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<div class="title">TriangularSolver.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> <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_SPARSETRIANGULARSOLVER_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_SPARSETRIANGULARSOLVER_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="l00013"></a><span class="lineno"> 13</span> <span class="keyword">namespace </span>Eigen { </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> <span class="keyword">namespace </span>internal {</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> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode,</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  <span class="keywordtype">int</span> UpLo = (Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>)</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  ? <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  : (Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Upper</a>)</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  ? Upper</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  : -1,</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keywordtype">int</span> StorageOrder = int(traits<Lhs>::Flags) & <a class="code" href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">RowMajorBit</a>></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">struct </span>sparse_solve_triangular_selector;</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> <span class="comment">// forward substitution, row-major</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">struct </span>sparse_solve_triangular_selector<Lhs,Rhs,Mode,<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>,<a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">RowMajor</a>></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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Rhs::Scalar Scalar;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">const</span> Lhs& lhs, Rhs& other)</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>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> col=0 ; col<other.cols() ; ++col)</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>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i<lhs.rows(); ++i)</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>  Scalar tmp = other.coeff(i,col);</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  Scalar lastVal(0);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordtype">int</span> lastIndex = 0;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span>(<span class="keyword">typename</span> Lhs::InnerIterator it(lhs, i); it; ++it)</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  {</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  lastVal = it.value();</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  lastIndex = it.index();</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">if</span>(lastIndex==i)</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  tmp -= lastVal * other.coeff(lastIndex,col);</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="keywordflow">if</span> (Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bab051342541ee4cd3d2d7d710ba7c8a2d">UnitDiag</a>)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  other.coeffRef(i,col) = tmp;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">else</span></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>  eigen_assert(lastIndex==i);</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  other.coeffRef(i,col) = tmp/lastVal;</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>  }</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>  }</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"> 60</span> <span class="comment">// backward substitution, row-major</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">struct </span>sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,<a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">RowMajor</a>></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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Rhs::Scalar Scalar;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">const</span> Lhs& lhs, Rhs& other)</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> col=0 ; col<other.cols() ; ++col)</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="keywordflow">for</span>(<span class="keywordtype">int</span> i=lhs.rows()-1 ; i>=0 ; --i)</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>  Scalar tmp = other.coeff(i,col);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  Scalar l_ii = 0;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">typename</span> Lhs::InnerIterator it(lhs, i);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">while</span>(it && it.index()<i)</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  ++it;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span>(!(Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bab051342541ee4cd3d2d7d710ba7c8a2d">UnitDiag</a>))</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>  eigen_assert(it && it.index()==i);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  l_ii = it.value();</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  ++it;</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>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (it && it.index() == i)</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  ++it;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">for</span>(; it; ++it)</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>  tmp -= it.value() * other.coeff(it.index(),col);</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">if</span> (Mode & UnitDiag)</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  other.coeffRef(i,col) = tmp;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  other.coeffRef(i,col) = tmp/l_ii;</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="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> <span class="comment">// forward substitution, col-major</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">struct </span>sparse_solve_triangular_selector<Lhs,Rhs,Mode,<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>,<a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf">ColMajor</a>></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="keyword">typedef</span> <span class="keyword">typename</span> Rhs::Scalar Scalar;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">const</span> Lhs& lhs, Rhs& other)</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>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> col=0 ; col<other.cols() ; ++col)</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="keywordflow">for</span>(<span class="keywordtype">int</span> i=0; i<lhs.cols(); ++i)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Scalar& tmp = other.coeffRef(i,col);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">if</span> (tmp!=Scalar(0)) <span class="comment">// optimization when other is actually sparse</span></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>  <span class="keyword">typename</span> Lhs::InnerIterator it(lhs, i);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">while</span>(it && it.index()<i)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  ++it;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">if</span>(!(Mode & UnitDiag))</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>  eigen_assert(it && it.index()==i);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  tmp /= it.value();</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>  <span class="keywordflow">if</span> (it && it.index()==i)</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  ++it;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">for</span>(; it; ++it)</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  other.coeffRef(it.index(), col) -= tmp * it.value();</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>  }</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> };</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// backward substitution, col-major</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">struct </span>sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,<a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf">ColMajor</a>></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="keyword">typedef</span> <span class="keyword">typename</span> Rhs::Scalar Scalar;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">const</span> Lhs& lhs, Rhs& other)</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">for</span>(<span class="keywordtype">int</span> col=0 ; col<other.cols() ; ++col)</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>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=lhs.cols()-1; i>=0; --i)</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>  Scalar& tmp = other.coeffRef(i,col);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">if</span> (tmp!=Scalar(0)) <span class="comment">// optimization when other is actually sparse</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  {</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span>(!(Mode & UnitDiag))</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>  <span class="comment">// TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keyword">typename</span> Lhs::ReverseInnerIterator it(lhs, i);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">while</span>(it && it.index()!=i)</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  --it;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  eigen_assert(it && it.index()==i);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  other.coeffRef(i,col) /= it.value();</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="keyword">typename</span> Lhs::InnerIterator it(lhs, i);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordflow">for</span>(; it && it.index()<i; ++it)</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  other.coeffRef(it.index(), col) -= tmp * it.value();</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>  }</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="l00160"></a><span class="lineno"> 160</span> };</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> } <span class="comment">// end namespace internal</span></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> <span class="keyword">template</span><<span class="keyword">typename</span> ExpressionType,<span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="keywordtype">void</span> SparseTriangularView<ExpressionType,Mode>::solveInPlace(MatrixBase<OtherDerived>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  eigen_assert((!(Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910ba72b90f18314e6abbe9193224547df48d">ZeroDiag</a>)) && <span class="keywordtype">bool</span>(Mode & (Upper|<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>)));</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>  <span class="keyword">enum</span> { copy = internal::traits<OtherDerived>::Flags & <a class="code" href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">RowMajorBit</a> };</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::conditional<copy,</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">typename</span> internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  OtherCopy otherCopy(other.derived());</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(m_matrix, otherCopy);</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>  <span class="keywordflow">if</span> (copy)</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  other = otherCopy;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</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="keyword">template</span><<span class="keyword">typename</span> ExpressionType,<span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="keyword">typename</span> internal::plain_matrix_type_column_major<OtherDerived>::type</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> SparseTriangularView<ExpressionType,Mode>::solve(<span class="keyword">const</span> MatrixBase<OtherDerived>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">typename</span> internal::plain_matrix_type_column_major<OtherDerived>::type res(other);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  solveInPlace(res);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">return</span> res;</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> <span class="comment">// pure sparse path</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode,</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordtype">int</span> UpLo = (Mode & <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>)</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  ? <a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  : (Mode & Upper)</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  ? Upper</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  : -1,</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">int</span> StorageOrder = int(Lhs::Flags) & (<a class="code" href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">RowMajorBit</a>)></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="keyword">struct</span> sparse_solve_triangular_sparse_selector;</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// forward substitution, col-major</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">template</span><<span class="keyword">typename</span> Lhs, <span class="keyword">typename</span> Rhs, <span class="keywordtype">int</span> Mode, <span class="keywordtype">int</span> UpLo></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">struct </span>sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor></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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Rhs::Scalar Scalar;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> promote_index_type<typename traits<Lhs>::Index,</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">typename</span> traits<Rhs>::Index>::type Index;</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">const</span> Lhs& lhs, Rhs& other)</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  {</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> IsLower = (UpLo==<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  AmbiVector<Scalar,Index> tempVector(other.rows()*2);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  tempVector.setBounds(0,other.rows());</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>  Rhs res(other.rows(), other.cols());</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  res.reserve(other.nonZeros());</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="keywordflow">for</span>(<span class="keywordtype">int</span> col=0 ; col<other.cols() ; ++col)</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  {</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="comment">// FIXME estimate number of non zeros</span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  tempVector.init(.99<span class="comment">/*float(other.col(col).nonZeros())/float(other.rows())*/</span>);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  tempVector.setZero();</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  tempVector.restart();</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  {</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  tempVector.coeffRef(rhsIt.index()) = rhsIt.value();</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> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=IsLower?0:lhs.cols()-1;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  IsLower?i<lhs.cols():i>=0;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  i+=IsLower?1:-1)</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>  tempVector.restart();</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  Scalar& ci = tempVector.coeffRef(i);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">if</span> (ci!=Scalar(0))</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">// find</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keyword">typename</span> Lhs::InnerIterator it(lhs, i);</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">if</span>(!(Mode & UnitDiag))</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="keywordflow">if</span> (IsLower)</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>  eigen_assert(it.index()==i);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  ci /= it.value();</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  }</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  ci /= lhs.coeff(i,i);</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>  tempVector.restart();</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">if</span> (IsLower)</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>  <span class="keywordflow">if</span> (it.index()==i)</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  ++it;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">for</span>(; it; ++it)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  tempVector.coeffRef(it.index()) -= ci * it.value();</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  }</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">else</span></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>(; it && it.index()<i; ++it)</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  tempVector.coeffRef(it.index()) -= ci * it.value();</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  }</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>  }</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// FIXME compute a reference value to filter zeros</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> AmbiVector<Scalar,Index>::Iterator it(tempVector<span class="comment">/*,1e-12*/</span>); it; ++it)</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>  ++ count;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="comment">// std::cerr << "fill " << it.index() << ", " << col << "\n";</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="comment">// std::cout << it.value() << " ";</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// FIXME use insertBack</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  res.insert(it.index(), col) = it.value();</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> <span class="comment">// std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";</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>  res.finalize();</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  other = res.markAsRValue();</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> </div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> } <span class="comment">// end namespace internal</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"> 289</span> <span class="keyword">template</span><<span class="keyword">typename</span> ExpressionType,<span class="keywordtype">int</span> Mode></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="keywordtype">void</span> SparseTriangularView<ExpressionType,Mode>::solveInPlace(SparseMatrixBase<OtherDerived>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  eigen_assert( (!(Mode & ZeroDiag)) && <span class="keywordtype">bool</span>(Mode & (Upper|<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>)));</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment">// enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment">// typedef typename internal::conditional<copy,</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment">// typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment">// OtherCopy otherCopy(other.derived());</span></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>  internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(m_matrix, other.derived());</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> <span class="comment">// if (copy)</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment">// other = otherCopy;</span></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> <span class="preprocessor">#ifdef EIGEN2_SUPPORT</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment">// deprecated stuff:</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keywordtype">void</span> SparseMatrixBase<Derived>::solveTriangularInPlace(MatrixBase<OtherDerived>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  this-><span class="keyword">template</span> triangular<Flags&(Upper|Lower)>().solveInPlace(other);</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> </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="keyword">typename</span> internal::plain_matrix_type_column_major<OtherDerived>::type</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> SparseMatrixBase<Derived>::solveTriangular(<span class="keyword">const</span> MatrixBase<OtherDerived>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keyword">typename</span> internal::plain_matrix_type_column_major<OtherDerived>::type res(other);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  derived().solveTriangularInPlace(res);</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">return</span> res;</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> <span class="preprocessor">#endif // EIGEN2_SUPPORT</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> </div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="preprocessor">#endif // EIGEN_SPARSETRIANGULARSOLVER_H</span></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">Eigen::RowMajor</a></div><div class="ttdef"><b>Definition:</b> Constants.h:266</div></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf">Eigen::ColMajor</a></div><div class="ttdef"><b>Definition:</b> Constants.h:264</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910bab051342541ee4cd3d2d7d710ba7c8a2d"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910bab051342541ee4cd3d2d7d710ba7c8a2d">Eigen::UnitDiag</a></div><div class="ttdef"><b>Definition:</b> Constants.h:171</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Eigen::Upper</a></div><div class="ttdef"><b>Definition:</b> Constants.h:169</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Eigen::Lower</a></div><div class="ttdef"><b>Definition:</b> Constants.h:167</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910ba72b90f18314e6abbe9193224547df48d"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910ba72b90f18314e6abbe9193224547df48d">Eigen::ZeroDiag</a></div><div class="ttdef"><b>Definition:</b> Constants.h:173</div></div>
<div class="ttc" id="group__flags_html_ga7bd49e7b260e869e10fb9dc4fd081a85"><div class="ttname"><a href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:53</div></div>
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