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<a href="../../d1/dbe/lu__decomposition_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">/**</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * @file lu_decomposition.h</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * @author [Krishna Vedala](https://github.com/kvedala)</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * @brief Functions associated with [LU</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * Decomposition](https://en.wikipedia.org/wiki/LU_decomposition)</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * of a square matrix.</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> */</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#include &lt;valarray&gt;</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"></span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">/** Define matrix type as a `std::vector` of `std::valarray` */</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5"> 19</a></span><span class="keyword">using</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt;;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment"></span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">/** Perform LU decomposition on matrix</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment"> * \param[in] A matrix to decompose</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment"> * \param[out] L output L matrix</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment"> * \param[out] U output U matrix</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> * \returns 0 if no errors</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment"> * \returns negative if error occurred</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment"> */</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509"> 29</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *L, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *U) {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> != A[0].size()) {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Not a square matrix!\n&quot;</span>;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// regularize each row</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">for</span> (row = 0; row &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; row++) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (col = row; col &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">for</span> (col = row; col &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (row == col) {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> L[0][row][col] = 1.;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> lu_sum += L[0][col][j] * U[0][j][row];</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> }</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> }</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span>}</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment"></span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">/**</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment"> * Compute determinant of an NxN square matrix using LU decomposition.</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment"> * Using LU decomposition, the determinant is given by the product of diagonal</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment"> * elements of matrices L and U.</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment"> *</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment"> * @tparam T datatype of input matrix - int, unsigned int, double, etc</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment"> * @param A input square matrix</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment"> * @return determinant of matrix A</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment"> */</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f"> 90</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U) &lt; 0)</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">double</span> result = 1.f;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> result *= L[i][i] * U[i][i];</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
<div class="ttc" id="alu__decomposition_8h_html_a3108d43bd32c6fb3b3c158476c51ba7f"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a></div><div class="ttdeci">double determinant_lu(const matrix&lt; T &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:90</div></div>
<div class="ttc" id="alu__decomposition_8h_html_a75b8a228c6419ecda6077255d6d60509"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a></div><div class="ttdeci">int lu_decomposition(const matrix&lt; T &gt; &amp;A, matrix&lt; double &gt; *L, matrix&lt; double &gt; *U)</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:29</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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