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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 id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/**</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * @file</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * \brief Library functions to compute [QR</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of a given</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * matrix.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * \author [Krishna Vedala](https://github.com/kvedala)</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> */</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span> </div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#ifndef QR_DECOMPOSE_H</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#define QR_DECOMPOSE_H</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;math.h&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;stdio.h&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;stdlib.h&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"></span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">/**</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment"> * function to display matrix on stdout</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment"> */</span></div>
<div class="line"><a id="l00022" 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 hl_function" href="../../d4/d68/qr__decompose_8h.html#a90562ce8c3707401e9c5809dece68d6a">print_matrix</a>(<span class="keywordtype">double</span> **A, <span class="comment">/**&lt; matrix to print */</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordtype">int</span> M, <span class="comment">/**&lt; number of rows of matrix */</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordtype">int</span> N) <span class="comment">/**&lt; number of columns of matrix */</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span>{</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row = 0; row &lt; M; row++)</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col = 0; col &lt; N; col++) printf(<span class="stringliteral">&quot;% 9.3g\t&quot;</span>, A[row][col]);</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> putchar(<span class="charliteral">&#39;\n&#39;</span>);</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> }</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> putchar(<span class="charliteral">&#39;\n&#39;</span>);</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span>}</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment"></span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">/**</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment"> * Compute dot product of two vectors of equal lengths</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment"> *</span></div>
<div class="line"><a id="l00037" 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>
<div class="line"><a id="l00038" 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>
<div class="line"><a id="l00039" 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>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment"> *</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment"> */</span></div>
<div class="line"><a id="l00043" 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 hl_function" 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 hl_struct" href="../../df/db3/struct_l.html">L</a>)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span>{</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">double</span> mag = 0.f;</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordtype">int</span> i;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor">#pragma omp parallel for reduction(+ : mag)</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>; i++) mag += a[i] * b[i];</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> mag;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>}</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment"></span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">/**</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"> * Compute magnitude of vector.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment"> *</span></div>
<div class="line"><a id="l00059" 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>
<div class="line"><a id="l00060" 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>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment"> *</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment"> */</span></div>
<div class="line"><a id="l00064" 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 hl_function" 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 hl_struct" href="../../df/db3/struct_l.html">L</a>)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>{</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordtype">double</span> dot = <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(vector, vector, <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">return</span> sqrt(dot);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span>}</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment"></span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">/**</span></div>
<div class="line"><a id="l00071" 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>
<div class="line"><a id="l00072" 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>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment"> *</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment"> */</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a2ed4977f38642dca8b10c16a823c740b"> 76</a></span><span class="keywordtype">double</span> *<a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a2ed4977f38642dca8b10c16a823c740b">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 hl_struct" href="../../df/db3/struct_l.html">L</a>)</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>{</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">const</span> <span class="keywordtype">double</span> num = <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(a, b, <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">const</span> <span class="keywordtype">double</span> deno = <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(b, b, <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>);</div>
<div class="line"><a id="l00080" 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>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">return</span> NULL;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">const</span> <span class="keywordtype">double</span> scalar = num / deno;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordtype">int</span> i;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>; i++) out[i] = scalar * b[i];</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment"></span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">/**</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment"> * Compute vector subtraction</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment"> *</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment"> * \f$\vec{c}=\vec{a}-\vec{b}\f$</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment"> *</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment"> * \returns pointer to output vector</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment"> */</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="../../d4/d68/qr__decompose_8h.html#a5ee39e7c8fce8a604dcf7009ce101c02"> 101</a></span><span class="keywordtype">double</span> *<a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a5ee39e7c8fce8a604dcf7009ce101c02">vector_sub</a>(<span class="keywordtype">double</span> *a, <span class="comment">/**&lt; minuend */</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">double</span> *b, <span class="comment">/**&lt; subtrahend */</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">double</span> *out, <span class="comment">/**&lt; resultant vector */</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordtype">int</span> <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a> <span class="comment">/**&lt; length of vectors */</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>)</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span>{</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">int</span> i;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_struct" href="../../df/db3/struct_l.html">L</a>; i++) out[i] = a[i] - b[i];</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="comment"></span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">/**</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment"> * Decompose matrix \f$A\f$ using [Gram-Schmidt</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"> *process](https://en.wikipedia.org/wiki/QR_decomposition).</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment"> *</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> * \f{eqnarray*}{</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment"> * \text{given that}\quad A &amp;=&amp;</span></div>
<div class="line"><a id="l00123" 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>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment"> * \text{where}\quad\mathbf{a}_i &amp;=&amp;</span></div>
<div class="line"><a id="l00125" 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>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment"> *vectors)}\\</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment"> * \text{then}\quad\mathbf{u}_i &amp;=&amp; \mathbf{a}_i</span></div>
<div class="line"><a id="l00128" 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>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment"> * \mathbf{e}_i &amp;=&amp;\frac{\mathbf{u}_i}{\left|\mathbf{u}_i\right|}\\</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment"> * Q &amp;=&amp; \begin{bmatrix}\mathbf{e}_0 &amp; \mathbf{e}_1 &amp; \mathbf{e}_2 &amp; \dots &amp;</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment"> *\mathbf{e}_{N-1}\end{bmatrix}\\</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="comment"> * R &amp;=&amp; \begin{bmatrix}\langle\mathbf{e}_0\,,\mathbf{a}_0\rangle &amp;</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="comment"> *\langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="comment"> *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots \\</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="comment"> * 0 &amp; \langle\mathbf{e}_1\,,\mathbf{a}_1\rangle &amp;</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="comment"> *\langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\</span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment"> * 0 &amp; 0 &amp; \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &amp; \dots\\</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment"> * \vdots &amp; \vdots &amp; \vdots &amp; \ddots</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="comment"> * \end{bmatrix}\\</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment"> * \f}</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment"> */</span></div>
<div class="line"><a id="l00142" 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 hl_function" href="../../d4/d68/qr__decompose_8h.html#a45c7640d9d22c89c11beb1f567843c56">qr_decompose</a>(<span class="keywordtype">double</span> **A, <span class="comment">/**&lt; input matrix to decompose */</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordtype">double</span> **Q, <span class="comment">/**&lt; output decomposed matrix */</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordtype">double</span> **R, <span class="comment">/**&lt; output decomposed matrix */</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordtype">int</span> M, <span class="comment">/**&lt; number of rows of matrix A */</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordtype">int</span> N <span class="comment">/**&lt; number of columns of matrix A */</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span>)</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span>{</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordtype">double</span> *col_vector = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordtype">double</span> *col_vector2 = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">double</span> *tmp_vector = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(M * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> i++) <span class="comment">/* for each column =&gt; R is a square matrix of NxN */</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> {</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordtype">int</span> j;</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) <span class="comment">/* second dimension of column */</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> R[i][j] = 0.; <span class="comment">/* make R upper triangular */</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">/* get corresponding Q vector */</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">for</span> (j = 0; j &lt; M; j++)</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> {</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> tmp_vector[j] = A[j][i]; <span class="comment">/* accumulator for uk */</span></div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> col_vector[j] = A[j][i];</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">for</span> (j = 0; j &lt; i; j++)</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> {</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; M; k++) col_vector2[k] = Q[k][j];</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a2ed4977f38642dca8b10c16a823c740b">vector_proj</a>(col_vector, col_vector2, col_vector2, M);</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a5ee39e7c8fce8a604dcf7009ce101c02">vector_sub</a>(tmp_vector, col_vector2, tmp_vector, M);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> }</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordtype">double</span> mag = <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#abeec1f78a7a7e7251687e75340331212">vector_mag</a>(tmp_vector, M);</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="comment">// parallelize on threads</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordflow">for</span> (j = 0; j &lt; M; j++) Q[j][i] = tmp_vector[j] / mag;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">/* compute upper triangular values of R */</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; M; kk++) col_vector[kk] = Q[kk][i];</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; k &lt; N; k++)</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> {</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; M; kk++) col_vector2[kk] = A[kk][k];</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> R[i][k] = <a class="code hl_function" href="../../d4/d68/qr__decompose_8h.html#a3a584b79941a43d775f9d4ce446dbe05">vector_dot</a>(col_vector, col_vector2, M);</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> }</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(col_vector);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(col_vector2);</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(tmp_vector);</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span>}</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="preprocessor">#endif </span><span class="comment">// QR_DECOMPOSE_H</span></div>
<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>
<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>
<div class="ttc" id="aqr__decompose_8h_html_a2ed4977f38642dca8b10c16a823c740b"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a2ed4977f38642dca8b10c16a823c740b">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>
<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>
<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>
<div class="ttc" id="aqr__decompose_8h_html_a5ee39e7c8fce8a604dcf7009ce101c02"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html#a5ee39e7c8fce8a604dcf7009ce101c02">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>
<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>
<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>
<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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