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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr</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> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_ITERSCALING_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_ITERSCALING_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">using</span> std::abs; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">class </span>IterScaling</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">typedef</span> _MatrixType MatrixType; </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  IterScaling() { init(); }</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  IterScaling(<span class="keyword">const</span> MatrixType& matrix)</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>  init();</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  compute(matrix);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  ~IterScaling() { }</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">void</span> compute (<span class="keyword">const</span> MatrixType& mat)</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordtype">int</span> m = mat.rows(); </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordtype">int</span> n = mat.cols();</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  eigen_assert((m>0 && m == n) && <span class="stringliteral">"Please give a non - empty matrix"</span>);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  m_left.resize(m); </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  m_right.resize(n);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  m_left.setOnes();</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  m_right.setOnes();</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  m_matrix = mat;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  VectorXd Dr, Dc, DrRes, DcRes; <span class="comment">// Temporary Left and right scaling vectors</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  Dr.resize(m); Dc.resize(n);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  DrRes.resize(m); DcRes.resize(n);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">double</span> EpsRow = 1.0, EpsCol = 1.0;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">int</span> its = 0; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">do</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  { <span class="comment">// Iterate until the infinite norm of each row and column is approximately 1</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="comment">// Get the maximum value in each row and column</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  Dr.setZero(); Dc.setZero();</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k=0; k<m_matrix.outerSize(); ++k)</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixType::InnerIterator it(m_matrix, k); it; ++it)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span> ( Dr(it.row()) < abs(it.value()) )</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  Dr(it.row()) = abs(it.value());</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> ( Dc(it.col()) < abs(it.value()) )</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  Dc(it.col()) = abs(it.value());</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="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < m; ++i) </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  Dr(i) = std::sqrt(Dr(i));</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  Dc(i) = std::sqrt(Dc(i));</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// Save the scaling factors </span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < m; ++i) </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  {</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  m_left(i) /= Dr(i);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  m_right(i) /= Dc(i);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// Scale the rows and the columns of the matrix</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  DrRes.setZero(); DcRes.setZero(); </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k=0; k<m_matrix.outerSize(); ++k)</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>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixType::InnerIterator it(m_matrix, k); it; ++it)</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>  it.valueRef() = it.value()/( Dr(it.row()) * Dc(it.col()) );</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// Accumulate the norms of the row and column vectors </span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">if</span> ( DrRes(it.row()) < abs(it.value()) )</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  DrRes(it.row()) = abs(it.value());</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">if</span> ( DcRes(it.col()) < abs(it.value()) )</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  DcRes(it.col()) = abs(it.value());</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>  } </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  DrRes.array() = (1-DrRes.array()).abs();</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  EpsRow = DrRes.maxCoeff();</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  DcRes.array() = (1-DcRes.array()).abs();</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  EpsCol = DcRes.maxCoeff();</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  its++;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  }<span class="keywordflow">while</span> ( (EpsRow >m_tol || EpsCol > m_tol) && (its < m_maxits) );</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordtype">void</span> computeRef (MatrixType& mat)</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  {</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  compute (mat);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  mat = m_matrix;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  }</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  VectorXd& LeftScaling()</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="keywordflow">return</span> m_left;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  VectorXd& RightScaling()</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">return</span> m_right;</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  }</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordtype">void</span> setTolerance(<span class="keywordtype">double</span> tol)</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>  m_tol = tol; </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</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>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordtype">void</span> init()</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  {</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  m_tol = 1e-10;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  m_maxits = 5;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  m_isInitialized = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  }</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  MatrixType m_matrix;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">mutable</span> ComputationInfo m_info; </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordtype">bool</span> m_isInitialized; </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  VectorXd m_left; <span class="comment">// Left scaling vector</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  VectorXd m_right; <span class="comment">// m_right scaling vector</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordtype">double</span> m_tol; </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordtype">int</span> m_maxits; <span class="comment">// Maximum number of iterations allowed</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> };</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> }</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="preprocessor">#endif</span></div>
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</html>
