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Documentation for c26eea874d
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realstealthninja
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<title>TheAlgorithms/C++: qr_algorithm Namespace Reference</title>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834" id="r_adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834" id="r_adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#adfbdf47277c8cfee229b05b72f1f7834">operator<<</a> (std::ostream &out, std::valarray< std::valarray< T > > const &v)</td></tr>
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<tr class="memitem:a257425cb2365359da51c6fe6741834d8" id="r_a257425cb2365359da51c6fe6741834d8"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a257425cb2365359da51c6fe6741834d8" id="r_a257425cb2365359da51c6fe6741834d8"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:a257425cb2365359da51c6fe6741834d8"><td class="memTemplItemLeft" align="right" valign="top">std::ostream & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a257425cb2365359da51c6fe6741834d8">operator<<</a> (std::ostream &out, std::valarray< T > const &v)</td></tr>
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<tr class="memitem:a8ea313a1a1b5f9d0e3e332c29c6446ec"><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a> (const std::valarray< T > &a, const std::valarray< T > &b)</td></tr>
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<tr class="memitem:ad16da2183db22378435042f26af43d5f" id="r_ad16da2183db22378435042f26af43d5f"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ad16da2183db22378435042f26af43d5f" id="r_ad16da2183db22378435042f26af43d5f"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:ad16da2183db22378435042f26af43d5f"><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#ad16da2183db22378435042f26af43d5f">vector_mag</a> (const std::valarray< T > &a)</td></tr>
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<tr class="memitem:a6d3c7dce1f142141f509d09f6c0e25dc"><td class="memTemplItemLeft" align="right" valign="top">std::valarray< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a> (const std::valarray< T > &a, const std::valarray< T > &b)</td></tr>
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<tr class="memitem:a73ce637634fc49e1d10d190eb388ebf1" id="r_a73ce637634fc49e1d10d190eb388ebf1"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:a73ce637634fc49e1d10d190eb388ebf1"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a> (const std::valarray< std::valarray< T > > &A, std::valarray< std::valarray< T > > *Q, std::valarray< std::valarray< T > > *R)</td></tr>
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<div class="line"><span class="lineno"> 123</span> A[0][i][i] -= last_eig; <span class="comment">/* A - cI */</span></div>
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<div class="line"><span class="lineno"> 124</span> }</div>
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<div class="line"><span class="lineno"> 125</span> </div>
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<div class="line"><span class="lineno"> 126</span> qr_decompose(*A, &Q, &R);</div>
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<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(*A, &Q, &R);</div>
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<div class="line"><span class="lineno"> 127</span> </div>
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<div class="line"><span class="lineno"> 128</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
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<div class="line"><span class="lineno"> 129</span> std::cout << *A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 163</span> </div>
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<div class="line"><span class="lineno"> 164</span> <span class="keywordflow">return</span> eigen_vals;</div>
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<div class="line"><span class="lineno"> 165</span>}</div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a73ce637634fc49e1d10d190eb388ebf1"><div class="ttname"><a href="#a73ce637634fc49e1d10d190eb388ebf1">qr_algorithm::qr_decompose</a></div><div class="ttdeci">void qr_decompose(const std::valarray< std::valarray< T > > &A, std::valarray< std::valarray< T > > *Q, std::valarray< std::valarray< T > > *R)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00146">qr_decompose.h:146</a></div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_abb8bf4c55e10685a5eb2ad3797fde1ae"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a></div><div class="ttdeci">void mat_mul(const std::valarray< std::valarray< double > > &A, const std::valarray< std::valarray< double > > &B, std::valarray< std::valarray< double > > *OUT)</div><div class="ttdef"><b>Definition</b> <a href="../../de/d75/qr__eigen__values_8cpp_source.html#l00054">qr_eigen_values.cpp:54</a></div></div>
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<td class="memname">void qr_algorithm::qr_decompose </td>
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<p>Decompose matrix \(A\) using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">Gram-Schmidt process</a>.</p>
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<p class="formulaDsp">
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\begin{eqnarray*}
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\text{given that}\quad A &=&
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\begin{eqnarray*} \text{given that}\quad A &=&
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*\left[\mathbf{a}_1,\mathbf{a}_2,\ldots,\mathbf{a}_{N-1},\right]\\
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\text{where}\quad\mathbf{a}_i &=&
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\left[a_{0i},a_{1i},a_{2i},\ldots,a_{(M-1)i}\right]^T\quad\ldots\mbox{(column
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0 & 0 & \langle\mathbf{e}_2\,,\mathbf{a}_2\rangle &
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\dots\\ \vdots & \vdots & \vdots & \ddots
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\end{bmatrix}\\
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition</b> <a href="../../d8/d95/vector__ops_8hpp_source.html#l00232">vector_ops.hpp:232</a></div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a6d3c7dce1f142141f509d09f6c0e25dc"><div class="ttname"><a href="#a6d3c7dce1f142141f509d09f6c0e25dc">qr_algorithm::vector_proj</a></div><div class="ttdeci">std::valarray< T > vector_proj(const std::valarray< T > &a, const std::valarray< T > &b)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00104">qr_decompose.h:104</a></div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_ad16da2183db22378435042f26af43d5f"><div class="ttname"><a href="#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a></div><div class="ttdeci">double vector_mag(const std::valarray< T > &a)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00092">qr_decompose.h:92</a></div></div>
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<div class="ttc" id="avector__cross__product_8cpp_html_a4b2a9757a87c18e1642d72410ecfaba8"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a></div><div class="ttdeci">double mag(const std::array< double, 3 > &vec)</div><div class="ttdoc">Calculates the magnitude of the mathematical vector from it's direction ratios.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d66/vector__cross__product_8cpp_source.html#l00083">vector_cross_product.cpp:83</a></div></div>
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<div class="ttc" id="avector__cross__product_8cpp_html_a4b2a9757a87c18e1642d72410ecfaba8"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a></div><div class="ttdeci">double mag(const std::array< double, 3 > &vec)</div><div class="ttdoc">Calculates the magnitude of the mathematical vector from it's direction ratios.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d66/vector__cross__product_8cpp_source.html#l00083">vector_cross_product.cpp:83</a></div></div>
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<div class="fragment"><div class="line"><span class="lineno"> 105</span> {</div>
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<div class="line"><span class="lineno"> 106</span> <span class="keywordtype">double</span> num = <a class="code hl_function" href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, b);</div>
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<div class="line"><span class="lineno"> 107</span> <span class="keywordtype">double</span> deno = <a class="code hl_function" href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(b, b);</div>
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<div class="line"><span class="lineno"> 108</span> </div>
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<div class="line"><span class="lineno"> 110</span> <span class="keywordflow">if</span> (deno <= std::numeric_limits<double>::epsilon()) {</div>
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<div class="line"><span class="lineno"> 111</span> std::cerr << <span class="stringliteral">"["</span> << __func__ << <span class="stringliteral">"] Possible division by zero\n"</span>;</div>
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<div class="line"><span class="lineno"> 112</span> <span class="keywordflow">return</span> a; <span class="comment">// return vector a back</span></div>
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<li class="navelem"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.12.0 </li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.13.2 </li>
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