Repository: commons-complex Updated Branches: refs/heads/master f4195fec7 -> b3576eeb6
http://git-wip-us.apache.org/repos/asf/commons-complex/blob/b3576eeb/site-content/.svn/pristine/06/0640bc70df1ed91181aa7f85d2220b0021526e77.svn-base ---------------------------------------------------------------------- diff --git a/site-content/.svn/pristine/06/0640bc70df1ed91181aa7f85d2220b0021526e77.svn-base b/site-content/.svn/pristine/06/0640bc70df1ed91181aa7f85d2220b0021526e77.svn-base deleted file mode 100644 index 803ca12..0000000 --- a/site-content/.svn/pristine/06/0640bc70df1ed91181aa7f85d2220b0021526e77.svn-base +++ /dev/null @@ -1,795 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd";> -<html xmlns="http://www.w3.org/1999/xhtml"; xml:lang="en" lang="en"> -<head><meta http-equiv="content-type" content="text/html; charset=UTF-8" /> -<title>EigenDecompositionTest xref</title> -<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" /> -</head> -<body> -<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/math3/linear/EigenDecompositionTest.html">View Javadoc</a></div><pre> -<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em> -<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em> -<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em> -<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em> -<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em> -<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em> -<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em> -<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em> -<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2."; target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.</a>0</em> -<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em> -<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em> -<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em> -<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em> -<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em> -<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em> -<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em> -<a class="jxr_linenumber" name="L17" href="#L17">17</a> -<a class="jxr_linenumber" name="L18" href="#L18">18</a> <strong class="jxr_keyword">package</strong> org.apache.commons.math3.linear; -<a class="jxr_linenumber" name="L19" href="#L19">19</a> -<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> java.util.Arrays; -<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> java.util.Random; -<a class="jxr_linenumber" name="L22" href="#L22">22</a> -<a class="jxr_linenumber" name="L23" href="#L23">23</a> -<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.distribution.NormalDistribution; -<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath; -<a class="jxr_linenumber" name="L26" href="#L26">26</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.Precision; -<a class="jxr_linenumber" name="L27" href="#L27">27</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.MathArrays; -<a class="jxr_linenumber" name="L28" href="#L28">28</a> <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.MathUnsupportedOperationException; -<a class="jxr_linenumber" name="L29" href="#L29">29</a> <strong class="jxr_keyword">import</strong> org.junit.After; -<a class="jxr_linenumber" name="L30" href="#L30">30</a> <strong class="jxr_keyword">import</strong> org.junit.Assert; -<a class="jxr_linenumber" name="L31" href="#L31">31</a> <strong class="jxr_keyword">import</strong> org.junit.Before; -<a class="jxr_linenumber" name="L32" href="#L32">32</a> <strong class="jxr_keyword">import</strong> org.junit.Ignore; -<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">import</strong> org.junit.Test; -<a class="jxr_linenumber" name="L34" href="#L34">34</a> -<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../org/apache/commons/math3/linear/EigenDecompositionTest.html">EigenDecompositionTest</a> { -<a class="jxr_linenumber" name="L36" href="#L36">36</a> -<a class="jxr_linenumber" name="L37" href="#L37">37</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong>[] refValues; -<a class="jxr_linenumber" name="L38" href="#L38">38</a> <strong class="jxr_keyword">private</strong> RealMatrix matrix; -<a class="jxr_linenumber" name="L39" href="#L39">39</a> -<a class="jxr_linenumber" name="L40" href="#L40">40</a> @Test -<a class="jxr_linenumber" name="L41" href="#L41">41</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension1() { -<a class="jxr_linenumber" name="L42" href="#L42">42</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L43" href="#L43">43</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { { 1.5 } }); -<a class="jxr_linenumber" name="L44" href="#L44">44</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L45" href="#L45">45</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L46" href="#L46">46</a> Assert.assertEquals(1.5, ed.getRealEigenvalue(0), 1.0e-15); -<a class="jxr_linenumber" name="L47" href="#L47">47</a> } -<a class="jxr_linenumber" name="L48" href="#L48">48</a> -<a class="jxr_linenumber" name="L49" href="#L49">49</a> @Test -<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension2() { -<a class="jxr_linenumber" name="L51" href="#L51">51</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L52" href="#L52">52</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L53" href="#L53">53</a> { 59.0, 12.0 }, -<a class="jxr_linenumber" name="L54" href="#L54">54</a> { 12.0, 66.0 } -<a class="jxr_linenumber" name="L55" href="#L55">55</a> }); -<a class="jxr_linenumber" name="L56" href="#L56">56</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L57" href="#L57">57</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L58" href="#L58">58</a> Assert.assertEquals(75.0, ed.getRealEigenvalue(0), 1.0e-15); -<a class="jxr_linenumber" name="L59" href="#L59">59</a> Assert.assertEquals(50.0, ed.getRealEigenvalue(1), 1.0e-15); -<a class="jxr_linenumber" name="L60" href="#L60">60</a> } -<a class="jxr_linenumber" name="L61" href="#L61">61</a> -<a class="jxr_linenumber" name="L62" href="#L62">62</a> @Test -<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension3() { -<a class="jxr_linenumber" name="L64" href="#L64">64</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L65" href="#L65">65</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L66" href="#L66">66</a> { 39632.0, -4824.0, -16560.0 }, -<a class="jxr_linenumber" name="L67" href="#L67">67</a> { -4824.0, 8693.0, 7920.0 }, -<a class="jxr_linenumber" name="L68" href="#L68">68</a> { -16560.0, 7920.0, 17300.0 } -<a class="jxr_linenumber" name="L69" href="#L69">69</a> }); -<a class="jxr_linenumber" name="L70" href="#L70">70</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L71" href="#L71">71</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L72" href="#L72">72</a> Assert.assertEquals(50000.0, ed.getRealEigenvalue(0), 3.0e-11); -<a class="jxr_linenumber" name="L73" href="#L73">73</a> Assert.assertEquals(12500.0, ed.getRealEigenvalue(1), 3.0e-11); -<a class="jxr_linenumber" name="L74" href="#L74">74</a> Assert.assertEquals( 3125.0, ed.getRealEigenvalue(2), 3.0e-11); -<a class="jxr_linenumber" name="L75" href="#L75">75</a> } -<a class="jxr_linenumber" name="L76" href="#L76">76</a> -<a class="jxr_linenumber" name="L77" href="#L77">77</a> @Test -<a class="jxr_linenumber" name="L78" href="#L78">78</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension3MultipleRoot() { -<a class="jxr_linenumber" name="L79" href="#L79">79</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L80" href="#L80">80</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L81" href="#L81">81</a> { 5, 10, 15 }, -<a class="jxr_linenumber" name="L82" href="#L82">82</a> { 10, 20, 30 }, -<a class="jxr_linenumber" name="L83" href="#L83">83</a> { 15, 30, 45 } -<a class="jxr_linenumber" name="L84" href="#L84">84</a> }); -<a class="jxr_linenumber" name="L85" href="#L85">85</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L86" href="#L86">86</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L87" href="#L87">87</a> Assert.assertEquals(70.0, ed.getRealEigenvalue(0), 3.0e-11); -<a class="jxr_linenumber" name="L88" href="#L88">88</a> Assert.assertEquals(0.0, ed.getRealEigenvalue(1), 3.0e-11); -<a class="jxr_linenumber" name="L89" href="#L89">89</a> Assert.assertEquals(0.0, ed.getRealEigenvalue(2), 3.0e-11); -<a class="jxr_linenumber" name="L90" href="#L90">90</a> } -<a class="jxr_linenumber" name="L91" href="#L91">91</a> -<a class="jxr_linenumber" name="L92" href="#L92">92</a> @Test -<a class="jxr_linenumber" name="L93" href="#L93">93</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension4WithSplit() { -<a class="jxr_linenumber" name="L94" href="#L94">94</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L95" href="#L95">95</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L96" href="#L96">96</a> { 0.784, -0.288, 0.000, 0.000 }, -<a class="jxr_linenumber" name="L97" href="#L97">97</a> { -0.288, 0.616, 0.000, 0.000 }, -<a class="jxr_linenumber" name="L98" href="#L98">98</a> { 0.000, 0.000, 0.164, -0.048 }, -<a class="jxr_linenumber" name="L99" href="#L99">99</a> { 0.000, 0.000, -0.048, 0.136 } -<a class="jxr_linenumber" name="L100" href="#L100">100</a> }); -<a class="jxr_linenumber" name="L101" href="#L101">101</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L102" href="#L102">102</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L103" href="#L103">103</a> Assert.assertEquals(1.0, ed.getRealEigenvalue(0), 1.0e-15); -<a class="jxr_linenumber" name="L104" href="#L104">104</a> Assert.assertEquals(0.4, ed.getRealEigenvalue(1), 1.0e-15); -<a class="jxr_linenumber" name="L105" href="#L105">105</a> Assert.assertEquals(0.2, ed.getRealEigenvalue(2), 1.0e-15); -<a class="jxr_linenumber" name="L106" href="#L106">106</a> Assert.assertEquals(0.1, ed.getRealEigenvalue(3), 1.0e-15); -<a class="jxr_linenumber" name="L107" href="#L107">107</a> } -<a class="jxr_linenumber" name="L108" href="#L108">108</a> -<a class="jxr_linenumber" name="L109" href="#L109">109</a> @Test -<a class="jxr_linenumber" name="L110" href="#L110">110</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimension4WithoutSplit() { -<a class="jxr_linenumber" name="L111" href="#L111">111</a> RealMatrix matrix = -<a class="jxr_linenumber" name="L112" href="#L112">112</a> MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L113" href="#L113">113</a> { 0.5608, -0.2016, 0.1152, -0.2976 }, -<a class="jxr_linenumber" name="L114" href="#L114">114</a> { -0.2016, 0.4432, -0.2304, 0.1152 }, -<a class="jxr_linenumber" name="L115" href="#L115">115</a> { 0.1152, -0.2304, 0.3088, -0.1344 }, -<a class="jxr_linenumber" name="L116" href="#L116">116</a> { -0.2976, 0.1152, -0.1344, 0.3872 } -<a class="jxr_linenumber" name="L117" href="#L117">117</a> }); -<a class="jxr_linenumber" name="L118" href="#L118">118</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L119" href="#L119">119</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L120" href="#L120">120</a> Assert.assertEquals(1.0, ed.getRealEigenvalue(0), 1.0e-15); -<a class="jxr_linenumber" name="L121" href="#L121">121</a> Assert.assertEquals(0.4, ed.getRealEigenvalue(1), 1.0e-15); -<a class="jxr_linenumber" name="L122" href="#L122">122</a> Assert.assertEquals(0.2, ed.getRealEigenvalue(2), 1.0e-15); -<a class="jxr_linenumber" name="L123" href="#L123">123</a> Assert.assertEquals(0.1, ed.getRealEigenvalue(3), 1.0e-15); -<a class="jxr_linenumber" name="L124" href="#L124">124</a> } -<a class="jxr_linenumber" name="L125" href="#L125">125</a> -<a class="jxr_linenumber" name="L126" href="#L126">126</a> <em class="jxr_comment">// the following test triggered an ArrayIndexOutOfBoundsException in commons-math 2.0</em> -<a class="jxr_linenumber" name="L127" href="#L127">127</a> @Test -<a class="jxr_linenumber" name="L128" href="#L128">128</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMath308() { -<a class="jxr_linenumber" name="L129" href="#L129">129</a> -<a class="jxr_linenumber" name="L130" href="#L130">130</a> <strong class="jxr_keyword">double</strong>[] mainTridiagonal = { -<a class="jxr_linenumber" name="L131" href="#L131">131</a> 22.330154644539597, 46.65485522478641, 17.393672330044705, 54.46687435351116, 80.17800767709437 -<a class="jxr_linenumber" name="L132" href="#L132">132</a> }; -<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">double</strong>[] secondaryTridiagonal = { -<a class="jxr_linenumber" name="L134" href="#L134">134</a> 13.04450406501361, -5.977590941539671, 2.9040909856707517, 7.1570352792841225 -<a class="jxr_linenumber" name="L135" href="#L135">135</a> }; -<a class="jxr_linenumber" name="L136" href="#L136">136</a> -<a class="jxr_linenumber" name="L137" href="#L137">137</a> <em class="jxr_comment">// the reference values have been computed using routine DSTEMR</em> -<a class="jxr_linenumber" name="L138" href="#L138">138</a> <em class="jxr_comment">// from the fortran library LAPACK version 3.2.1</em> -<a class="jxr_linenumber" name="L139" href="#L139">139</a> <strong class="jxr_keyword">double</strong>[] refEigenValues = { -<a class="jxr_linenumber" name="L140" href="#L140">140</a> 82.044413207204002, 53.456697699894512, 52.536278520113882, 18.847969733754262, 14.138204224043099 -<a class="jxr_linenumber" name="L141" href="#L141">141</a> }; -<a class="jxr_linenumber" name="L142" href="#L142">142</a> RealVector[] refEigenVectors = { -<a class="jxr_linenumber" name="L143" href="#L143">143</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { -0.000462690386766, -0.002118073109055, 0.011530080757413, 0.252322434584915, 0.967572088232592 }), -<a class="jxr_linenumber" name="L144" href="#L144">144</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { 0.314647769490148, 0.750806415553905, -0.167700312025760, -0.537092972407375, 0.143854968127780 }), -<a class="jxr_linenumber" name="L145" href="#L145">145</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { 0.222368839324646, 0.514921891363332, -0.021377019336614, 0.801196801016305, -0.207446991247740 }), -<a class="jxr_linenumber" name="L146" href="#L146">146</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { -0.713933751051495, 0.190582113553930, -0.671410443368332, 0.056056055955050, -0.006541576993581 }), -<a class="jxr_linenumber" name="L147" href="#L147">147</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { -0.584677060845929, 0.367177264979103, 0.721453187784497, -0.052971054621812, 0.005740715188257 }) -<a class="jxr_linenumber" name="L148" href="#L148">148</a> }; -<a class="jxr_linenumber" name="L149" href="#L149">149</a> -<a class="jxr_linenumber" name="L150" href="#L150">150</a> EigenDecomposition decomposition; -<a class="jxr_linenumber" name="L151" href="#L151">151</a> decomposition = <strong class="jxr_keyword">new</strong> EigenDecomposition(mainTridiagonal, secondaryTridiagonal); -<a class="jxr_linenumber" name="L152" href="#L152">152</a> -<a class="jxr_linenumber" name="L153" href="#L153">153</a> <strong class="jxr_keyword">double</strong>[] eigenValues = decomposition.getRealEigenvalues(); -<a class="jxr_linenumber" name="L154" href="#L154">154</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < refEigenValues.length; ++i) { -<a class="jxr_linenumber" name="L155" href="#L155">155</a> Assert.assertEquals(refEigenValues[i], eigenValues[i], 1.0e-5); -<a class="jxr_linenumber" name="L156" href="#L156">156</a> Assert.assertEquals(0, refEigenVectors[i].subtract(decomposition.getEigenvector(i)).getNorm(), 2.0e-7); -<a class="jxr_linenumber" name="L157" href="#L157">157</a> } -<a class="jxr_linenumber" name="L158" href="#L158">158</a> -<a class="jxr_linenumber" name="L159" href="#L159">159</a> } -<a class="jxr_linenumber" name="L160" href="#L160">160</a> -<a class="jxr_linenumber" name="L161" href="#L161">161</a> @Test -<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMathpbx02() { -<a class="jxr_linenumber" name="L163" href="#L163">163</a> -<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">double</strong>[] mainTridiagonal = { -<a class="jxr_linenumber" name="L165" href="#L165">165</a> 7484.860960227216, 18405.28129035345, 13855.225609560746, -<a class="jxr_linenumber" name="L166" href="#L166">166</a> 10016.708722343366, 559.8117399576674, 6750.190788301587, -<a class="jxr_linenumber" name="L167" href="#L167">167</a> 71.21428769782159 -<a class="jxr_linenumber" name="L168" href="#L168">168</a> }; -<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">double</strong>[] secondaryTridiagonal = { -<a class="jxr_linenumber" name="L170" href="#L170">170</a> -4175.088570476366,1975.7955858241994,5193.178422374075, -<a class="jxr_linenumber" name="L171" href="#L171">171</a> 1995.286659169179,75.34535882933804,-234.0808002076056 -<a class="jxr_linenumber" name="L172" href="#L172">172</a> }; -<a class="jxr_linenumber" name="L173" href="#L173">173</a> -<a class="jxr_linenumber" name="L174" href="#L174">174</a> <em class="jxr_comment">// the reference values have been computed using routine DSTEMR</em> -<a class="jxr_linenumber" name="L175" href="#L175">175</a> <em class="jxr_comment">// from the fortran library LAPACK version 3.2.1</em> -<a class="jxr_linenumber" name="L176" href="#L176">176</a> <strong class="jxr_keyword">double</strong>[] refEigenValues = { -<a class="jxr_linenumber" name="L177" href="#L177">177</a> 20654.744890306974412,16828.208208485466457, -<a class="jxr_linenumber" name="L178" href="#L178">178</a> 6893.155912634994820,6757.083016675340332, -<a class="jxr_linenumber" name="L179" href="#L179">179</a> 5887.799885688558788,64.309089923240379, -<a class="jxr_linenumber" name="L180" href="#L180">180</a> 57.992628792736340 -<a class="jxr_linenumber" name="L181" href="#L181">181</a> }; -<a class="jxr_linenumber" name="L182" href="#L182">182</a> RealVector[] refEigenVectors = { -<a class="jxr_linenumber" name="L183" href="#L183">183</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.270356342026904, 0.852811091326997, 0.399639490702077, 0.198794657813990, 0.019739323307666, 0.000106983022327, -0.000001216636321}), -<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.179995273578326,-0.402807848153042,0.701870993525734,0.555058211014888,0.068079148898236,0.000509139115227,-0.000007112235617}), -<a class="jxr_linenumber" name="L185" href="#L185">185</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.399582721284727,-0.056629954519333,-0.514406488522827,0.711168164518580,0.225548081276367,0.125943999652923,-0.004321507456014}), -<a class="jxr_linenumber" name="L186" href="#L186">186</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.058515721572821,0.010200130057739,0.063516274916536,-0.090696087449378,-0.017148420432597,0.991318870265707,-0.034707338554096}), -<a class="jxr_linenumber" name="L187" href="#L187">187</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.855205995537564,0.327134656629775,-0.265382397060548,0.282690729026706,0.105736068025572,-0.009138126622039,0.000367751821196}), -<a class="jxr_linenumber" name="L188" href="#L188">188</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.002913069901144,-0.005177515777101,0.041906334478672,-0.109315918416258,0.436192305456741,0.026307315639535,0.891797507436344}), -<a class="jxr_linenumber" name="L189" href="#L189">189</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.005738311176435,-0.010207611670378,0.082662420517928,-0.215733886094368,0.861606487840411,-0.025478530652759,-0.451080697503958}) -<a class="jxr_linenumber" name="L190" href="#L190">190</a> }; -<a class="jxr_linenumber" name="L191" href="#L191">191</a> -<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_comment">// the following line triggers the exception</em> -<a class="jxr_linenumber" name="L193" href="#L193">193</a> EigenDecomposition decomposition; -<a class="jxr_linenumber" name="L194" href="#L194">194</a> decomposition = <strong class="jxr_keyword">new</strong> EigenDecomposition(mainTridiagonal, secondaryTridiagonal); -<a class="jxr_linenumber" name="L195" href="#L195">195</a> -<a class="jxr_linenumber" name="L196" href="#L196">196</a> <strong class="jxr_keyword">double</strong>[] eigenValues = decomposition.getRealEigenvalues(); -<a class="jxr_linenumber" name="L197" href="#L197">197</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < refEigenValues.length; ++i) { -<a class="jxr_linenumber" name="L198" href="#L198">198</a> Assert.assertEquals(refEigenValues[i], eigenValues[i], 1.0e-3); -<a class="jxr_linenumber" name="L199" href="#L199">199</a> <strong class="jxr_keyword">if</strong> (refEigenVectors[i].dotProduct(decomposition.getEigenvector(i)) < 0) { -<a class="jxr_linenumber" name="L200" href="#L200">200</a> Assert.assertEquals(0, refEigenVectors[i].add(decomposition.getEigenvector(i)).getNorm(), 1.0e-5); -<a class="jxr_linenumber" name="L201" href="#L201">201</a> } <strong class="jxr_keyword">else</strong> { -<a class="jxr_linenumber" name="L202" href="#L202">202</a> Assert.assertEquals(0, refEigenVectors[i].subtract(decomposition.getEigenvector(i)).getNorm(), 1.0e-5); -<a class="jxr_linenumber" name="L203" href="#L203">203</a> } -<a class="jxr_linenumber" name="L204" href="#L204">204</a> } -<a class="jxr_linenumber" name="L205" href="#L205">205</a> -<a class="jxr_linenumber" name="L206" href="#L206">206</a> } -<a class="jxr_linenumber" name="L207" href="#L207">207</a> -<a class="jxr_linenumber" name="L208" href="#L208">208</a> @Test -<a class="jxr_linenumber" name="L209" href="#L209">209</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMathpbx03() { -<a class="jxr_linenumber" name="L210" href="#L210">210</a> -<a class="jxr_linenumber" name="L211" href="#L211">211</a> <strong class="jxr_keyword">double</strong>[] mainTridiagonal = { -<a class="jxr_linenumber" name="L212" href="#L212">212</a> 1809.0978259647177,3395.4763425956166,1832.1894584712693,3804.364873592377, -<a class="jxr_linenumber" name="L213" href="#L213">213</a> 806.0482458637571,2403.656427234185,28.48691431556015 -<a class="jxr_linenumber" name="L214" href="#L214">214</a> }; -<a class="jxr_linenumber" name="L215" href="#L215">215</a> <strong class="jxr_keyword">double</strong>[] secondaryTridiagonal = { -<a class="jxr_linenumber" name="L216" href="#L216">216</a> -656.8932064545833,-469.30804108920734,-1021.7714889369421, -<a class="jxr_linenumber" name="L217" href="#L217">217</a> -1152.540497328983,-939.9765163817368,-12.885877015422391 -<a class="jxr_linenumber" name="L218" href="#L218">218</a> }; -<a class="jxr_linenumber" name="L219" href="#L219">219</a> -<a class="jxr_linenumber" name="L220" href="#L220">220</a> <em class="jxr_comment">// the reference values have been computed using routine DSTEMR</em> -<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_comment">// from the fortran library LAPACK version 3.2.1</em> -<a class="jxr_linenumber" name="L222" href="#L222">222</a> <strong class="jxr_keyword">double</strong>[] refEigenValues = { -<a class="jxr_linenumber" name="L223" href="#L223">223</a> 4603.121913685183245,3691.195818048970978,2743.442955402465032,1657.596442107321764, -<a class="jxr_linenumber" name="L224" href="#L224">224</a> 1336.797819095331306,30.129865209677519,17.035352085224986 -<a class="jxr_linenumber" name="L225" href="#L225">225</a> }; -<a class="jxr_linenumber" name="L226" href="#L226">226</a> -<a class="jxr_linenumber" name="L227" href="#L227">227</a> RealVector[] refEigenVectors = { -<a class="jxr_linenumber" name="L228" href="#L228">228</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.036249830202337,0.154184732411519,-0.346016328392363,0.867540105133093,-0.294483395433451,0.125854235969548,-0.000354507444044}), -<a class="jxr_linenumber" name="L229" href="#L229">229</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.318654191697157,0.912992309960507,-0.129270874079777,-0.184150038178035,0.096521712579439,-0.070468788536461,0.000247918177736}), -<a class="jxr_linenumber" name="L230" href="#L230">230</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.051394668681147,0.073102235876933,0.173502042943743,-0.188311980310942,-0.327158794289386,0.905206581432676,-0.004296342252659}), -<a class="jxr_linenumber" name="L231" href="#L231">231</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.838150199198361,0.193305209055716,-0.457341242126146,-0.166933875895419,0.094512811358535,0.119062381338757,-0.000941755685226}), -<a class="jxr_linenumber" name="L232" href="#L232">232</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.438071395458547,0.314969169786246,0.768480630802146,0.227919171600705,-0.193317045298647,-0.170305467485594,0.001677380536009}), -<a class="jxr_linenumber" name="L233" href="#L233">233</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-0.003726503878741,-0.010091946369146,-0.067152015137611,-0.113798146542187,-0.313123000097908,-0.118940107954918,0.932862311396062}), -<a class="jxr_linenumber" name="L234" href="#L234">234</a> <strong class="jxr_keyword">new</strong> ArrayRealVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.009373003194332,0.025570377559400,0.170955836081348,0.291954519805750,0.807824267665706,0.320108347088646,0.360202112392266}), -<a class="jxr_linenumber" name="L235" href="#L235">235</a> }; -<a class="jxr_linenumber" name="L236" href="#L236">236</a> -<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_comment">// the following line triggers the exception</em> -<a class="jxr_linenumber" name="L238" href="#L238">238</a> EigenDecomposition decomposition; -<a class="jxr_linenumber" name="L239" href="#L239">239</a> decomposition = <strong class="jxr_keyword">new</strong> EigenDecomposition(mainTridiagonal, secondaryTridiagonal); -<a class="jxr_linenumber" name="L240" href="#L240">240</a> -<a class="jxr_linenumber" name="L241" href="#L241">241</a> <strong class="jxr_keyword">double</strong>[] eigenValues = decomposition.getRealEigenvalues(); -<a class="jxr_linenumber" name="L242" href="#L242">242</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < refEigenValues.length; ++i) { -<a class="jxr_linenumber" name="L243" href="#L243">243</a> Assert.assertEquals(refEigenValues[i], eigenValues[i], 1.0e-4); -<a class="jxr_linenumber" name="L244" href="#L244">244</a> <strong class="jxr_keyword">if</strong> (refEigenVectors[i].dotProduct(decomposition.getEigenvector(i)) < 0) { -<a class="jxr_linenumber" name="L245" href="#L245">245</a> Assert.assertEquals(0, refEigenVectors[i].add(decomposition.getEigenvector(i)).getNorm(), 1.0e-5); -<a class="jxr_linenumber" name="L246" href="#L246">246</a> } <strong class="jxr_keyword">else</strong> { -<a class="jxr_linenumber" name="L247" href="#L247">247</a> Assert.assertEquals(0, refEigenVectors[i].subtract(decomposition.getEigenvector(i)).getNorm(), 1.0e-5); -<a class="jxr_linenumber" name="L248" href="#L248">248</a> } -<a class="jxr_linenumber" name="L249" href="#L249">249</a> } -<a class="jxr_linenumber" name="L250" href="#L250">250</a> -<a class="jxr_linenumber" name="L251" href="#L251">251</a> } -<a class="jxr_linenumber" name="L252" href="#L252">252</a> -<a class="jxr_linenumber" name="L253" href="#L253">253</a> <em class="jxr_javadoccomment">/** test a matrix already in tridiagonal form. */</em> -<a class="jxr_linenumber" name="L254" href="#L254">254</a> @Test -<a class="jxr_linenumber" name="L255" href="#L255">255</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTridiagonal() { -<a class="jxr_linenumber" name="L256" href="#L256">256</a> Random r = <strong class="jxr_keyword">new</strong> Random(4366663527842l); -<a class="jxr_linenumber" name="L257" href="#L257">257</a> <strong class="jxr_keyword">double</strong>[] ref = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[30]; -<a class="jxr_linenumber" name="L258" href="#L258">258</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < ref.length; ++i) { -<a class="jxr_linenumber" name="L259" href="#L259">259</a> <strong class="jxr_keyword">if</strong> (i < 5) { -<a class="jxr_linenumber" name="L260" href="#L260">260</a> ref[i] = 2 * r.nextDouble() - 1; -<a class="jxr_linenumber" name="L261" href="#L261">261</a> } <strong class="jxr_keyword">else</strong> { -<a class="jxr_linenumber" name="L262" href="#L262">262</a> ref[i] = 0.0001 * r.nextDouble() + 6; -<a class="jxr_linenumber" name="L263" href="#L263">263</a> } -<a class="jxr_linenumber" name="L264" href="#L264">264</a> } -<a class="jxr_linenumber" name="L265" href="#L265">265</a> Arrays.sort(ref); -<a class="jxr_linenumber" name="L266" href="#L266">266</a> TriDiagonalTransformer t = -<a class="jxr_linenumber" name="L267" href="#L267">267</a> <strong class="jxr_keyword">new</strong> TriDiagonalTransformer(createTestMatrix(r, ref)); -<a class="jxr_linenumber" name="L268" href="#L268">268</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L269" href="#L269">269</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(t.getMainDiagonalRef(), t.getSecondaryDiagonalRef()); -<a class="jxr_linenumber" name="L270" href="#L270">270</a> <strong class="jxr_keyword">double</strong>[] eigenValues = ed.getRealEigenvalues(); -<a class="jxr_linenumber" name="L271" href="#L271">271</a> Assert.assertEquals(ref.length, eigenValues.length); -<a class="jxr_linenumber" name="L272" href="#L272">272</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < ref.length; ++i) { -<a class="jxr_linenumber" name="L273" href="#L273">273</a> Assert.assertEquals(ref[ref.length - i - 1], eigenValues[i], 2.0e-14); -<a class="jxr_linenumber" name="L274" href="#L274">274</a> } -<a class="jxr_linenumber" name="L275" href="#L275">275</a> -<a class="jxr_linenumber" name="L276" href="#L276">276</a> } -<a class="jxr_linenumber" name="L277" href="#L277">277</a> -<a class="jxr_linenumber" name="L278" href="#L278">278</a> <em class="jxr_javadoccomment">/** test dimensions */</em> -<a class="jxr_linenumber" name="L279" href="#L279">279</a> @Test -<a class="jxr_linenumber" name="L280" href="#L280">280</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDimensions() { -<a class="jxr_linenumber" name="L281" href="#L281">281</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = matrix.getRowDimension(); -<a class="jxr_linenumber" name="L282" href="#L282">282</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L283" href="#L283">283</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L284" href="#L284">284</a> Assert.assertEquals(m, ed.getV().getRowDimension()); -<a class="jxr_linenumber" name="L285" href="#L285">285</a> Assert.assertEquals(m, ed.getV().getColumnDimension()); -<a class="jxr_linenumber" name="L286" href="#L286">286</a> Assert.assertEquals(m, ed.getD().getColumnDimension()); -<a class="jxr_linenumber" name="L287" href="#L287">287</a> Assert.assertEquals(m, ed.getD().getColumnDimension()); -<a class="jxr_linenumber" name="L288" href="#L288">288</a> Assert.assertEquals(m, ed.getVT().getRowDimension()); -<a class="jxr_linenumber" name="L289" href="#L289">289</a> Assert.assertEquals(m, ed.getVT().getColumnDimension()); -<a class="jxr_linenumber" name="L290" href="#L290">290</a> } -<a class="jxr_linenumber" name="L291" href="#L291">291</a> -<a class="jxr_linenumber" name="L292" href="#L292">292</a> <em class="jxr_javadoccomment">/** test eigenvalues */</em> -<a class="jxr_linenumber" name="L293" href="#L293">293</a> @Test -<a class="jxr_linenumber" name="L294" href="#L294">294</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testEigenvalues() { -<a class="jxr_linenumber" name="L295" href="#L295">295</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L296" href="#L296">296</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L297" href="#L297">297</a> <strong class="jxr_keyword">double</strong>[] eigenValues = ed.getRealEigenvalues(); -<a class="jxr_linenumber" name="L298" href="#L298">298</a> Assert.assertEquals(refValues.length, eigenValues.length); -<a class="jxr_linenumber" name="L299" href="#L299">299</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < refValues.length; ++i) { -<a class="jxr_linenumber" name="L300" href="#L300">300</a> Assert.assertEquals(refValues[i], eigenValues[i], 3.0e-15); -<a class="jxr_linenumber" name="L301" href="#L301">301</a> } -<a class="jxr_linenumber" name="L302" href="#L302">302</a> } -<a class="jxr_linenumber" name="L303" href="#L303">303</a> -<a class="jxr_linenumber" name="L304" href="#L304">304</a> <em class="jxr_javadoccomment">/** test eigenvalues for a big matrix. */</em> -<a class="jxr_linenumber" name="L305" href="#L305">305</a> @Test -<a class="jxr_linenumber" name="L306" href="#L306">306</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testBigMatrix() { -<a class="jxr_linenumber" name="L307" href="#L307">307</a> Random r = <strong class="jxr_keyword">new</strong> Random(17748333525117l); -<a class="jxr_linenumber" name="L308" href="#L308">308</a> <strong class="jxr_keyword">double</strong>[] bigValues = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[200]; -<a class="jxr_linenumber" name="L309" href="#L309">309</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < bigValues.length; ++i) { -<a class="jxr_linenumber" name="L310" href="#L310">310</a> bigValues[i] = 2 * r.nextDouble() - 1; -<a class="jxr_linenumber" name="L311" href="#L311">311</a> } -<a class="jxr_linenumber" name="L312" href="#L312">312</a> Arrays.sort(bigValues); -<a class="jxr_linenumber" name="L313" href="#L313">313</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L314" href="#L314">314</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(createTestMatrix(r, bigValues)); -<a class="jxr_linenumber" name="L315" href="#L315">315</a> <strong class="jxr_keyword">double</strong>[] eigenValues = ed.getRealEigenvalues(); -<a class="jxr_linenumber" name="L316" href="#L316">316</a> Assert.assertEquals(bigValues.length, eigenValues.length); -<a class="jxr_linenumber" name="L317" href="#L317">317</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < bigValues.length; ++i) { -<a class="jxr_linenumber" name="L318" href="#L318">318</a> Assert.assertEquals(bigValues[bigValues.length - i - 1], eigenValues[i], 2.0e-14); -<a class="jxr_linenumber" name="L319" href="#L319">319</a> } -<a class="jxr_linenumber" name="L320" href="#L320">320</a> } -<a class="jxr_linenumber" name="L321" href="#L321">321</a> -<a class="jxr_linenumber" name="L322" href="#L322">322</a> @Test -<a class="jxr_linenumber" name="L323" href="#L323">323</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSymmetric() { -<a class="jxr_linenumber" name="L324" href="#L324">324</a> RealMatrix symmetric = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L325" href="#L325">325</a> {4, 1, 1}, -<a class="jxr_linenumber" name="L326" href="#L326">326</a> {1, 2, 3}, -<a class="jxr_linenumber" name="L327" href="#L327">327</a> {1, 3, 6} -<a class="jxr_linenumber" name="L328" href="#L328">328</a> }); -<a class="jxr_linenumber" name="L329" href="#L329">329</a> -<a class="jxr_linenumber" name="L330" href="#L330">330</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L331" href="#L331">331</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(symmetric); -<a class="jxr_linenumber" name="L332" href="#L332">332</a> -<a class="jxr_linenumber" name="L333" href="#L333">333</a> RealMatrix d = ed.getD(); -<a class="jxr_linenumber" name="L334" href="#L334">334</a> RealMatrix v = ed.getV(); -<a class="jxr_linenumber" name="L335" href="#L335">335</a> RealMatrix vT = ed.getVT(); -<a class="jxr_linenumber" name="L336" href="#L336">336</a> -<a class="jxr_linenumber" name="L337" href="#L337">337</a> <strong class="jxr_keyword">double</strong> norm = v.multiply(d).multiply(vT).subtract(symmetric).getNorm(); -<a class="jxr_linenumber" name="L338" href="#L338">338</a> Assert.assertEquals(0, norm, 6.0e-13); -<a class="jxr_linenumber" name="L339" href="#L339">339</a> } -<a class="jxr_linenumber" name="L340" href="#L340">340</a> -<a class="jxr_linenumber" name="L341" href="#L341">341</a> @Test -<a class="jxr_linenumber" name="L342" href="#L342">342</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSquareRoot() { -<a class="jxr_linenumber" name="L343" href="#L343">343</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] data = { -<a class="jxr_linenumber" name="L344" href="#L344">344</a> { 33, 24, 7 }, -<a class="jxr_linenumber" name="L345" href="#L345">345</a> { 24, 57, 11 }, -<a class="jxr_linenumber" name="L346" href="#L346">346</a> { 7, 11, 9 } -<a class="jxr_linenumber" name="L347" href="#L347">347</a> }; -<a class="jxr_linenumber" name="L348" href="#L348">348</a> -<a class="jxr_linenumber" name="L349" href="#L349">349</a> <strong class="jxr_keyword">final</strong> EigenDecomposition dec = <strong class="jxr_keyword">new</strong> EigenDecomposition(MatrixUtils.createRealMatrix(data)); -<a class="jxr_linenumber" name="L350" href="#L350">350</a> <strong class="jxr_keyword">final</strong> RealMatrix sqrtM = dec.getSquareRoot(); -<a class="jxr_linenumber" name="L351" href="#L351">351</a> -<a class="jxr_linenumber" name="L352" href="#L352">352</a> <em class="jxr_comment">// Reconstruct initial matrix.</em> -<a class="jxr_linenumber" name="L353" href="#L353">353</a> <strong class="jxr_keyword">final</strong> RealMatrix m = sqrtM.multiply(sqrtM); -<a class="jxr_linenumber" name="L354" href="#L354">354</a> -<a class="jxr_linenumber" name="L355" href="#L355">355</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> dim = data.length; -<a class="jxr_linenumber" name="L356" href="#L356">356</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> r = 0; r < dim; r++) { -<a class="jxr_linenumber" name="L357" href="#L357">357</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> c = 0; c < dim; c++) { -<a class="jxr_linenumber" name="L358" href="#L358">358</a> Assert.assertEquals(<span class="jxr_string">"m["</span> + r + <span class="jxr_string">"]["</span> + c + <span class="jxr_string">"]"</span>, -<a class="jxr_linenumber" name="L359" href="#L359">359</a> data[r][c], m.getEntry(r, c), 1e-13); -<a class="jxr_linenumber" name="L360" href="#L360">360</a> } -<a class="jxr_linenumber" name="L361" href="#L361">361</a> } -<a class="jxr_linenumber" name="L362" href="#L362">362</a> } -<a class="jxr_linenumber" name="L363" href="#L363">363</a> -<a class="jxr_linenumber" name="L364" href="#L364">364</a> @Test(expected=MathUnsupportedOperationException.<strong class="jxr_keyword">class</strong>) -<a class="jxr_linenumber" name="L365" href="#L365">365</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSquareRootNonSymmetric() { -<a class="jxr_linenumber" name="L366" href="#L366">366</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] data = { -<a class="jxr_linenumber" name="L367" href="#L367">367</a> { 1, 2, 4 }, -<a class="jxr_linenumber" name="L368" href="#L368">368</a> { 2, 3, 5 }, -<a class="jxr_linenumber" name="L369" href="#L369">369</a> { 11, 5, 9 } -<a class="jxr_linenumber" name="L370" href="#L370">370</a> }; -<a class="jxr_linenumber" name="L371" href="#L371">371</a> -<a class="jxr_linenumber" name="L372" href="#L372">372</a> <strong class="jxr_keyword">final</strong> EigenDecomposition dec = <strong class="jxr_keyword">new</strong> EigenDecomposition(MatrixUtils.createRealMatrix(data)); -<a class="jxr_linenumber" name="L373" href="#L373">373</a> @SuppressWarnings(<span class="jxr_string">"unused"</span>) -<a class="jxr_linenumber" name="L374" href="#L374">374</a> <strong class="jxr_keyword">final</strong> RealMatrix sqrtM = dec.getSquareRoot(); -<a class="jxr_linenumber" name="L375" href="#L375">375</a> } -<a class="jxr_linenumber" name="L376" href="#L376">376</a> -<a class="jxr_linenumber" name="L377" href="#L377">377</a> @Test(expected=MathUnsupportedOperationException.<strong class="jxr_keyword">class</strong>) -<a class="jxr_linenumber" name="L378" href="#L378">378</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testSquareRootNonPositiveDefinite() { -<a class="jxr_linenumber" name="L379" href="#L379">379</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] data = { -<a class="jxr_linenumber" name="L380" href="#L380">380</a> { 1, 2, 4 }, -<a class="jxr_linenumber" name="L381" href="#L381">381</a> { 2, 3, 5 }, -<a class="jxr_linenumber" name="L382" href="#L382">382</a> { 4, 5, -9 } -<a class="jxr_linenumber" name="L383" href="#L383">383</a> }; -<a class="jxr_linenumber" name="L384" href="#L384">384</a> -<a class="jxr_linenumber" name="L385" href="#L385">385</a> <strong class="jxr_keyword">final</strong> EigenDecomposition dec = <strong class="jxr_keyword">new</strong> EigenDecomposition(MatrixUtils.createRealMatrix(data)); -<a class="jxr_linenumber" name="L386" href="#L386">386</a> @SuppressWarnings(<span class="jxr_string">"unused"</span>) -<a class="jxr_linenumber" name="L387" href="#L387">387</a> <strong class="jxr_keyword">final</strong> RealMatrix sqrtM = dec.getSquareRoot(); -<a class="jxr_linenumber" name="L388" href="#L388">388</a> } -<a class="jxr_linenumber" name="L389" href="#L389">389</a> -<a class="jxr_linenumber" name="L390" href="#L390">390</a> @Test -<a class="jxr_linenumber" name="L391" href="#L391">391</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testUnsymmetric() { -<a class="jxr_linenumber" name="L392" href="#L392">392</a> <em class="jxr_comment">// Vandermonde matrix V(x;i,j) = x_i^{n - j} with x = (-1,-2,3,4)</em> -<a class="jxr_linenumber" name="L393" href="#L393">393</a> <strong class="jxr_keyword">double</strong>[][] vData = { { -1.0, 1.0, -1.0, 1.0 }, -<a class="jxr_linenumber" name="L394" href="#L394">394</a> { -8.0, 4.0, -2.0, 1.0 }, -<a class="jxr_linenumber" name="L395" href="#L395">395</a> { 27.0, 9.0, 3.0, 1.0 }, -<a class="jxr_linenumber" name="L396" href="#L396">396</a> { 64.0, 16.0, 4.0, 1.0 } }; -<a class="jxr_linenumber" name="L397" href="#L397">397</a> checkUnsymmetricMatrix(MatrixUtils.createRealMatrix(vData)); -<a class="jxr_linenumber" name="L398" href="#L398">398</a> -<a class="jxr_linenumber" name="L399" href="#L399">399</a> RealMatrix randMatrix = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L400" href="#L400">400</a> {0, 1, 0, 0}, -<a class="jxr_linenumber" name="L401" href="#L401">401</a> {1, 0, 2.e-7, 0}, -<a class="jxr_linenumber" name="L402" href="#L402">402</a> {0, -2.e-7, 0, 1}, -<a class="jxr_linenumber" name="L403" href="#L403">403</a> {0, 0, 1, 0} -<a class="jxr_linenumber" name="L404" href="#L404">404</a> }); -<a class="jxr_linenumber" name="L405" href="#L405">405</a> checkUnsymmetricMatrix(randMatrix); -<a class="jxr_linenumber" name="L406" href="#L406">406</a> -<a class="jxr_linenumber" name="L407" href="#L407">407</a> <em class="jxr_comment">// from http://eigen.tuxfamily.org/dox/classEigen_1_1RealSchur.html</em> -<a class="jxr_linenumber" name="L408" href="#L408">408</a> <strong class="jxr_keyword">double</strong>[][] randData2 = { -<a class="jxr_linenumber" name="L409" href="#L409">409</a> { 0.680, -0.3300, -0.2700, -0.717, -0.687, 0.0259 }, -<a class="jxr_linenumber" name="L410" href="#L410">410</a> { -0.211, 0.5360, 0.0268, 0.214, -0.198, 0.6780 }, -<a class="jxr_linenumber" name="L411" href="#L411">411</a> { 0.566, -0.4440, 0.9040, -0.967, -0.740, 0.2250 }, -<a class="jxr_linenumber" name="L412" href="#L412">412</a> { 0.597, 0.1080, 0.8320, -0.514, -0.782, -0.4080 }, -<a class="jxr_linenumber" name="L413" href="#L413">413</a> { 0.823, -0.0452, 0.2710, -0.726, 0.998, 0.2750 }, -<a class="jxr_linenumber" name="L414" href="#L414">414</a> { -0.605, 0.2580, 0.4350, 0.608, -0.563, 0.0486 } -<a class="jxr_linenumber" name="L415" href="#L415">415</a> }; -<a class="jxr_linenumber" name="L416" href="#L416">416</a> checkUnsymmetricMatrix(MatrixUtils.createRealMatrix(randData2)); -<a class="jxr_linenumber" name="L417" href="#L417">417</a> } -<a class="jxr_linenumber" name="L418" href="#L418">418</a> -<a class="jxr_linenumber" name="L419" href="#L419">419</a> @Test -<a class="jxr_linenumber" name="L420" href="#L420">420</a> @Ignore -<a class="jxr_linenumber" name="L421" href="#L421">421</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testRandomUnsymmetricMatrix() { -<a class="jxr_linenumber" name="L422" href="#L422">422</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> run = 0; run < 100; run++) { -<a class="jxr_linenumber" name="L423" href="#L423">423</a> Random r = <strong class="jxr_keyword">new</strong> Random(System.currentTimeMillis()); -<a class="jxr_linenumber" name="L424" href="#L424">424</a> -<a class="jxr_linenumber" name="L425" href="#L425">425</a> <em class="jxr_comment">// matrix size</em> -<a class="jxr_linenumber" name="L426" href="#L426">426</a> <strong class="jxr_keyword">int</strong> size = r.nextInt(20) + 4; -<a class="jxr_linenumber" name="L427" href="#L427">427</a> -<a class="jxr_linenumber" name="L428" href="#L428">428</a> <strong class="jxr_keyword">double</strong>[][] data = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[size][size]; -<a class="jxr_linenumber" name="L429" href="#L429">429</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < size; i++) { -<a class="jxr_linenumber" name="L430" href="#L430">430</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j < size; j++) { -<a class="jxr_linenumber" name="L431" href="#L431">431</a> data[i][j] = r.nextInt(100); -<a class="jxr_linenumber" name="L432" href="#L432">432</a> } -<a class="jxr_linenumber" name="L433" href="#L433">433</a> } -<a class="jxr_linenumber" name="L434" href="#L434">434</a> -<a class="jxr_linenumber" name="L435" href="#L435">435</a> RealMatrix m = MatrixUtils.createRealMatrix(data); -<a class="jxr_linenumber" name="L436" href="#L436">436</a> checkUnsymmetricMatrix(m); -<a class="jxr_linenumber" name="L437" href="#L437">437</a> } -<a class="jxr_linenumber" name="L438" href="#L438">438</a> } -<a class="jxr_linenumber" name="L439" href="#L439">439</a> -<a class="jxr_linenumber" name="L440" href="#L440">440</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L441" href="#L441">441</a> <em class="jxr_javadoccomment"> * Tests the porting of a bugfix in Jama-1.0.3 (from changelog):</em> -<a class="jxr_linenumber" name="L442" href="#L442">442</a> <em class="jxr_javadoccomment"> *</em> -<a class="jxr_linenumber" name="L443" href="#L443">443</a> <em class="jxr_javadoccomment"> * Patched hqr2 method in Jama.EigenvalueDecomposition to avoid infinite loop;</em> -<a class="jxr_linenumber" name="L444" href="#L444">444</a> <em class="jxr_javadoccomment"> * Thanks Frederic Devernay <[email protected]></em> -<a class="jxr_linenumber" name="L445" href="#L445">445</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L446" href="#L446">446</a> @Test -<a class="jxr_linenumber" name="L447" href="#L447">447</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMath1051() { -<a class="jxr_linenumber" name="L448" href="#L448">448</a> <strong class="jxr_keyword">double</strong>[][] data = { -<a class="jxr_linenumber" name="L449" href="#L449">449</a> {0,0,0,0,0}, -<a class="jxr_linenumber" name="L450" href="#L450">450</a> {0,0,0,0,1}, -<a class="jxr_linenumber" name="L451" href="#L451">451</a> {0,0,0,1,0}, -<a class="jxr_linenumber" name="L452" href="#L452">452</a> {1,1,0,0,1}, -<a class="jxr_linenumber" name="L453" href="#L453">453</a> {1,0,1,0,1} -<a class="jxr_linenumber" name="L454" href="#L454">454</a> }; -<a class="jxr_linenumber" name="L455" href="#L455">455</a> -<a class="jxr_linenumber" name="L456" href="#L456">456</a> RealMatrix m = MatrixUtils.createRealMatrix(data); -<a class="jxr_linenumber" name="L457" href="#L457">457</a> checkUnsymmetricMatrix(m); -<a class="jxr_linenumber" name="L458" href="#L458">458</a> } -<a class="jxr_linenumber" name="L459" href="#L459">459</a> -<a class="jxr_linenumber" name="L460" href="#L460">460</a> @Test -<a class="jxr_linenumber" name="L461" href="#L461">461</a> @Ignore -<a class="jxr_linenumber" name="L462" href="#L462">462</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testNormalDistributionUnsymmetricMatrix() { -<a class="jxr_linenumber" name="L463" href="#L463">463</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> run = 0; run < 100; run++) { -<a class="jxr_linenumber" name="L464" href="#L464">464</a> Random r = <strong class="jxr_keyword">new</strong> Random(System.currentTimeMillis()); -<a class="jxr_linenumber" name="L465" href="#L465">465</a> NormalDistribution dist = <strong class="jxr_keyword">new</strong> NormalDistribution(0.0, r.nextDouble() * 5); -<a class="jxr_linenumber" name="L466" href="#L466">466</a> -<a class="jxr_linenumber" name="L467" href="#L467">467</a> <em class="jxr_comment">// matrix size</em> -<a class="jxr_linenumber" name="L468" href="#L468">468</a> <strong class="jxr_keyword">int</strong> size = r.nextInt(20) + 4; -<a class="jxr_linenumber" name="L469" href="#L469">469</a> -<a class="jxr_linenumber" name="L470" href="#L470">470</a> <strong class="jxr_keyword">double</strong>[][] data = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[size][size]; -<a class="jxr_linenumber" name="L471" href="#L471">471</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < size; i++) { -<a class="jxr_linenumber" name="L472" href="#L472">472</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j < size; j++) { -<a class="jxr_linenumber" name="L473" href="#L473">473</a> data[i][j] = dist.sample(); -<a class="jxr_linenumber" name="L474" href="#L474">474</a> } -<a class="jxr_linenumber" name="L475" href="#L475">475</a> } -<a class="jxr_linenumber" name="L476" href="#L476">476</a> -<a class="jxr_linenumber" name="L477" href="#L477">477</a> RealMatrix m = MatrixUtils.createRealMatrix(data); -<a class="jxr_linenumber" name="L478" href="#L478">478</a> checkUnsymmetricMatrix(m); -<a class="jxr_linenumber" name="L479" href="#L479">479</a> } -<a class="jxr_linenumber" name="L480" href="#L480">480</a> } -<a class="jxr_linenumber" name="L481" href="#L481">481</a> -<a class="jxr_linenumber" name="L482" href="#L482">482</a> @Test -<a class="jxr_linenumber" name="L483" href="#L483">483</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testMath848() { -<a class="jxr_linenumber" name="L484" href="#L484">484</a> <strong class="jxr_keyword">double</strong>[][] data = { -<a class="jxr_linenumber" name="L485" href="#L485">485</a> { 0.1849449280, -0.0646971046, 0.0774755812, -0.0969651755, -0.0692648806, 0.3282344352, -0.0177423074, 0.2063136340}, -<a class="jxr_linenumber" name="L486" href="#L486">486</a> {-0.0742700134, -0.0289063030, -0.0017269460, -0.0375550146, -0.0487737922, -0.2616837868, -0.0821201295, -0.2530000167}, -<a class="jxr_linenumber" name="L487" href="#L487">487</a> { 0.2549910127, 0.0995733692, -0.0009718388, 0.0149282808, 0.1791878897, -0.0823182816, 0.0582629256, 0.3219545182}, -<a class="jxr_linenumber" name="L488" href="#L488">488</a> {-0.0694747557, -0.1880649148, -0.2740630911, 0.0720096468, -0.1800836914, -0.3518996425, 0.2486747833, 0.6257938167}, -<a class="jxr_linenumber" name="L489" href="#L489">489</a> { 0.0536360918, -0.1339297778, 0.2241579764, -0.0195327484, -0.0054103808, 0.0347564518, 0.5120802482, -0.0329902864}, -<a class="jxr_linenumber" name="L490" href="#L490">490</a> {-0.5933332356, -0.2488721082, 0.2357173629, 0.0177285473, 0.0856630593, -0.3567126300, -0.1600668126, -0.1010899621}, -<a class="jxr_linenumber" name="L491" href="#L491">491</a> {-0.0514349819, -0.0854319435, 0.1125050061, 0.0063453560, -0.2250000688, -0.2209343090, 0.1964623477, -0.1512329924}, -<a class="jxr_linenumber" name="L492" href="#L492">492</a> { 0.0197395947, -0.1997170581, -0.1425959019, -0.2749477910, -0.0969467073, 0.0603688520, -0.2826905192, 0.1794315473}}; -<a class="jxr_linenumber" name="L493" href="#L493">493</a> RealMatrix m = MatrixUtils.createRealMatrix(data); -<a class="jxr_linenumber" name="L494" href="#L494">494</a> checkUnsymmetricMatrix(m); -<a class="jxr_linenumber" name="L495" href="#L495">495</a> } -<a class="jxr_linenumber" name="L496" href="#L496">496</a> -<a class="jxr_linenumber" name="L497" href="#L497">497</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L498" href="#L498">498</a> <em class="jxr_javadoccomment"> * Checks that the eigen decomposition of a general (unsymmetric) matrix is valid by</em> -<a class="jxr_linenumber" name="L499" href="#L499">499</a> <em class="jxr_javadoccomment"> * checking: A*V = V*D</em> -<a class="jxr_linenumber" name="L500" href="#L500">500</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L501" href="#L501">501</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">void</strong> checkUnsymmetricMatrix(<strong class="jxr_keyword">final</strong> RealMatrix m) { -<a class="jxr_linenumber" name="L502" href="#L502">502</a> <strong class="jxr_keyword">try</strong> { -<a class="jxr_linenumber" name="L503" href="#L503">503</a> EigenDecomposition ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(m); -<a class="jxr_linenumber" name="L504" href="#L504">504</a> -<a class="jxr_linenumber" name="L505" href="#L505">505</a> RealMatrix d = ed.getD(); -<a class="jxr_linenumber" name="L506" href="#L506">506</a> RealMatrix v = ed.getV(); -<a class="jxr_linenumber" name="L507" href="#L507">507</a> <em class="jxr_comment">//RealMatrix vT = ed.getVT();</em> -<a class="jxr_linenumber" name="L508" href="#L508">508</a> -<a class="jxr_linenumber" name="L509" href="#L509">509</a> RealMatrix x = m.multiply(v); -<a class="jxr_linenumber" name="L510" href="#L510">510</a> RealMatrix y = v.multiply(d); -<a class="jxr_linenumber" name="L511" href="#L511">511</a> -<a class="jxr_linenumber" name="L512" href="#L512">512</a> <strong class="jxr_keyword">double</strong> diffNorm = x.subtract(y).getNorm(); -<a class="jxr_linenumber" name="L513" href="#L513">513</a> Assert.assertTrue(<span class="jxr_string">"The norm of (X-Y) is too large: "</span> + diffNorm + <span class="jxr_string">", matrix="</span> + m.toString(), -<a class="jxr_linenumber" name="L514" href="#L514">514</a> x.subtract(y).getNorm() < 1000 * Precision.EPSILON * FastMath.max(x.getNorm(), y.getNorm())); -<a class="jxr_linenumber" name="L515" href="#L515">515</a> -<a class="jxr_linenumber" name="L516" href="#L516">516</a> RealMatrix invV = <strong class="jxr_keyword">new</strong> LUDecomposition(v).getSolver().getInverse(); -<a class="jxr_linenumber" name="L517" href="#L517">517</a> <strong class="jxr_keyword">double</strong> norm = v.multiply(d).multiply(invV).subtract(m).getNorm(); -<a class="jxr_linenumber" name="L518" href="#L518">518</a> Assert.assertEquals(0.0, norm, 1.0e-10); -<a class="jxr_linenumber" name="L519" href="#L519">519</a> } <strong class="jxr_keyword">catch</strong> (Exception e) { -<a class="jxr_linenumber" name="L520" href="#L520">520</a> Assert.fail(<span class="jxr_string">"Failed to create EigenDecomposition for matrix "</span> + m.toString() + <span class="jxr_string">", ex="</span> + e.toString()); -<a class="jxr_linenumber" name="L521" href="#L521">521</a> } -<a class="jxr_linenumber" name="L522" href="#L522">522</a> } -<a class="jxr_linenumber" name="L523" href="#L523">523</a> -<a class="jxr_linenumber" name="L524" href="#L524">524</a> <em class="jxr_javadoccomment">/** test eigenvectors */</em> -<a class="jxr_linenumber" name="L525" href="#L525">525</a> @Test -<a class="jxr_linenumber" name="L526" href="#L526">526</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testEigenvectors() { -<a class="jxr_linenumber" name="L527" href="#L527">527</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L528" href="#L528">528</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L529" href="#L529">529</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < matrix.getRowDimension(); ++i) { -<a class="jxr_linenumber" name="L530" href="#L530">530</a> <strong class="jxr_keyword">double</strong> lambda = ed.getRealEigenvalue(i); -<a class="jxr_linenumber" name="L531" href="#L531">531</a> RealVector v = ed.getEigenvector(i); -<a class="jxr_linenumber" name="L532" href="#L532">532</a> RealVector mV = matrix.operate(v); -<a class="jxr_linenumber" name="L533" href="#L533">533</a> Assert.assertEquals(0, mV.subtract(v.mapMultiplyToSelf(lambda)).getNorm(), 1.0e-13); -<a class="jxr_linenumber" name="L534" href="#L534">534</a> } -<a class="jxr_linenumber" name="L535" href="#L535">535</a> } -<a class="jxr_linenumber" name="L536" href="#L536">536</a> -<a class="jxr_linenumber" name="L537" href="#L537">537</a> <em class="jxr_javadoccomment">/** test A = VDVt */</em> -<a class="jxr_linenumber" name="L538" href="#L538">538</a> @Test -<a class="jxr_linenumber" name="L539" href="#L539">539</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testAEqualVDVt() { -<a class="jxr_linenumber" name="L540" href="#L540">540</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L541" href="#L541">541</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix); -<a class="jxr_linenumber" name="L542" href="#L542">542</a> RealMatrix v = ed.getV(); -<a class="jxr_linenumber" name="L543" href="#L543">543</a> RealMatrix d = ed.getD(); -<a class="jxr_linenumber" name="L544" href="#L544">544</a> RealMatrix vT = ed.getVT(); -<a class="jxr_linenumber" name="L545" href="#L545">545</a> <strong class="jxr_keyword">double</strong> norm = v.multiply(d).multiply(vT).subtract(matrix).getNorm(); -<a class="jxr_linenumber" name="L546" href="#L546">546</a> Assert.assertEquals(0, norm, 6.0e-13); -<a class="jxr_linenumber" name="L547" href="#L547">547</a> } -<a class="jxr_linenumber" name="L548" href="#L548">548</a> -<a class="jxr_linenumber" name="L549" href="#L549">549</a> <em class="jxr_javadoccomment">/** test that V is orthogonal */</em> -<a class="jxr_linenumber" name="L550" href="#L550">550</a> @Test -<a class="jxr_linenumber" name="L551" href="#L551">551</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testVOrthogonal() { -<a class="jxr_linenumber" name="L552" href="#L552">552</a> RealMatrix v = <strong class="jxr_keyword">new</strong> EigenDecomposition(matrix).getV(); -<a class="jxr_linenumber" name="L553" href="#L553">553</a> RealMatrix vTv = v.transpose().multiply(v); -<a class="jxr_linenumber" name="L554" href="#L554">554</a> RealMatrix id = MatrixUtils.createRealIdentityMatrix(vTv.getRowDimension()); -<a class="jxr_linenumber" name="L555" href="#L555">555</a> Assert.assertEquals(0, vTv.subtract(id).getNorm(), 2.0e-13); -<a class="jxr_linenumber" name="L556" href="#L556">556</a> } -<a class="jxr_linenumber" name="L557" href="#L557">557</a> -<a class="jxr_linenumber" name="L558" href="#L558">558</a> <em class="jxr_javadoccomment">/** test diagonal matrix */</em> -<a class="jxr_linenumber" name="L559" href="#L559">559</a> @Test -<a class="jxr_linenumber" name="L560" href="#L560">560</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDiagonal() { -<a class="jxr_linenumber" name="L561" href="#L561">561</a> <strong class="jxr_keyword">double</strong>[] diagonal = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] { -3.0, -2.0, 2.0, 5.0 }; -<a class="jxr_linenumber" name="L562" href="#L562">562</a> RealMatrix m = MatrixUtils.createRealDiagonalMatrix(diagonal); -<a class="jxr_linenumber" name="L563" href="#L563">563</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L564" href="#L564">564</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(m); -<a class="jxr_linenumber" name="L565" href="#L565">565</a> Assert.assertEquals(diagonal[0], ed.getRealEigenvalue(3), 2.0e-15); -<a class="jxr_linenumber" name="L566" href="#L566">566</a> Assert.assertEquals(diagonal[1], ed.getRealEigenvalue(2), 2.0e-15); -<a class="jxr_linenumber" name="L567" href="#L567">567</a> Assert.assertEquals(diagonal[2], ed.getRealEigenvalue(1), 2.0e-15); -<a class="jxr_linenumber" name="L568" href="#L568">568</a> Assert.assertEquals(diagonal[3], ed.getRealEigenvalue(0), 2.0e-15); -<a class="jxr_linenumber" name="L569" href="#L569">569</a> } -<a class="jxr_linenumber" name="L570" href="#L570">570</a> -<a class="jxr_linenumber" name="L571" href="#L571">571</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L572" href="#L572">572</a> <em class="jxr_javadoccomment"> * Matrix with eigenvalues {8, -1, -1}</em> -<a class="jxr_linenumber" name="L573" href="#L573">573</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L574" href="#L574">574</a> @Test -<a class="jxr_linenumber" name="L575" href="#L575">575</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testRepeatedEigenvalue() { -<a class="jxr_linenumber" name="L576" href="#L576">576</a> RealMatrix repeated = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L577" href="#L577">577</a> {3, 2, 4}, -<a class="jxr_linenumber" name="L578" href="#L578">578</a> {2, 0, 2}, -<a class="jxr_linenumber" name="L579" href="#L579">579</a> {4, 2, 3} -<a class="jxr_linenumber" name="L580" href="#L580">580</a> }); -<a class="jxr_linenumber" name="L581" href="#L581">581</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L582" href="#L582">582</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(repeated); -<a class="jxr_linenumber" name="L583" href="#L583">583</a> checkEigenValues((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {8, -1, -1}), ed, 1E-12); -<a class="jxr_linenumber" name="L584" href="#L584">584</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {2, 1, 2}), ed, 1E-12); -<a class="jxr_linenumber" name="L585" href="#L585">585</a> } -<a class="jxr_linenumber" name="L586" href="#L586">586</a> -<a class="jxr_linenumber" name="L587" href="#L587">587</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L588" href="#L588">588</a> <em class="jxr_javadoccomment"> * Matrix with eigenvalues {2, 0, 12}</em> -<a class="jxr_linenumber" name="L589" href="#L589">589</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L590" href="#L590">590</a> @Test -<a class="jxr_linenumber" name="L591" href="#L591">591</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testDistinctEigenvalues() { -<a class="jxr_linenumber" name="L592" href="#L592">592</a> RealMatrix distinct = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L593" href="#L593">593</a> {3, 1, -4}, -<a class="jxr_linenumber" name="L594" href="#L594">594</a> {1, 3, -4}, -<a class="jxr_linenumber" name="L595" href="#L595">595</a> {-4, -4, 8} -<a class="jxr_linenumber" name="L596" href="#L596">596</a> }); -<a class="jxr_linenumber" name="L597" href="#L597">597</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L598" href="#L598">598</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(distinct); -<a class="jxr_linenumber" name="L599" href="#L599">599</a> checkEigenValues((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {2, 0, 12}), ed, 1E-12); -<a class="jxr_linenumber" name="L600" href="#L600">600</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1, -1, 0}), ed, 1E-12); -<a class="jxr_linenumber" name="L601" href="#L601">601</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1, 1, 1}), ed, 1E-12); -<a class="jxr_linenumber" name="L602" href="#L602">602</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-1, -1, 2}), ed, 1E-12); -<a class="jxr_linenumber" name="L603" href="#L603">603</a> } -<a class="jxr_linenumber" name="L604" href="#L604">604</a> -<a class="jxr_linenumber" name="L605" href="#L605">605</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L606" href="#L606">606</a> <em class="jxr_javadoccomment"> * Verifies operation on indefinite matrix</em> -<a class="jxr_linenumber" name="L607" href="#L607">607</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L608" href="#L608">608</a> @Test -<a class="jxr_linenumber" name="L609" href="#L609">609</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testZeroDivide() { -<a class="jxr_linenumber" name="L610" href="#L610">610</a> RealMatrix indefinite = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong> [][] { -<a class="jxr_linenumber" name="L611" href="#L611">611</a> { 0.0, 1.0, -1.0 }, -<a class="jxr_linenumber" name="L612" href="#L612">612</a> { 1.0, 1.0, 0.0 }, -<a class="jxr_linenumber" name="L613" href="#L613">613</a> { -1.0,0.0, 1.0 } -<a class="jxr_linenumber" name="L614" href="#L614">614</a> }); -<a class="jxr_linenumber" name="L615" href="#L615">615</a> EigenDecomposition ed; -<a class="jxr_linenumber" name="L616" href="#L616">616</a> ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(indefinite); -<a class="jxr_linenumber" name="L617" href="#L617">617</a> checkEigenValues((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {2, 1, -1}), ed, 1E-12); -<a class="jxr_linenumber" name="L618" href="#L618">618</a> <strong class="jxr_keyword">double</strong> isqrt3 = 1/FastMath.sqrt(3.0); -<a class="jxr_linenumber" name="L619" href="#L619">619</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {isqrt3,isqrt3,-isqrt3}), ed, 1E-12); -<a class="jxr_linenumber" name="L620" href="#L620">620</a> <strong class="jxr_keyword">double</strong> isqrt2 = 1/FastMath.sqrt(2.0); -<a class="jxr_linenumber" name="L621" href="#L621">621</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {0.0,-isqrt2,-isqrt2}), ed, 1E-12); -<a class="jxr_linenumber" name="L622" href="#L622">622</a> <strong class="jxr_keyword">double</strong> isqrt6 = 1/FastMath.sqrt(6.0); -<a class="jxr_linenumber" name="L623" href="#L623">623</a> checkEigenVector((<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {2*isqrt6,-isqrt6,isqrt6}), ed, 1E-12); -<a class="jxr_linenumber" name="L624" href="#L624">624</a> } -<a class="jxr_linenumber" name="L625" href="#L625">625</a> -<a class="jxr_linenumber" name="L626" href="#L626">626</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L627" href="#L627">627</a> <em class="jxr_javadoccomment"> * Verifies operation on very small values.</em> -<a class="jxr_linenumber" name="L628" href="#L628">628</a> <em class="jxr_javadoccomment"> * Matrix with eigenvalues {2e-100, 0, 12e-100}</em> -<a class="jxr_linenumber" name="L629" href="#L629">629</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L630" href="#L630">630</a> @Test -<a class="jxr_linenumber" name="L631" href="#L631">631</a> <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">void</strong> testTinyValues() { -<a class="jxr_linenumber" name="L632" href="#L632">632</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> tiny = 1e-100; -<a class="jxr_linenumber" name="L633" href="#L633">633</a> RealMatrix distinct = MatrixUtils.createRealMatrix(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[][] { -<a class="jxr_linenumber" name="L634" href="#L634">634</a> {3, 1, -4}, -<a class="jxr_linenumber" name="L635" href="#L635">635</a> {1, 3, -4}, -<a class="jxr_linenumber" name="L636" href="#L636">636</a> {-4, -4, 8} -<a class="jxr_linenumber" name="L637" href="#L637">637</a> }); -<a class="jxr_linenumber" name="L638" href="#L638">638</a> distinct = distinct.scalarMultiply(tiny); -<a class="jxr_linenumber" name="L639" href="#L639">639</a> -<a class="jxr_linenumber" name="L640" href="#L640">640</a> <strong class="jxr_keyword">final</strong> EigenDecomposition ed = <strong class="jxr_keyword">new</strong> EigenDecomposition(distinct); -<a class="jxr_linenumber" name="L641" href="#L641">641</a> checkEigenValues(MathArrays.scale(tiny, <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {2, 0, 12}), ed, 1e-12 * tiny); -<a class="jxr_linenumber" name="L642" href="#L642">642</a> checkEigenVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1, -1, 0}, ed, 1e-12); -<a class="jxr_linenumber" name="L643" href="#L643">643</a> checkEigenVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1, 1, 1}, ed, 1e-12); -<a class="jxr_linenumber" name="L644" href="#L644">644</a> checkEigenVector(<strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {-1, -1, 2}, ed, 1e-12); -<a class="jxr_linenumber" name="L645" href="#L645">645</a> } -<a class="jxr_linenumber" name="L646" href="#L646">646</a> -<a class="jxr_linenumber" name="L647" href="#L647">647</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L648" href="#L648">648</a> <em class="jxr_javadoccomment"> * Verifies that the given EigenDecomposition has eigenvalues equivalent to</em> -<a class="jxr_linenumber" name="L649" href="#L649">649</a> <em class="jxr_javadoccomment"> * the targetValues, ignoring the order of the values and allowing</em> -<a class="jxr_linenumber" name="L650" href="#L650">650</a> <em class="jxr_javadoccomment"> * values to differ by tolerance.</em> -<a class="jxr_linenumber" name="L651" href="#L651">651</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L652" href="#L652">652</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">void</strong> checkEigenValues(<strong class="jxr_keyword">double</strong>[] targetValues, -<a class="jxr_linenumber" name="L653" href="#L653">653</a> EigenDecomposition ed, <strong class="jxr_keyword">double</strong> tolerance) { -<a class="jxr_linenumber" name="L654" href="#L654">654</a> <strong class="jxr_keyword">double</strong>[] observed = ed.getRealEigenvalues(); -<a class="jxr_linenumber" name="L655" href="#L655">655</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i < observed.length; i++) { -<a class="jxr_linenumber" name="L656" href="#L656">656</a> Assert.assertTrue(isIncludedValue(observed[i], targetValues, tolerance)); -<a class="jxr_linenumber" name="L657" href="#L657">657</a> Assert.assertTrue(isIncludedValue(targetValues[i], observed, tolerance)); -<a class="jxr_linenumber" name="L658" href="#L658">658</a> } -<a class="jxr_linenumber" name="L659" href="#L659">659</a> } -<a class="jxr_linenumber" name="L660" href="#L660">660</a> -<a class="jxr_linenumber" name="L661" href="#L661">661</a> -<a class="jxr_linenumber" name="L662" href="#L662">662</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L663" href="#L663">663</a> <em class="jxr_javadoccomment"> * Returns true iff there is an entry within tolerance of value in</em> -<a class="jxr_linenumber" name="L664" href="#L664">664</a> <em class="jxr_javadoccomment"> * searchArray.</em> -<a class="jxr_linenumber" name="L665" href="#L665">665</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L666" href="#L666">666</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">boolean</strong> isIncludedValue(<strong class="jxr_keyword">double</strong> value, <strong class="jxr_keyword">double</strong>[] searchArray, -<a class="jxr_linenumber" name="L667" href="#L667">667</a> <strong class="jxr_keyword">double</strong> tolerance) { -<a class="jxr_linenumber" name="L668" href="#L668">668</a> <strong class="jxr_keyword">boolean</strong> found = false; -<a class="jxr_linenumber" name="L669" href="#L669">669</a> <strong class="jxr_keyword">int</strong> i = 0; -<a class="jxr_linenumber" name="L670" href="#L670">670</a> <strong class="jxr_keyword">while</strong> (!found && i < searchArray.length) { -<a class="jxr_linenumber" name="L671" href="#L671">671</a> <strong class="jxr_keyword">if</strong> (FastMath.abs(value - searchArray[i]) < tolerance) { -<a class="jxr_linenumber" name="L672" href="#L672">672</a> found = <strong class="jxr_keyword">true</strong>; -<a class="jxr_linenumber" name="L673" href="#L673">673</a> } -<a class="jxr_linenumber" name="L674" href="#L674">674</a> i++; -<a class="jxr_linenumber" name="L675" href="#L675">675</a> } -<a class="jxr_linenumber" name="L676" href="#L676">676</a> <strong class="jxr_keyword">return</strong> found; -<a class="jxr_linenumber" name="L677" href="#L677">677</a> } -<a class="jxr_linenumber" name="L678" href="#L678">678</a> -<a class="jxr_linenumber" name="L679" href="#L679">679</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L680" href="#L680">680</a> <em class="jxr_javadoccomment"> * Returns true iff eigenVector is a scalar multiple of one of the columns</em> -<a class="jxr_linenumber" name="L681" href="#L681">681</a> <em class="jxr_javadoccomment"> * of ed.getV(). Does not try linear combinations - i.e., should only be</em> -<a class="jxr_linenumber" name="L682" href="#L682">682</a> <em class="jxr_javadoccomment"> * used to find vectors in one-dimensional eigenspaces.</em> -<a class="jxr_linenumber" name="L683" href="#L683">683</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L684" href="#L684">684</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">void</strong> checkEigenVector(<strong class="jxr_keyword">double</strong>[] eigenVector, -<a class="jxr_linenumber" name="L685" href="#L685">685</a> EigenDecomposition ed, <strong class="jxr_keyword">double</strong> tolerance) { -<a class="jxr_linenumber" name="L686" href="#L686">686</a> Assert.assertTrue(isIncludedColumn(eigenVector, ed.getV(), tolerance)); -<a class="jxr_linenumber" name="L687" href="#L687">687</a> } -<a class="jxr_linenumber" name="L688" href="#L688">688</a> -<a class="jxr_linenumber" name="L689" href="#L689">689</a> <em class="jxr_javadoccomment">/**</em> -<a class="jxr_linenumber" name="L690" href="#L690">690</a> <em class="jxr_javadoccomment"> * Returns true iff there is a column that is a scalar multiple of column</em> -<a class="jxr_linenumber" name="L691" href="#L691">691</a> <em class="jxr_javadoccomment"> * in searchMatrix (modulo tolerance)</em> -<a class="jxr_linenumber" name="L692" href="#L692">692</a> <em class="jxr_javadoccomment"> */</em> -<a class="jxr_linenumber" name="L693" href="#L693">693</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">boolean</strong> isIncludedColumn(<strong class="jxr_keyword">double</strong>[] column, RealMatrix searchMatrix, -<a class="jxr_linenumber" name="L694" href="#L694">694</a> <strong class="jxr_keyword">double</strong> tolerance) { -<a class="jxr_linenumber" name="L695" href="#L695">695</a> <strong class="jxr_keyword">boolean</strong> found = false; -<a class="jxr_linenumber" name="L696" href="#L696">696</a> <strong class="jxr_keyword">int</strong> i = 0; -<a class="jxr_linenumber" name="L697" href="#L697">697</a> <strong class="jxr_keyword">while</strong> (!found && i < searchMatrix.getColumnDimension()) { -<a class="jxr_linenumber" name="L698" href="#L698">698</a> <strong class="jxr_keyword">double</strong> multiplier = 1.0; -<a class="jxr_linenumber" name="L699" href="#L699">699</a> <strong class="jxr_keyword">boolean</strong> matching = <strong class="jxr_keyword">true</strong>; -<a class="jxr_linenumber" name="L700" href="#L700">700</a> <strong class="jxr_keyword">int</strong> j = 0; -<a class="jxr_linenumber" name="L701" href="#L701">701</a> <strong class="jxr_keyword">while</strong> (matching && j < searchMatrix.getRowDimension()) { -<a class="jxr_linenumber" name="L702" href="#L702">702</a> <st <TRUNCATED>
