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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> /**</div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>  * This program is free software: you can redistribute it and/or modify</div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  * it under the terms of the GNU Lesser General Public License as</div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>  * published by the Free Software Foundation, either version 3 of the</div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>  * License, or (at your option) any later version.</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>  * This program is distributed in the hope that it will be useful,</div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  * but WITHOUT ANY WARRANTY; without even the implied warranty of</div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  * GNU General Public License for more details.</div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  *</div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  * You should have received a copy of the GNU General Public License</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  * along with this program. If not, see <http://www.gnu.org/licenses/>.</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"> 16</span>  </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> /**</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  * @file ATVu2v0.ih</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  * @author Jacques-Olivier Lachaud (\c [email protected] )</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  * Laboratory of Mathematics (CNRS, UMR 5127), University of Savoie, France</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  * @author Marion Foare (\c [email protected] )</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  * Laboratory of Mathematics (CNRS, UMR 5127), University of Savoie, France</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>  * @date 2016/10/12</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  *</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  * Implementation of inline methods defined in ATVu2v0.h</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  *</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  * This file is part of the DGtal library.</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  */</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> #include <cstdlib></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> //////////////////////////////////////////////////////////////////////////////</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> ///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> // IMPLEMENTATION of inline methods.</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> ///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> ///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> // ----------------------- Standard services ------------------------------</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> ATVu2v0( int _verbose )</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  : Base( _verbose ),</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  M01( calculus ), M12( calculus ),</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  primal_AD2( calculus ), primal_L0( calculus ),</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  v0( calculus ), former_v0( calculus ), </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  alpha_Id2( calculus ), left_V0( calculus ), </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  l_1( calculus ), l_over_e_1( calculus ), </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  l_over_e_Id0( calculus ),</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  metric_average( false )</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>  </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> void</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> init( Clone<KSpace> aKSpace )</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  Base::init( aKSpace );</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  if ( verbose > 0 ) trace.beginBlock( "Initialize DEC specific operators" );</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  if ( verbose > 1 ) trace.info() << "M01" << std::endl;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  M01 = calculus.template derivative<0, PRIMAL>();</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  M01.myContainer = .5 * M01.myContainer.cwiseAbs();</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  if ( verbose > 1 ) trace.info() << "M12" << std::endl;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  M12 = calculus.template derivative<1, PRIMAL>();</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  M12.myContainer = .25 * M12.myContainer.cwiseAbs(); </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  if ( verbose > 1 ) trace.info() << "primal_AD2" << std::endl;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  primal_AD2 = calculus.template antiderivative<2,PRIMAL>();</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  if ( verbose > 1 ) trace.info() << "primal_L0" << std::endl;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  primal_L0 = calculus.template laplace<PRIMAL>();</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  if ( verbose > 1 ) trace.info() << "v0" << std::endl;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  v0 = KForm<Calculus, 0, PRIMAL>::ones( calculus );</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  if ( verbose > 0 ) trace.endBlock();</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</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> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> template <typename Image, typename Function></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> void </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> addInput( const Image& image, </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  const Function& f,</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  bool perfect_data )</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  if ( perfect_data ) i2.push_back( PrimalForm2( calculus ) );</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  else g2.push_back( PrimalForm2( calculus ) );</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  PrimalForm2& g = perfect_data ? i2.back() : g2.back();</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  const KSpace& K = calculus.myKSpace; </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  for ( Index index = 0; index < g.myContainer.rows(); index++)</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>  SCell cell = g.getSCell( index );</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  g.myContainer( index ) = f( image( K.sCoords( cell ) ) );</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> }</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> typename DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::Scalar</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> computeSNR() const</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  Scalar MSE = 0.0;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  for ( Dimension i = 0; i < i2.size(); ++i )</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  Scalar MSEi = 0.0;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  const PrimalForm2 u_minus_i_snr = u2[ i ] - i2[ i ];</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  for ( Index j = 0; j < u_minus_i_snr.length(); ++j )</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  MSEi += u_minus_i_snr.myContainer( j ) * u_minus_i_snr.myContainer( j );</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  MSE += MSEi / (Scalar) u_minus_i_snr.length();</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  MSE /= 3.0;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  return 10.0 * log10(1.0 / MSE);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> }</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> void </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> setMetricAverage( bool average )</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> {</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  metric_average = average;</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>  </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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> void </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> setAlpha( Scalar _alpha )</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>  ASSERT( _alpha >= 0.0 );</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  alpha = _alpha;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  // Building alpha_Id2</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  alpha_Id2 = _alpha * calculus.template identity<2, PRIMAL>();</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  alpha_g2.clear();</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  for ( unsigned int i = 0; i < g2.size(); i++ )</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  alpha_g2.push_back( alpha_Id2 * g2[ i ] );</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> }</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> void </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> setAlpha( Scalar _alpha, const PrimalForm2& m )</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  ASSERT( _alpha >= 0.0 );</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  alpha = _alpha;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  // Building alpha_Id0</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  alpha_Id2 = _alpha * functions::dec::diagonal( m ) * calculus.template identity<2, PRIMAL>();</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  alpha_g2.clear();</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  for ( unsigned int i = 0; i < g2.size(); i++ )</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  alpha_g2.push_back( alpha_Id2 * g2[ i ] );</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> }</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> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> void </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> setLambda( Scalar _lambda )</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>  ASSERT( _lambda >= 0.0 );</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  lambda = _lambda;</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  if ( metric_average )</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  l_1 = lambda</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  * M01.transpose() * M12.transpose()</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  * M12 * M01</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  * KForm< Calculus, 0, PRIMAL >::ones( calculus );</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  else</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  l_1 = lambda * KForm< Calculus, 0, PRIMAL >::ones( calculus );</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>  </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> void </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> setEpsilon( Scalar _epsilon )</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> {</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  ASSERT( _epsilon > 0.0 );</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  epsilon = _epsilon;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  if ( metric_average )</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  left_V0 = ( lambda/epsilon )</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  * M01.transpose() * M12.transpose()</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  * M12 * M01</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  + (lambda*epsilon*epsilon*epsilon) * primal_L0.transpose() * primal_L0;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  else</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  left_V0 = ( lambda/epsilon )</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  * calculus.template identity<0, PRIMAL>()</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  + (lambda*epsilon*epsilon*epsilon) * primal_L0.transpose() * primal_L0;</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  l_over_e_1 = (1.0/epsilon) * l_1;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  </div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> void </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> setUFromInput()</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  u2 = g2;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> }</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  </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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> void </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> setUFromInputAndMask()</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> {</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  setUFromInput();</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  for ( int i = 0; i < u2.size(); ++i )</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  {</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  const Index nb = u2[ i ].length();</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  for ( Index index = 0; index < nb; index++)</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>  if ( alpha_g2[ i ].myContainer( index ) == 0.0 )</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  u2[ i ].myContainer( index ) = ((double) rand()) / (double) RAND_MAX;</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  } </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  }</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>  </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> bool</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> solveU()</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>  if ( verbose > 0 ) trace.beginBlock("Solving for u");</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  if ( verbose > 1 ) trace.info() << "- building matrix M : = alpha_Id2 - tB'_Diag(M01 v)^2_B'" << std::endl;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  </div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  const PrimalIdentity1 diag_Mv_squared = functions::dec::squaredDiagonal( M01 * v0 );</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  // JOL: clarify sign below.</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  const PrimalIdentity2 M = alpha_Id2</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  + primal_AD2.transpose() * diag_Mv_squared * primal_AD2;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  if ( verbose > 1 ) trace.info() << "- prefactoring matrix M" << std::endl;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  solver_u.compute( M );</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  bool ok = true;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  for ( Dimension i = 0; i < u2.size(); ++i )</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  {</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  if ( verbose > 1 ) trace.info() << "- solving M u[" << i << "] = alpha g[" << i << "]" << std::endl;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  u2[ i ] = solver_u.solve( alpha_g2[ i ] );</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  if ( verbose > 1 ) trace.info() << ( solver_u.isValid() ? "=> OK" : "ERROR" ) << " " << solver_u.myLinearAlgebraSolver.info() << std::endl;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  ok = ok && solver_u.isValid();</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  if ( verbose > 0 ) trace.endBlock();</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  return ok;</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>  </div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> bool</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> solveV()</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> {</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  former_v0 = v0;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  if ( verbose > 0 ) trace.beginBlock("Solving for v");</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  if ( verbose > 1 ) trace.info() << "- building matrix N := l/e Id0 + le^3 L^t L + M01^t sum Diag(B' u_i)^2 M01" << std::endl;</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  PrimalForm1 squared_norm_D_u2 = PrimalForm1::zeros(calculus);</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>  PrimalIdentity1 U2 = functions::dec::squaredDiagonal( primal_AD2 * u2[ 0 ] );</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  for ( Dimension i = 1; i < u2.size(); ++i )</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  U2.myContainer += functions::dec::squaredDiagonal( primal_AD2 * u2[ i ] ).myContainer;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  const PrimalIdentity0 N = left_V0 + M01.transpose() * U2 * M01;</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>  typedef typename PrimalIdentity0::Container Matrix; </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  const Matrix & M = N.myContainer;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  if ( verbose > 2 )</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  for (int k = 0; k < M.outerSize(); ++k)</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  for ( typename Matrix::InnerIterator it( M, k ); it; ++it )</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  if ( ( verbose > 3 ) || ( it.row() == it.col() ) )</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  trace.info() << "[" << it.row() << "," << it.col() << "] = " << it.value() << std::endl;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  if ( verbose > 1 ) trace.info() << "- prefactoring matrix N" << std::endl;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  solver_v.compute( N );</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  if ( verbose > 1 ) trace.info() << "- solving N v = l/e 1" << std::endl;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  v0 = solver_v.solve( l_over_e_1 );</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  if ( verbose > 1 ) trace.info() << ( solver_v.isValid() ? "OK" : "ERROR" )</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  << " " << solver_v.myLinearAlgebraSolver.info()</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  << std::endl;</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  if ( verbose > 0 ) trace.endBlock();</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  return solver_v.isValid();</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> }</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  </div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> //-----------------------------------------------------------------------------</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> typename DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::Scalar</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> computeVariation()</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> {</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  if ( verbose > 0 ) trace.beginBlock( "Compute variation of v.");</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  delta_v_l1 = 0.0;</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  delta_v_l2 = 0.0;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  delta_v_loo = 0.0;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  for ( Index index = 0; index < size0(); index++)</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>  delta_v_loo = std::max( delta_v_loo,</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  std::fabs( v0.myContainer( index )</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  - former_v0.myContainer( index ) ) );</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  delta_v_l2 += ( v0.myContainer( index ) - former_v0.myContainer( index ) )</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  * ( v0.myContainer( index ) - former_v0.myContainer( index ) );</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  delta_v_l1 += fabs( v0.myContainer( index )</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  - former_v0.myContainer( index ) );</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  }</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  delta_v_l1 /= size0();</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  delta_v_l2 = sqrt( delta_v_l2 / size0() );</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  if ( verbose > 0 )</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  {</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  trace.info() << "Variation |v^k+1 - v^k|_oo = " << delta_v_loo << std::endl;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  trace.info() << "Variation |v^k+1 - v^k|_2 = " << delta_v_l2 << std::endl;</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  trace.info() << "Variation |v^k+1 - v^k|_1 = " << delta_v_l1 << std::endl;</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  if ( verbose > 0 ) trace.endBlock();</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  return delta_v_loo;</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>  </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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> typename DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::Scalar</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> checkV()</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> {</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  if ( verbose > 0 ) trace.beginBlock("Checking v");</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  Scalar m1 = 1.0;</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  Scalar m2 = 0.0;</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  Scalar ma = 0.0;</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  for ( Index index = 0; index < size0(); index++)</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>  Scalar val = v0.myContainer( index );</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  m1 = std::min( m1, val );</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  m2 = std::max( m2, val );</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  ma += val;</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  if ( verbose > 0 ) </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  trace.info() << "1-form v: min=" << m1 << " avg=" << ( ma / size0() )</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  << " max=" << m2 << std::endl;</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  if ( verbose > 0 ) trace.endBlock();</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  return std::max( std::fabs( m1 ), std::fabs( m2 - 1.0 ) );</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> }</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  </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> // Interface - public :</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>  * Writes/Displays the object on an output stream.</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  * @param out the output stream where the object is written.</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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> inline</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> void</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::selfDisplay ( std::ostream & out ) const</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>  out << "[ ATVu2v0 #g=" << g2.size() << " dec=" << calculus << " ]";</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> }</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> /**</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  * Checks the validity/consistency of the object.</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  * @return 'true' if the object is valid, 'false' otherwise.</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> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> inline</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> bool</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> DGtal::ATVu2v0<TKSpace, TLinearAlgebra>::isValid() const</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> {</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  return true;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> }</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  </div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  </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> // Implementation of inline functions //</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> template <typename TKSpace, typename TLinearAlgebra></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> inline</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> std::ostream&</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> DGtal::operator<< ( std::ostream & out,</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  const ATVu2v0<TKSpace, TLinearAlgebra> & object )</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> {</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  object.selfDisplay( out );</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  return out;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> }</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  </div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> // //</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> ///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  </div>
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