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<div class="title">qr_decompose.h File Reference</div> </div>
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<div class="contents">
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<p>Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">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 <math.h></code><br />
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<code>#include <stdio.h></code><br />
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<code>#include <stdlib.h></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for qr_decompose.h:</div>
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<p><a href="../../d4/d68/qr__decompose_8h_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 name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a90562ce8c3707401e9c5809dece68d6a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a">print_matrix</a> (double **A, int M, int <a class="el" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>)</td></tr>
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<tr class="memdesc:a90562ce8c3707401e9c5809dece68d6a"><td class="mdescLeft"> </td><td class="mdescRight">function to display matrix on stdout <a href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a">More...</a><br /></td></tr>
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<tr class="separator:a90562ce8c3707401e9c5809dece68d6a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3a584b79941a43d775f9d4ce446dbe05"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a> (double *a, double *b, int <a class="el" href="../../df/db3/struct_l.html">L</a>)</td></tr>
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<tr class="memdesc:a3a584b79941a43d775f9d4ce446dbe05"><td class="mdescLeft"> </td><td class="mdescRight">Compute dot product of two vectors of equal lengths. <a href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">More...</a><br /></td></tr>
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<tr class="separator:a3a584b79941a43d775f9d4ce446dbe05"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:abeec1f78a7a7e7251687e75340331212"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">vector_mag</a> (double *vector, int <a class="el" href="../../df/db3/struct_l.html">L</a>)</td></tr>
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<tr class="memdesc:abeec1f78a7a7e7251687e75340331212"><td class="mdescLeft"> </td><td class="mdescRight">Compute magnitude of vector. <a href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">More...</a><br /></td></tr>
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<tr class="separator:abeec1f78a7a7e7251687e75340331212"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a82b20e027437df768d7e994cf4cae29f"><td class="memItemLeft" align="right" valign="top">double * </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f">vector_proj</a> (double *a, double *b, double *out, int <a class="el" href="../../df/db3/struct_l.html">L</a>)</td></tr>
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<tr class="memdesc:a82b20e027437df768d7e994cf4cae29f"><td class="mdescLeft"> </td><td class="mdescRight">Compute projection of vector \(\vec{a}\) on \(\vec{b}\) defined as. <a href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f">More...</a><br /></td></tr>
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<tr class="separator:a82b20e027437df768d7e994cf4cae29f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6b6a0e75e75ff7919057dd275bb69145"><td class="memItemLeft" align="right" valign="top">double * </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145">vector_sub</a> (double *a, double *b, double *out, int <a class="el" href="../../df/db3/struct_l.html">L</a>)</td></tr>
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<tr class="memdesc:a6b6a0e75e75ff7919057dd275bb69145"><td class="mdescLeft"> </td><td class="mdescRight">Compute vector subtraction. <a href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145">More...</a><br /></td></tr>
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<tr class="separator:a6b6a0e75e75ff7919057dd275bb69145"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a45c7640d9d22c89c11beb1f567843c56"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56">qr_decompose</a> (double **A, double **Q, double **R, int M, int <a class="el" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>)</td></tr>
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<tr class="memdesc:a45c7640d9d22c89c11beb1f567843c56"><td class="mdescLeft"> </td><td class="mdescRight">Decompose matrix \(A\) using <a href="https://en.wikipedia.org/wiki/QR_decomposition">Gram-Schmidt process</a>. <a href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56">More...</a><br /></td></tr>
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<tr class="separator:a45c7640d9d22c89c11beb1f567843c56"><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>Library functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition">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">Krishna Vedala</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a90562ce8c3707401e9c5809dece68d6a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a90562ce8c3707401e9c5809dece68d6a">◆ </a></span>print_matrix()</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 print_matrix </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>M</em>, </td>
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<td class="paramkey"></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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<td></td>
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<td>)</td>
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<td></td><td></td>
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</table>
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</div><div class="memdoc">
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<p>function to display matrix on stdout </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>matrix to print </td></tr>
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<tr><td class="paramname">M</td><td>number of rows of matrix </td></tr>
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<tr><td class="paramname">N</td><td>number of columns of matrix </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="l00025"></a><span class="lineno"> 25</span> {</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row < M; row++)</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  {</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col < <a class="code" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>; col++) printf(<span class="stringliteral">"% 9.3g\t"</span>, A[row][col]);</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  putchar(<span class="charliteral">'\n'</span>);</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  }</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  putchar(<span class="charliteral">'\n'</span>);</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a45c7640d9d22c89c11beb1f567843c56"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a45c7640d9d22c89c11beb1f567843c56">◆ </a></span>qr_decompose()</h2>
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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 qr_decompose </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>Q</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>R</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">int </td>
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<td class="paramname"><em>M</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">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>Decompose matrix \(A\) using <a href="https://en.wikipedia.org/wiki/QR_decomposition">Gram-Schmidt process</a>. </p>
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<p class="formulaDsp">
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\begin{eqnarray*} \text{given that}\quad A &=& *\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\ \text{where}\quad\mathbf{a}_i &=& *\left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column *vectors)}\\ \text{then}\quad\mathbf{u}_i &=& \mathbf{a}_i *-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\ \mathbf{e}_i &=&\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\ Q &=& \begin{bmatrix}\mathbf{e}_0 & \mathbf{e}_1 & \mathbf{e}_2 & \dots & *\mathbf{e}_{N-1}\end{bmatrix}\\ R &=& \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle & *\langle\mathbf{e}_1\,,\mathbf{a}_1\rangle & *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots \\ 0 & \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle & *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\ 0 & 0 & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\ \vdots & \vdots & \vdots & \ddots \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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<tr><td class="paramname">M</td><td>number of rows of matrix A </td></tr>
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<tr><td class="paramname">N</td><td>number of columns of matrix A </td></tr>
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</table>
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</dd>
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<div class="fragment"><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> {</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordtype">double</span> *col_vector = (<span class="keywordtype">double</span> *)malloc(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordtype">double</span> *col_vector2 = (<span class="keywordtype">double</span> *)malloc(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordtype">double</span> *tmp_vector = (<span class="keywordtype">double</span> *)malloc(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</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>;</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  i++) <span class="comment">/* for each column => R is a square matrix of NxN */</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  {</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordtype">int</span> j;</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">for</span> (j = 0; j < i; j++) <span class="comment">/* second dimension of column */</span></div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  R[i][j] = 0.; <span class="comment">/* make R upper triangular */</span></div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  </div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">/* get corresponding Q vector */</span></div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">for</span> (j = 0; j < M; j++)</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  {</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  col_vector[j] = A[j][i];</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  }</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">for</span> (j = 0; j < i; j++)</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  {</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < M; k++) col_vector2[k] = Q[k][j];</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f">vector_proj</a>(col_vector, col_vector2, col_vector2, M);</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <a class="code" href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145">vector_sub</a>(tmp_vector, col_vector2, tmp_vector, M);</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordtype">double</span> mag = <a class="code" href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">vector_mag</a>(tmp_vector, M);</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">for</span> (j = 0; j < M; j++) Q[j][i] = tmp_vector[j] / mag;</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">/* compute upper triangular values of R */</span></div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk < M; kk++) col_vector[kk] = Q[kk][i];</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; k < <a class="code" href="../../db/d01/problem__13_2sol1_8c.html#a0240ac851181b84ac374872dc5434ee4">N</a>; k++)</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  {</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk < M; kk++) col_vector2[kk] = A[kk][k];</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  R[i][k] = <a class="code" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(col_vector, col_vector2, M);</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  }</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  }</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  </div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  free(col_vector);</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  free(col_vector2);</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  free(tmp_vector);</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3a584b79941a43d775f9d4ce446dbe05">◆ </a></span>vector_dot()</h2>
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<td class="memname">double vector_dot </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="paramtype">double * </td>
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<p>Compute dot product of two vectors of equal lengths. </p>
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<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) and \(\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\) then \(\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\)</p>
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<dl class="section return"><dt>Returns</dt><dd>\(\vec{a}\cdot\vec{b}\) </dd></dl>
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<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordtype">double</span> mag = 0.f;</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordtype">int</span> i;</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#pragma omp parallel for reduction(+ : mag)</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../df/db3/struct_l.html">L</a>; i++) mag += a[i] * b[i];</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>  <span class="keywordflow">return</span> mag;</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#abeec1f78a7a7e7251687e75340331212">◆ </a></span>vector_mag()</h2>
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<td class="memname">double vector_mag </td>
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<td class="paramname"><em>vector</em>, </td>
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<p>Compute magnitude of vector. </p>
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<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) then \(\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\)</p>
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<dl class="section return"><dt>Returns</dt><dd>\(\left|\vec{a}\right|\) </dd></dl>
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<div class="fragment"><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="keywordtype">double</span> dot = <a class="code" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(vector, vector, <a class="code" href="../../df/db3/struct_l.html">L</a>);</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">return</span> sqrt(dot);</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a82b20e027437df768d7e994cf4cae29f">◆ </a></span>vector_proj()</h2>
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<td class="memname">double* vector_proj </td>
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<p>Compute projection of vector \(\vec{a}\) on \(\vec{b}\) defined as. </p>
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<p class="formulaDsp">
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\[\text{proj}_\vec{b}\vec{a}=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|^2}\vec{b}\]
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</p>
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<dl class="section return"><dt>Returns</dt><dd>NULL if error, otherwise pointer to output </dd></dl>
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<p>check for division by zero</p>
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<div class="fragment"><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>  <span class="keyword">const</span> <span class="keywordtype">double</span> num = <a class="code" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(a, b, <a class="code" href="../../df/db3/struct_l.html">L</a>);</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> deno = <a class="code" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(b, b, <a class="code" href="../../df/db3/struct_l.html">L</a>);</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> (deno == 0) <span class="comment">/*! check for division by zero */</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">return</span> NULL;</div>
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<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="keyword">const</span> <span class="keywordtype">double</span> scalar = num / deno;</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">int</span> i;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../df/db3/struct_l.html">L</a>; i++) out[i] = scalar * b[i];</div>
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<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>  <span class="keywordflow">return</span> out;</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6b6a0e75e75ff7919057dd275bb69145">◆ </a></span>vector_sub()</h2>
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<p>Compute vector subtraction. </p>
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<p>\(\vec{c}=\vec{a}-\vec{b}\)</p>
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<dl class="section return"><dt>Returns</dt><dd>pointer to output vector </dd></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>minuend </td></tr>
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<tr><td class="paramname">b</td><td>subtrahend </td></tr>
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<tr><td class="paramname">out</td><td>resultant vector </td></tr>
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<tr><td class="paramname"><a class="el" href="../../df/db3/struct_l.html">L</a></td><td>length of vectors </td></tr>
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<div class="fragment"><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>  <span class="keywordtype">int</span> i;</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// parallelize on threads</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../df/db3/struct_l.html">L</a>; i++) out[i] = a[i] - b[i];</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  </div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">return</span> out;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> }</div>
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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="aqr__decompose_8h_html_abeec1f78a7a7e7251687e75340331212"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">vector_mag</a></div><div class="ttdeci">double vector_mag(double *vector, int L)</div><div class="ttdoc">Compute magnitude of vector.</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:64</div></div>
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<div class="ttc" id="aqr__decompose_8h_html_a82b20e027437df768d7e994cf4cae29f"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f">vector_proj</a></div><div class="ttdeci">double * vector_proj(double *a, double *b, double *out, int L)</div><div class="ttdoc">Compute projection of vector on defined as.</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:76</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="ttdoc">number of digits of the large number</div><div class="ttdef"><b>Definition:</b> sol1.c:109</div></div>
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<div class="ttc" id="aqr__decompose_8h_html_a3a584b79941a43d775f9d4ce446dbe05"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a></div><div class="ttdeci">double vector_dot(double *a, double *b, int L)</div><div class="ttdoc">Compute dot product of two vectors of equal lengths.</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:43</div></div>
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<div class="ttc" id="aqr__decompose_8h_html_a6b6a0e75e75ff7919057dd275bb69145"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145">vector_sub</a></div><div class="ttdeci">double * vector_sub(double *a, double *b, double *out, int L)</div><div class="ttdoc">Compute vector subtraction.</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:101</div></div>
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