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From er...@apache.org
Subject [18/51] [partial] commons-complex git commit: Removed "site-content" directory.
Date Fri, 06 Jan 2017 17:09:58 GMT
http://git-wip-us.apache.org/repos/asf/commons-complex/blob/b3576eeb/site-content/.svn/pristine/04/04c235c553e4747ac4d82b8d31891fb1317fd80b.svn-base
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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-<title>QRDecomposition xref</title>
-<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
-</head>
-<body>
-<div id="overview"><a href="../../../../../../apidocs/org/apache/commons/math3/linear/QRDecomposition.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>  
-<a class="jxr_linenumber" name="L22" href="#L22">22</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.exception.DimensionMismatchException;
-<a class="jxr_linenumber" name="L23" href="#L23">23</a>  <strong class="jxr_keyword">import</strong> org.apache.commons.math3.util.FastMath;
-<a class="jxr_linenumber" name="L24" href="#L24">24</a>  
-<a class="jxr_linenumber" name="L25" href="#L25">25</a>  
-<a class="jxr_linenumber" name="L26" href="#L26">26</a>  <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L27" href="#L27">27</a>  <em class="jxr_javadoccomment"> * Calculates the QR-decomposition of a matrix.</em>
-<a class="jxr_linenumber" name="L28" href="#L28">28</a>  <em class="jxr_javadoccomment"> * &lt;p&gt;The QR-decomposition of a matrix A consists of two matrices Q and R</em>
-<a class="jxr_linenumber" name="L29" href="#L29">29</a>  <em class="jxr_javadoccomment"> * that satisfy: A = QR, Q is orthogonal (Q&lt;sup&gt;T&lt;/sup&gt;Q = I), and R is</em>
-<a class="jxr_linenumber" name="L30" href="#L30">30</a>  <em class="jxr_javadoccomment"> * upper triangular. If A is m&amp;times;n, Q is m&amp;times;m and R m&amp;times;n.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L31" href="#L31">31</a>  <em class="jxr_javadoccomment"> * &lt;p&gt;This class compute the decomposition using Householder reflectors.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L32" href="#L32">32</a>  <em class="jxr_javadoccomment"> * &lt;p&gt;For efficiency purposes, the decomposition in packed form is transposed.</em>
-<a class="jxr_linenumber" name="L33" href="#L33">33</a>  <em class="jxr_javadoccomment"> * This allows inner loop to iterate inside rows, which is much more cache-efficient</em>
-<a class="jxr_linenumber" name="L34" href="#L34">34</a>  <em class="jxr_javadoccomment"> * in Java.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L35" href="#L35">35</a>  <em class="jxr_javadoccomment"> * &lt;p&gt;This class is based on the class with similar name from the</em>
-<a class="jxr_linenumber" name="L36" href="#L36">36</a>  <em class="jxr_javadoccomment"> * &lt;a href="<a href="http://math.nist.gov/javanumerics/jama/" target="alexandria_uri">http://math.nist.gov/javanumerics/jama/</a>"&gt;JAMA&lt;/a&gt; library, with the</em>
-<a class="jxr_linenumber" name="L37" href="#L37">37</a>  <em class="jxr_javadoccomment"> * following changes:&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L38" href="#L38">38</a>  <em class="jxr_javadoccomment"> * &lt;ul&gt;</em>
-<a class="jxr_linenumber" name="L39" href="#L39">39</a>  <em class="jxr_javadoccomment"> *   &lt;li&gt;a {@link #getQT() getQT} method has been added,&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L40" href="#L40">40</a>  <em class="jxr_javadoccomment"> *   &lt;li&gt;the {@code solve} and {@code isFullRank} methods have been replaced</em>
-<a class="jxr_linenumber" name="L41" href="#L41">41</a>  <em class="jxr_javadoccomment"> *   by a {@link #getSolver() getSolver} method and the equivalent methods</em>
-<a class="jxr_linenumber" name="L42" href="#L42">42</a>  <em class="jxr_javadoccomment"> *   provided by the returned {@link DecompositionSolver}.&lt;/li&gt;</em>
-<a class="jxr_linenumber" name="L43" href="#L43">43</a>  <em class="jxr_javadoccomment"> * &lt;/ul&gt;</em>
-<a class="jxr_linenumber" name="L44" href="#L44">44</a>  <em class="jxr_javadoccomment"> *</em>
-<a class="jxr_linenumber" name="L45" href="#L45">45</a>  <em class="jxr_javadoccomment"> * @see &lt;a href="<a href="http://mathworld.wolfram.com/QRDecomposition.html" target="alexandria_uri">http://mathworld.wolfram.com/QRDecomposition.html</a>"&gt;MathWorld&lt;/a&gt;</em>
-<a class="jxr_linenumber" name="L46" href="#L46">46</a>  <em class="jxr_javadoccomment"> * @see &lt;a href="<a href="http://en.wikipedia.org/wiki/QR_decomposition" target="alexandria_uri">http://en.wikipedia.org/wiki/QR_decomposition</a>"&gt;Wikipedia&lt;/a&gt;</em>
-<a class="jxr_linenumber" name="L47" href="#L47">47</a>  <em class="jxr_javadoccomment"> *</em>
-<a class="jxr_linenumber" name="L48" href="#L48">48</a>  <em class="jxr_javadoccomment"> * @since 1.2 (changed to concrete class in 3.0)</em>
-<a class="jxr_linenumber" name="L49" href="#L49">49</a>  <em class="jxr_javadoccomment"> */</em>
-<a class="jxr_linenumber" name="L50" href="#L50">50</a>  <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">QRDecomposition</a> {
-<a class="jxr_linenumber" name="L51" href="#L51">51</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L52" href="#L52">52</a>  <em class="jxr_javadoccomment">     * A packed TRANSPOSED representation of the QR decomposition.</em>
-<a class="jxr_linenumber" name="L53" href="#L53">53</a>  <em class="jxr_javadoccomment">     * &lt;p&gt;The elements BELOW the diagonal are the elements of the UPPER triangular</em>
-<a class="jxr_linenumber" name="L54" href="#L54">54</a>  <em class="jxr_javadoccomment">     * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors</em>
-<a class="jxr_linenumber" name="L55" href="#L55">55</a>  <em class="jxr_javadoccomment">     * from which an explicit form of Q can be recomputed if desired.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L56" href="#L56">56</a>  <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L57" href="#L57">57</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong>[][] qrt;
-<a class="jxr_linenumber" name="L58" href="#L58">58</a>      <em class="jxr_javadoccomment">/** The diagonal elements of R. */</em>
-<a class="jxr_linenumber" name="L59" href="#L59">59</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong>[] rDiag;
-<a class="jxr_linenumber" name="L60" href="#L60">60</a>      <em class="jxr_javadoccomment">/** Cached value of Q. */</em>
-<a class="jxr_linenumber" name="L61" href="#L61">61</a>      <strong class="jxr_keyword">private</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> cachedQ;
-<a class="jxr_linenumber" name="L62" href="#L62">62</a>      <em class="jxr_javadoccomment">/** Cached value of QT. */</em>
-<a class="jxr_linenumber" name="L63" href="#L63">63</a>      <strong class="jxr_keyword">private</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> cachedQT;
-<a class="jxr_linenumber" name="L64" href="#L64">64</a>      <em class="jxr_javadoccomment">/** Cached value of R. */</em>
-<a class="jxr_linenumber" name="L65" href="#L65">65</a>      <strong class="jxr_keyword">private</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> cachedR;
-<a class="jxr_linenumber" name="L66" href="#L66">66</a>      <em class="jxr_javadoccomment">/** Cached value of H. */</em>
-<a class="jxr_linenumber" name="L67" href="#L67">67</a>      <strong class="jxr_keyword">private</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> cachedH;
-<a class="jxr_linenumber" name="L68" href="#L68">68</a>      <em class="jxr_javadoccomment">/** Singularity threshold. */</em>
-<a class="jxr_linenumber" name="L69" href="#L69">69</a>      <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> threshold;
-<a class="jxr_linenumber" name="L70" href="#L70">70</a>  
-<a class="jxr_linenumber" name="L71" href="#L71">71</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L72" href="#L72">72</a>  <em class="jxr_javadoccomment">     * Calculates the QR-decomposition of the given matrix.</em>
-<a class="jxr_linenumber" name="L73" href="#L73">73</a>  <em class="jxr_javadoccomment">     * The singularity threshold defaults to zero.</em>
-<a class="jxr_linenumber" name="L74" href="#L74">74</a>  <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L75" href="#L75">75</a>  <em class="jxr_javadoccomment">     * @param matrix The matrix to decompose.</em>
-<a class="jxr_linenumber" name="L76" href="#L76">76</a>  <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L77" href="#L77">77</a>  <em class="jxr_javadoccomment">     * @see #QRDecomposition(RealMatrix,double)</em>
-<a class="jxr_linenumber" name="L78" href="#L78">78</a>  <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L79" href="#L79">79</a>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">QRDecomposition</a>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> matrix) {
-<a class="jxr_linenumber" name="L80" href="#L80">80</a>          <strong class="jxr_keyword">this</strong>(matrix, 0d);
-<a class="jxr_linenumber" name="L81" href="#L81">81</a>      }
-<a class="jxr_linenumber" name="L82" href="#L82">82</a>  
-<a class="jxr_linenumber" name="L83" href="#L83">83</a>      <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L84" href="#L84">84</a>  <em class="jxr_javadoccomment">     * Calculates the QR-decomposition of the given matrix.</em>
-<a class="jxr_linenumber" name="L85" href="#L85">85</a>  <em class="jxr_javadoccomment">     *</em>
-<a class="jxr_linenumber" name="L86" href="#L86">86</a>  <em class="jxr_javadoccomment">     * @param matrix The matrix to decompose.</em>
-<a class="jxr_linenumber" name="L87" href="#L87">87</a>  <em class="jxr_javadoccomment">     * @param threshold Singularity threshold.</em>
-<a class="jxr_linenumber" name="L88" href="#L88">88</a>  <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L89" href="#L89">89</a>      <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">QRDecomposition</a>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> matrix,
-<a class="jxr_linenumber" name="L90" href="#L90">90</a>                             <strong class="jxr_keyword">double</strong> threshold) {
-<a class="jxr_linenumber" name="L91" href="#L91">91</a>          <strong class="jxr_keyword">this</strong>.threshold = threshold;
-<a class="jxr_linenumber" name="L92" href="#L92">92</a>  
-<a class="jxr_linenumber" name="L93" href="#L93">93</a>          <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = matrix.getRowDimension();
-<a class="jxr_linenumber" name="L94" href="#L94">94</a>          <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = matrix.getColumnDimension();
-<a class="jxr_linenumber" name="L95" href="#L95">95</a>          qrt = matrix.transpose().getData();
-<a class="jxr_linenumber" name="L96" href="#L96">96</a>          rDiag = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[FastMath.min(m, n)];
-<a class="jxr_linenumber" name="L97" href="#L97">97</a>          cachedQ  = <strong class="jxr_keyword">null</strong>;
-<a class="jxr_linenumber" name="L98" href="#L98">98</a>          cachedQT = <strong class="jxr_keyword">null</strong>;
-<a class="jxr_linenumber" name="L99" href="#L99">99</a>          cachedR  = <strong class="jxr_keyword">null</strong>;
-<a class="jxr_linenumber" name="L100" href="#L100">100</a>         cachedH  = <strong class="jxr_keyword">null</strong>;
-<a class="jxr_linenumber" name="L101" href="#L101">101</a> 
-<a class="jxr_linenumber" name="L102" href="#L102">102</a>         decompose(qrt);
-<a class="jxr_linenumber" name="L103" href="#L103">103</a> 
-<a class="jxr_linenumber" name="L104" href="#L104">104</a>     }
-<a class="jxr_linenumber" name="L105" href="#L105">105</a> 
-<a class="jxr_linenumber" name="L106" href="#L106">106</a>     <em class="jxr_javadoccomment">/** Decompose matrix.</em>
-<a class="jxr_linenumber" name="L107" href="#L107">107</a> <em class="jxr_javadoccomment">     * @param matrix transposed matrix</em>
-<a class="jxr_linenumber" name="L108" href="#L108">108</a> <em class="jxr_javadoccomment">     * @since 3.2</em>
-<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L110" href="#L110">110</a>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">void</strong> decompose(<strong class="jxr_keyword">double</strong>[][] matrix) {
-<a class="jxr_linenumber" name="L111" href="#L111">111</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> minor = 0; minor &lt; FastMath.min(matrix.length, matrix[0].length); minor++) {
-<a class="jxr_linenumber" name="L112" href="#L112">112</a>             performHouseholderReflection(minor, matrix);
-<a class="jxr_linenumber" name="L113" href="#L113">113</a>         }
-<a class="jxr_linenumber" name="L114" href="#L114">114</a>     }
-<a class="jxr_linenumber" name="L115" href="#L115">115</a> 
-<a class="jxr_linenumber" name="L116" href="#L116">116</a>     <em class="jxr_javadoccomment">/** Perform Householder reflection for a minor A(minor, minor) of A.</em>
-<a class="jxr_linenumber" name="L117" href="#L117">117</a> <em class="jxr_javadoccomment">     * @param minor minor index</em>
-<a class="jxr_linenumber" name="L118" href="#L118">118</a> <em class="jxr_javadoccomment">     * @param matrix transposed matrix</em>
-<a class="jxr_linenumber" name="L119" href="#L119">119</a> <em class="jxr_javadoccomment">     * @since 3.2</em>
-<a class="jxr_linenumber" name="L120" href="#L120">120</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L121" href="#L121">121</a>     <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">void</strong> performHouseholderReflection(<strong class="jxr_keyword">int</strong> minor, <strong class="jxr_keyword">double</strong>[][] matrix) {
-<a class="jxr_linenumber" name="L122" href="#L122">122</a> 
-<a class="jxr_linenumber" name="L123" href="#L123">123</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtMinor = matrix[minor];
-<a class="jxr_linenumber" name="L124" href="#L124">124</a> 
-<a class="jxr_linenumber" name="L125" href="#L125">125</a>         <em class="jxr_comment">/*</em>
-<a class="jxr_linenumber" name="L126" href="#L126">126</a> <em class="jxr_comment">         * Let x be the first column of the minor, and a^2 = |x|^2.</em>
-<a class="jxr_linenumber" name="L127" href="#L127">127</a> <em class="jxr_comment">         * x will be in the positions qr[minor][minor] through qr[m][minor].</em>
-<a class="jxr_linenumber" name="L128" href="#L128">128</a> <em class="jxr_comment">         * The first column of the transformed minor will be (a,0,0,..)'</em>
-<a class="jxr_linenumber" name="L129" href="#L129">129</a> <em class="jxr_comment">         * The sign of a is chosen to be opposite to the sign of the first</em>
-<a class="jxr_linenumber" name="L130" href="#L130">130</a> <em class="jxr_comment">         * component of x. Let's find a:</em>
-<a class="jxr_linenumber" name="L131" href="#L131">131</a> <em class="jxr_comment">         */</em>
-<a class="jxr_linenumber" name="L132" href="#L132">132</a>         <strong class="jxr_keyword">double</strong> xNormSqr = 0;
-<a class="jxr_linenumber" name="L133" href="#L133">133</a>         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; qrtMinor.length; row++) {
-<a class="jxr_linenumber" name="L134" href="#L134">134</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> c = qrtMinor[row];
-<a class="jxr_linenumber" name="L135" href="#L135">135</a>             xNormSqr += c * c;
-<a class="jxr_linenumber" name="L136" href="#L136">136</a>         }
-<a class="jxr_linenumber" name="L137" href="#L137">137</a>         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> a = (qrtMinor[minor] &gt; 0) ? -FastMath.sqrt(xNormSqr) : FastMath.sqrt(xNormSqr);
-<a class="jxr_linenumber" name="L138" href="#L138">138</a>         rDiag[minor] = a;
-<a class="jxr_linenumber" name="L139" href="#L139">139</a> 
-<a class="jxr_linenumber" name="L140" href="#L140">140</a>         <strong class="jxr_keyword">if</strong> (a != 0.0) {
-<a class="jxr_linenumber" name="L141" href="#L141">141</a> 
-<a class="jxr_linenumber" name="L142" href="#L142">142</a>             <em class="jxr_comment">/*</em>
-<a class="jxr_linenumber" name="L143" href="#L143">143</a> <em class="jxr_comment">             * Calculate the normalized reflection vector v and transform</em>
-<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_comment">             * the first column. We know the norm of v beforehand: v = x-ae</em>
-<a class="jxr_linenumber" name="L145" href="#L145">145</a> <em class="jxr_comment">             * so |v|^2 = &lt;x-ae,x-ae&gt; = &lt;x,x&gt;-2a&lt;x,e&gt;+a^2&lt;e,e&gt; =</em>
-<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_comment">             * a^2+a^2-2a&lt;x,e&gt; = 2a*(a - &lt;x,e&gt;).</em>
-<a class="jxr_linenumber" name="L147" href="#L147">147</a> <em class="jxr_comment">             * Here &lt;x, e&gt; is now qr[minor][minor].</em>
-<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_comment">             * v = x-ae is stored in the column at qr:</em>
-<a class="jxr_linenumber" name="L149" href="#L149">149</a> <em class="jxr_comment">             */</em>
-<a class="jxr_linenumber" name="L150" href="#L150">150</a>             qrtMinor[minor] -= a; <em class="jxr_comment">// now |v|^2 = -2a*(qr[minor][minor])</em>
-<a class="jxr_linenumber" name="L151" href="#L151">151</a> 
-<a class="jxr_linenumber" name="L152" href="#L152">152</a>             <em class="jxr_comment">/*</em>
-<a class="jxr_linenumber" name="L153" href="#L153">153</a> <em class="jxr_comment">             * Transform the rest of the columns of the minor:</em>
-<a class="jxr_linenumber" name="L154" href="#L154">154</a> <em class="jxr_comment">             * They will be transformed by the matrix H = I-2vv'/|v|^2.</em>
-<a class="jxr_linenumber" name="L155" href="#L155">155</a> <em class="jxr_comment">             * If x is a column vector of the minor, then</em>
-<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_comment">             * Hx = (I-2vv'/|v|^2)x = x-2vv'x/|v|^2 = x - 2&lt;x,v&gt;/|v|^2 v.</em>
-<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_comment">             * Therefore the transformation is easily calculated by</em>
-<a class="jxr_linenumber" name="L158" href="#L158">158</a> <em class="jxr_comment">             * subtracting the column vector (2&lt;x,v&gt;/|v|^2)v from x.</em>
-<a class="jxr_linenumber" name="L159" href="#L159">159</a> <em class="jxr_comment">             *</em>
-<a class="jxr_linenumber" name="L160" href="#L160">160</a> <em class="jxr_comment">             * Let 2&lt;x,v&gt;/|v|^2 = alpha. From above we have</em>
-<a class="jxr_linenumber" name="L161" href="#L161">161</a> <em class="jxr_comment">             * |v|^2 = -2a*(qr[minor][minor]), so</em>
-<a class="jxr_linenumber" name="L162" href="#L162">162</a> <em class="jxr_comment">             * alpha = -&lt;x,v&gt;/(a*qr[minor][minor])</em>
-<a class="jxr_linenumber" name="L163" href="#L163">163</a> <em class="jxr_comment">             */</em>
-<a class="jxr_linenumber" name="L164" href="#L164">164</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> col = minor+1; col &lt; matrix.length; col++) {
-<a class="jxr_linenumber" name="L165" href="#L165">165</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtCol = matrix[col];
-<a class="jxr_linenumber" name="L166" href="#L166">166</a>                 <strong class="jxr_keyword">double</strong> alpha = 0;
-<a class="jxr_linenumber" name="L167" href="#L167">167</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; qrtCol.length; row++) {
-<a class="jxr_linenumber" name="L168" href="#L168">168</a>                     alpha -= qrtCol[row] * qrtMinor[row];
-<a class="jxr_linenumber" name="L169" href="#L169">169</a>                 }
-<a class="jxr_linenumber" name="L170" href="#L170">170</a>                 alpha /= a * qrtMinor[minor];
-<a class="jxr_linenumber" name="L171" href="#L171">171</a> 
-<a class="jxr_linenumber" name="L172" href="#L172">172</a>                 <em class="jxr_comment">// Subtract the column vector alpha*v from x.</em>
-<a class="jxr_linenumber" name="L173" href="#L173">173</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; qrtCol.length; row++) {
-<a class="jxr_linenumber" name="L174" href="#L174">174</a>                     qrtCol[row] -= alpha * qrtMinor[row];
-<a class="jxr_linenumber" name="L175" href="#L175">175</a>                 }
-<a class="jxr_linenumber" name="L176" href="#L176">176</a>             }
-<a class="jxr_linenumber" name="L177" href="#L177">177</a>         }
-<a class="jxr_linenumber" name="L178" href="#L178">178</a>     }
-<a class="jxr_linenumber" name="L179" href="#L179">179</a> 
-<a class="jxr_linenumber" name="L180" href="#L180">180</a> 
-<a class="jxr_linenumber" name="L181" href="#L181">181</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L182" href="#L182">182</a> <em class="jxr_javadoccomment">     * Returns the matrix R of the decomposition.</em>
-<a class="jxr_linenumber" name="L183" href="#L183">183</a> <em class="jxr_javadoccomment">     * &lt;p&gt;R is an upper-triangular matrix&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L184" href="#L184">184</a> <em class="jxr_javadoccomment">     * @return the R matrix</em>
-<a class="jxr_linenumber" name="L185" href="#L185">185</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L186" href="#L186">186</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> getR() {
-<a class="jxr_linenumber" name="L187" href="#L187">187</a> 
-<a class="jxr_linenumber" name="L188" href="#L188">188</a>         <strong class="jxr_keyword">if</strong> (cachedR == <strong class="jxr_keyword">null</strong>) {
-<a class="jxr_linenumber" name="L189" href="#L189">189</a> 
-<a class="jxr_linenumber" name="L190" href="#L190">190</a>             <em class="jxr_comment">// R is supposed to be m x n</em>
-<a class="jxr_linenumber" name="L191" href="#L191">191</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = qrt.length;
-<a class="jxr_linenumber" name="L192" href="#L192">192</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = qrt[0].length;
-<a class="jxr_linenumber" name="L193" href="#L193">193</a>             <strong class="jxr_keyword">double</strong>[][] ra = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[m][n];
-<a class="jxr_linenumber" name="L194" href="#L194">194</a>             <em class="jxr_comment">// copy the diagonal from rDiag and the upper triangle of qr</em>
-<a class="jxr_linenumber" name="L195" href="#L195">195</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = FastMath.min(m, n) - 1; row &gt;= 0; row--) {
-<a class="jxr_linenumber" name="L196" href="#L196">196</a>                 ra[row][row] = rDiag[row];
-<a class="jxr_linenumber" name="L197" href="#L197">197</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> col = row + 1; col &lt; n; col++) {
-<a class="jxr_linenumber" name="L198" href="#L198">198</a>                     ra[row][col] = qrt[col][row];
-<a class="jxr_linenumber" name="L199" href="#L199">199</a>                 }
-<a class="jxr_linenumber" name="L200" href="#L200">200</a>             }
-<a class="jxr_linenumber" name="L201" href="#L201">201</a>             cachedR = MatrixUtils.createRealMatrix(ra);
-<a class="jxr_linenumber" name="L202" href="#L202">202</a>         }
-<a class="jxr_linenumber" name="L203" href="#L203">203</a> 
-<a class="jxr_linenumber" name="L204" href="#L204">204</a>         <em class="jxr_comment">// return the cached matrix</em>
-<a class="jxr_linenumber" name="L205" href="#L205">205</a>         <strong class="jxr_keyword">return</strong> cachedR;
-<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>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_javadoccomment">     * Returns the matrix Q of the decomposition.</em>
-<a class="jxr_linenumber" name="L210" href="#L210">210</a> <em class="jxr_javadoccomment">     * &lt;p&gt;Q is an orthogonal matrix&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L211" href="#L211">211</a> <em class="jxr_javadoccomment">     * @return the Q matrix</em>
-<a class="jxr_linenumber" name="L212" href="#L212">212</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L213" href="#L213">213</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> getQ() {
-<a class="jxr_linenumber" name="L214" href="#L214">214</a>         <strong class="jxr_keyword">if</strong> (cachedQ == <strong class="jxr_keyword">null</strong>) {
-<a class="jxr_linenumber" name="L215" href="#L215">215</a>             cachedQ = getQT().transpose();
-<a class="jxr_linenumber" name="L216" href="#L216">216</a>         }
-<a class="jxr_linenumber" name="L217" href="#L217">217</a>         <strong class="jxr_keyword">return</strong> cachedQ;
-<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_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_javadoccomment">     * Returns the transpose of the matrix Q of the decomposition.</em>
-<a class="jxr_linenumber" name="L222" href="#L222">222</a> <em class="jxr_javadoccomment">     * &lt;p&gt;Q is an orthogonal matrix&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L223" href="#L223">223</a> <em class="jxr_javadoccomment">     * @return the transpose of the Q matrix, Q&lt;sup&gt;T&lt;/sup&gt;</em>
-<a class="jxr_linenumber" name="L224" href="#L224">224</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L225" href="#L225">225</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> getQT() {
-<a class="jxr_linenumber" name="L226" href="#L226">226</a>         <strong class="jxr_keyword">if</strong> (cachedQT == <strong class="jxr_keyword">null</strong>) {
-<a class="jxr_linenumber" name="L227" href="#L227">227</a> 
-<a class="jxr_linenumber" name="L228" href="#L228">228</a>             <em class="jxr_comment">// QT is supposed to be m x m</em>
-<a class="jxr_linenumber" name="L229" href="#L229">229</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = qrt.length;
-<a class="jxr_linenumber" name="L230" href="#L230">230</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = qrt[0].length;
-<a class="jxr_linenumber" name="L231" href="#L231">231</a>             <strong class="jxr_keyword">double</strong>[][] qta = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[m][m];
-<a class="jxr_linenumber" name="L232" href="#L232">232</a> 
-<a class="jxr_linenumber" name="L233" href="#L233">233</a>             <em class="jxr_comment">/*</em>
-<a class="jxr_linenumber" name="L234" href="#L234">234</a> <em class="jxr_comment">             * Q = Q1 Q2 ... Q_m, so Q is formed by first constructing Q_m and then</em>
-<a class="jxr_linenumber" name="L235" href="#L235">235</a> <em class="jxr_comment">             * applying the Householder transformations Q_(m-1),Q_(m-2),...,Q1 in</em>
-<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_comment">             * succession to the result</em>
-<a class="jxr_linenumber" name="L237" href="#L237">237</a> <em class="jxr_comment">             */</em>
-<a class="jxr_linenumber" name="L238" href="#L238">238</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> minor = m - 1; minor &gt;= FastMath.min(m, n); minor--) {
-<a class="jxr_linenumber" name="L239" href="#L239">239</a>                 qta[minor][minor] = 1.0d;
-<a class="jxr_linenumber" name="L240" href="#L240">240</a>             }
-<a class="jxr_linenumber" name="L241" href="#L241">241</a> 
-<a class="jxr_linenumber" name="L242" href="#L242">242</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> minor = FastMath.min(m, n)-1; minor &gt;= 0; minor--){
-<a class="jxr_linenumber" name="L243" href="#L243">243</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtMinor = qrt[minor];
-<a class="jxr_linenumber" name="L244" href="#L244">244</a>                 qta[minor][minor] = 1.0d;
-<a class="jxr_linenumber" name="L245" href="#L245">245</a>                 <strong class="jxr_keyword">if</strong> (qrtMinor[minor] != 0.0) {
-<a class="jxr_linenumber" name="L246" href="#L246">246</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> col = minor; col &lt; m; col++) {
-<a class="jxr_linenumber" name="L247" href="#L247">247</a>                         <strong class="jxr_keyword">double</strong> alpha = 0;
-<a class="jxr_linenumber" name="L248" href="#L248">248</a>                         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; row++) {
-<a class="jxr_linenumber" name="L249" href="#L249">249</a>                             alpha -= qta[col][row] * qrtMinor[row];
-<a class="jxr_linenumber" name="L250" href="#L250">250</a>                         }
-<a class="jxr_linenumber" name="L251" href="#L251">251</a>                         alpha /= rDiag[minor] * qrtMinor[minor];
-<a class="jxr_linenumber" name="L252" href="#L252">252</a> 
-<a class="jxr_linenumber" name="L253" href="#L253">253</a>                         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; row++) {
-<a class="jxr_linenumber" name="L254" href="#L254">254</a>                             qta[col][row] += -alpha * qrtMinor[row];
-<a class="jxr_linenumber" name="L255" href="#L255">255</a>                         }
-<a class="jxr_linenumber" name="L256" href="#L256">256</a>                     }
-<a class="jxr_linenumber" name="L257" href="#L257">257</a>                 }
-<a class="jxr_linenumber" name="L258" href="#L258">258</a>             }
-<a class="jxr_linenumber" name="L259" href="#L259">259</a>             cachedQT = MatrixUtils.createRealMatrix(qta);
-<a class="jxr_linenumber" name="L260" href="#L260">260</a>         }
-<a class="jxr_linenumber" name="L261" href="#L261">261</a> 
-<a class="jxr_linenumber" name="L262" href="#L262">262</a>         <em class="jxr_comment">// return the cached matrix</em>
-<a class="jxr_linenumber" name="L263" href="#L263">263</a>         <strong class="jxr_keyword">return</strong> cachedQT;
-<a class="jxr_linenumber" name="L264" href="#L264">264</a>     }
-<a class="jxr_linenumber" name="L265" href="#L265">265</a> 
-<a class="jxr_linenumber" name="L266" href="#L266">266</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L267" href="#L267">267</a> <em class="jxr_javadoccomment">     * Returns the Householder reflector vectors.</em>
-<a class="jxr_linenumber" name="L268" href="#L268">268</a> <em class="jxr_javadoccomment">     * &lt;p&gt;H is a lower trapezoidal matrix whose columns represent</em>
-<a class="jxr_linenumber" name="L269" href="#L269">269</a> <em class="jxr_javadoccomment">     * each successive Householder reflector vector. This matrix is used</em>
-<a class="jxr_linenumber" name="L270" href="#L270">270</a> <em class="jxr_javadoccomment">     * to compute Q.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L271" href="#L271">271</a> <em class="jxr_javadoccomment">     * @return a matrix containing the Householder reflector vectors</em>
-<a class="jxr_linenumber" name="L272" href="#L272">272</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L273" href="#L273">273</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> getH() {
-<a class="jxr_linenumber" name="L274" href="#L274">274</a>         <strong class="jxr_keyword">if</strong> (cachedH == <strong class="jxr_keyword">null</strong>) {
-<a class="jxr_linenumber" name="L275" href="#L275">275</a> 
-<a class="jxr_linenumber" name="L276" href="#L276">276</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = qrt.length;
-<a class="jxr_linenumber" name="L277" href="#L277">277</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = qrt[0].length;
-<a class="jxr_linenumber" name="L278" href="#L278">278</a>             <strong class="jxr_keyword">double</strong>[][] ha = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[m][n];
-<a class="jxr_linenumber" name="L279" href="#L279">279</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; m; ++i) {
-<a class="jxr_linenumber" name="L280" href="#L280">280</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> j = 0; j &lt; FastMath.min(i + 1, n); ++j) {
-<a class="jxr_linenumber" name="L281" href="#L281">281</a>                     ha[i][j] = qrt[j][i] / -rDiag[j];
-<a class="jxr_linenumber" name="L282" href="#L282">282</a>                 }
-<a class="jxr_linenumber" name="L283" href="#L283">283</a>             }
-<a class="jxr_linenumber" name="L284" href="#L284">284</a>             cachedH = MatrixUtils.createRealMatrix(ha);
-<a class="jxr_linenumber" name="L285" href="#L285">285</a>         }
-<a class="jxr_linenumber" name="L286" href="#L286">286</a> 
-<a class="jxr_linenumber" name="L287" href="#L287">287</a>         <em class="jxr_comment">// return the cached matrix</em>
-<a class="jxr_linenumber" name="L288" href="#L288">288</a>         <strong class="jxr_keyword">return</strong> cachedH;
-<a class="jxr_linenumber" name="L289" href="#L289">289</a>     }
-<a class="jxr_linenumber" name="L290" href="#L290">290</a> 
-<a class="jxr_linenumber" name="L291" href="#L291">291</a>     <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L292" href="#L292">292</a> <em class="jxr_javadoccomment">     * Get a solver for finding the A &amp;times; X = B solution in least square sense.</em>
-<a class="jxr_linenumber" name="L293" href="#L293">293</a> <em class="jxr_javadoccomment">     * &lt;p&gt;</em>
-<a class="jxr_linenumber" name="L294" href="#L294">294</a> <em class="jxr_javadoccomment">     * Least Square sense means a solver can be computed for an overdetermined system,</em>
-<a class="jxr_linenumber" name="L295" href="#L295">295</a> <em class="jxr_javadoccomment">     * (i.e. a system with more equations than unknowns, which corresponds to a tall A</em>
-<a class="jxr_linenumber" name="L296" href="#L296">296</a> <em class="jxr_javadoccomment">     * matrix with more rows than columns). In any case, if the matrix is singular</em>
-<a class="jxr_linenumber" name="L297" href="#L297">297</a> <em class="jxr_javadoccomment">     * within the tolerance set at {@link QRDecomposition#QRDecomposition(RealMatrix,</em>
-<a class="jxr_linenumber" name="L298" href="#L298">298</a> <em class="jxr_javadoccomment">     * double) construction}, an error will be triggered when</em>
-<a class="jxr_linenumber" name="L299" href="#L299">299</a> <em class="jxr_javadoccomment">     * the {@link DecompositionSolver#solve(RealVector) solve} method will be called.</em>
-<a class="jxr_linenumber" name="L300" href="#L300">300</a> <em class="jxr_javadoccomment">     * &lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L301" href="#L301">301</a> <em class="jxr_javadoccomment">     * @return a solver</em>
-<a class="jxr_linenumber" name="L302" href="#L302">302</a> <em class="jxr_javadoccomment">     */</em>
-<a class="jxr_linenumber" name="L303" href="#L303">303</a>     <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html">DecompositionSolver</a> getSolver() {
-<a class="jxr_linenumber" name="L304" href="#L304">304</a>         <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">Solver</a>(qrt, rDiag, threshold);
-<a class="jxr_linenumber" name="L305" href="#L305">305</a>     }
-<a class="jxr_linenumber" name="L306" href="#L306">306</a> 
-<a class="jxr_linenumber" name="L307" href="#L307">307</a>     <em class="jxr_javadoccomment">/** Specialized solver. */</em>
-<a class="jxr_linenumber" name="L308" href="#L308">308</a>     <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">class</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">Solver</a> <strong class="jxr_keyword">implements</strong> <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html">DecompositionSolver</a> {
-<a class="jxr_linenumber" name="L309" href="#L309">309</a>         <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L310" href="#L310">310</a> <em class="jxr_javadoccomment">         * A packed TRANSPOSED representation of the QR decomposition.</em>
-<a class="jxr_linenumber" name="L311" href="#L311">311</a> <em class="jxr_javadoccomment">         * &lt;p&gt;The elements BELOW the diagonal are the elements of the UPPER triangular</em>
-<a class="jxr_linenumber" name="L312" href="#L312">312</a> <em class="jxr_javadoccomment">         * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors</em>
-<a class="jxr_linenumber" name="L313" href="#L313">313</a> <em class="jxr_javadoccomment">         * from which an explicit form of Q can be recomputed if desired.&lt;/p&gt;</em>
-<a class="jxr_linenumber" name="L314" href="#L314">314</a> <em class="jxr_javadoccomment">         */</em>
-<a class="jxr_linenumber" name="L315" href="#L315">315</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] qrt;
-<a class="jxr_linenumber" name="L316" href="#L316">316</a>         <em class="jxr_javadoccomment">/** The diagonal elements of R. */</em>
-<a class="jxr_linenumber" name="L317" href="#L317">317</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] rDiag;
-<a class="jxr_linenumber" name="L318" href="#L318">318</a>         <em class="jxr_javadoccomment">/** Singularity threshold. */</em>
-<a class="jxr_linenumber" name="L319" href="#L319">319</a>         <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> threshold;
-<a class="jxr_linenumber" name="L320" href="#L320">320</a> 
-<a class="jxr_linenumber" name="L321" href="#L321">321</a>         <em class="jxr_javadoccomment">/**</em>
-<a class="jxr_linenumber" name="L322" href="#L322">322</a> <em class="jxr_javadoccomment">         * Build a solver from decomposed matrix.</em>
-<a class="jxr_linenumber" name="L323" href="#L323">323</a> <em class="jxr_javadoccomment">         *</em>
-<a class="jxr_linenumber" name="L324" href="#L324">324</a> <em class="jxr_javadoccomment">         * @param qrt Packed TRANSPOSED representation of the QR decomposition.</em>
-<a class="jxr_linenumber" name="L325" href="#L325">325</a> <em class="jxr_javadoccomment">         * @param rDiag Diagonal elements of R.</em>
-<a class="jxr_linenumber" name="L326" href="#L326">326</a> <em class="jxr_javadoccomment">         * @param threshold Singularity threshold.</em>
-<a class="jxr_linenumber" name="L327" href="#L327">327</a> <em class="jxr_javadoccomment">         */</em>
-<a class="jxr_linenumber" name="L328" href="#L328">328</a>         <strong class="jxr_keyword">private</strong> <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html">Solver</a>(<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] qrt,
-<a class="jxr_linenumber" name="L329" href="#L329">329</a>                        <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] rDiag,
-<a class="jxr_linenumber" name="L330" href="#L330">330</a>                        <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> threshold) {
-<a class="jxr_linenumber" name="L331" href="#L331">331</a>             <strong class="jxr_keyword">this</strong>.qrt   = qrt;
-<a class="jxr_linenumber" name="L332" href="#L332">332</a>             <strong class="jxr_keyword">this</strong>.rDiag = rDiag;
-<a class="jxr_linenumber" name="L333" href="#L333">333</a>             <strong class="jxr_keyword">this</strong>.threshold = threshold;
-<a class="jxr_linenumber" name="L334" href="#L334">334</a>         }
-<a class="jxr_linenumber" name="L335" href="#L335">335</a> 
-<a class="jxr_linenumber" name="L336" href="#L336">336</a>         <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L337" href="#L337">337</a>         <strong class="jxr_keyword">public</strong> <strong class="jxr_keyword">boolean</strong> isNonSingular() {
-<a class="jxr_linenumber" name="L338" href="#L338">338</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">double</strong> diag : rDiag) {
-<a class="jxr_linenumber" name="L339" href="#L339">339</a>                 <strong class="jxr_keyword">if</strong> (FastMath.abs(diag) &lt;= threshold) {
-<a class="jxr_linenumber" name="L340" href="#L340">340</a>                     <strong class="jxr_keyword">return</strong> false;
-<a class="jxr_linenumber" name="L341" href="#L341">341</a>                 }
-<a class="jxr_linenumber" name="L342" href="#L342">342</a>             }
-<a class="jxr_linenumber" name="L343" href="#L343">343</a>             <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">true</strong>;
-<a class="jxr_linenumber" name="L344" href="#L344">344</a>         }
-<a class="jxr_linenumber" name="L345" href="#L345">345</a> 
-<a class="jxr_linenumber" name="L346" href="#L346">346</a>         <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L347" href="#L347">347</a>         <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealVector.html">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html">RealVector</a> b) {
-<a class="jxr_linenumber" name="L348" href="#L348">348</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = qrt.length;
-<a class="jxr_linenumber" name="L349" href="#L349">349</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = qrt[0].length;
-<a class="jxr_linenumber" name="L350" href="#L350">350</a>             <strong class="jxr_keyword">if</strong> (b.getDimension() != m) {
-<a class="jxr_linenumber" name="L351" href="#L351">351</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html">DimensionMismatchException</a>(b.getDimension(), m);
-<a class="jxr_linenumber" name="L352" href="#L352">352</a>             }
-<a class="jxr_linenumber" name="L353" href="#L353">353</a>             <strong class="jxr_keyword">if</strong> (!isNonSingular()) {
-<a class="jxr_linenumber" name="L354" href="#L354">354</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html">SingularMatrixException</a>();
-<a class="jxr_linenumber" name="L355" href="#L355">355</a>             }
-<a class="jxr_linenumber" name="L356" href="#L356">356</a> 
-<a class="jxr_linenumber" name="L357" href="#L357">357</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[n];
-<a class="jxr_linenumber" name="L358" href="#L358">358</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] y = b.toArray();
-<a class="jxr_linenumber" name="L359" href="#L359">359</a> 
-<a class="jxr_linenumber" name="L360" href="#L360">360</a>             <em class="jxr_comment">// apply Householder transforms to solve Q.y = b</em>
-<a class="jxr_linenumber" name="L361" href="#L361">361</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> minor = 0; minor &lt; FastMath.min(m, n); minor++) {
-<a class="jxr_linenumber" name="L362" href="#L362">362</a> 
-<a class="jxr_linenumber" name="L363" href="#L363">363</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtMinor = qrt[minor];
-<a class="jxr_linenumber" name="L364" href="#L364">364</a>                 <strong class="jxr_keyword">double</strong> dotProduct = 0;
-<a class="jxr_linenumber" name="L365" href="#L365">365</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; row++) {
-<a class="jxr_linenumber" name="L366" href="#L366">366</a>                     dotProduct += y[row] * qrtMinor[row];
-<a class="jxr_linenumber" name="L367" href="#L367">367</a>                 }
-<a class="jxr_linenumber" name="L368" href="#L368">368</a>                 dotProduct /= rDiag[minor] * qrtMinor[minor];
-<a class="jxr_linenumber" name="L369" href="#L369">369</a> 
-<a class="jxr_linenumber" name="L370" href="#L370">370</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; row++) {
-<a class="jxr_linenumber" name="L371" href="#L371">371</a>                     y[row] += dotProduct * qrtMinor[row];
-<a class="jxr_linenumber" name="L372" href="#L372">372</a>                 }
-<a class="jxr_linenumber" name="L373" href="#L373">373</a>             }
-<a class="jxr_linenumber" name="L374" href="#L374">374</a> 
-<a class="jxr_linenumber" name="L375" href="#L375">375</a>             <em class="jxr_comment">// solve triangular system R.x = y</em>
-<a class="jxr_linenumber" name="L376" href="#L376">376</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = rDiag.length - 1; row &gt;= 0; --row) {
-<a class="jxr_linenumber" name="L377" href="#L377">377</a>                 y[row] /= rDiag[row];
-<a class="jxr_linenumber" name="L378" href="#L378">378</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> yRow = y[row];
-<a class="jxr_linenumber" name="L379" href="#L379">379</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtRow = qrt[row];
-<a class="jxr_linenumber" name="L380" href="#L380">380</a>                 x[row] = yRow;
-<a class="jxr_linenumber" name="L381" href="#L381">381</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 0; i &lt; row; i++) {
-<a class="jxr_linenumber" name="L382" href="#L382">382</a>                     y[i] -= yRow * qrtRow[i];
-<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> 
-<a class="jxr_linenumber" name="L386" href="#L386">386</a>             <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/linear/ArrayRealVector.html">ArrayRealVector</a>(x, false);
-<a class="jxr_linenumber" name="L387" href="#L387">387</a>         }
-<a class="jxr_linenumber" name="L388" href="#L388">388</a> 
-<a class="jxr_linenumber" name="L389" href="#L389">389</a>         <em class="jxr_javadoccomment">/** {@inheritDoc} */</em>
-<a class="jxr_linenumber" name="L390" href="#L390">390</a>         <strong class="jxr_keyword">public</strong> <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html">RealMatrix</a> b) {
-<a class="jxr_linenumber" name="L391" href="#L391">391</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> n = qrt.length;
-<a class="jxr_linenumber" name="L392" href="#L392">392</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> m = qrt[0].length;
-<a class="jxr_linenumber" name="L393" href="#L393">393</a>             <strong class="jxr_keyword">if</strong> (b.getRowDimension() != m) {
-<a class="jxr_linenumber" name="L394" href="#L394">394</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html">DimensionMismatchException</a>(b.getRowDimension(), m);
-<a class="jxr_linenumber" name="L395" href="#L395">395</a>             }
-<a class="jxr_linenumber" name="L396" href="#L396">396</a>             <strong class="jxr_keyword">if</strong> (!isNonSingular()) {
-<a class="jxr_linenumber" name="L397" href="#L397">397</a>                 <strong class="jxr_keyword">throw</strong> <strong class="jxr_keyword">new</strong> <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html">SingularMatrixException</a>();
-<a class="jxr_linenumber" name="L398" href="#L398">398</a>             }
-<a class="jxr_linenumber" name="L399" href="#L399">399</a> 
-<a class="jxr_linenumber" name="L400" href="#L400">400</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> columns        = b.getColumnDimension();
-<a class="jxr_linenumber" name="L401" href="#L401">401</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> blockSize      = BlockRealMatrix.BLOCK_SIZE;
-<a class="jxr_linenumber" name="L402" href="#L402">402</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> cBlocks        = (columns + blockSize - 1) / blockSize;
-<a class="jxr_linenumber" name="L403" href="#L403">403</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] xBlocks = BlockRealMatrix.createBlocksLayout(n, columns);
-<a class="jxr_linenumber" name="L404" href="#L404">404</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[][] y       = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[b.getRowDimension()][blockSize];
-<a class="jxr_linenumber" name="L405" href="#L405">405</a>             <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[]   alpha   = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[blockSize];
-<a class="jxr_linenumber" name="L406" href="#L406">406</a> 
-<a class="jxr_linenumber" name="L407" href="#L407">407</a>             <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> kBlock = 0; kBlock &lt; cBlocks; ++kBlock) {
-<a class="jxr_linenumber" name="L408" href="#L408">408</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> kStart = kBlock * blockSize;
-<a class="jxr_linenumber" name="L409" href="#L409">409</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> kEnd   = FastMath.min(kStart + blockSize, columns);
-<a class="jxr_linenumber" name="L410" href="#L410">410</a>                 <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> kWidth = kEnd - kStart;
-<a class="jxr_linenumber" name="L411" href="#L411">411</a> 
-<a class="jxr_linenumber" name="L412" href="#L412">412</a>                 <em class="jxr_comment">// get the right hand side vector</em>
-<a class="jxr_linenumber" name="L413" href="#L413">413</a>                 b.copySubMatrix(0, m - 1, kStart, kEnd - 1, y);
-<a class="jxr_linenumber" name="L414" href="#L414">414</a> 
-<a class="jxr_linenumber" name="L415" href="#L415">415</a>                 <em class="jxr_comment">// apply Householder transforms to solve Q.y = b</em>
-<a class="jxr_linenumber" name="L416" href="#L416">416</a>                 <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> minor = 0; minor &lt; FastMath.min(m, n); minor++) {
-<a class="jxr_linenumber" name="L417" href="#L417">417</a>                     <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] qrtMinor = qrt[minor];
-<a class="jxr_linenumber" name="L418" href="#L418">418</a>                     <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> factor     = 1.0 / (rDiag[minor] * qrtMinor[minor]);
-<a class="jxr_linenumber" name="L419" href="#L419">419</a> 
-<a class="jxr_linenumber" name="L420" href="#L420">420</a>                     Arrays.fill(alpha, 0, kWidth, 0.0);
-<a class="jxr_linenumber" name="L421" href="#L421">421</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; ++row) {
-<a class="jxr_linenumber" name="L422" href="#L422">422</a>                         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>   d    = qrtMinor[row];
-<a class="jxr_linenumber" name="L423" href="#L423">423</a>                         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] yRow = y[row];
-<a class="jxr_linenumber" name="L424" href="#L424">424</a>                         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 0; k &lt; kWidth; ++k) {
-<a class="jxr_linenumber" name="L425" href="#L425">425</a>                             alpha[k] += d * yRow[k];
-<a class="jxr_linenumber" name="L426" href="#L426">426</a>                         }
-<a class="jxr_linenumber" name="L427" href="#L427">427</a>                     }
-<a class="jxr_linenumber" name="L428" href="#L428">428</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 0; k &lt; kWidth; ++k) {
-<a class="jxr_linenumber" name="L429" href="#L429">429</a>                         alpha[k] *= factor;
-<a class="jxr_linenumber" name="L430" href="#L430">430</a>                     }
-<a class="jxr_linenumber" name="L431" href="#L431">431</a> 
-<a class="jxr_linenumber" name="L432" href="#L432">432</a>                     <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> row = minor; row &lt; m; ++row) {
-<a class="jxr_linenumber" name="L433" href="#L433">433</a>                         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>   d    = qrtMinor[row];
-<a class="jxr_linenumber" name="L434" href="#L434">434</a>                         <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] yRow = y[row];
-<a class="jxr_linenumber" name="L435" href="#L435">435</a>                         <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> k = 0; k &lt; kWidth; ++k) {
-<a class="jxr_linenumber" name="L436" href="#L436">436</a>                             yRow[k] += alpha[k] * d;
-<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> 
-<a class="jxr_linenumber" name="L441" href="#L441">441</a>                 <em class="jxr_comment">// solve triangular system R.x = y</em>
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