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<p>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition">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 <iostream></code><br />
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<code>#include <valarray></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for lu_decomposition.h:</div>
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Typedefs</h2></td></tr>
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<tr class="memitem:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memTemplItemLeft" align="right" valign="top">using </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>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > ></td></tr>
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<tr class="separator:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memSeparator" colspan="2"> </td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:a75b8a228c6419ecda6077255d6d60509"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a75b8a228c6419ecda6077255d6d60509"><td class="memTemplItemLeft" align="right" valign="top">int </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>< T > &A, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< double > *L, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< double > *U)</td></tr>
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<tr class="separator:a75b8a228c6419ecda6077255d6d60509"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="memTemplItemLeft" align="right" valign="top">double </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>< T > &A)</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>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition">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">Typedef Documentation</h2>
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<a id="aed8766713ee9b561a4acdcdff5f90ea5"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aed8766713ee9b561a4acdcdff5f90ea5">◆ </a></span>matrix</h2>
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<div class="memtemplate">
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template<typename T > </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><<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a><T> ></td>
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</div><div class="memdoc">
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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" title="STL class.">std::vector</a></code> of <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html" title="STL class.">std::valarray</a></code> </p>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a3108d43bd32c6fb3b3c158476c51ba7f"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3108d43bd32c6fb3b3c158476c51ba7f">◆ </a></span>determinant_lu()</h2>
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template<typename T > </div>
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<td class="memname">double determinant_lu </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< T > & </td>
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<td class="paramname"><em>A</em></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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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>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>datatype of input matrix - int, unsigned int, double, etc </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">A</td><td>input square matrix </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>determinant of matrix A </dd></dl>
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<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  {</div>
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<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>
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<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>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  </div>
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<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>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordtype">double</span> result = 1.f;</div>
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<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>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  result *= L[i][i] * U[i][i];</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  }</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">return</span> result;</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</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="center"><iframe scrolling="no" frameborder="0" src="../../d1/dbe/lu__decomposition_8h_a3108d43bd32c6fb3b3c158476c51ba7f_cgraph.svg" width="452" height="63"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="a75b8a228c6419ecda6077255d6d60509"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a75b8a228c6419ecda6077255d6d60509">◆ </a></span>lu_decomposition()</h2>
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template<typename T > </div>
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<td class="memname">int lu_decomposition </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< T > & </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"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< double > * </td>
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<td class="paramname"><em>L</em>, </td>
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<td></td>
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<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>< double > * </td>
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<td class="paramname"><em>U</em> </td>
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<td>)</td>
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<td></td><td></td>
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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">L</td><td>output L 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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<dl class="section return"><dt>Returns</dt><dd>0 if no errors </dd>
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<dd>
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negative if error occurred </dd></dl>
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<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  {</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordtype">int</span> row, col, j;</div>
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<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>
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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="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> != A[0].size()) {</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">// check matrix is a square matrix</span></div>
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<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>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> -1;</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>  </div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">// regularize each row</span></div>
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<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>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">// Upper triangular matrix</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="preprocessor">#endif</span></div>
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<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>
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<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>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++) {</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  lu_sum += L[0][row][j] * U[0][j][col];</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  }</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// Evaluate U[i,k]</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  U[0][row][col] = A[row][col] - lu_sum;</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// Lower triangular matrix</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="preprocessor">#endif</span></div>
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<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>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">if</span> (row == col) {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  L[0][row][col] = 1.;</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  }</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<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>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">double</span> lu_sum = 0.;</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">for</span> (j = 0; j < row; j++) {</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  lu_sum += L[0][col][j] * U[0][j][row];</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</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="comment">// Evaluate U[i,k]</span></div>
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<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>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</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>  </div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> }</div>
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