#214">214</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0; x < 2; x += 0.2) {
-<a class="jxr_linenumber" name="215" href="#215">215</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 0, x);
-<a class="jxr_linenumber" name="216" href="#216">216</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0; y < 2; y += 0.2) {
-<a class="jxr_linenumber" name="217" href="#217">217</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 1, y);
-<a class="jxr_linenumber" name="218" href="#218">218</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = 0; z >- 2; z -= 0.2) {
-<a class="jxr_linenumber" name="219" href="#219">219</a> DerivativeStructure dsZ = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 2, z);
-<a class="jxr_linenumber" name="220" href="#220">220</a>
-<a class="jxr_linenumber" name="221" href="#221">221</a> <em class="jxr_comment">// f(x, y, z) = x + 5 x y - 2 z + (8 z x - y)^3</em>
-<a class="jxr_linenumber" name="222" href="#222">222</a> DerivativeStructure ds =
-<a class="jxr_linenumber" name="223" href="#223">223</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(1, dsX,
-<a class="jxr_linenumber" name="224" href="#224">224</a> 5, dsX.multiply(dsY),
-<a class="jxr_linenumber" name="225" href="#225">225</a> -2, dsZ,
-<a class="jxr_linenumber" name="226" href="#226">226</a> 1, <strong class="jxr_keyword">new</strong> DerivativeStructure(8, dsZ.multiply(dsX),
-<a class="jxr_linenumber" name="227" href="#227">227</a> -1, dsY).pow(3));
-<a class="jxr_linenumber" name="228" href="#228">228</a> DerivativeStructure dsOther =
+<a class="jxr_linenumber" name="64" href="#64">64</a> @Test(expected=NumberIsTooLargeException.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="65" href="#65">65</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariableWithoutDerivative1() {
+<a class="jxr_linenumber" name="66" href="#66">66</a> DerivativeStructure v = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, 0, 0, 1.0);
+<a class="jxr_linenumber" name="67" href="#67">67</a> Assert.assertEquals(1.0, v.getPartialDerivative(1), 1.0e-15);
+<a class="jxr_linenumber" name="68" href="#68">68</a> }
+<a class="jxr_linenumber" name="69" href="#69">69</a>
+<a class="jxr_linenumber" name="70" href="#70">70</a> @Test
+<a class="jxr_linenumber" name="71" href="#71">71</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVariable() {
+<a class="jxr_linenumber" name="72" href="#72">72</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="73" href="#73">73</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0),
+<a class="jxr_linenumber" name="74" href="#74">74</a> 1.0, 1.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="75" href="#75">75</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0),
+<a class="jxr_linenumber" name="76" href="#76">76</a> 2.0, 0.0, 1.0, 0.0);
+<a class="jxr_linenumber" name="77" href="#77">77</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0),
+<a class="jxr_linenumber" name="78" href="#78">78</a> 3.0, 0.0, 0.0, 1.0);
+<a class="jxr_linenumber" name="79" href="#79">79</a> }
+<a class="jxr_linenumber" name="80" href="#80">80</a> }
+<a class="jxr_linenumber" name="81" href="#81">81</a>
+<a class="jxr_linenumber" name="82" href="#82">82</a> @Test
+<a class="jxr_linenumber" name="83" href="#83">83</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testConstant() {
+<a class="jxr_linenumber" name="84" href="#84">84</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="85" href="#85">85</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, FastMath.PI),
+<a class="jxr_linenumber" name="86" href="#86">86</a> FastMath.PI, 0.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="87" href="#87">87</a> }
+<a class="jxr_linenumber" name="88" href="#88">88</a> }
+<a class="jxr_linenumber" name="89" href="#89">89</a>
+<a class="jxr_linenumber" name="90" href="#90">90</a> @Test
+<a class="jxr_linenumber" name="91" href="#91">91</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveAdd() {
+<a class="jxr_linenumber" name="92" href="#92">92</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="93" href="#93">93</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).add(5), 6.0, 1.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="94" href="#94">94</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).add(5), 7.0, 0.0, 1.0, 0.0);
+<a class="jxr_linenumber" name="95" href="#95">95</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).add(5), 8.0, 0.0, 0.0, 1.0);
+<a class="jxr_linenumber" name="96" href="#96">96</a> }
+<a class="jxr_linenumber" name="97" href="#97">97</a> }
+<a class="jxr_linenumber" name="98" href="#98">98</a>
+<a class="jxr_linenumber" name="99" href="#99">99</a> @Test
+<a class="jxr_linenumber" name="100" href="#100">100</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAdd() {
+<a class="jxr_linenumber" name="101" href="#101">101</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="102" href="#102">102</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
+<a class="jxr_linenumber" name="103" href="#103">103</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
+<a class="jxr_linenumber" name="104" href="#104">104</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
+<a class="jxr_linenumber" name="105" href="#105">105</a> DerivativeStructure xyz = x.add(y.add(z));
+<a class="jxr_linenumber" name="106" href="#106">106</a> checkF0F1(xyz, x.getValue() + y.getValue() + z.getValue(), 1.0, 1.0, 1.0);
+<a class="jxr_linenumber" name="107" href="#107">107</a> }
+<a class="jxr_linenumber" name="108" href="#108">108</a> }
+<a class="jxr_linenumber" name="109" href="#109">109</a>
+<a class="jxr_linenumber" name="110" href="#110">110</a> @Test
+<a class="jxr_linenumber" name="111" href="#111">111</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveSubtract() {
+<a class="jxr_linenumber" name="112" href="#112">112</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="113" href="#113">113</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).subtract(5), -4.0, 1.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="114" href="#114">114</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).subtract(5), -3.0, 0.0, 1.0, 0.0);
+<a class="jxr_linenumber" name="115" href="#115">115</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).subtract(5), -2.0, 0.0, 0.0, 1.0);
+<a class="jxr_linenumber" name="116" href="#116">116</a> }
+<a class="jxr_linenumber" name="117" href="#117">117</a> }
+<a class="jxr_linenumber" name="118" href="#118">118</a>
+<a class="jxr_linenumber" name="119" href="#119">119</a> @Test
+<a class="jxr_linenumber" name="120" href="#120">120</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSubtract() {
+<a class="jxr_linenumber" name="121" href="#121">121</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="122" href="#122">122</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
+<a class="jxr_linenumber" name="123" href="#123">123</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
+<a class="jxr_linenumber" name="124" href="#124">124</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
+<a class="jxr_linenumber" name="125" href="#125">125</a> DerivativeStructure xyz = x.subtract(y.subtract(z));
+<a class="jxr_linenumber" name="126" href="#126">126</a> checkF0F1(xyz, x.getValue() - (y.getValue() - z.getValue()), 1.0, -1.0, 1.0);
+<a class="jxr_linenumber" name="127" href="#127">127</a> }
+<a class="jxr_linenumber" name="128" href="#128">128</a> }
+<a class="jxr_linenumber" name="129" href="#129">129</a>
+<a class="jxr_linenumber" name="130" href="#130">130</a> @Test
+<a class="jxr_linenumber" name="131" href="#131">131</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPrimitiveMultiply() {
+<a class="jxr_linenumber" name="132" href="#132">132</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="133" href="#133">133</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).multiply(5), 5.0, 5.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="134" href="#134">134</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).multiply(5), 10.0, 0.0, 5.0, 0.0);
+<a class="jxr_linenumber" name="135" href="#135">135</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).multiply(5), 15.0, 0.0, 0.0, 5.0);
+<a class="jxr_linenumber" name="136" href="#136">136</a> }
+<a class="jxr_linenumber" name="137" href="#137">137</a> }
+<a class="jxr_linenumber" name="138" href="#138">138</a>
+<a class="jxr_linenumber" name="139" href="#139">139</a> @Test
+<a class="jxr_linenumber" name="140" href="#140">140</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMultiply() {
+<a class="jxr_linenumber" name="141" href="#141">141</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="142" href="#142">142</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
+<a class="jxr_linenumber" name="143" href="#143">143</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
+<a class="jxr_linenumber" name="144" href="#144">144</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
+<a class="jxr_linenumber" name="145" href="#145">145</a> DerivativeStructure xyz = x.multiply(y.multiply(z));
+<a class="jxr_linenumber" name="146" href="#146">146</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i <= maxOrder; ++i) {
+<a class="jxr_linenumber" name="147" href="#147">147</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j <= maxOrder; ++j) {
+<a class="jxr_linenumber" name="148" href="#148">148</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 0; k <= maxOrder; ++k) {
+<a class="jxr_linenumber" name="149" href="#149">149</a> <strong class="jxr_keyword">if</strong> (i + j + k <= maxOrder) {
+<a class="jxr_linenumber" name="150" href="#150">150</a> Assert.assertEquals((i == 0 ? x.getValue() : (i == 1 ? 1.0 : 0.0)) *
+<a class="jxr_linenumber" name="151" href="#151">151</a> (j == 0 ? y.getValue() : (j == 1 ? 1.0 : 0.0)) *
+<a class="jxr_linenumber" name="152" href="#152">152</a> (k == 0 ? z.getValue() : (k == 1 ? 1.0 : 0.0)),
+<a class="jxr_linenumber" name="153" href="#153">153</a> xyz.getPartialDerivative(i, j, k),
+<a class="jxr_linenumber" name="154" href="#154">154</a> 1.0e-15);
+<a class="jxr_linenumber" name="155" href="#155">155</a> }
+<a class="jxr_linenumber" name="156" href="#156">156</a> }
+<a class="jxr_linenumber" name="157" href="#157">157</a> }
+<a class="jxr_linenumber" name="158" href="#158">158</a> }
+<a class="jxr_linenumber" name="159" href="#159">159</a> }
+<a class="jxr_linenumber" name="160" href="#160">160</a> }
+<a class="jxr_linenumber" name="161" href="#161">161</a>
+<a class="jxr_linenumber" name="162" href="#162">162</a> @Test
+<a class="jxr_linenumber" name="163" href="#163">163</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNegate() {
+<a class="jxr_linenumber" name="164" href="#164">164</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="165" href="#165">165</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0).negate(), -1.0, -1.0, 0.0, 0.0);
+<a class="jxr_linenumber" name="166" href="#166">166</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0).negate(), -2.0, 0.0, -1.0, 0.0);
+<a class="jxr_linenumber" name="167" href="#167">167</a> checkF0F1(<strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0).negate(), -3.0, 0.0, 0.0, -1.0);
+<a class="jxr_linenumber" name="168" href="#168">168</a> }
+<a class="jxr_linenumber" name="169" href="#169">169</a> }
+<a class="jxr_linenumber" name="170" href="#170">170</a>
+<a class="jxr_linenumber" name="171" href="#171">171</a> @Test
+<a class="jxr_linenumber" name="172" href="#172">172</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testReciprocal() {
+<a class="jxr_linenumber" name="173" href="#173">173</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
+<a class="jxr_linenumber" name="174" href="#174">174</a> DerivativeStructure r = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, 6, 0, x).reciprocal();
+<a class="jxr_linenumber" name="175" href="#175">175</a> Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
+<a class="jxr_linenumber" name="176" href="#176">176</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 1; i < r.getOrder(); ++i) {
+<a class="jxr_linenumber" name="177" href="#177">177</a> <strong class="jxr_keyword">double</strong> expected = ArithmeticUtils.pow(-1, i) * ArithmeticUtils.factorial(i) /
+<a class="jxr_linenumber" name="178" href="#178">178</a> FastMath.pow(x, i + 1);
+<a class="jxr_linenumber" name="179" href="#179">179</a> Assert.assertEquals(expected, r.getPartialDerivative(i), 1.0e-15 * FastMath.abs(expected));
+<a class="jxr_linenumber" name="180" href="#180">180</a> }
+<a class="jxr_linenumber" name="181" href="#181">181</a> }
+<a class="jxr_linenumber" name="182" href="#182">182</a> }
+<a class="jxr_linenumber" name="183" href="#183">183</a>
+<a class="jxr_linenumber" name="184" href="#184">184</a> @Test
+<a class="jxr_linenumber" name="185" href="#185">185</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testPow() {
+<a class="jxr_linenumber" name="186" href="#186">186</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 1; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="187" href="#187">187</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> n = 0; n < 10; ++n) {
+<a class="jxr_linenumber" name="188" href="#188">188</a>
+<a class="jxr_linenumber" name="189" href="#189">189</a> DerivativeStructure x = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, 1.0);
+<a class="jxr_linenumber" name="190" href="#190">190</a> DerivativeStructure y = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, 2.0);
+<a class="jxr_linenumber" name="191" href="#191">191</a> DerivativeStructure z = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, 3.0);
+<a class="jxr_linenumber" name="192" href="#192">192</a> List<DerivativeStructure> list = Arrays.asList(x, y, z,
+<a class="jxr_linenumber" name="193" href="#193">193</a> x.add(y).add(z),
+<a class="jxr_linenumber" name="194" href="#194">194</a> x.multiply(y).multiply(z));
+<a class="jxr_linenumber" name="195" href="#195">195</a>
+<a class="jxr_linenumber" name="196" href="#196">196</a> <strong class="jxr_keyword">if</strong> (n == 0) {
+<a class="jxr_linenumber" name="197" href="#197">197</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
+<a class="jxr_linenumber" name="198" href="#198">198</a> checkEquals(ds.getField().getOne(), ds.pow(n), 1.0e-15);
+<a class="jxr_linenumber" name="199" href="#199">199</a> }
+<a class="jxr_linenumber" name="200" href="#200">200</a> } <strong class="jxr_keyword">else</strong> <strong class="jxr_keyword">if</strong> (n == 1) {
+<a class="jxr_linenumber" name="201" href="#201">201</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
+<a class="jxr_linenumber" name="202" href="#202">202</a> checkEquals(ds, ds.pow(n), 1.0e-15);
+<a class="jxr_linenumber" name="203" href="#203">203</a> }
+<a class="jxr_linenumber" name="204" href="#204">204</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="205" href="#205">205</a> <strong class="jxr_keyword">for</strong> (DerivativeStructure ds : list) {
+<a class="jxr_linenumber" name="206" href="#206">206</a> DerivativeStructure p = ds.getField().getOne();
+<a class="jxr_linenumber" name="207" href="#207">207</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < n; ++i) {
+<a class="jxr_linenumber" name="208" href="#208">208</a> p = p.multiply(ds);
+<a class="jxr_linenumber" name="209" href="#209">209</a> }
+<a class="jxr_linenumber" name="210" href="#210">210</a> checkEquals(p, ds.pow(n), 1.0e-15);
+<a class="jxr_linenumber" name="211" href="#211">211</a> }
+<a class="jxr_linenumber" name="212" href="#212">212</a> }
+<a class="jxr_linenumber" name="213" href="#213">213</a> }
+<a class="jxr_linenumber" name="214" href="#214">214</a> }
+<a class="jxr_linenumber" name="215" href="#215">215</a> }
+<a class="jxr_linenumber" name="216" href="#216">216</a>
+<a class="jxr_linenumber" name="217" href="#217">217</a> @Test
+<a class="jxr_linenumber" name="218" href="#218">218</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testExpression() {
+<a class="jxr_linenumber" name="219" href="#219">219</a> <strong class="jxr_keyword">double</strong> epsilon = 2.5e-13;
+<a class="jxr_linenumber" name="220" href="#220">220</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0; x < 2; x += 0.2) {
+<a class="jxr_linenumber" name="221" href="#221">221</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 0, x);
+<a class="jxr_linenumber" name="222" href="#222">222</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0; y < 2; y += 0.2) {
+<a class="jxr_linenumber" name="223" href="#223">223</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 1, y);
+<a class="jxr_linenumber" name="224" href="#224">224</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = 0; z >- 2; z -= 0.2) {
+<a class="jxr_linenumber" name="225" href="#225">225</a> DerivativeStructure dsZ = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, 5, 2, z);
+<a class="jxr_linenumber" name="226" href="#226">226</a>
+<a class="jxr_linenumber" name="227" href="#227">227</a> <em class="jxr_comment">// f(x, y, z) = x + 5 x y - 2 z + (8 z x - y)^3</em>
+<a class="jxr_linenumber" name="228" href="#228">228</a> DerivativeStructure ds =
<a class="jxr_linenumber" name="229" href="#229">229</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(1, dsX,
<a class="jxr_linenumber" name="230" href="#230">230</a> 5, dsX.multiply(dsY),
-<a class="jxr_linenumber" name="231" href="#231">231</a> -2, dsZ).add(<strong class="jxr_keyword">new</strong> DerivativeStructure(8, dsZ.multiply(dsX),
-<a class="jxr_linenumber" name="232" href="#232">232</a> -1, dsY).pow(3));
-<a class="jxr_linenumber" name="233" href="#233">233</a> <strong class="jxr_keyword">double</strong> f = x + 5 * x * y - 2 * z + FastMath.pow(8 * z * x - y, 3);
-<a class="jxr_linenumber" name="234" href="#234">234</a> Assert.assertEquals(f, ds.getValue(),
-<a class="jxr_linenumber" name="235" href="#235">235</a> FastMath.abs(epsilon * f));
-<a class="jxr_linenumber" name="236" href="#236">236</a> Assert.assertEquals(f, dsOther.getValue(),
-<a class="jxr_linenumber" name="237" href="#237">237</a> FastMath.abs(epsilon * f));
-<a class="jxr_linenumber" name="238" href="#238">238</a>
-<a class="jxr_linenumber" name="239" href="#239">239</a> <em class="jxr_comment">// df/dx = 1 + 5 y + 24 (8 z x - y)^2 z</em>
-<a class="jxr_linenumber" name="240" href="#240">240</a> <strong class="jxr_keyword">double</strong> dfdx = 1 + 5 * y + 24 * z * FastMath.pow(8 * z * x - y, 2);
-<a class="jxr_linenumber" name="241" href="#241">241</a> Assert.assertEquals(dfdx, ds.getPartialDerivative(1, 0, 0),
-<a class="jxr_linenumber" name="242" href="#242">242</a> FastMath.abs(epsilon * dfdx));
-<a class="jxr_linenumber" name="243" href="#243">243</a> Assert.assertEquals(dfdx, dsOther.getPartialDerivative(1, 0, 0),
-<a class="jxr_linenumber" name="244" href="#244">244</a> FastMath.abs(epsilon * dfdx));
-<a class="jxr_linenumber" name="245" href="#245">245</a>
-<a class="jxr_linenumber" name="246" href="#246">246</a> <em class="jxr_comment">// df/dxdy = 5 + 48 z*(y - 8 z x)</em>
-<a class="jxr_linenumber" name="247" href="#247">247</a> <strong class="jxr_keyword">double</strong> dfdxdy = 5 + 48 * z * (y - 8 * z * x);
-<a class="jxr_linenumber" name="248" href="#248">248</a> Assert.assertEquals(dfdxdy, ds.getPartialDerivative(1, 1, 0),
-<a class="jxr_linenumber" name="249" href="#249">249</a> FastMath.abs(epsilon * dfdxdy));
-<a class="jxr_linenumber" name="250" href="#250">250</a> Assert.assertEquals(dfdxdy, dsOther.getPartialDerivative(1, 1, 0),
-<a class="jxr_linenumber" name="251" href="#251">251</a> FastMath.abs(epsilon * dfdxdy));
-<a class="jxr_linenumber" name="252" href="#252">252</a>
-<a class="jxr_linenumber" name="253" href="#253">253</a> <em class="jxr_comment">// df/dxdydz = 48 (y - 16 z x)</em>
-<a class="jxr_linenumber" name="254" href="#254">254</a> <strong class="jxr_keyword">double</strong> dfdxdydz = 48 * (y - 16 * z * x);
-<a class="jxr_linenumber" name="255" href="#255">255</a> Assert.assertEquals(dfdxdydz, ds.getPartialDerivative(1, 1, 1),
-<a class="jxr_linenumber" name="256" href="#256">256</a> FastMath.abs(epsilon * dfdxdydz));
-<a class="jxr_linenumber" name="257" href="#257">257</a> Assert.assertEquals(dfdxdydz, dsOther.getPartialDerivative(1, 1, 1),
-<a class="jxr_linenumber" name="258" href="#258">258</a> FastMath.abs(epsilon * dfdxdydz));
-<a class="jxr_linenumber" name="259" href="#259">259</a>
-<a class="jxr_linenumber" name="260" href="#260">260</a> }
-<a class="jxr_linenumber" name="261" href="#261">261</a>
-<a class="jxr_linenumber" name="262" href="#262">262</a> }
-<a class="jxr_linenumber" name="263" href="#263">263</a> }
-<a class="jxr_linenumber" name="264" href="#264">264</a> }
+<a class="jxr_linenumber" name="231" href="#231">231</a> -2, dsZ,
+<a class="jxr_linenumber" name="232" href="#232">232</a> 1, <strong class="jxr_keyword">new</strong> DerivativeStructure(8, dsZ.multiply(dsX),
+<a class="jxr_linenumber" name="233" href="#233">233</a> -1, dsY).pow(3));
+<a class="jxr_linenumber" name="234" href="#234">234</a> DerivativeStructure dsOther =
+<a class="jxr_linenumber" name="235" href="#235">235</a> <strong class="jxr_keyword">new</strong> DerivativeStructure(1, dsX,
+<a class="jxr_linenumber" name="236" href="#236">236</a> 5, dsX.multiply(dsY),
+<a class="jxr_linenumber" name="237" href="#237">237</a> -2, dsZ).add(<strong class="jxr_keyword">new</strong> DerivativeStructure(8, dsZ.multiply(dsX),
+<a class="jxr_linenumber" name="238" href="#238">238</a> -1, dsY).pow(3));
+<a class="jxr_linenumber" name="239" href="#239">239</a> <strong class="jxr_keyword">double</strong> f = x + 5 * x * y - 2 * z + FastMath.pow(8 * z * x - y, 3);
+<a class="jxr_linenumber" name="240" href="#240">240</a> Assert.assertEquals(f, ds.getValue(),
+<a class="jxr_linenumber" name="241" href="#241">241</a> FastMath.abs(epsilon * f));
+<a class="jxr_linenumber" name="242" href="#242">242</a> Assert.assertEquals(f, dsOther.getValue(),
+<a class="jxr_linenumber" name="243" href="#243">243</a> FastMath.abs(epsilon * f));
+<a class="jxr_linenumber" name="244" href="#244">244</a>
+<a class="jxr_linenumber" name="245" href="#245">245</a> <em class="jxr_comment">// df/dx = 1 + 5 y + 24 (8 z x - y)^2 z</em>
+<a class="jxr_linenumber" name="246" href="#246">246</a> <strong class="jxr_keyword">double</strong> dfdx = 1 + 5 * y + 24 * z * FastMath.pow(8 * z * x - y, 2);
+<a class="jxr_linenumber" name="247" href="#247">247</a> Assert.assertEquals(dfdx, ds.getPartialDerivative(1, 0, 0),
+<a class="jxr_linenumber" name="248" href="#248">248</a> FastMath.abs(epsilon * dfdx));
+<a class="jxr_linenumber" name="249" href="#249">249</a> Assert.assertEquals(dfdx, dsOther.getPartialDerivative(1, 0, 0),
+<a class="jxr_linenumber" name="250" href="#250">250</a> FastMath.abs(epsilon * dfdx));
+<a class="jxr_linenumber" name="251" href="#251">251</a>
+<a class="jxr_linenumber" name="252" href="#252">252</a> <em class="jxr_comment">// df/dxdy = 5 + 48 z*(y - 8 z x)</em>
+<a class="jxr_linenumber" name="253" href="#253">253</a> <strong class="jxr_keyword">double</strong> dfdxdy = 5 + 48 * z * (y - 8 * z * x);
+<a class="jxr_linenumber" name="254" href="#254">254</a> Assert.assertEquals(dfdxdy, ds.getPartialDerivative(1, 1, 0),
+<a class="jxr_linenumber" name="255" href="#255">255</a> FastMath.abs(epsilon * dfdxdy));
+<a class="jxr_linenumber" name="256" href="#256">256</a> Assert.assertEquals(dfdxdy, dsOther.getPartialDerivative(1, 1, 0),
+<a class="jxr_linenumber" name="257" href="#257">257</a> FastMath.abs(epsilon * dfdxdy));
+<a class="jxr_linenumber" name="258" href="#258">258</a>
+<a class="jxr_linenumber" name="259" href="#259">259</a> <em class="jxr_comment">// df/dxdydz = 48 (y - 16 z x)</em>
+<a class="jxr_linenumber" name="260" href="#260">260</a> <strong class="jxr_keyword">double</strong> dfdxdydz = 48 * (y - 16 * z * x);
+<a class="jxr_linenumber" name="261" href="#261">261</a> Assert.assertEquals(dfdxdydz, ds.getPartialDerivative(1, 1, 1),
+<a class="jxr_linenumber" name="262" href="#262">262</a> FastMath.abs(epsilon * dfdxdydz));
+<a class="jxr_linenumber" name="263" href="#263">263</a> Assert.assertEquals(dfdxdydz, dsOther.getPartialDerivative(1, 1, 1),
+<a class="jxr_linenumber" name="264" href="#264">264</a> FastMath.abs(epsilon * dfdxdydz));
<a class="jxr_linenumber" name="265" href="#265">265</a>
-<a class="jxr_linenumber" name="266" href="#266">266</a> @Test
-<a class="jxr_linenumber" name="267" href="#267">267</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCompositionOneVariableX() {
-<a class="jxr_linenumber" name="268" href="#268">268</a> <strong class="jxr_keyword">double</strong> epsilon = 1.0e-13;
-<a class="jxr_linenumber" name="269" href="#269">269</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="270" href="#270">270</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
-<a class="jxr_linenumber" name="271" href="#271">271</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, 0, x);
-<a class="jxr_linenumber" name="272" href="#272">272</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0.1; y < 1.2; y += 0.1) {
-<a class="jxr_linenumber" name="273" href="#273">273</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, y);
-<a class="jxr_linenumber" name="274" href="#274">274</a> DerivativeStructure f = dsX.divide(dsY).sqrt();
-<a class="jxr_linenumber" name="275" href="#275">275</a> <strong class="jxr_keyword">double</strong> f0 = FastMath.sqrt(x / y);
-<a class="jxr_linenumber" name="276" href="#276">276</a> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
-<a class="jxr_linenumber" name="277" href="#277">277</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 0) {
-<a class="jxr_linenumber" name="278" href="#278">278</a> <strong class="jxr_keyword">double</strong> f1 = 1 / (2 * FastMath.sqrt(x * y));
-<a class="jxr_linenumber" name="279" href="#279">279</a> Assert.assertEquals(f1, f.getPartialDerivative(1), FastMath.abs(epsilon * f1));
-<a class="jxr_linenumber" name="280" href="#280">280</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 1) {
-<a class="jxr_linenumber" name="281" href="#281">281</a> <strong class="jxr_keyword">double</strong> f2 = -f1 / (2 * x);
-<a class="jxr_linenumber" name="282" href="#282">282</a> Assert.assertEquals(f2, f.getPartialDerivative(2), FastMath.abs(epsilon * f2));
-<a class="jxr_linenumber" name="283" href="#283">283</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 2) {
-<a class="jxr_linenumber" name="284" href="#284">284</a> <strong class="jxr_keyword">double</strong> f3 = (f0 + x / (2 * y * f0)) / (4 * x * x * x);
-<a class="jxr_linenumber" name="285" href="#285">285</a> Assert.assertEquals(f3, f.getPartialDerivative(3), FastMath.abs(epsilon * f3));
-<a class="jxr_linenumber" name="286" href="#286">286</a> }
-<a class="jxr_linenumber" name="287" href="#287">287</a> }
-<a class="jxr_linenumber" name="288" href="#288">288</a> }
-<a class="jxr_linenumber" name="289" href="#289">289</a> }
-<a class="jxr_linenumber" name="290" href="#290">290</a> }
-<a class="jxr_linenumber" name="291" href="#291">291</a> }
-<a class="jxr_linenumber" name="292" href="#292">292</a> }
-<a class="jxr_linenumber" name="293" href="#293">293</a>
-<a class="jxr_linenumber" name="294" href="#294">294</a> @Test
-<a class="jxr_linenumber" name="295" href="#295">295</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTrigo() {
-<a class="jxr_linenumber" name="296" href="#296">296</a> <strong class="jxr_keyword">double</strong> epsilon = 2.0e-12;
-<a class="jxr_linenumber" name="297" href="#297">297</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="298" href="#298">298</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
-<a class="jxr_linenumber" name="299" href="#299">299</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, x);
-<a class="jxr_linenumber" name="300" href="#300">300</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0.1; y < 1.2; y += 0.1) {
-<a class="jxr_linenumber" name="301" href="#301">301</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, y);
-<a class="jxr_linenumber" name="302" href="#302">302</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = 0.1; z < 1.2; z += 0.1) {
-<a class="jxr_linenumber" name="303" href="#303">303</a> DerivativeStructure dsZ = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, z);
-<a class="jxr_linenumber" name="304" href="#304">304</a> DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();
-<a class="jxr_linenumber" name="305" href="#305">305</a> <strong class="jxr_keyword">double</strong> a = FastMath.cos(y) + FastMath.tan(z);
-<a class="jxr_linenumber" name="306" href="#306">306</a> <strong class="jxr_keyword">double</strong> f0 = FastMath.sin(x / a);
-<a class="jxr_linenumber" name="307" href="#307">307</a> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
-<a class="jxr_linenumber" name="308" href="#308">308</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 0) {
-<a class="jxr_linenumber" name="309" href="#309">309</a> <strong class="jxr_keyword">double</strong> dfdx = FastMath.cos(x / a) / a;
-<a class="jxr_linenumber" name="310" href="#310">310</a> Assert.assertEquals(dfdx, f.getPartialDerivative(1, 0, 0), FastMath.abs(epsilon * dfdx));
-<a class="jxr_linenumber" name="311" href="#311">311</a> <strong class="jxr_keyword">double</strong> dfdy = x * FastMath.sin(y) * dfdx / a;
-<a class="jxr_linenumber" name="312" href="#312">312</a> Assert.assertEquals(dfdy, f.getPartialDerivative(0, 1, 0), FastMath.abs(epsilon * dfdy));
-<a class="jxr_linenumber" name="313" href="#313">313</a> <strong class="jxr_keyword">double</strong> cz = FastMath.cos(z);
-<a class="jxr_linenumber" name="314" href="#314">314</a> <strong class="jxr_keyword">double</strong> cz2 = cz * cz;
-<a class="jxr_linenumber" name="315" href="#315">315</a> <strong class="jxr_keyword">double</strong> dfdz = -x * dfdx / (a * cz2);
-<a class="jxr_linenumber" name="316" href="#316">316</a> Assert.assertEquals(dfdz, f.getPartialDerivative(0, 0, 1), FastMath.abs(epsilon * dfdz));
-<a class="jxr_linenumber" name="317" href="#317">317</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 1) {
-<a class="jxr_linenumber" name="318" href="#318">318</a> <strong class="jxr_keyword">double</strong> df2dx2 = -(f0 / (a * a));
-<a class="jxr_linenumber" name="319" href="#319">319</a> Assert.assertEquals(df2dx2, f.getPartialDerivative(2, 0, 0), FastMath.abs(epsilon * df2dx2));
-<a class="jxr_linenumber" name="320" href="#320">320</a> <strong class="jxr_keyword">double</strong> df2dy2 = x * FastMath.cos(y) * dfdx / a -
-<a class="jxr_linenumber" name="321" href="#321">321</a> x * x * FastMath.sin(y) * FastMath.sin(y) * f0 / (a * a * a * a) +
-<a class="jxr_linenumber" name="322" href="#322">322</a> 2 * FastMath.sin(y) * dfdy / a;
-<a class="jxr_linenumber" name="323" href="#323">323</a> Assert.assertEquals(df2dy2, f.getPartialDerivative(0, 2, 0), FastMath.abs(epsilon * df2dy2));
-<a class="jxr_linenumber" name="324" href="#324">324</a> <strong class="jxr_keyword">double</strong> c4 = cz2 * cz2;
-<a class="jxr_linenumber" name="325" href="#325">325</a> <strong class="jxr_keyword">double</strong> df2dz2 = x * (2 * a * (1 - a * cz * FastMath.sin(z)) * dfdx - x * f0 / a ) / (a * a * a * c4);
-<a class="jxr_linenumber" name="326" href="#326">326</a> Assert.assertEquals(df2dz2, f.getPartialDerivative(0, 0, 2), FastMath.abs(epsilon * df2dz2));
-<a class="jxr_linenumber" name="327" href="#327">327</a> <strong class="jxr_keyword">double</strong> df2dxdy = dfdy / x - x * FastMath.sin(y) * f0 / (a * a * a);
-<a class="jxr_linenumber" name="328" href="#328">328</a> Assert.assertEquals(df2dxdy, f.getPartialDerivative(1, 1, 0), FastMath.abs(epsilon * df2dxdy));
-<a class="jxr_linenumber" name="329" href="#329">329</a> }
-<a class="jxr_linenumber" name="330" href="#330">330</a> }
-<a class="jxr_linenumber" name="331" href="#331">331</a> }
-<a class="jxr_linenumber" name="332" href="#332">332</a> }
-<a class="jxr_linenumber" name="333" href="#333">333</a> }
-<a class="jxr_linenumber" name="334" href="#334">334</a> }
-<a class="jxr_linenumber" name="335" href="#335">335</a> }
-<a class="jxr_linenumber" name="336" href="#336">336</a>
-<a class="jxr_linenumber" name="337" href="#337">337</a> @Test
-<a class="jxr_linenumber" name="338" href="#338">338</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSqrtDefinition() {
-<a class="jxr_linenumber" name="339" href="#339">339</a> <strong class="jxr_keyword">double</strong>[] epsilon = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { 5.0e-16, 5.0e-16, 2.0e-15, 5.0e-14, 2.0e-12 };
-<a class="jxr_linenumber" name="340" href="#340">340</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 5; ++maxOrder) {
-<a class="jxr_linenumber" name="341" href="#341">341</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.001) {
-<a class="jxr_linenumber" name="342" href="#342">342</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, 0, x);
-<a class="jxr_linenumber" name="343" href="#343">343</a> DerivativeStructure sqrt1 = dsX.pow(0.5);
-<a class="jxr_linenumber" name="344" href="#344">344</a> DerivativeStructure sqrt2 = dsX.sqrt();
-<a class="jxr_linenumber" name="345" href="#345">345</a> DerivativeStructure zero = sqrt1.subtract(sqrt2);
-<a class="jxr_linenumber" name="346" href="#346">346</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> n = 0; n <= maxOrder; ++n) {
-<a class="jxr_linenumber" name="347" href="#347">347</a> Assert.assertEquals(0, zero.getPartialDerivative(n), epsilon[n]);
-<a class="jxr_linenumber" name="348" href="#348">348</a> }
-<a class="jxr_linenumber" name="349" href="#349">349</a> }
-<a class="jxr_linenumber" name="350" href="#350">350</a> }
-<a class="jxr_linenumber" name="351" href="#351">351</a> }
-<a class="jxr_linenumber" name="352" href="#352">352</a>
-<a class="jxr_linenumber" name="353" href="#353">353</a> @Test
-<a class="jxr_linenumber" name="354" href="#354">354</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testRootNSingularity() {
-<a class="jxr_linenumber" name="355" href="#355">355</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> n = 2; n < 10; ++n) {
-<a class="jxr_linenumber" name="356" href="#356">356</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 12; ++maxOrder) {
-<a class="jxr_linenumber" name="357" href="#357">357</a> DerivativeStructure dsZero = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, 0, 0.0);
-<a class="jxr_linenumber" name="358" href="#358">358</a> DerivativeStructure rootN = dsZero.rootN(n);
-<a class="jxr_linenumber" name="359" href="#359">359</a> Assert.assertEquals(0.0, rootN.getValue(), 1.0e-20);
-<a class="jxr_linenumber" name="360" href="#360">360</a> <strong class="jxr_keyword">if</strong> (maxOrder > 0) {
-<a class="jxr_linenumber" name="361" href="#361">361</a> Assert.assertTrue(Double.isInfinite(rootN.getPartialDerivative(1)));
-<a class="jxr_linenumber" name="362" href="#362">362</a> Assert.assertTrue(rootN.getPartialDerivative(1) > 0);
-<a class="jxr_linenumber" name="363" href="#363">363</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> order = 2; order <= maxOrder; ++order) {
-<a class="jxr_linenumber" name="364" href="#364">364</a> <em class="jxr_comment">// the following checks shows a LIMITATION of the current implementation</em>
-<a class="jxr_linenumber" name="365" href="#365">365</a> <em class="jxr_comment">// we have no way to tell dsZero is a pure linear variable x = 0</em>
-<a class="jxr_linenumber" name="366" href="#366">366</a> <em class="jxr_comment">// we only say: "dsZero is a structure with value = 0.0,</em>
-<a class="jxr_linenumber" name="367" href="#367">367</a> <em class="jxr_comment">// first derivative = 1.0, second and higher derivatives = 0.0".</em>
-<a class="jxr_linenumber" name="368" href="#368">368</a> <em class="jxr_comment">// Function composition rule for second derivatives is:</em>
-<a class="jxr_linenumber" name="369" href="#369">369</a> <em class="jxr_comment">// d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)</em>
-<a class="jxr_linenumber" name="370" href="#370">370</a> <em class="jxr_comment">// when function f is the nth root and x = 0 we have:</em>
-<a class="jxr_linenumber" name="371" href="#371">371</a> <em class="jxr_comment">// f(0) = 0, f'(0) = +infinity, f''(0) = -infinity (and higher</em>
-<a class="jxr_linenumber" name="372" href="#372">372</a> <em class="jxr_comment">// derivatives keep switching between +infinity and -infinity)</em>
-<a class="jxr_linenumber" name="373" href="#373">373</a> <em class="jxr_comment">// so given that in our case dsZero represents g, we have g(x) = 0,</em>
-<a class="jxr_linenumber" name="374" href="#374">374</a> <em class="jxr_comment">// g'(x) = 1 and g''(x) = 0</em>
-<a class="jxr_linenumber" name="375" href="#375">375</a> <em class="jxr_comment">// applying the composition rules gives:</em>
-<a class="jxr_linenumber" name="376" href="#376">376</a> <em class="jxr_comment">// d2[f(g(x))]/dx2 = f''(g(x)) * [g'(x)]^2 + f'(g(x)) * g''(x)</em>
-<a class="jxr_linenumber" name="377" href="#377">377</a> <em class="jxr_comment">// = -infinity * 1^2 + +infinity * 0</em>
-<a class="jxr_linenumber" name="378" href="#378">378</a> <em class="jxr_comment">// = -infinity + NaN</em>
-<a class="jxr_linenumber" name="379" href="#379">379</a> <em class="jxr_comment">// = NaN</em>
-<a class="jxr_linenumber" name="380" href="#380">380</a> <em class="jxr_comment">// if we knew dsZero is really the x variable and not the identity</em>
-<a class="jxr_linenumber" name="381" href="#381">381</a> <em class="jxr_comment">// function applied to x, we would not have computed f'(g(x)) * g''(x)</em>
-<a class="jxr_linenumber" name="382" href="#382">382</a> <em class="jxr_comment">// and we would have found that the result was -infinity and not NaN</em>
-<a class="jxr_linenumber" name="383" href="#383">383</a> Assert.assertTrue(Double.isNaN(rootN.getPartialDerivative(order)));
-<a class="jxr_linenumber" name="384" href="#384">384</a> }
-<a class="jxr_linenumber" name="385" href="#385">385</a> }
-<a class="jxr_linenumber" name="386" href="#386">386</a>
-<a class="jxr_linenumber" name="387" href="#387">387</a> <em class="jxr_comment">// the following shows that the limitation explained above is NOT a bug...</em>
-<a class="jxr_linenumber" name="388" href="#388">388</a> <em class="jxr_comment">// if we set up the higher order derivatives for g appropriately, we do</em>
-<a class="jxr_linenumber" name="389" href="#389">389</a> <em class="jxr_comment">// compute the higher order derivatives of the composition correctly</em>
-<a class="jxr_linenumber" name="390" href="#390">390</a> <strong class="jxr_keyword">double</strong>[] gDerivatives = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[ 1 + maxOrder];
-<a class="jxr_linenumber" name="391" href="#391">391</a> gDerivatives[0] = 0.0;
-<a class="jxr_linenumber" name="392" href="#392">392</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 1; k <= maxOrder; ++k) {
-<a class="jxr_linenumber" name="393" href="#393">393</a> gDerivatives[k] = FastMath.pow(-1.0, k + 1);
-<a class="jxr_linenumber" name="394" href="#394">394</a> }
-<a class="jxr_linenumber" name="395" href="#395">395</a> DerivativeStructure correctRoot = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, gDerivatives).rootN(n);
-<a class="jxr_linenumber" name="396" href="#396">396</a> Assert.assertEquals(0.0, correctRoot.getValue(), 1.0e-20);
-<a class="jxr_linenumber" name="397" href="#397">397</a> <strong class="jxr_keyword">if</strong> (maxOrder > 0) {
-<a class="jxr_linenumber" name="398" href="#398">398</a> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(1)));
-<a class="jxr_linenumber" name="399" href="#399">399</a> Assert.assertTrue(correctRoot.getPartialDerivative(1) > 0);
-<a class="jxr_linenumber" name="400" href="#400">400</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> order = 2; order <= maxOrder; ++order) {
-<a class="jxr_linenumber" name="401" href="#401">401</a> Assert.assertTrue(Double.isInfinite(correctRoot.getPartialDerivative(order)));
-<a class="jxr_linenumber" name="402" href="#402">402</a> <strong class="jxr_keyword">if</strong> ((order % 2) == 0) {
-<a class="jxr_linenumber" name="403" href="#403">403</a> Assert.assertTrue(correctRoot.getPartialDerivative(order) < 0);
-<a class="jxr_linenumber" name="404" href="#404">404</a> } <strong class="jxr_keyword">else</strong> {
-<a class="jxr_linenumber" name="405" href="#405">405</a> Assert.assertTrue(correctRoot.getPartialDerivative(order) > 0);
-<a class="jxr_linenumber" name="406" href="#406">406</a> }
-<a class="jxr_linenumber" name="407" href="#407">407</a> }
-<a class="jxr_linenumber" name="408" href="#408">408</a> }
-<a class="jxr_linenumber" name="409" href="#409">409</a>
-<a class="jxr_linenumber" name="410" href="#410">410</a> }
-<a class="jxr_linenumber" name="411" href="#411">411</a>
-<a class="jxr_linenumber" name="412" href="#412">412</a> }
-<a class="jxr_linenumber" name="413" href="#413">413</a>
-<a class="jxr_linenumber" name="414" href="#414">414</a> }
+<a class="jxr_linenumber" name="266" href="#266">266</a> }
+<a class="jxr_linenumber" name="267" href="#267">267</a>
+<a class="jxr_linenumber" name="268" href="#268">268</a> }
+<a class="jxr_linenumber" name="269" href="#269">269</a> }
+<a class="jxr_linenumber" name="270" href="#270">270</a> }
+<a class="jxr_linenumber" name="271" href="#271">271</a>
+<a class="jxr_linenumber" name="272" href="#272">272</a> @Test
+<a class="jxr_linenumber" name="273" href="#273">273</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testCompositionOneVariableX() {
+<a class="jxr_linenumber" name="274" href="#274">274</a> <strong class="jxr_keyword">double</strong> epsilon = 1.0e-13;
+<a class="jxr_linenumber" name="275" href="#275">275</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="276" href="#276">276</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
+<a class="jxr_linenumber" name="277" href="#277">277</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, 0, x);
+<a class="jxr_linenumber" name="278" href="#278">278</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0.1; y < 1.2; y += 0.1) {
+<a class="jxr_linenumber" name="279" href="#279">279</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(1, maxOrder, y);
+<a class="jxr_linenumber" name="280" href="#280">280</a> DerivativeStructure f = dsX.divide(dsY).sqrt();
+<a class="jxr_linenumber" name="281" href="#281">281</a> <strong class="jxr_keyword">double</strong> f0 = FastMath.sqrt(x / y);
+<a class="jxr_linenumber" name="282" href="#282">282</a> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
+<a class="jxr_linenumber" name="283" href="#283">283</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 0) {
+<a class="jxr_linenumber" name="284" href="#284">284</a> <strong class="jxr_keyword">double</strong> f1 = 1 / (2 * FastMath.sqrt(x * y));
+<a class="jxr_linenumber" name="285" href="#285">285</a> Assert.assertEquals(f1, f.getPartialDerivative(1), FastMath.abs(epsilon * f1));
+<a class="jxr_linenumber" name="286" href="#286">286</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 1) {
+<a class="jxr_linenumber" name="287" href="#287">287</a> <strong class="jxr_keyword">double</strong> f2 = -f1 / (2 * x);
+<a class="jxr_linenumber" name="288" href="#288">288</a> Assert.assertEquals(f2, f.getPartialDerivative(2), FastMath.abs(epsilon * f2));
+<a class="jxr_linenumber" name="289" href="#289">289</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 2) {
+<a class="jxr_linenumber" name="290" href="#290">290</a> <strong class="jxr_keyword">double</strong> f3 = (f0 + x / (2 * y * f0)) / (4 * x * x * x);
+<a class="jxr_linenumber" name="291" href="#291">291</a> Assert.assertEquals(f3, f.getPartialDerivative(3), FastMath.abs(epsilon * f3));
+<a class="jxr_linenumber" name="292" href="#292">292</a> }
+<a class="jxr_linenumber" name="293" href="#293">293</a> }
+<a class="jxr_linenumber" name="294" href="#294">294</a> }
+<a class="jxr_linenumber" name="295" href="#295">295</a> }
+<a class="jxr_linenumber" name="296" href="#296">296</a> }
+<a class="jxr_linenumber" name="297" href="#297">297</a> }
+<a class="jxr_linenumber" name="298" href="#298">298</a> }
+<a class="jxr_linenumber" name="299" href="#299">299</a>
+<a class="jxr_linenumber" name="300" href="#300">300</a> @Test
+<a class="jxr_linenumber" name="301" href="#301">301</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTrigo() {
+<a class="jxr_linenumber" name="302" href="#302">302</a> <strong class="jxr_keyword">double</strong> epsilon = 2.0e-12;
+<a class="jxr_linenumber" name="303" href="#303">303</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> maxOrder = 0; maxOrder < 5; ++maxOrder) {
+<a class="jxr_linenumber" name="304" href="#304">304</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> x = 0.1; x < 1.2; x += 0.1) {
+<a class="jxr_linenumber" name="305" href="#305">305</a> DerivativeStructure dsX = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 0, x);
+<a class="jxr_linenumber" name="306" href="#306">306</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> y = 0.1; y < 1.2; y += 0.1) {
+<a class="jxr_linenumber" name="307" href="#307">307</a> DerivativeStructure dsY = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 1, y);
+<a class="jxr_linenumber" name="308" href="#308">308</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> z = 0.1; z < 1.2; z += 0.1) {
+<a class="jxr_linenumber" name="309" href="#309">309</a> DerivativeStructure dsZ = <strong class="jxr_keyword">new</strong> DerivativeStructure(3, maxOrder, 2, z);
+<a class="jxr_linenumber" name="310" href="#310">310</a> DerivativeStructure f = dsX.divide(dsY.cos().add(dsZ.tan())).sin();
+<a class="jxr_linenumber" name="311" href="#311">311</a> <strong class="jxr_keyword">double</strong> a = FastMath.cos(y) + FastMath.tan(z);
+<a class="jxr_linenumber" name="312" href="#312">312</a> <strong class="jxr_keyword">double</strong> f0 = FastMath.sin(x / a);
+<a class="jxr_linenumber" name="313" href="#313">313</a> Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
+<a class="jxr_linenumber" name="314" href="#314">314</a> <strong class="jxr_keyword">if</strong> (f.getOrder() > 0) {
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