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<a href="#func-members">Functions</a> </div>
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<div class="title">lu_decompose.c File Reference</div> </div>
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</div><!--header-->
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<div class="contents">
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<p><a href="https://en.wikipedia.org/wiki/LU_decompositon">LU decomposition</a> of a square matrix
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <stdio.h></code><br />
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<code>#include <stdlib.h></code><br />
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<code>#include <time.h></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for lu_decompose.c:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:aae40b90a8efd645c749128cf8072bbb4"><td class="memItemLeft" align="right" valign="top">int </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>
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<tr class="separator:aae40b90a8efd645c749128cf8072bbb4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0789beb8d3396582d77b7aedf5e5554a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a> (double **A, int <a class="el" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>)</td></tr>
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<tr class="separator:a0789beb8d3396582d77b7aedf5e5554a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </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>
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<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/LU_decompositon">LU decomposition</a> of a square matrix </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a0789beb8d3396582d77b7aedf5e5554a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a0789beb8d3396582d77b7aedf5e5554a">◆ </a></span>display()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">void display </td>
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<td>(</td>
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<td class="paramtype">double ** </td>
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<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>N</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Function to display square matrix </p>
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<div class="fragment"><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>; i++)</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  {</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < <a class="code" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>; j++)</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  {</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  printf(<span class="stringliteral">"% 3.3g \t"</span>, A[i][j]);</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  }</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  putchar(<span class="charliteral">'\n'</span>);</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="aae40b90a8efd645c749128cf8072bbb4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aae40b90a8efd645c749128cf8072bbb4">◆ </a></span>lu_decomposition()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">int lu_decomposition </td>
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<td>(</td>
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<td class="paramtype">double ** </td>
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<td class="paramname"><em>A</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double ** </td>
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<td class="paramname"><em>L</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double ** </td>
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<td class="paramname"><em>U</em>, </td>
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</tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>mat_size</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Perform LU decomposition on matrix </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix to decompose </td></tr>
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<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>
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<tr><td class="paramdir">[out]</td><td class="paramname">U</td><td>output U matrix </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">mat_size</td><td>input square matrix size </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keywordtype">int</span> row, col, j;</div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="comment">// regularize each row</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keywordflow">for</span> (row = 0; row < mat_size; row++)</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  {</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="comment">// Upper triangular matrix</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">for</span> (col = row; col < mat_size; col++)</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  {</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++)</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  lu_sum += <a class="code" href="../../df/db3/struct_l.html">L</a>[row][j] * U[j][col];</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="comment">// Evaluate U[i,k]</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  U[row][col] = A[row][col] - lu_sum;</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  }</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  </div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="comment">// Lower triangular matrix</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">for</span> (col = row; col < mat_size; col++)</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  {</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">if</span> (row == col)</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  {</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <a class="code" href="../../df/db3/struct_l.html">L</a>[row][col] = 1.;</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  }</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  </div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++)</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  lu_sum += <a class="code" href="../../df/db3/struct_l.html">L</a>[col][j] * U[j][row];</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// Evaluate U[i,k]</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <a class="code" href="../../df/db3/struct_l.html">L</a>[col][row] = (A[col][row] - lu_sum) / U[row][row];</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  }</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  }</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> }</div>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>argc</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">char ** </td>
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<td class="paramname"><em>argv</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Main function </p>
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<div class="fragment"><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> {</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordtype">int</span> mat_size = 3; <span class="comment">// default matrix size</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="../../df/dea/structdata.html">range</a> = 10;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = <a class="code" href="../../df/dea/structdata.html">range</a> >> 1;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  </div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">if</span> (argc == 2)</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  mat_size = atoi(argv[1]);</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  srand(time(NULL)); <span class="comment">// random number initializer</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  </div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">/* Create a square matrix with random values */</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordtype">double</span> **A = (<span class="keywordtype">double</span> **)malloc(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *));</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">double</span> **<a class="code" href="../../df/db3/struct_l.html">L</a> = (<span class="keywordtype">double</span> **)malloc(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *)); <span class="comment">// output</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">double</span> **U = (<span class="keywordtype">double</span> **)malloc(mat_size * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span> *)); <span class="comment">// output</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < mat_size; i++)</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  {</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// calloc so that all valeus are '0' by default</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  A[i] = (<span class="keywordtype">double</span> *)calloc(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="../../df/db3/struct_l.html">L</a>[i] = (<span class="keywordtype">double</span> *)calloc(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  U[i] = (<span class="keywordtype">double</span> *)calloc(mat_size, <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < mat_size; j++)</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  A[i][j] = (<span class="keywordtype">double</span>)(rand() % <a class="code" href="../../df/dea/structdata.html">range</a> - range2);</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  }</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <a class="code" href="../../dc/d2e/lu__decompose_8c.html#aae40b90a8efd645c749128cf8072bbb4">lu_decomposition</a>(A, <a class="code" href="../../df/db3/struct_l.html">L</a>, U, mat_size);</div>
|
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  </div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  printf(<span class="stringliteral">"A = \n"</span>);</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(A, mat_size);</div>
|
||
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  printf(<span class="stringliteral">"\nL = \n"</span>);</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(<a class="code" href="../../df/db3/struct_l.html">L</a>, mat_size);</div>
|
||
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  printf(<span class="stringliteral">"\nU = \n"</span>);</div>
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||
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <a class="code" href="../../dc/d2e/lu__decompose_8c.html#a0789beb8d3396582d77b7aedf5e5554a">display</a>(U, mat_size);</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div>
|
||
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">/* Free dynamically allocated memory */</span></div>
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||
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < mat_size; i++)</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  {</div>
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||
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  free(A[i]);</div>
|
||
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  free(<a class="code" href="../../df/db3/struct_l.html">L</a>[i]);</div>
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||
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|
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  free(U[i]);</div>
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||
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  }</div>
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||
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  free(A);</div>
|
||
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  free(<a class="code" href="../../df/db3/struct_l.html">L</a>);</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  free(U);</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d2e/lu__decompose_8c_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="232" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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</div><!-- contents -->
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</div><!-- doc-content -->
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<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>
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<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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<div class="ttc" id="aproblem__13_2sol1_8c_html_a0240ac851181b84ac374872dc5434ee4"><div class="ttname"><a href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a></div><div class="ttdeci">#define N</div><div class="ttdef"><b>Definition:</b> sol1.c:111</div></div>
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<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="ttdef"><b>Definition:</b> lu_decompose.c:20</div></div>
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<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="ttdef"><b>Definition:</b> lu_decompose.c:68</div></div>
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