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<div class="title">qr_decompose.h</div> </div>
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<a href="../../d4/d68/qr__decompose_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * @file</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * \brief Library functions to compute [QR</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of a given</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * matrix.</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * \author [Krishna Vedala](https://github.com/kvedala)</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  </div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="preprocessor">#ifndef QR_DECOMPOSE_H</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#define QR_DECOMPOSE_H</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  </div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include <math.h></span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include <stdio.h></span></div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <stdlib.h></span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <omp.h></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> * function to display matrix on stdout</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a"> 22</a></span> <span class="keywordtype">void</span> <a class="code" href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a">print_matrix</a>(<span class="keywordtype">double</span> **A, <span class="comment">/**< matrix to print */</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keywordtype">int</span> M, <span class="comment">/**< number of rows of matrix */</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keywordtype">int</span> N) <span class="comment">/**< number of columns of matrix */</span></div>
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<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 < N; 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 class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> * Compute dot product of two vectors of equal lengths</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> * If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ and</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> * \f$\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\f$ then</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> * \f$\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\f$</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05"> 43</a></span> <span class="keywordtype">double</span> <a class="code" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(<span class="keywordtype">double</span> *a, <span class="keywordtype">double</span> *b, <span class="keywordtype">int</span> <a class="code" href="../../df/db3/struct_l.html">L</a>)</div>
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<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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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> * Compute magnitude of vector.</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> * If \f$\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\f$ then</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> * \f$\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\f$</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212"> 64</a></span> <span class="keywordtype">double</span> <a class="code" href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">vector_mag</a>(<span class="keywordtype">double</span> *vector, <span class="keywordtype">int</span> <a class="code" href="../../df/db3/struct_l.html">L</a>)</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="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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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> * Compute projection of vector \f$\vec{a}\f$ on \f$\vec{b}\f$ defined as</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> * \f[\text{proj}_\vec{b}\vec{a}=\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|^2}\vec{b}\f]</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f"> 76</a></span> <span class="keywordtype">double</span> *<a class="code" href="../../d4/d68/qr__decompose_8h.html#a82b20e027437df768d7e994cf4cae29f">vector_proj</a>(<span class="keywordtype">double</span> *a, <span class="keywordtype">double</span> *b, <span class="keywordtype">double</span> *out, <span class="keywordtype">int</span> <a class="code" href="../../df/db3/struct_l.html">L</a>)</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> {</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <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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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> * Compute vector subtraction</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> * \f$\vec{c}=\vec{a}-\vec{b}\f$</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> * \returns pointer to output vector</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145"> 101</a></span> <span class="keywordtype">double</span> *<a class="code" href="../../d4/d68/qr__decompose_8h.html#a6b6a0e75e75ff7919057dd275bb69145">vector_sub</a>(<span class="keywordtype">double</span> *a, <span class="comment">/**< minuend */</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordtype">double</span> *b, <span class="comment">/**< subtrahend */</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">double</span> *out, <span class="comment">/**< resultant vector */</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">int</span> <a class="code" href="../../df/db3/struct_l.html">L</a> <span class="comment">/**< length of vectors */</span></div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> )</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <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="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment">/**</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> * Decompose matrix \f$A\f$ using [Gram-Schmidt</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> *process](https://en.wikipedia.org/wiki/QR_decomposition).</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"> *</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"> * \f{eqnarray*}{</span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> * \text{given that}\quad A &=&</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"> *\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\</span></div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment"> * \text{where}\quad\mathbf{a}_i &=&</span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment"> *\left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"> *vectors)}\\</span></div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> * \text{then}\quad\mathbf{u}_i &=& \mathbf{a}_i</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"> *-\sum_{j=0}^{i-1}\text{proj}_{\mathbf{u}_j}\mathbf{a}_i\\</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> * \mathbf{e}_i &=&\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> * Q &=& \begin{bmatrix}\mathbf{e}_0 & \mathbf{e}_1 & \mathbf{e}_2 & \dots &</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> *\mathbf{e}_{N-1}\end{bmatrix}\\</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> * R &=& \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> *\langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &</span></div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots \\</span></div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> * 0 & \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\</span></div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> * 0 & 0 & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle & \dots\\</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> * \vdots & \vdots & \vdots & \ddots</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> * \end{bmatrix}\\</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> * \f}</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56"> 142</a></span> <span class="keywordtype">void</span> <a class="code" href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56">qr_decompose</a>(<span class="keywordtype">double</span> **A, <span class="comment">/**< input matrix to decompose */</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordtype">double</span> **Q, <span class="comment">/**< output decomposed matrix */</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordtype">double</span> **R, <span class="comment">/**< output decomposed matrix */</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordtype">int</span> M, <span class="comment">/**< number of rows of matrix A */</span></div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordtype">int</span> N <span class="comment">/**< number of columns of matrix A */</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> )</div>
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<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> *)<a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(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> *)<a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(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> *)<a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(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 < N;</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>
|
|
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// parallelize on threads</span></div>
|
|
<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>
|
|
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
|
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// parallelize on threads</span></div>
|
|
<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>
|
|
<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>
|
|
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// parallelize on threads</span></div>
|
|
<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>
|
|
<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 < N; 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>  <a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(col_vector);</div>
|
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(col_vector2);</div>
|
|
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <a class="code" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(tmp_vector);</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> }</div>
|
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  </div>
|
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="preprocessor">#endif </span><span class="comment">// QR_DECOMPOSE_H</span></div>
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<div class="ttc" id="amalloc__dbg_8h_html_a725f50ecaf1959d96de79b36b4788fee"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a></div><div class="ttdeci">#define malloc(bytes)</div><div class="ttdoc">This macro replace the standard malloc function with malloc_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:18</div></div>
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<div class="ttc" id="amalloc__dbg_8h_html_a9cc854374299a1dd933bf62029761768"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a></div><div class="ttdeci">#define free(ptr)</div><div class="ttdoc">This macro replace the standard free function with free_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:26</div></div>
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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_a45c7640d9d22c89c11beb1f567843c56"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56">qr_decompose</a></div><div class="ttdeci">void qr_decompose(double **A, double **Q, double **R, int M, int N)</div><div class="ttdoc">Decompose matrix using Gram-Schmidt process.</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:142</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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<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="aqr__decompose_8h_html_a90562ce8c3707401e9c5809dece68d6a"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a">print_matrix</a></div><div class="ttdeci">void print_matrix(double **A, int M, int N)</div><div class="ttdoc">function to display matrix on stdout</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:22</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="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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