mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-03-22 04:42:10 +08:00
217 lines
23 KiB
HTML
217 lines
23 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
|
|
<meta name="generator" content="Doxygen 1.9.1"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>Algorithms_in_C++: numerical_methods/lu_decomposition.h Source File</title>
|
|
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="../../jquery.js"></script>
|
|
<script type="text/javascript" src="../../dynsections.js"></script>
|
|
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="../../resize.js"></script>
|
|
<script type="text/javascript" src="../../navtreedata.js"></script>
|
|
<script type="text/javascript" src="../../navtree.js"></script>
|
|
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="../../search/searchdata.js"></script>
|
|
<script type="text/javascript" src="../../search/search.js"></script>
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
|
|
jax: ["input/TeX","output/HTML-CSS"],
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
|
|
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
|
|
</head>
|
|
<body>
|
|
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
|
|
<div id="titlearea">
|
|
<table cellspacing="0" cellpadding="0">
|
|
<tbody>
|
|
<tr style="height: 56px;">
|
|
<td id="projectalign" style="padding-left: 0.5em;">
|
|
<div id="projectname">Algorithms_in_C++
|
|
 <span id="projectnumber">1.0.0</span>
|
|
</div>
|
|
<div id="projectbrief">Set of algorithms implemented in C++.</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<!-- end header part -->
|
|
<!-- Generated by Doxygen 1.9.1 -->
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
var searchBox = new SearchBox("searchBox", "../../search",false,'Search','.html');
|
|
/* @license-end */
|
|
</script>
|
|
<script type="text/javascript" src="../../menudata.js"></script>
|
|
<script type="text/javascript" src="../../menu.js"></script>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(function() {
|
|
initMenu('../../',true,false,'search.php','Search');
|
|
$(document).ready(function() { init_search(); });
|
|
});
|
|
/* @license-end */</script>
|
|
<div id="main-nav"></div>
|
|
</div><!-- top -->
|
|
<div id="side-nav" class="ui-resizable side-nav-resizable">
|
|
<div id="nav-tree">
|
|
<div id="nav-tree-contents">
|
|
<div id="nav-sync" class="sync"></div>
|
|
</div>
|
|
</div>
|
|
<div id="splitbar" style="-moz-user-select:none;"
|
|
class="ui-resizable-handle">
|
|
</div>
|
|
</div>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(document).ready(function(){initNavTree('d1/dbe/lu__decomposition_8h_source.html','../../'); initResizable(); });
|
|
/* @license-end */
|
|
</script>
|
|
<div id="doc-content">
|
|
<!-- window showing the filter options -->
|
|
<div id="MSearchSelectWindow"
|
|
onmouseover="return searchBox.OnSearchSelectShow()"
|
|
onmouseout="return searchBox.OnSearchSelectHide()"
|
|
onkeydown="return searchBox.OnSearchSelectKey(event)">
|
|
</div>
|
|
|
|
<!-- iframe showing the search results (closed by default) -->
|
|
<div id="MSearchResultsWindow">
|
|
<iframe src="javascript:void(0)" frameborder="0"
|
|
name="MSearchResults" id="MSearchResults">
|
|
</iframe>
|
|
</div>
|
|
|
|
<div class="header">
|
|
<div class="headertitle">
|
|
<div class="title">lu_decomposition.h</div> </div>
|
|
</div><!--header-->
|
|
<div class="contents">
|
|
<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> <span class="comment">/**</span></div>
|
|
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * @file lu_decomposition.h</span></div>
|
|
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @author [Krishna Vedala](https://github.com/kvedala)</span></div>
|
|
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * @brief Functions associated with [LU</span></div>
|
|
<div class="line"><a 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 name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * of a square matrix.</span></div>
|
|
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> */</span></div>
|
|
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="preprocessor">#pragma once</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">#include <iostream></span></div>
|
|
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#include <valarray></span></div>
|
|
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include <vector></span></div>
|
|
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <omp.h></span></div>
|
|
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#endif</span></div>
|
|
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span> </div>
|
|
<div class="line"><a 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 name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></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> <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<std::valarray<T></a>>;</div>
|
|
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span> </div>
|
|
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">/** Perform LU decomposition on matrix</span></div>
|
|
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> * \param[in] A matrix to decompose</span></div>
|
|
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> * \param[out] L output L matrix</span></div>
|
|
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> * \param[out] U output U matrix</span></div>
|
|
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> * \returns 0 if no errors</span></div>
|
|
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> * \returns negative if error occurred</span></div>
|
|
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> */</span></div>
|
|
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></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> <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<T></a> &A, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix<double></a> *L, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix<double></a> *U) {</div>
|
|
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordtype">int</span> row, col, j;</div>
|
|
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <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>  </div>
|
|
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <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>  <span class="comment">// check matrix is a square matrix</span></div>
|
|
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> << <span class="stringliteral">"Not a square matrix!\n"</span>;</div>
|
|
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> -1;</div>
|
|
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  }</div>
|
|
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  </div>
|
|
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">// regularize each row</span></div>
|
|
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span> (row = 0; row < <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>  <span class="comment">// Upper triangular matrix</span></div>
|
|
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#pragma omp for</span></div>
|
|
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#endif</span></div>
|
|
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">for</span> (col = row; col < <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>  <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>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
|
|
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++) {</div>
|
|
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  lu_sum += L[0][row][j] * U[0][j][col];</div>
|
|
<div class="line"><a name="l00050"></a><span class="lineno"> 50</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>  <span class="comment">// Evaluate U[i,k]</span></div>
|
|
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  U[0][row][col] = A[row][col] - lu_sum;</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>  <span class="comment">// Lower triangular matrix</span></div>
|
|
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="preprocessor">#pragma omp for</span></div>
|
|
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="preprocessor">#endif</span></div>
|
|
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">for</span> (col = row; col < <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>  <span class="keywordflow">if</span> (row == col) {</div>
|
|
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  L[0][row][col] = 1.;</div>
|
|
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">continue</span>;</div>
|
|
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  }</div>
|
|
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
|
|
<div class="line"><a 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 name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
|
|
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++) {</div>
|
|
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  lu_sum += L[0][col][j] * U[0][j][row];</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>  </div>
|
|
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// Evaluate U[i,k]</span></div>
|
|
<div class="line"><a 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 name="l00074"></a><span class="lineno"> 74</span>  }</div>
|
|
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  }</div>
|
|
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
|
|
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">return</span> 0;</div>
|
|
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> }</div>
|
|
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span> </div>
|
|
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">/**</span></div>
|
|
<div class="line"><a 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 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 name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> * elements of matrices L and U.</span></div>
|
|
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"> *</span></div>
|
|
<div class="line"><a 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 name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> * @param A input square matrix</span></div>
|
|
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> * @return determinant of matrix A</span></div>
|
|
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> */</span></div>
|
|
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></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> <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<T></a> &A) {</div>
|
|
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix<double></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<double></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>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix<double></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<double></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>  </div>
|
|
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &L, &U) < 0)</div>
|
|
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> 0;</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>  <span class="keywordtype">double</span> result = 1.f;</div>
|
|
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < 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>  result *= L[i][i] * U[i][i];</div>
|
|
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  }</div>
|
|
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">return</span> result;</div>
|
|
<div class="line"><a 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< T > &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< T > &A, matrix< double > *L, matrix< double > *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< double ></a></div></div>
|
|
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
|
|
</div><!-- fragment --></div><!-- contents -->
|
|
</div><!-- doc-content -->
|
|
<!-- start footer part -->
|
|
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
|
<ul>
|
|
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html">lu_decomposition.h</a></li>
|
|
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|