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<tr class="memdesc:d2/d3b/namespaceqr__algorithm"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of any rectangular matrix. <br /></td></tr>
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d4/d68/qr__decompose_8h_source.html
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@@ -3,7 +3,7 @@
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
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<title>Algorithms_in_C++: numerical_methods/qr_decompose.h Source File</title>
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -132,6 +137,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment"> * operator to print a matrix</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment"> */</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00033" data-start="{" data-end="}">
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#adfbdf47277c8cfee229b05b72f1f7834"> 33</a></span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;<a class="code hl_function" href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a7075a0fccad9b2d79be0275bfe8948d4">operator&lt;&lt;</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out,</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; <span class="keyword">const</span> &amp;v) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">return</span> out;</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment"></span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">/**</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment"> * operator to print a vector</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment"> */</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
@@ -164,6 +172,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span> out;</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment"></span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">/**</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> * Compute dot product of two vectors of equal lengths</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec"> 76</a></span><span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;b) {</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> (a * b).sum();</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// could also use following</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="comment"></span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">/**</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment"> * Compute magnitude of vector.</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment"> */</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordtype">double</span> dot = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, a);</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment"></span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">/**</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment"> * Compute projection of vector \f$\vec{a}\f$ on \f$\vec{b}\f$ defined as</span></div>
@@ -203,6 +216,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment"> */</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00104" data-start="{" data-end="}">
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc"> 104</a></span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a>(<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;a,</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;b) {</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordtype">double</span> num = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, b);</div>
@@ -218,6 +232,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> b * scalar;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>}</div>
</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment"></span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">/**</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> * Decompose matrix \f$A\f$ using [Gram-Schmidt</span></div>
@@ -245,6 +260,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment"> * \f}</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment"> */</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00146" data-start="{" data-end="}">
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1"> 146</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; &amp;A, <span class="comment">/**&lt; input matrix to decompose */</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a>&gt; *Q, <span class="comment">/**&lt; output decomposed matrix */</span></div>
@@ -307,6 +323,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> }</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span>}</div>
</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span>} <span class="comment">// namespace qr_algorithm</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="preprocessor">#endif </span><span class="comment">// NUMERICAL_METHODS_QR_DECOMPOSE_H_</span></div>
@@ -332,7 +349,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
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