<!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">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.12"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Engauge Digitizer: Matrix/Matrix.cpp Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">Engauge Digitizer
 <span id="projectnumber">2</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.12 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
$(function() {
initMenu('',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
</script>
<div id="main-nav"></div>
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div id="nav-path" class="navpath">
<ul>
<li class="navelem"><a class="el" href="dir_d60f6684020cb105011de41729268593.html">Matrix</a></li> </ul>
</div>
</div><!-- top -->
<div class="header">
<div class="headertitle">
<div class="title">Matrix.cpp</div> </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/******************************************************************************************************</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * (C) 2016 markummitchell@github.com. This file is part of Engauge Digitizer, which is released *</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * under GNU General Public License version 2 (GPLv2) or (at your option) any later version. See file *</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * LICENSE or go to gnu.org/licenses for details. Distribution requires prior written permission. *</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> ******************************************************************************************************/</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> </div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#include "EngaugeAssert.h"</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="preprocessor">#include "Matrix.h"</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="preprocessor">#include <QTextStream></span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div><div class="line"><a name="l00011"></a><span class="lineno"><a class="line" href="classMatrix.html#aa9d5b60eef1b5eed3aa3ceb95f026e2c"> 11</a></span> <a class="code" href="classMatrix.html#aa9d5b60eef1b5eed3aa3ceb95f026e2c">Matrix::Matrix</a> (<span class="keywordtype">int</span> N)</div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> {</div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  initialize (N, N);</div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> }</div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"><a class="line" href="classMatrix.html#a7213414e405fd1c81c394d5053721fa7"> 16</a></span> <a class="code" href="classMatrix.html#aa9d5b60eef1b5eed3aa3ceb95f026e2c">Matrix::Matrix</a> (<span class="keywordtype">int</span> <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a>,</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  <span class="keywordtype">int</span> <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a>)</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> {</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  initialize (rows, cols);</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> }</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div><div class="line"><a name="l00022"></a><span class="lineno"><a class="line" href="classMatrix.html#abcf708e864ed3d9db2c3b317c5e529ab"> 22</a></span> <a class="code" href="classMatrix.html#aa9d5b60eef1b5eed3aa3ceb95f026e2c">Matrix::Matrix</a> (<span class="keyword">const</span> <a class="code" href="classMatrix.html">Matrix</a> &other)</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> {</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  m_rows = other.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a>();</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  m_cols = other.<a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a>();</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  m_vector.resize (m_rows * m_cols);</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">set</span> (row, col, other.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (row, col));</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  }</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  }</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> }</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="classMatrix.html#a45e4814b752129bed1f1316632f8543a"> 34</a></span> <a class="code" href="classMatrix.html">Matrix</a> &<a class="code" href="classMatrix.html#a45e4814b752129bed1f1316632f8543a">Matrix::operator= </a>(<span class="keyword">const</span> <a class="code" href="classMatrix.html">Matrix</a> &other)</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> {</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  m_rows = other.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a>();</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  m_cols = other.<a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a>();</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  m_vector.resize (m_rows * m_cols);</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">set</span> (row, col, other.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (row, col));</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  }</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> }</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="keywordtype">void</span> Matrix::addRowToAnotherWithScaling (<span class="keywordtype">int</span> rowFrom,</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordtype">int</span> rowTo,</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordtype">double</span> factor)</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> {</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">double</span> oldValueFrom = <span class="keyword">get</span> (rowFrom, col);</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">double</span> oldValueTo = <span class="keyword">get</span> (rowTo, col);</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">double</span> newValueTo = oldValueFrom * factor + oldValueTo;</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">set</span> (rowTo, col, newValueTo);</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> }</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc"> 60</a></span> <span class="keywordtype">int</span> <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">Matrix::cols</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword"></span>{</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">return</span> m_cols;</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> }</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div><div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5"> 65</a></span> <span class="keywordtype">double</span> <a class="code" href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5">Matrix::determinant</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="keyword"></span>{</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  ENGAUGE_ASSERT (m_rows == m_cols);</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordtype">double</span> rtn;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">if</span> (m_rows == 1) {</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  rtn = m_vector [0];</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> COL = 0; <span class="comment">// We arbitrarily iterate through the first column</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// This is a recursive algorithm</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  rtn = 0.0;</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordtype">double</span> multiplier = +1;</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <a class="code" href="classMatrix.html">Matrix</a> min = <a class="code" href="classMatrix.html#a5a2b2b981f044207ef30269edf0acc4f">minorReduced</a> (row, COL);</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  rtn += multiplier * <span class="keyword">get</span> (row, COL) * min.<a class="code" href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5">determinant</a> ();</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  multiplier *= -1.0;</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  }</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">return</span> rtn;</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> }</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="keywordtype">int</span> Matrix::fold2dIndexes (<span class="keywordtype">int</span> row, <span class="keywordtype">int</span> col)<span class="keyword"> const</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="keyword"></span>{</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">return</span> row * m_cols + col;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> }</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div><div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478"> 97</a></span> <span class="keywordtype">double</span> <a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">Matrix::get</a> (<span class="keywordtype">int</span> row, <span class="keywordtype">int</span> col)<span class="keyword"> const</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="keyword"></span>{</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">return</span> m_vector [fold2dIndexes (row, col)];</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> }</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">void</span> Matrix::initialize (<span class="keywordtype">int</span> <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a>,</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">int</span> <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a>)</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> {</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  m_rows = <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a>;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  m_cols = <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a>;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  m_vector.resize (<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> * cols);</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> </div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// Identity matrix for square matrix, otherwise zero matrix</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">if</span> (row == col && m_rows == m_cols) {</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">set</span> (row, col, 1.0);</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">set</span> (row, col, 0.0);</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  }</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  }</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  }</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> }</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div><div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="classMatrix.html#aab07edad1c28dbd2b521bf195d33cb06"> 121</a></span> <a class="code" href="classMatrix.html">Matrix</a> <a class="code" href="classMatrix.html#aab07edad1c28dbd2b521bf195d33cb06">Matrix::inverse</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="keyword"></span>{</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// Available algorithms are inverseCramersRule and inverseGaussianElimination</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">return</span> inverseGaussianElimination ();</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> }</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <a class="code" href="classMatrix.html">Matrix</a> Matrix::inverseCramersRule ()<span class="keyword"> const</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="keyword"></span>{</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  ENGAUGE_ASSERT (m_rows == m_cols);</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> </div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="classMatrix.html">Matrix</a> inv (m_rows);</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordtype">int</span> row, col;</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  </div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">if</span> (m_rows > 1) {</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> </div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">// Compute cofactor matrix</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordtype">double</span> multiplierStartForRow = 1.0;</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="code" href="classMatrix.html">Matrix</a> cofactor (m_rows);</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">for</span> (row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">double</span> multiplier = multiplierStartForRow;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">for</span> (col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <a class="code" href="classMatrix.html">Matrix</a> min = <a class="code" href="classMatrix.html#a5a2b2b981f044207ef30269edf0acc4f">minorReduced</a> (row, col);</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordtype">double</span> element = multiplier * min.<a class="code" href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5">determinant</a> ();</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  multiplier *= -1.0;</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  cofactor.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (row, col, element);</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  }</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  multiplierStartForRow *= -1.0;</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> </div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// Compute adjoint</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <a class="code" href="classMatrix.html">Matrix</a> adjoint = cofactor.<a class="code" href="classMatrix.html#a759661b75b9681f3a89ff75e27933b3a">transpose</a> ();</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordtype">double</span> determ = <a class="code" href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5">determinant</a> ();</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// Inverse is the adjoint divided by the determinant</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">for</span> (row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">for</span> (col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  inv.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (row, col, adjoint.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (row, col) / determ);</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  }</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  }</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  inv.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (0, 0, 1.0 / <span class="keyword">get</span> (0, 0));</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  }</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">return</span> inv;</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span> }</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <a class="code" href="classMatrix.html">Matrix</a> Matrix::inverseGaussianElimination ()<span class="keyword"> const</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="keyword"></span>{</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// From https://en.wikipedia.org/wiki/Gaussian_elimination</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordtype">int</span> row, col, rowFrom, rowTo;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> </div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="comment">// Track the row switches that may or may not be performed below</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  QVector<int> rowIndexes (<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> ());</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">for</span> (row = 0; row < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row++) {</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  rowIndexes [row] = row;</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="comment">// Creat the working matrix and populate the left half. Number of columns in the working matrix is twice the number</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="comment">// of cols in this matrix, but we will not populate the right half until after the bubble sort below</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="classMatrix.html">Matrix</a> working (rows (), 2 * <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> ());</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">for</span> (row = 0; row < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row++) {</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">for</span> (col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordtype">double</span> value = <span class="keyword">get</span> (row, col);</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  working.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (row, col, value);</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  }</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// Simple bubble sort to rearrange the rows with 0 leading zeros at start, followed by rows with 1 leading zero at start, ...</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row1 = 0; row1 < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row1++) {</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row2 = row1 + 1; row2 < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row2++) {</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> (working.leadingZeros (row1) > working.leadingZeros (row2)) {</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  working.switchRows (row1, row2);</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// Remember this switch</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordtype">int</span> row1Index = rowIndexes [row1];</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordtype">int</span> row2Index = rowIndexes [row2];</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  rowIndexes [row1] = row2Index;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  rowIndexes [row2] = row1Index;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  }</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  }</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="comment">// Populate the right half now</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">for</span> (row = 0; row < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row++) {</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">for</span> (col = <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col < 2 * <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordtype">int</span> colIdentitySubmatrix = col - <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> ();</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keywordtype">double</span> value = (row == colIdentitySubmatrix) ? 1 : 0;</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  working.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (row, col, value);</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> \</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">// Loop through the "from" row going down. This results in the lower off-diagonal terms becoming zero, in the left half</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">for</span> (rowFrom = 0; rowFrom < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); rowFrom++) {</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordtype">int</span> colFirstWithNonZero = rowFrom;</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> </div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// In pathological situations we have (rowFrom, colFirstWithNonzero) = 0 in which case the solution cannot be obtained</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">// so we exit</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">if</span> (working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowFrom, colFirstWithNonZero) == 0) {</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="comment">// Fail</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// Normalize the 'from' row with first nonzero term set to 1</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  working.normalizeRow (rowFrom, colFirstWithNonZero);</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">// Apply the 'from' row to all the 'to' rows</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">for</span> (rowTo = rowFrom + 1; rowTo < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); rowTo++) {</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowTo, colFirstWithNonZero) != 0) {</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> </div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="comment">// We need to merge rowFrom and rowTo into rowTo</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordtype">double</span> factor = -1.0 * working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowTo, colFirstWithNonZero) / working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowFrom, colFirstWithNonZero);</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  working.addRowToAnotherWithScaling (rowFrom, rowTo, factor);</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  }</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  }</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> </div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="comment">// Loop through the "from" row doing up. This results in the upper off-diagonal terms becoming zero, in the left half</span></div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">for</span> (rowFrom = rows () - 1; rowFrom >= 0; rowFrom--) {</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordtype">int</span> colFirstWithNonZero = rowFrom; <span class="comment">// This is true since we should have 1s all down the diagonal at this point</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">// Normalize the 'from' row with diagonal term set to 1. The first term should be like 0.9999 or 1.0001 but we want exactly one</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  working.normalizeRow (rowFrom, colFirstWithNonZero);</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span> </div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">// Apply the 'from' row to all the 'to' rows</span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">for</span> (rowTo = rowFrom - 1; rowTo >= 0; rowTo--) {</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">if</span> (working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowTo, colFirstWithNonZero) != 0) {</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="comment">// We need to merge rowFro and rowTo into rowTo</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordtype">double</span> factor = -1.0 * working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowTo, colFirstWithNonZero) / working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowFrom, colFirstWithNonZero);</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  working.addRowToAnotherWithScaling (rowFrom, rowTo, factor);</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  }</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="comment">// Extract right half of rectangular matrix which is the inverse</span></div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <a class="code" href="classMatrix.html">Matrix</a> inv (working.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> ());</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">for</span> (row = 0; row < working.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row++) {</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordtype">int</span> rowBeforeSort = rowIndexes [row];</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> </div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">for</span> (col = 0; col < working.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); col++) {</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordtype">int</span> colRightHalf = col + inv.<a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> ();</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keywordtype">double</span> value = working.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (rowBeforeSort, colRightHalf);</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  inv.set (row, col, value);</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  }</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  }</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> </div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">return</span> inv;</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> }</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Matrix::leadingZeros (<span class="keywordtype">int</span> row)<span class="keyword"> const</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="keyword"></span>{</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> sum = 0;</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keywordflow">if</span> (<span class="keyword">get</span> (row, col) != 0) {</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  ++sum;</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  }</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  }</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">return</span> sum;</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> }</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div><div class="line"><a name="l00289"></a><span class="lineno"><a class="line" href="classMatrix.html#a5a2b2b981f044207ef30269edf0acc4f"> 289</a></span> <a class="code" href="classMatrix.html">Matrix</a> <a class="code" href="classMatrix.html#a5a2b2b981f044207ef30269edf0acc4f">Matrix::minorReduced</a> (<span class="keywordtype">int</span> rowOmit, <span class="keywordtype">int</span> colOmit)<span class="keyword"> const</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="keyword"></span>{</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  ENGAUGE_ASSERT (m_rows == m_cols);</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> </div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <a class="code" href="classMatrix.html">Matrix</a> outMinor (m_rows - 1);</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordtype">int</span> rowMinor = 0;</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  </div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span> (row != rowOmit) {</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  </div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordtype">int</span> colMinor = 0;</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">if</span> (col != colOmit) {</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span> </div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  outMinor.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (rowMinor, colMinor, <span class="keyword">get</span> (row, col));</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  ++colMinor;</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  }</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  ++rowMinor;</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  }</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  }</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">return</span> outMinor;</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span> }</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keywordtype">void</span> Matrix::normalizeRow (<span class="keywordtype">int</span> rowToNormalize,</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordtype">int</span> colToNormalize)</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> {</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  ENGAUGE_ASSERT (<span class="keyword">get</span> (rowToNormalize, colToNormalize) != 0);</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordtype">double</span> factor = 1.0 / <span class="keyword">get</span> (rowToNormalize, colToNormalize);</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordtype">double</span> value = <span class="keyword">get</span> (rowToNormalize, col);</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keyword">set</span> (rowToNormalize, col, factor * value);</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  }</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span> }</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span> </div><div class="line"><a name="l00327"></a><span class="lineno"><a class="line" href="classMatrix.html#ab4f8e22e8db0983d75e090542f4d1f7a"> 327</a></span> <a class="code" href="classMatrix.html">Matrix</a> <a class="code" href="classMatrix.html#ab4f8e22e8db0983d75e090542f4d1f7a">Matrix::operator* </a>(<span class="keyword">const</span> <a class="code" href="classMatrix.html">Matrix</a> &other)<span class="keyword"> const</span></div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword"></span>{</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  ENGAUGE_ASSERT (m_cols == other.<a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> ());</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <a class="code" href="classMatrix.html">Matrix</a> out (m_rows, other.<a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> ());</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < other.<a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordtype">double</span> sum = 0;</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> index = 0; index < m_cols; index++) {</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  sum += <span class="keyword">get</span> (row, index) * other.<a class="code" href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">get</a> (index, col);</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  out.set (row, col, sum);</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span> </div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">return</span> out;</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> }</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="classMatrix.html#aef629e2461c502ce6daa21006d06c782"> 346</a></span> QVector<double> <a class="code" href="classMatrix.html#ab4f8e22e8db0983d75e090542f4d1f7a">Matrix::operator* </a>(<span class="keyword">const</span> QVector<double> other)<span class="keyword"> const</span></div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="keyword"></span>{</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  ENGAUGE_ASSERT (m_cols == other.size ());</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  QVector<double> out;</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  out.resize (m_rows);</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="keywordtype">double</span> sum = 0;</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  sum += <span class="keyword">get</span> (row, col) * other [col];</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  }</div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span> </div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  out [row] = sum;</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  }</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordflow">return</span> out;</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span> }</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span> </div><div class="line"><a name="l00364"></a><span class="lineno"><a class="line" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15"> 364</a></span> <span class="keywordtype">int</span> <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">Matrix::rows</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="keyword"></span>{</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">return</span> m_rows;</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span> }</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div><div class="line"><a name="l00369"></a><span class="lineno"><a class="line" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78"> 369</a></span> <span class="keywordtype">void</span> <a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">Matrix::set</a> (<span class="keywordtype">int</span> row, <span class="keywordtype">int</span> col, <span class="keywordtype">double</span> value)</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span> {</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  m_vector [fold2dIndexes (row, col)] = value;</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span> }</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="keywordtype">void</span> Matrix::switchRows (<span class="keywordtype">int</span> row1,</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordtype">int</span> row2)</div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span> {</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">// Switch rows</span></div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordtype">double</span> temp1 = <span class="keyword">get</span> (row1, col);</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keywordtype">double</span> temp2 = <span class="keyword">get</span> (row2, col);</div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keyword">set</span> (row2, col, temp2);</div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keyword">set</span> (row1, col, temp1);</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  }</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span> }</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span> </div><div class="line"><a name="l00386"></a><span class="lineno"><a class="line" href="classMatrix.html#ae7734ca9c95e03ba832d675a7595b408"> 386</a></span> QString <a class="code" href="classMatrix.html#ae7734ca9c95e03ba832d675a7595b408">Matrix::toString</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="keyword"></span>{</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  QString out;</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  QTextStream str (&out);</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span> </div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  str << <span class="stringliteral">"("</span>;</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < <a class="code" href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">rows</a> (); row++) {</div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">if</span> (row > 0) {</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  str << <span class="stringliteral">", "</span>;</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  str << <span class="stringliteral">"("</span>;</div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">cols</a> (); col++) {</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordflow">if</span> (col > 0) {</div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  str << <span class="stringliteral">", "</span>;</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  }</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  str << <span class="keyword">get</span> (row, col);</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  }</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  str << <span class="stringliteral">")"</span>;</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  }</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  str << <span class="stringliteral">")"</span>;</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="keywordflow">return</span> out;</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span> }</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span> </div><div class="line"><a name="l00410"></a><span class="lineno"><a class="line" href="classMatrix.html#a759661b75b9681f3a89ff75e27933b3a"> 410</a></span> <a class="code" href="classMatrix.html">Matrix</a> <a class="code" href="classMatrix.html#a759661b75b9681f3a89ff75e27933b3a">Matrix::transpose</a> ()<span class="keyword"> const</span></div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="keyword"></span>{</div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <a class="code" href="classMatrix.html">Matrix</a> out (m_cols, m_rows);</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < m_rows; row++) {</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < m_cols; col++) {</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  out.<a class="code" href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">set</a> (col, row, <span class="keyword">get</span> (row, col));</div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  }</div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  }</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> </div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keywordflow">return</span> out;</div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> }</div><div class="ttc" id="classMatrix_html_aab07edad1c28dbd2b521bf195d33cb06"><div class="ttname"><a href="classMatrix.html#aab07edad1c28dbd2b521bf195d33cb06">Matrix::inverse</a></div><div class="ttdeci">Matrix inverse() const</div><div class="ttdoc">Return the inverse of this matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00121">Matrix.cpp:121</a></div></div>
<div class="ttc" id="classMatrix_html_ab4f8e22e8db0983d75e090542f4d1f7a"><div class="ttname"><a href="classMatrix.html#ab4f8e22e8db0983d75e090542f4d1f7a">Matrix::operator*</a></div><div class="ttdeci">Matrix operator*(const Matrix &other) const</div><div class="ttdoc">Multiplication operator with a matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00327">Matrix.cpp:327</a></div></div>
<div class="ttc" id="classMatrix_html_a759661b75b9681f3a89ff75e27933b3a"><div class="ttname"><a href="classMatrix.html#a759661b75b9681f3a89ff75e27933b3a">Matrix::transpose</a></div><div class="ttdeci">Matrix transpose() const</div><div class="ttdoc">Return the transpose of the current matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00410">Matrix.cpp:410</a></div></div>
<div class="ttc" id="classMatrix_html_a45e4814b752129bed1f1316632f8543a"><div class="ttname"><a href="classMatrix.html#a45e4814b752129bed1f1316632f8543a">Matrix::operator=</a></div><div class="ttdeci">Matrix & operator=(const Matrix &matrix)</div><div class="ttdoc">Assignment operator. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00034">Matrix.cpp:34</a></div></div>
<div class="ttc" id="classMatrix_html_a5a2b2b981f044207ef30269edf0acc4f"><div class="ttname"><a href="classMatrix.html#a5a2b2b981f044207ef30269edf0acc4f">Matrix::minorReduced</a></div><div class="ttdeci">Matrix minorReduced(int rowOmit, int colOmit) const</div><div class="ttdoc">Return minor matrix which is the original with the specified row and column omitted. The name &#39;minor&#39; is a reserved word. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00289">Matrix.cpp:289</a></div></div>
<div class="ttc" id="classMatrix_html_a0b959a2e367c53ebde140772ea9281b5"><div class="ttname"><a href="classMatrix.html#a0b959a2e367c53ebde140772ea9281b5">Matrix::determinant</a></div><div class="ttdeci">double determinant() const</div><div class="ttdoc">Return the determinant of this matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00065">Matrix.cpp:65</a></div></div>
<div class="ttc" id="classMatrix_html_aa9d5b60eef1b5eed3aa3ceb95f026e2c"><div class="ttname"><a href="classMatrix.html#aa9d5b60eef1b5eed3aa3ceb95f026e2c">Matrix::Matrix</a></div><div class="ttdeci">Matrix(int N)</div><div class="ttdoc">Simple constructor of square matrix with initialization to identity matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00011">Matrix.cpp:11</a></div></div>
<div class="ttc" id="classMatrix_html_ae836a1433ba6902a4a2ee9105a92b4fc"><div class="ttname"><a href="classMatrix.html#ae836a1433ba6902a4a2ee9105a92b4fc">Matrix::cols</a></div><div class="ttdeci">int cols() const</div><div class="ttdoc">Width of matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00060">Matrix.cpp:60</a></div></div>
<div class="ttc" id="classMatrix_html"><div class="ttname"><a href="classMatrix.html">Matrix</a></div><div class="ttdoc">Matrix class that supports arbitrary NxN size. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8h_source.html#l00014">Matrix.h:14</a></div></div>
<div class="ttc" id="classMatrix_html_a243417b7fe6c8acb70b5393ebe113a15"><div class="ttname"><a href="classMatrix.html#a243417b7fe6c8acb70b5393ebe113a15">Matrix::rows</a></div><div class="ttdeci">int rows() const</div><div class="ttdoc">Height of matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00364">Matrix.cpp:364</a></div></div>
<div class="ttc" id="classMatrix_html_abb30328c4f3132dcfb0b7a9ffdfad478"><div class="ttname"><a href="classMatrix.html#abb30328c4f3132dcfb0b7a9ffdfad478">Matrix::get</a></div><div class="ttdeci">double get(int row, int col) const</div><div class="ttdoc">Return (row, col) element. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00097">Matrix.cpp:97</a></div></div>
<div class="ttc" id="classMatrix_html_a5c337cdd8313e5f97ddf042359ec7e78"><div class="ttname"><a href="classMatrix.html#a5c337cdd8313e5f97ddf042359ec7e78">Matrix::set</a></div><div class="ttdeci">void set(int row, int col, double value)</div><div class="ttdoc">Set (row, col) element. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00369">Matrix.cpp:369</a></div></div>
<div class="ttc" id="classMatrix_html_ae7734ca9c95e03ba832d675a7595b408"><div class="ttname"><a href="classMatrix.html#ae7734ca9c95e03ba832d675a7595b408">Matrix::toString</a></div><div class="ttdeci">QString toString() const</div><div class="ttdoc">Dump matrix to a string. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8cpp_source.html#l00386">Matrix.cpp:386</a></div></div>
</div><!-- fragment --></div><!-- contents -->
<!-- start footer part -->
<hr class="footer"/><address class="footer"><small>
Generated on Sun Dec 25 2016 20:54:09 for Engauge Digitizer by  <a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/>
</a> 1.8.12
</small></address>
</body>
</html>
