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<a href="#func-members">Functions</a> </div>
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<div class="contents">
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<p>Program to compute the <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of a given matrix.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <array></code><br />
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<code>#include <cmath></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <ctime></code><br />
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<code>#include <iostream></code><br />
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<code>#include "<a class="el" href="../../d4/d68/qr__decompose_8h_source.html">./qr_decompose.h</a>"</code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for qr_decomposition.cpp:</div>
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<div class="dyncontent">
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<p><a href="../../d3/d24/qr__decomposition_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a840291bc02cba5474a4cb46a9b9566fe" id="r_a840291bc02cba5474a4cb46a9b9566fe"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a840291bc02cba5474a4cb46a9b9566fe">main</a> (void)</td></tr>
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<tr class="separator:a840291bc02cba5474a4cb46a9b9566fe"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a73ce637634fc49e1d10d190eb388ebf1" id="r_a73ce637634fc49e1d10d190eb388ebf1"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:a73ce637634fc49e1d10d190eb388ebf1"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a> (const std::valarray< std::valarray< T > > &A, std::valarray< std::valarray< T > > *Q, std::valarray< std::valarray< T > > *R)</td></tr>
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<tr class="separator:a73ce637634fc49e1d10d190eb388ebf1"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834" id="r_adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#adfbdf47277c8cfee229b05b72f1f7834">operator<<</a> (std::ostream &out, std::valarray< std::valarray< T > > const &v)</td></tr>
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<tr class="separator:adfbdf47277c8cfee229b05b72f1f7834"><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>Program to compute the <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of a given matrix. </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../d3/d24/qr__decomposition_8cpp_source.html">qr_decomposition.cpp</a>.</p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a840291bc02cba5474a4cb46a9b9566fe" name="a840291bc02cba5474a4cb46a9b9566fe"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a840291bc02cba5474a4cb46a9b9566fe">◆ </a></span>main()</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 main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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<p>main function </p>
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<p class="definition">Definition at line <a class="el" href="../../d3/d24/qr__decomposition_8cpp_source.html#l00023">23</a> of file <a class="el" href="../../d3/d24/qr__decomposition_8cpp_source.html">qr_decomposition.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 23</span> {</div>
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<div class="line"><span class="lineno"> 24</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ROWS, COLUMNS;</div>
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<div class="line"><span class="lineno"> 25</span> </div>
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<div class="line"><span class="lineno"> 26</span> std::cout << <span class="stringliteral">"Enter the number of rows and columns: "</span>;</div>
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<div class="line"><span class="lineno"> 27</span> std::cin >> ROWS >> COLUMNS;</div>
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<div class="line"><span class="lineno"> 28</span> </div>
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<div class="line"><span class="lineno"> 29</span> std::cout << <span class="stringliteral">"Enter matrix elements row-wise:\n"</span>;</div>
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<div class="line"><span class="lineno"> 30</span> </div>
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<div class="line"><span class="lineno"> 31</span> std::valarray<std::valarray<double>> A(ROWS);</div>
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<div class="line"><span class="lineno"> 32</span> std::valarray<std::valarray<double>> Q(ROWS);</div>
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<div class="line"><span class="lineno"> 33</span> std::valarray<std::valarray<double>> R(COLUMNS);</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < std::max(ROWS, COLUMNS); i++) {</div>
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<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">if</span> (i < ROWS) {</div>
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<div class="line"><span class="lineno"> 36</span> A[i] = std::valarray<double>(COLUMNS);</div>
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<div class="line"><span class="lineno"> 37</span> Q[i] = std::valarray<double>(COLUMNS);</div>
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<div class="line"><span class="lineno"> 38</span> }</div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">if</span> (i < COLUMNS) {</div>
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<div class="line"><span class="lineno"> 40</span> R[i] = std::valarray<double>(COLUMNS);</div>
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<div class="line"><span class="lineno"> 41</span> }</div>
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<div class="line"><span class="lineno"> 42</span> }</div>
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<div class="line"><span class="lineno"> 43</span> </div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < ROWS; i++)</div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < COLUMNS; j++) std::cin >> A[i][j];</div>
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<div class="line"><span class="lineno"> 46</span> </div>
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<div class="line"><span class="lineno"> 47</span> std::cout << A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 48</span> </div>
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<div class="line"><span class="lineno"> 49</span> clock_t t1 = clock();</div>
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<div class="line"><span class="lineno"> 50</span> <a class="code hl_function" href="#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(A, &Q, &R);</div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(clock() - t1) / CLOCKS_PER_SEC;</div>
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<div class="line"><span class="lineno"> 52</span> </div>
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<div class="line"><span class="lineno"> 53</span> std::cout << Q << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 54</span> std::cout << R << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 55</span> std::cout << <span class="stringliteral">"Time taken to compute: "</span> << dtime << <span class="stringliteral">" sec\n "</span>;</div>
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<div class="line"><span class="lineno"> 56</span> </div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 58</span>}</div>
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<div class="ttc" id="aqr__decomposition_8cpp_html_a73ce637634fc49e1d10d190eb388ebf1"><div class="ttname"><a href="#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a></div><div class="ttdeci">void qr_decompose(const std::valarray< std::valarray< T > > &A, std::valarray< std::valarray< T > > *Q, std::valarray< std::valarray< T > > *R)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00146">qr_decompose.h:146</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="adfbdf47277c8cfee229b05b72f1f7834" name="adfbdf47277c8cfee229b05b72f1f7834"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#adfbdf47277c8cfee229b05b72f1f7834">◆ </a></span>operator<<()</h2>
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<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
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template<typename T> </div>
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<td class="memname">std::ostream & qr_algorithm::operator<< </td>
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<td>(</td>
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<td class="paramtype">std::ostream &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::valarray< std::valarray< T > > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
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</div><div class="memdoc">
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<p>operator to print a matrix </p>
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00033">33</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 34</span> {</div>
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<div class="line"><span class="lineno"> 35</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
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<div class="line"><span class="lineno"> 36</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">' '</span>;</div>
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<div class="line"><span class="lineno"> 37</span> </div>
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<div class="line"><span class="lineno"> 38</span> out.precision(4);</div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row < v.size(); row++) {</div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col < v[row].size(); col++)</div>
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<div class="line"><span class="lineno"> 41</span> out << std::right << std::setw(width) << std::setfill(separator)</div>
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<div class="line"><span class="lineno"> 42</span> << v[row][col];</div>
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<div class="line"><span class="lineno"> 43</span> out << std::endl;</div>
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<div class="line"><span class="lineno"> 44</span> }</div>
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<div class="line"><span class="lineno"> 45</span> </div>
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<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">return</span> out;</div>
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<div class="line"><span class="lineno"> 47</span>}</div>
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</div><!-- fragment -->
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</div>
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<a id="a73ce637634fc49e1d10d190eb388ebf1" name="a73ce637634fc49e1d10d190eb388ebf1"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a73ce637634fc49e1d10d190eb388ebf1">◆ </a></span>qr_decompose()</h2>
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<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
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template<typename T> </div>
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<td class="memname">void qr_algorithm::qr_decompose </td>
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<td>(</td>
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<td class="paramtype">const std::valarray< std::valarray< T > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </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">std::valarray< std::valarray< T > > *</td> <td class="paramname"><span class="paramname"><em>Q</em></span>, </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">std::valarray< std::valarray< T > > *</td> <td class="paramname"><span class="paramname"><em>R</em></span> )</td>
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</tr>
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</div><div class="memdoc">
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<p>Decompose matrix \(A\) using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">Gram-Schmidt process</a>.</p>
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<p class="formulaDsp">
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\begin{eqnarray*} \text{given that}\quad A &=&
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*\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\
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\text{where}\quad\mathbf{a}_i &=&
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\left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column
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vectors)}\\
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\text{then}\quad\mathbf{u}_i &=& \mathbf{a}_i
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*-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\
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\mathbf{e}_i &=&\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\
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Q &=& \begin{bmatrix}\mathbf{e}_0 & \mathbf{e}_1 & \mathbf{e}_2 & \dots &
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\mathbf{e}_{N-1}\end{bmatrix}\\
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R &=& \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &
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\langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &
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|
\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots \\
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|
0 & \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &
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|
\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\
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|
0 & 0 & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &
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|
\dots\\ \vdots & \vdots & \vdots & \ddots
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|
\end{bmatrix}\\
|
|
\end{eqnarray*}
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|
</p>
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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 matrix to decompose </td></tr>
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|
<tr><td class="paramname">Q</td><td>output decomposed matrix </td></tr>
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|
<tr><td class="paramname">R</td><td>output decomposed matrix </td></tr>
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</table>
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|
</dd>
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</dl>
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00146">146</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 150</span> {</div>
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<div class="line"><span class="lineno"> 151</span> std::size_t ROWS = A.size(); <span class="comment">// number of rows of A</span></div>
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<div class="line"><span class="lineno"> 152</span> std::size_t COLUMNS = A[0].size(); <span class="comment">// number of columns of A</span></div>
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<div class="line"><span class="lineno"> 153</span> std::valarray<T> col_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 154</span> std::valarray<T> col_vector2(ROWS);</div>
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<div class="line"><span class="lineno"> 155</span> std::valarray<T> tmp_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 156</span> </div>
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<div class="line"><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < COLUMNS; i++) {</div>
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<div class="line"><span class="lineno"> 158</span> <span class="comment">/* for each column => R is a square matrix of NxN */</span></div>
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<div class="line"><span class="lineno"> 159</span> <span class="keywordtype">int</span> j;</div>
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|
<div class="line"><span class="lineno"> 160</span> R[0][i] = 0.; <span class="comment">/* make R upper triangular */</span></div>
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<div class="line"><span class="lineno"> 161</span> </div>
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<div class="line"><span class="lineno"> 162</span> <span class="comment">/* get corresponding Q vector */</span></div>
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<div class="line"><span class="lineno"> 163</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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|
<div class="line"><span class="lineno"> 164</span><span class="comment">// parallelize on threads</span></div>
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<div class="line"><span class="lineno"> 165</span><span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><span class="lineno"> 166</span><span class="preprocessor">#endif</span></div>
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|
<div class="line"><span class="lineno"> 167</span> <span class="keywordflow">for</span> (j = 0; j < ROWS; j++) {</div>
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|
<div class="line"><span class="lineno"> 168</span> tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
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|
<div class="line"><span class="lineno"> 169</span> col_vector[j] = A[j][i];</div>
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|
<div class="line"><span class="lineno"> 170</span> }</div>
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|
<div class="line"><span class="lineno"> 171</span> <span class="keywordflow">for</span> (j = 0; j < i; j++) {</div>
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|
<div class="line"><span class="lineno"> 172</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < ROWS; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
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<div class="line"><span class="lineno"> 173</span> col_vector2[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = Q[0][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j];</div>
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<div class="line"><span class="lineno"> 174</span> }</div>
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<div class="line"><span class="lineno"> 175</span> col_vector2 = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a>(col_vector, col_vector2);</div>
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<div class="line"><span class="lineno"> 176</span> tmp_vector -= col_vector2;</div>
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<div class="line"><span class="lineno"> 177</span> }</div>
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<div class="line"><span class="lineno"> 178</span> </div>
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<div class="line"><span class="lineno"> 179</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">mag</a> = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
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|
<div class="line"><span class="lineno"> 180</span> </div>
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|
<div class="line"><span class="lineno"> 181</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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|
<div class="line"><span class="lineno"> 182</span><span class="comment">// parallelize on threads</span></div>
|
|
<div class="line"><span class="lineno"> 183</span><span class="preprocessor">#pragma omp for</span></div>
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|
<div class="line"><span class="lineno"> 184</span><span class="preprocessor">#endif</span></div>
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|
<div class="line"><span class="lineno"> 185</span> <span class="keywordflow">for</span> (j = 0; j < ROWS; j++) Q[0][j][i] = tmp_vector[j] / mag;</div>
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|
<div class="line"><span class="lineno"> 186</span> </div>
|
|
<div class="line"><span class="lineno"> 187</span> <span class="comment">/* compute upper triangular values of R */</span></div>
|
|
<div class="line"><span class="lineno"> 188</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><span class="lineno"> 189</span><span class="comment">// parallelize on threads</span></div>
|
|
<div class="line"><span class="lineno"> 190</span><span class="preprocessor">#pragma omp for</span></div>
|
|
<div class="line"><span class="lineno"> 191</span><span class="preprocessor">#endif</span></div>
|
|
<div class="line"><span class="lineno"> 192</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk < ROWS; kk++) {</div>
|
|
<div class="line"><span class="lineno"> 193</span> col_vector[kk] = Q[0][kk][i];</div>
|
|
<div class="line"><span class="lineno"> 194</span> }</div>
|
|
<div class="line"><span class="lineno"> 195</span> </div>
|
|
<div class="line"><span class="lineno"> 196</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><span class="lineno"> 197</span><span class="comment">// parallelize on threads</span></div>
|
|
<div class="line"><span class="lineno"> 198</span><span class="preprocessor">#pragma omp for</span></div>
|
|
<div class="line"><span class="lineno"> 199</span><span class="preprocessor">#endif</span></div>
|
|
<div class="line"><span class="lineno"> 200</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < COLUMNS; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
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|
<div class="line"><span class="lineno"> 201</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk < ROWS; kk++) {</div>
|
|
<div class="line"><span class="lineno"> 202</span> col_vector2[kk] = A[kk][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>];</div>
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|
<div class="line"><span class="lineno"> 203</span> }</div>
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<div class="line"><span class="lineno"> 204</span> R[0][i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] = (col_vector * col_vector2).<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>();</div>
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|
<div class="line"><span class="lineno"> 205</span> }</div>
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<div class="line"><span class="lineno"> 206</span> }</div>
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<div class="line"><span class="lineno"> 207</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition</b> <a href="../../d8/d95/vector__ops_8hpp_source.html#l00232">vector_ops.hpp:232</a></div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a6d3c7dce1f142141f509d09f6c0e25dc"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">qr_algorithm::vector_proj</a></div><div class="ttdeci">std::valarray< T > vector_proj(const std::valarray< T > &a, const std::valarray< T > &b)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00104">qr_decompose.h:104</a></div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_ad16da2183db22378435042f26af43d5f"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a></div><div class="ttdeci">double vector_mag(const std::valarray< T > &a)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00092">qr_decompose.h:92</a></div></div>
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<div class="ttc" id="avector__cross__product_8cpp_html_a4b2a9757a87c18e1642d72410ecfaba8"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a></div><div class="ttdeci">double mag(const std::array< double, 3 > &vec)</div><div class="ttdoc">Calculates the magnitude of the mathematical vector from it's direction ratios.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d66/vector__cross__product_8cpp_source.html#l00083">vector_cross_product.cpp:83</a></div></div>
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