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<p>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition" target="_blank">LU Decomposition</a> of a square matrix.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;valarray&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Typedefs</h2></td></tr>
<tr class="memitem:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memTemplItemLeft" align="right" valign="top">using&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &gt;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a75b8a228c6419ecda6077255d6d60509"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a75b8a228c6419ecda6077255d6d60509"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a> (const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;A, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *L, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *U)</td></tr>
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<tr class="memitem:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a> (const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;A)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition" target="_blank">LU Decomposition</a> of a square matrix. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Typedef Documentation</h2>
<a id="aed8766713ee9b561a4acdcdff5f90ea5" name="aed8766713ee9b561a4acdcdff5f90ea5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aed8766713ee9b561a4acdcdff5f90ea5">&#9670;&#160;</a></span>matrix</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">using <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;T&gt; &gt;</td>
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<p>Define matrix type as a <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></code> of <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></code> </p>
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<h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a3108d43bd32c6fb3b3c158476c51ba7f">&#9670;&#160;</a></span>determinant_lu()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">double determinant_lu </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
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<p>Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U.</p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>datatype of input matrix - int, unsigned int, double, etc </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>input square matrix </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>determinant of matrix A </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 90</span> {</div>
<div class="line"><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"><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"><span class="lineno"> 93</span> </div>
<div class="line"><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"><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1.f;</div>
<div class="line"><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"><span class="lineno"> 99</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> *= L[i][i] * U[i][i];</div>
<div class="line"><span class="lineno"> 100</span> }</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 102</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</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="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</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a75b8a228c6419ecda6077255d6d60509">&#9670;&#160;</a></span>lu_decomposition()</h2>
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<td class="memname">int lu_decomposition </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>U</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Perform LU decomposition on matrix </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix to decompose </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">L</td><td>output L matrix </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">U</td><td>output U matrix </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 if no errors </dd>
<dd>
negative if error occurred </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
<div class="line"><span class="lineno"> 30</span> <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><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"><span class="lineno"> 32</span> </div>
<div class="line"><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"><span class="lineno"> 34</span> <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><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"><span class="lineno"> 36</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><span class="lineno"> 37</span> }</div>
<div class="line"><span class="lineno"> 38</span> </div>
<div class="line"><span class="lineno"> 39</span> <span class="comment">// regularize each row</span></div>
<div class="line"><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"><span class="lineno"> 41</span> <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><span class="lineno"> 42</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><span class="lineno"> 43</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><span class="lineno"> 44</span><span class="preprocessor">#endif</span></div>
<div class="line"><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"><span class="lineno"> 46</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><span class="lineno"> 49</span> lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><span class="lineno"> 50</span> }</div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><span class="lineno"> 53</span> U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><span class="lineno"> 57</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><span class="lineno"> 58</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><span class="lineno"> 59</span><span class="preprocessor">#endif</span></div>
<div class="line"><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"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (row == col) {</div>
<div class="line"><span class="lineno"> 62</span> L[0][row][col] = 1.;</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><span class="lineno"> 64</span> }</div>
<div class="line"><span class="lineno"> 65</span> </div>
<div class="line"><span class="lineno"> 66</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><span class="lineno"> 69</span> lu_sum += L[0][col][j] * U[0][j][row];</div>
<div class="line"><span class="lineno"> 70</span> }</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><span class="lineno"> 73</span> L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
<div class="line"><span class="lineno"> 74</span> }</div>
<div class="line"><span class="lineno"> 75</span> }</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 78</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="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>
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