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<div class="title">ConstrainedConjGrad.h</div> </div>
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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) 2008 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> </div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">/* NOTE The functions of this file have been adapted from the GMM++ library */</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> </div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">//========================================================================</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">//</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// Copyright (C) 2002-2007 Yves Renard</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">//</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// This file is a part of GETFEM++</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">//</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// Getfem++ is free software; you can redistribute it and/or modify</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// it under the terms of the GNU Lesser General Public License as</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// published by the Free Software Foundation; version 2.1 of the License.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">//</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// This program is distributed in the hope that it will be useful,</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// GNU Lesser General Public License for more details.</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// You should have received a copy of the GNU Lesser General Public</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// License along with this program; if not, write to the Free Software</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// USA.</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">//</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">//========================================================================</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "../../../../Eigen/src/Core/util/NonMPL2.h"</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> <span class="preprocessor">#ifndef EIGEN_CONSTRAINEDCG_H</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_CONSTRAINEDCG_H</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include <Eigen/Core></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> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">template</span> <<span class="keyword">typename</span> CMatrix, <span class="keyword">typename</span> CINVMatrix></div>
<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="group__IterativeSolvers__Module.html#ga58a0ccf0e71d88beeb5dcf72ed0bdd5f"> 47</a></span> <span class="keywordtype">void</span> <a class="code" href="group__IterativeSolvers__Module.html#ga58a0ccf0e71d88beeb5dcf72ed0bdd5f">pseudo_inverse</a>(<span class="keyword">const</span> CMatrix &C, CINVMatrix &CINV)</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="comment">// optimisable : copie de la ligne, precalcul de C * trans(C).</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> CMatrix::Scalar Scalar;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> CMatrix::Index Index;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// FIXME use sparse vectors ?</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1> TmpVec;</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>  Index rows = C.rows(), cols = C.cols();</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>  TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  Scalar rho, rho_1, alpha;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  d.setZero();</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  CINV.startFill(); <span class="comment">// FIXME estimate the number of non-zeros</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">for</span> (Index i = 0; i < rows; ++i)</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>  d[i] = 1.0;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  rho = 1.0;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  e.setZero();</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  r = d;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  p = d;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">while</span> (rho >= 1e-38)</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  { <span class="comment">/* conjugate gradient to compute e */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">/* which is the i-th row of inv(C * trans(C)) */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  l = C.transpose() * p;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  q = C * l;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  alpha = rho / p.dot(q);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  e += alpha * p;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  r += -alpha * q;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  rho_1 = rho;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  rho = r.dot(r);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  p = (rho/rho_1) * p + r;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  l = C.transpose() * e; <span class="comment">// l is the i-th row of CINV</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// FIXME add a generic "prune/filter" expression for both dense and sparse object to sparse</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">for</span> (Index j=0; j<l.size(); ++j)</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (l[j]<1e-15)</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  CINV.fill(i,j) = l[j];</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>  d[i] = 0.0;</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>  CINV.endFill();</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> </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="l00101"></a><span class="lineno"> 101</span> <span class="keyword">template</span><<span class="keyword">typename</span> TMatrix, <span class="keyword">typename</span> CMatrix,</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keyword">typename</span> VectorX, <span class="keyword">typename</span> VectorB, <span class="keyword">typename</span> VectorF></div>
<div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="group__IterativeSolvers__Module.html#ga1c2f99746877fd46158af4a6b7dce2f9"> 103</a></span> <span class="keywordtype">void</span> <a class="code" href="group__IterativeSolvers__Module.html#ga1c2f99746877fd46158af4a6b7dce2f9">constrained_cg</a>(<span class="keyword">const</span> TMatrix& A, <span class="keyword">const</span> CMatrix& C, VectorX& x,</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keyword">const</span> VectorB& b, <span class="keyword">const</span> VectorF& f, <a class="code" href="classEigen_1_1IterationController.html">IterationController</a> &iter)</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> TMatrix::Scalar Scalar;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> TMatrix::Index Index;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1> TmpVec;</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>  Scalar rho = 1.0, rho_1, lambda, gamma;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  Index xSize = x.size();</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  TmpVec p(xSize), q(xSize), q2(xSize),</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  r(xSize), old_z(xSize), z(xSize),</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  memox(xSize);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  std::vector<bool> satured(C.rows());</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  p.setZero();</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  iter.setRhsNorm(sqrt(b.dot(b))); <span class="comment">// gael vect_sp(PS, b, b)</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">if</span> (iter.rhsNorm() == 0.0) iter.setRhsNorm(1.0);</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>  SparseMatrix<Scalar,RowMajor> CINV(C.rows(), C.cols());</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="code" href="group__IterativeSolvers__Module.html#ga58a0ccf0e71d88beeb5dcf72ed0bdd5f">pseudo_inverse</a>(C, CINV);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">while</span>(<span class="keyword">true</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>  <span class="comment">// computation of residual</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  old_z = z;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  memox = x;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  r = b;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  r += A * -x;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  z = r;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">bool</span> transition = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">for</span> (Index i = 0; i < C.rows(); ++i)</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>  Scalar al = C.row(i).dot(x) - f.coeff(i);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">if</span> (al >= -1.0E-15)</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  {</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">if</span> (!satured[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>  satured[i] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  transition = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  }</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  Scalar bb = CINV.row(i).dot(z);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">if</span> (bb > 0.0)</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// FIXME: we should allow that: z += -bb * C.row(i);</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> CMatrix::InnerIterator it(C,i); it; ++it)</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  z.coeffRef(it.index()) -= bb*it.value();</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  }</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  satured[i] = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</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>  <span class="comment">// descent direction</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  rho_1 = rho;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  rho = r.dot(z);</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>  <span class="keywordflow">if</span> (iter.finished(rho)) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">if</span> (iter.noiseLevel() > 0 && transition) std::cerr << <span class="stringliteral">"CCG: transition\n"</span>;</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">if</span> (transition || iter.first()) gamma = 0.0;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">else</span> gamma = (std::max)(0.0, (rho - old_z.dot(z)) / rho_1);</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  p = z + gamma*p;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  ++iter;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="comment">// one dimensionnal optimization</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  q = A * p;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  lambda = rho / q.dot(p);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">for</span> (Index i = 0; i < C.rows(); ++i)</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="keywordflow">if</span> (!satured[i])</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>  Scalar bb = C.row(i).dot(p) - f[i];</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span> (bb > 0.0)</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  lambda = (std::min)(lambda, (f.coeff(i)-C.row(i).dot(x)) / bb);</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>  x += lambda * p;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  memox -= x;</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> </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> } <span class="comment">// end namespace Eigen</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 // EIGEN_CONSTRAINEDCG_H</span></div>
<div class="ttc" id="group__IterativeSolvers__Module_html_ga1c2f99746877fd46158af4a6b7dce2f9"><div class="ttname"><a href="group__IterativeSolvers__Module.html#ga1c2f99746877fd46158af4a6b7dce2f9">Eigen::internal::constrained_cg</a></div><div class="ttdeci">void constrained_cg(const TMatrix &A, const CMatrix &C, VectorX &x, const VectorB &b, const VectorF &f, IterationController &iter)</div><div class="ttdef"><b>Definition:</b> ConstrainedConjGrad.h:103</div></div>
<div class="ttc" id="group__IterativeSolvers__Module_html_ga58a0ccf0e71d88beeb5dcf72ed0bdd5f"><div class="ttname"><a href="group__IterativeSolvers__Module.html#ga58a0ccf0e71d88beeb5dcf72ed0bdd5f">Eigen::internal::pseudo_inverse</a></div><div class="ttdeci">void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)</div><div class="ttdef"><b>Definition:</b> ConstrainedConjGrad.h:47</div></div>
<div class="ttc" id="classEigen_1_1IterationController_html"><div class="ttname"><a href="classEigen_1_1IterationController.html">Eigen::IterationController</a></div><div class="ttdoc">Controls the iterations of the iterative solvers. </div><div class="ttdef"><b>Definition:</b> IterationController.h:71</div></div>
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