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<div class="title">lu_decomposition.h</div> </div>
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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 name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment"> * @file lu_decomposition.h</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment"> * @author [Krishna Vedala](https://github.com/kvedala)</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment"> * @brief Functions associated with [LU</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment"> * Decomposition](https://en.wikipedia.org/wiki/LU_decomposition)</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment"> * of a square matrix.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="preprocessor">#include &lt;valarray&gt;</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="comment">/** Define matrix type as a `std::vector` of `std::valarray` */</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00019"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5"> 19</a></span>&#160;<span class="keyword">using</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a> = <a class="codeRef" 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 name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="comment">/** Perform LU decomposition on matrix</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="comment"> * \param[in] A matrix to decompose</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="comment"> * \param[out] L output L matrix</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="comment"> * \param[out] U output U matrix</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;<span class="comment"> * \returns 0 if no errors</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;<span class="comment"> * \returns negative if error occurred</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509"> 29</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *L, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *U) {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> != A[0].size()) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" 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 name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="comment">// regularize each row</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (row = 0; row &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; row++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (row == col) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; L[0][row][col] = 1.;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; }</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; lu_sum += L[0][col][j] * U[0][j][row];</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; }</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;}</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment"> * Compute determinant of an NxN square matrix using LU decomposition.</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"> * Using LU decomposition, the determinant is given by the product of diagonal</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> * elements of matrices L and U.</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> * @tparam T datatype of input matrix - int, unsigned int, double, etc</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> * @param A input square matrix</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> * @return determinant of matrix A</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f"> 90</a></span>&#160;<span class="keywordtype">double</span> <a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A) {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U) &lt; 0)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">double</span> result = 1.f;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; result *= L[i][i] * U[i][i];</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</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>
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
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