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  108.   <div class="headertitle"><div class="title">GaussianElimination.h</div></div>
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    110. 

  110. <div class="contents">
    111. 

  111. <a href="_gaussian_elimination_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)</span></div>
    112. 

  112. <div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">// SPDX-FileCopyrightText: 2021 Jorrit Rouwe</span></div>
    113. 

  113. <div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment">// SPDX-License-Identifier: MIT</span></div>
    114. 

  114. <div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span> </div>
    115. 

  115. <div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="preprocessor">#pragma once</span></div>
    116. 

  116. <div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span> </div>
    117. 

  117. <div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><a class="code hl_define" href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div>
    118. 

  118. <div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span> </div>
    119. 

  119. <div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="keyword">template</span> &lt;<span class="keyword">class</span> MatrixA, <span class="keyword">class</span> MatrixB&gt;</div>
    120. 

  120. <div class="foldopen" id="foldopen00019" data-start="{" data-end="}">
    121. 

  121. <div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="_gaussian_elimination_8h.html#a292d56457a5c67858f083798c34b111c">   19</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="_gaussian_elimination_8h.html#a292d56457a5c67858f083798c34b111c">GaussianElimination</a>(MatrixA &amp;ioA, MatrixB &amp;ioB, <span class="keywordtype">float</span> inTolerance = 1.0e-16f)</div>
    122. 

  122. <div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>{</div>
    123. 

  123. <div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <span class="comment">// Get problem dimensions</span></div>
    124. 

  124. <div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <span class="keyword">const</span> <a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> n = ioA.GetCols();</div>
    125. 

  125. <div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <span class="keyword">const</span> <a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> m = ioB.GetCols();</div>
    126. 

  126. <div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span> </div>
    127. 

  127. <div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    <span class="comment">// Check matrix requirement</span></div>
    128. 

  128. <div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <a class="code hl_define" href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a>(ioA.GetRows() == n);</div>
    129. 

  129. <div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <a class="code hl_define" href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a>(ioB.GetRows() == n);</div>
    130. 

  130. <div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span> </div>
    131. 

  131. <div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="comment">// Create array for bookkeeping on pivoting</span></div>
    132. 

  132. <div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <span class="keywordtype">int</span> *ipiv = (<span class="keywordtype">int</span> *)<a class="code hl_define" href="_core_8h.html#a438e7b853f86742bcbdf0faeaa2094a2">JPH_STACK_ALLOC</a>(n * <span class="keyword">sizeof</span>(<span class="keywordtype">int</span>));</div>
    133. 

  133. <div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    memset(ipiv, 0, n * <span class="keyword">sizeof</span>(<span class="keywordtype">int</span>));</div>
    134. 

  134. <div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
    135. 

  135. <div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> i = 0; i &lt; n; ++i)</div>
    136. 

  136. <div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    {</div>
    137. 

  137. <div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        <span class="comment">// Initialize pivot element as the diagonal</span></div>
    138. 

  138. <div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> pivot_row = i, pivot_col = i;</div>
    139. 

  139. <div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
    140. 

  140. <div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>        <span class="comment">// Determine pivot element</span></div>
    141. 

  141. <div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>        <span class="keywordtype">float</span> largest_element = 0.0f;</div>
    142. 

  142. <div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; n; ++j)</div>
    143. 

  143. <div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>            <span class="keywordflow">if</span> (ipiv[j] != 1)</div>
    144. 

  144. <div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>                <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> k = 0; k &lt; n; ++k)</div>
    145. 

  145. <div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>                {</div>
    146. 

  146. <div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>                    <span class="keywordflow">if</span> (ipiv[k] == 0)</div>
    147. 

  147. <div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>                    {</div>
    148. 

  148. <div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>                        <span class="keywordtype">float</span> element = abs(ioA(j, k));</div>
    149. 

  149. <div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>                        <span class="keywordflow">if</span> (element &gt;= largest_element)</div>
    150. 

  150. <div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>                        {</div>
    151. 

  151. <div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>                            largest_element = element;</div>
    152. 

  152. <div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>                            pivot_row = j;</div>
    153. 

  153. <div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>                            pivot_col = k;</div>
    154. 

  154. <div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>                        }</div>
    155. 

  155. <div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>                    }</div>
    156. 

  156. <div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (ipiv[k] &gt; 1)</div>
    157. 

  157. <div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>                    {</div>
    158. 

  158. <div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>                        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
    159. 

  159. <div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>                    }</div>
    160. 

  160. <div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>                }</div>
    161. 

  161. <div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
    162. 

  162. <div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="comment">// Mark this column as used</span></div>
    163. 

  163. <div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        ++ipiv[pivot_col];</div>
    164. 

  164. <div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span> </div>
    165. 

  165. <div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="comment">// Exchange rows when needed so that the pivot element is at ioA(pivot_col, pivot_col) instead of at ioA(pivot_row, pivot_col)</span></div>
    166. 

  166. <div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        <span class="keywordflow">if</span> (pivot_row != pivot_col)</div>
    167. 

  167. <div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>        {</div>
    168. 

  168. <div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>            <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; n; ++j)</div>
    169. 

  169. <div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                std::swap(ioA(pivot_row, j), ioA(pivot_col, j));</div>
    170. 

  170. <div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>            <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; m; ++j)</div>
    171. 

  171. <div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                std::swap(ioB(pivot_row, j), ioB(pivot_col, j));</div>
    172. 

  172. <div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        }</div>
    173. 

  173. <div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span> </div>
    174. 

  174. <div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <span class="comment">// Get diagonal element that we are about to set to 1</span></div>
    175. 

  175. <div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        <span class="keywordtype">float</span> diagonal_element = ioA(pivot_col, pivot_col);</div>
    176. 

  176. <div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <span class="keywordflow">if</span> (abs(diagonal_element) &lt; inTolerance)</div>
    177. 

  177. <div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
    178. 

  178. <div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
    179. 

  179. <div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <span class="comment">// Divide the whole row by the pivot element, making ioA(pivot_col, pivot_col) = 1</span></div>
    180. 

  180. <div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; n; ++j)</div>
    181. 

  181. <div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>            ioA(pivot_col, j) /= diagonal_element;</div>
    182. 

  182. <div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; m; ++j)</div>
    183. 

  183. <div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            ioB(pivot_col, j) /= diagonal_element;</div>
    184. 

  184. <div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        ioA(pivot_col, pivot_col) = 1.0f;</div>
    185. 

  185. <div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span> </div>
    186. 

  186. <div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>        <span class="comment">// Next reduce the rows, except for the pivot one,</span></div>
    187. 

  187. <div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="comment">// after this step the pivot_col column is zero except for the pivot element which is 1</span></div>
    188. 

  188. <div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> j = 0; j &lt; n; ++j)</div>
    189. 

  189. <div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="keywordflow">if</span> (j != pivot_col)</div>
    190. 

  190. <div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            {</div>
    191. 

  191. <div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                <span class="keywordtype">float</span> element = ioA(j, pivot_col);</div>
    192. 

  192. <div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>                <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> k = 0; k &lt; n; ++k)</div>
    193. 

  193. <div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                    ioA(j, k) -= ioA(pivot_col, k) * element;</div>
    194. 

  194. <div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                <span class="keywordflow">for</span> (<a class="code hl_typedef" href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a> k = 0; k &lt; m; ++k)</div>
    195. 

  195. <div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>                    ioB(j, k) -= ioB(pivot_col, k) * element;</div>
    196. 

  196. <div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>                ioA(j, pivot_col) = 0.0f;</div>
    197. 

  197. <div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            }</div>
    198. 

  198. <div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>    }</div>
    199. 

  199. <div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span> </div>
    200. 

  200. <div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="comment">// Success</span></div>
    201. 

  201. <div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
    202. 

  202. <div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>}</div>
    203. 

  203. </div>
    204. 

  204. <div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span> </div>
    205. 

  205. <div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><a class="code hl_define" href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div>
    206. 

  206. <div class="ttc" id="a_core_8h_html_a438e7b853f86742bcbdf0faeaa2094a2"><div class="ttname"><a href="_core_8h.html#a438e7b853f86742bcbdf0faeaa2094a2">JPH_STACK_ALLOC</a></div><div class="ttdeci">#define JPH_STACK_ALLOC(n)</div><div class="ttdef"><b>Definition</b> Core.h:558</div></div>
    207. 

  207. <div class="ttc" id="a_core_8h_html_a69aa29b598b851b0640aa225a9e5d61d"><div class="ttname"><a href="_core_8h.html#a69aa29b598b851b0640aa225a9e5d61d">uint</a></div><div class="ttdeci">unsigned int uint</div><div class="ttdef"><b>Definition</b> Core.h:500</div></div>
    208. 

  208. <div class="ttc" id="a_core_8h_html_a73da8725998b00321a9db341202d650d"><div class="ttname"><a href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div><div class="ttdeci">#define JPH_NAMESPACE_END</div><div class="ttdef"><b>Definition</b> Core.h:425</div></div>
    209. 

  209. <div class="ttc" id="a_core_8h_html_ad14098b68b8c44ea6112601031268405"><div class="ttname"><a href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div><div class="ttdeci">#define JPH_NAMESPACE_BEGIN</div><div class="ttdef"><b>Definition</b> Core.h:419</div></div>
    210. 

  210. <div class="ttc" id="a_gaussian_elimination_8h_html_a292d56457a5c67858f083798c34b111c"><div class="ttname"><a href="_gaussian_elimination_8h.html#a292d56457a5c67858f083798c34b111c">GaussianElimination</a></div><div class="ttdeci">JPH_NAMESPACE_BEGIN bool GaussianElimination(MatrixA &amp;ioA, MatrixB &amp;ioB, float inTolerance=1.0e-16f)</div><div class="ttdef"><b>Definition</b> GaussianElimination.h:19</div></div>
    211. 

  211. <div class="ttc" id="a_issue_reporting_8h_html_aaf6b1df827e11b7ca5f6f8778bd8f8cd"><div class="ttname"><a href="_issue_reporting_8h.html#aaf6b1df827e11b7ca5f6f8778bd8f8cd">JPH_ASSERT</a></div><div class="ttdeci">#define JPH_ASSERT(...)</div><div class="ttdef"><b>Definition</b> IssueReporting.h:33</div></div>
    212. 

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