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<p><a href="https://en.wikipedia.org/wiki/LU_decompositon" target="_blank">LU decomposition</a> of a square matrix
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;time.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for lu_decompose.c:</div>
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Functions</h2></td></tr>
<tr class="memitem:aae40b90a8efd645c749128cf8072bbb4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d2e/lu__decompose_8c.html#aae40b90a8efd645c749128cf8072bbb4">lu_decomposition</a> (double **A, double **<a class="el" href="../../df/db3/struct_l.html">L</a>, double **U, int mat_size)</td></tr>
<tr class="memdesc:aae40b90a8efd645c749128cf8072bbb4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Perform LU decomposition on matrix. <a href="../../dc/d2e/lu__decompose_8c.html#aae40b90a8efd645c749128cf8072bbb4">More...</a><br /></td></tr>
<tr class="separator:aae40b90a8efd645c749128cf8072bbb4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0789beb8d3396582d77b7aedf5e5554a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a> (double **A, int N)</td></tr>
<tr class="memdesc:a0789beb8d3396582d77b7aedf5e5554a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to display square matrix. <a href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">More...</a><br /></td></tr>
<tr class="separator:a0789beb8d3396582d77b7aedf5e5554a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d2e/lu__decompose_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../dc/d2e/lu__decompose_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">More...</a><br /></td></tr>
<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/LU_decompositon" 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">Function Documentation</h2>
<a id="a0789beb8d3396582d77b7aedf5e5554a" name="a0789beb8d3396582d77b7aedf5e5554a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0789beb8d3396582d77b7aedf5e5554a">&#9670;&#160;</a></span>display()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void display </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to display square matrix. </p>
<div class="fragment"><div class="line"><span class="lineno"> 67</span>{</div>
<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; i++)</div>
<div class="line"><span class="lineno"> 69</span> {</div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; N; j++)</div>
<div class="line"><span class="lineno"> 71</span> {</div>
<div class="line"><span class="lineno"> 72</span> printf(<span class="stringliteral">&quot;% 3.3g \t&quot;</span>, A[i][j]);</div>
<div class="line"><span class="lineno"> 73</span> }</div>
<div class="line"><span class="lineno"> 74</span> putchar(<span class="charliteral">&#39;\n&#39;</span>);</div>
<div class="line"><span class="lineno"> 75</span> }</div>
<div class="line"><span class="lineno"> 76</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="aae40b90a8efd645c749128cf8072bbb4" name="aae40b90a8efd645c749128cf8072bbb4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aae40b90a8efd645c749128cf8072bbb4">&#9670;&#160;</a></span>lu_decomposition()</h2>
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<td class="memname">int lu_decomposition </td>
<td>(</td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double **&#160;</td>
<td class="paramname"><em>U</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>mat_size</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<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"><a class="el" href="../../df/db3/struct_l.html">L</a></td><td>output <a class="el" href="../../df/db3/struct_l.html">L</a> matrix </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">U</td><td>output U matrix </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">mat_size</td><td>input square matrix size </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 21</span>{</div>
<div class="line"><span class="lineno"> 22</span> <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><span class="lineno"> 23</span> </div>
<div class="line"><span class="lineno"> 24</span> <span class="comment">// regularize each row</span></div>
<div class="line"><span class="lineno"> 25</span> <span class="keywordflow">for</span> (row = 0; row &lt; mat_size; row++)</div>
<div class="line"><span class="lineno"> 26</span> {</div>
<div class="line"><span class="lineno"> 27</span> <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><span class="lineno"> 28</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><span class="lineno"> 29</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><span class="lineno"> 30</span><span class="preprocessor">#endif</span></div>
<div class="line"><span class="lineno"> 31</span> <span class="keywordflow">for</span> (col = row; col &lt; mat_size; col++)</div>
<div class="line"><span class="lineno"> 32</span> {</div>
<div class="line"><span class="lineno"> 33</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[row][j] * U[j][col];</div>
<div class="line"><span class="lineno"> 36</span> </div>
<div class="line"><span class="lineno"> 37</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><span class="lineno"> 38</span> U[row][col] = A[row][col] - lu_sum;</div>
<div class="line"><span class="lineno"> 39</span> }</div>
<div class="line"><span class="lineno"> 40</span> </div>
<div class="line"><span class="lineno"> 41</span> <span class="comment">// Lower 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; mat_size; col++)</div>
<div class="line"><span class="lineno"> 46</span> {</div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">if</span> (row == col)</div>
<div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[row][col] = 1.;</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><span class="lineno"> 51</span> }</div>
<div class="line"><span class="lineno"> 52</span> </div>
<div class="line"><span class="lineno"> 53</span> <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[col][j] * U[j][row];</div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><span class="lineno"> 58</span> <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[col][row] = (A[col][row] - lu_sum) / U[row][row];</div>
<div class="line"><span class="lineno"> 59</span> }</div>
<div class="line"><span class="lineno"> 60</span> }</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 63</span>}</div>
<div class="ttc" id="astruct_l_html"><div class="ttname"><a href="../../df/db3/struct_l.html">L</a></div><div class="ttdef"><b>Definition:</b> list.h:8</div></div>
</div><!-- fragment -->
</div>
</div>
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<div class="fragment"><div class="line"><span class="lineno"> 80</span>{</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordtype">int</span> mat_size = 3; <span class="comment">// default matrix size</span></div>
<div class="line"><span class="lineno"> 82</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_struct" href="../../df/dea/structdata.html">range</a> = 10;</div>
<div class="line"><span class="lineno"> 83</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = <a class="code hl_struct" href="../../df/dea/structdata.html">range</a> &gt;&gt; 1;</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (argc == 2)</div>
<div class="line"><span class="lineno"> 86</span> mat_size = atoi(argv[1]);</div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> srand(time(NULL)); <span class="comment">// random number initializer</span></div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <span class="comment">/* Create a square matrix with random values */</span></div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordtype">double</span> **A = (<span class="keywordtype">double</span> **)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *));</div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordtype">double</span> **<a class="code hl_struct" href="../../df/db3/struct_l.html">L</a> = (<span class="keywordtype">double</span> **)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordtype">double</span> **U = (<span class="keywordtype">double</span> **)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; mat_size; i++)</div>
<div class="line"><span class="lineno"> 95</span> {</div>
<div class="line"><span class="lineno"> 96</span> <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
<div class="line"><span class="lineno"> 97</span> A[i] = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#afdddaa949a93c1ef559a638e98f9c21b">calloc</a>(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><span class="lineno"> 98</span> <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[i] = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#afdddaa949a93c1ef559a638e98f9c21b">calloc</a>(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><span class="lineno"> 99</span> U[i] = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#afdddaa949a93c1ef559a638e98f9c21b">calloc</a>(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; mat_size; j++)</div>
<div class="line"><span class="lineno"> 101</span> <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
<div class="line"><span class="lineno"> 102</span> A[i][j] = (<span class="keywordtype">double</span>)(rand() % <a class="code hl_struct" href="../../df/dea/structdata.html">range</a> - range2);</div>
<div class="line"><span class="lineno"> 103</span> }</div>
<div class="line"><span class="lineno"> 104</span> </div>
<div class="line"><span class="lineno"> 105</span> <a class="code hl_function" href="../../dc/d2e/lu__decompose_8c.html#aae40b90a8efd645c749128cf8072bbb4">lu_decomposition</a>(A, <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>, U, mat_size);</div>
<div class="line"><span class="lineno"> 106</span> </div>
<div class="line"><span class="lineno"> 107</span> printf(<span class="stringliteral">&quot;A = \n&quot;</span>);</div>
<div class="line"><span class="lineno"> 108</span> <a class="code hl_function" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(A, mat_size);</div>
<div class="line"><span class="lineno"> 109</span> printf(<span class="stringliteral">&quot;\nL = \n&quot;</span>);</div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_function" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(<a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>, mat_size);</div>
<div class="line"><span class="lineno"> 111</span> printf(<span class="stringliteral">&quot;\nU = \n&quot;</span>);</div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_function" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(U, mat_size);</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> <span class="comment">/* Free dynamically allocated memory */</span></div>
<div class="line"><span class="lineno"> 115</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; mat_size; i++)</div>
<div class="line"><span class="lineno"> 116</span> {</div>
<div class="line"><span class="lineno"> 117</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(A[i]);</div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(<a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>[i]);</div>
<div class="line"><span class="lineno"> 119</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(U[i]);</div>
<div class="line"><span class="lineno"> 120</span> }</div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(A);</div>
<div class="line"><span class="lineno"> 122</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(<a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>);</div>
<div class="line"><span class="lineno"> 123</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(U);</div>
<div class="line"><span class="lineno"> 124</span> </div>
<div class="line"><span class="lineno"> 125</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 126</span>}</div>
<div class="ttc" id="alu__decompose_8c_html_a0789beb8d3396582d77b7aedf5e5554a"><div class="ttname"><a href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a></div><div class="ttdeci">void display(double **A, int N)</div><div class="ttdoc">Function to display square matrix.</div><div class="ttdef"><b>Definition:</b> lu_decompose.c:66</div></div>
<div class="ttc" id="alu__decompose_8c_html_aae40b90a8efd645c749128cf8072bbb4"><div class="ttname"><a href="../../dc/d2e/lu__decompose_8c.html#aae40b90a8efd645c749128cf8072bbb4">lu_decomposition</a></div><div class="ttdeci">int lu_decomposition(double **A, double **L, double **U, int mat_size)</div><div class="ttdoc">Perform LU decomposition on matrix.</div><div class="ttdef"><b>Definition:</b> lu_decompose.c:20</div></div>
<div class="ttc" id="amalloc__dbg_8h_html_a725f50ecaf1959d96de79b36b4788fee"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a></div><div class="ttdeci">#define malloc(bytes)</div><div class="ttdoc">This macro replace the standard malloc function with malloc_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:18</div></div>
<div class="ttc" id="amalloc__dbg_8h_html_a9cc854374299a1dd933bf62029761768"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a></div><div class="ttdeci">#define free(ptr)</div><div class="ttdoc">This macro replace the standard free function with free_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:26</div></div>
<div class="ttc" id="amalloc__dbg_8h_html_afdddaa949a93c1ef559a638e98f9c21b"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#afdddaa949a93c1ef559a638e98f9c21b">calloc</a></div><div class="ttdeci">#define calloc(elemCount, elemSize)</div><div class="ttdoc">This macro replace the standard calloc function with calloc_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:22</div></div>
<div class="ttc" id="astructdata_html"><div class="ttname"><a href="../../df/dea/structdata.html">data</a></div><div class="ttdef"><b>Definition:</b> prime_factoriziation.c:25</div></div>
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