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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div id="projectbrief">All the algorithms implemented in C++</div>
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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"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#adfbdf47277c8cfee229b05b72f1f7834">operator<<</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &out, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > > const &v)</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"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a257425cb2365359da51c6fe6741834d8">operator<<</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &out, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > const &v)</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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &a, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &b)</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"><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#ad16da2183db22378435042f26af43d5f">vector_mag</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &a)</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"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a6d3c7dce1f142141f509d09f6c0e25dc">vector_proj</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &a, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &b)</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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > > &A, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > > *Q, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > > *R)</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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<tr class="memitem:a28e2fa3e803abaea6c568dc45d69d8cc" id="r_a28e2fa3e803abaea6c568dc45d69d8cc"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a28e2fa3e803abaea6c568dc45d69d8cc">eigen_values</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > > *A, bool print_intermediates=false)</td></tr>
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<tr class="memitem:a28e2fa3e803abaea6c568dc45d69d8cc" id="r_a28e2fa3e803abaea6c568dc45d69d8cc"><td class="memItemLeft" align="right" valign="top">std::valarray< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a28e2fa3e803abaea6c568dc45d69d8cc">eigen_values</a> (std::valarray< std::valarray< double > > *A, bool print_intermediates=false)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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@@ -146,9 +163,9 @@ Functions</h2></td></tr>
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<div class="memproto">
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > qr_algorithm::eigen_values </td>
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<td class="memname">std::valarray< double > qr_algorithm::eigen_values </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > > *</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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<td class="paramtype">std::valarray< std::valarray< double > > *</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00098">98</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 99</span> {</div>
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<div class="line"><span class="lineno"> 100</span> <span class="keywordtype">int</span> rows = A->size();</div>
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<div class="line"><span class="lineno"> 101</span> <span class="keywordtype">int</span> columns = rows;</div>
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<div class="line"><span class="lineno"> 102</span> <span class="keywordtype">int</span> counter = 0, num_eigs = rows - 1;</div>
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<div class="line"><span class="lineno"> 103</span> <span class="keywordtype">double</span> last_eig = 0;</div>
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<div class="line"><span class="lineno"> 104</span> </div>
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<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> Q(rows);</div>
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<div class="line"><span class="lineno"> 106</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> R(columns);</div>
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<div class="line"><span class="lineno"> 105</span> std::valarray<std::valarray<double>> Q(rows);</div>
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<div class="line"><span class="lineno"> 106</span> std::valarray<std::valarray<double>> R(columns);</div>
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<div class="line"><span class="lineno"> 107</span> </div>
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<div class="line"><span class="lineno"> 108</span> <span class="comment">/* number of eigen values = matrix size */</span></div>
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<div class="line"><span class="lineno"> 109</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eigen_vals(rows);</div>
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<div class="line"><span class="lineno"> 109</span> std::valarray<double> eigen_vals(rows);</div>
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<div class="line"><span class="lineno"> 110</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
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<div class="line"><span class="lineno"> 111</span> Q[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a>(columns);</div>
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<div class="line"><span class="lineno"> 112</span> R[i] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a>(columns);</div>
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<div class="line"><span class="lineno"> 111</span> Q[i] = std::valarray<double>(columns);</div>
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<div class="line"><span class="lineno"> 112</span> R[i] = std::valarray<double>(columns);</div>
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<div class="line"><span class="lineno"> 113</span> }</div>
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<div class="line"><span class="lineno"> 114</span> </div>
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<div class="line"><span class="lineno"> 115</span> <span class="comment">/* continue till all eigen values are found */</span></div>
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<div class="line"><span class="lineno"> 116</span> <span class="keywordflow">while</span> (num_eigs > 0) {</div>
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<div class="line"><span class="lineno"> 117</span> <span class="comment">/* iterate with QR decomposition */</span></div>
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<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">while</span> (std::abs(A[0][num_eigs][num_eigs - 1]) ></div>
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<div class="line"><span class="lineno"> 119</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits<double>::epsilon</a>()) {</div>
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<div class="line"><span class="lineno"> 119</span> std::numeric_limits<double>::epsilon()) {</div>
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<div class="line"><span class="lineno"> 120</span> <span class="comment">// initial approximation = last diagonal element</span></div>
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<div class="line"><span class="lineno"> 121</span> last_eig = A[0][num_eigs][num_eigs];</div>
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<div class="line"><span class="lineno"> 122</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
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@@ -213,10 +232,10 @@ Functions</h2></td></tr>
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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"> 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> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << *A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << Q << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << R << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 132</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">printf</a>(<span class="stringliteral">"-------------------- %d ---------------------\n"</span>,</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"> 130</span> std::cout << Q << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 131</span> std::cout << R << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 132</span> printf(<span class="stringliteral">"-------------------- %d ---------------------\n"</span>,</div>
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<div class="line"><span class="lineno"> 133</span> ++counter);</div>
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||||
<div class="line"><span class="lineno"> 134</span> }</div>
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<div class="line"><span class="lineno"> 135</span> </div>
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@@ -232,9 +251,9 @@ Functions</h2></td></tr>
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||||
<div class="line"><span class="lineno"> 145</span> eigen_vals[num_eigs] = last_eig;</div>
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<div class="line"><span class="lineno"> 146</span> <span class="comment">// A[0][num_eigs][num_eigs];</span></div>
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<div class="line"><span class="lineno"> 147</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
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<div class="line"><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"========================\n"</span>;</div>
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<div class="line"><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Eigen value: "</span> << last_eig << <span class="stringliteral">",\n"</span>;</div>
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<div class="line"><span class="lineno"> 150</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"========================\n"</span>;</div>
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<div class="line"><span class="lineno"> 148</span> std::cout << <span class="stringliteral">"========================\n"</span>;</div>
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<div class="line"><span class="lineno"> 149</span> std::cout << <span class="stringliteral">"Eigen value: "</span> << last_eig << <span class="stringliteral">",\n"</span>;</div>
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<div class="line"><span class="lineno"> 150</span> std::cout << <span class="stringliteral">"========================\n"</span>;</div>
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<div class="line"><span class="lineno"> 151</span> }</div>
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<div class="line"><span class="lineno"> 152</span> </div>
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<div class="line"><span class="lineno"> 153</span> num_eigs--;</div>
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<div class="line"><span class="lineno"> 157</span> eigen_vals[0] = A[0][0][0];</div>
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<div class="line"><span class="lineno"> 158</span> </div>
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<div class="line"><span class="lineno"> 159</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
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<div class="line"><span class="lineno"> 160</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << Q << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 161</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << R << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 160</span> std::cout << Q << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 161</span> std::cout << R << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 162</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="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="afprintf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::printf</a></div><div class="ttdeci">T printf(T... args)</div></div>
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<div class="ttc" id="anumeric_limits_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</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> qr_eigen_values.cpp:54</div></div>
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<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</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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@@ -272,43 +282,35 @@ Here is the call graph for this function:</div>
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template<typename T > </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> & qr_algorithm::operator<< </td>
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<td class="memname">std::ostream & qr_algorithm::operator<< </td>
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||||
<td>(</td>
|
||||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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<td class="paramtype">std::ostream &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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<td class="paramkey"></td>
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||||
<td></td>
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||||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
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||||
<td class="paramtype">std::valarray< std::valarray< T > > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
|
||||
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||||
</table>
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||||
</div><div class="memdoc">
|
||||
<p>operator to print a matrix </p>
|
||||
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||||
<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00033">33</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 34</span> {</div>
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<div class="line"><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"><span class="lineno"> 36</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">' '</span>;</div>
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<div class="line"><span class="lineno"> 37</span> </div>
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<div class="line"><span class="lineno"> 38</span> out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
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||||
<div class="line"><span class="lineno"> 38</span> out.precision(4);</div>
|
||||
<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row < v.size(); row++) {</div>
|
||||
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col < v[row].size(); col++)</div>
|
||||
<div class="line"><span class="lineno"> 41</span> out << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
|
||||
<div class="line"><span class="lineno"> 41</span> out << std::right << std::setw(width) << std::setfill(separator)</div>
|
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<div class="line"><span class="lineno"> 42</span> << v[row][col];</div>
|
||||
<div class="line"><span class="lineno"> 43</span> out << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><span class="lineno"> 43</span> out << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 44</span> }</div>
|
||||
<div class="line"><span class="lineno"> 45</span> </div>
|
||||
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">return</span> out;</div>
|
||||
<div class="line"><span class="lineno"> 47</span>}</div>
|
||||
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a></div><div class="ttdeci">T right(T... args)</div></div>
|
||||
<div class="ttc" id="aprecision_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">std::ostream::precision</a></div><div class="ttdeci">T precision(T... args)</div></div>
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<div class="ttc" id="asetfill_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a></div><div class="ttdeci">T setfill(T... args)</div></div>
|
||||
<div class="ttc" id="asetw_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a></div><div class="ttdeci">T setw(T... args)</div></div>
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template<typename T > </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> & qr_algorithm::operator<< </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
|
||||
<td class="paramtype">std::ostream &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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||||
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||||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
|
||||
<td class="paramtype">std::valarray< T > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
|
||||
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||||
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|
||||
<p>operator to print a vector </p>
|
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00053">53</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 53</span> {</div>
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<div class="line"><span class="lineno"> 54</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
|
||||
<div class="line"><span class="lineno"> 55</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">' '</span>;</div>
|
||||
<div class="line"><span class="lineno"> 56</span> </div>
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||||
<div class="line"><span class="lineno"> 57</span> out.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/precision.html">precision</a>(4);</div>
|
||||
<div class="line"><span class="lineno"> 57</span> out.precision(4);</div>
|
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<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row < v.size(); row++) {</div>
|
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<div class="line"><span class="lineno"> 59</span> out << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::right</a> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
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||||
<div class="line"><span class="lineno"> 59</span> out << std::right << std::setw(width) << std::setfill(separator)</div>
|
||||
<div class="line"><span class="lineno"> 60</span> << v[row];</div>
|
||||
<div class="line"><span class="lineno"> 61</span> }</div>
|
||||
<div class="line"><span class="lineno"> 62</span> </div>
|
||||
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span> out;</div>
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<td>(</td>
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|
||||
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|
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00146">146</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 150</span> {</div>
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<div class="line"><span class="lineno"> 151</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> ROWS = A.size(); <span class="comment">// number of rows of A</span></div>
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<div class="line"><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> COLUMNS = A[0].size(); <span class="comment">// number of columns of A</span></div>
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<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<T></a> col_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<T></a> col_vector2(ROWS);</div>
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<div class="line"><span class="lineno"> 155</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<T></a> tmp_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 151</span> std::size_t ROWS = A.size(); <span class="comment">// number of rows of A</span></div>
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<div class="line"><span class="lineno"> 152</span> std::size_t COLUMNS = A[0].size(); <span class="comment">// number of columns of A</span></div>
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<div class="line"><span class="lineno"> 153</span> std::valarray<T> col_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 155</span> std::valarray<T> tmp_vector(ROWS);</div>
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<div class="line"><span class="lineno"> 156</span> </div>
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<div class="line"><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < COLUMNS; i++) {</div>
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<div class="line"><span class="lineno"> 158</span> <span class="comment">/* for each column => R is a square matrix of NxN */</span></div>
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@@ -466,18 +467,12 @@ template<typename T > </div>
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<div class="line"><span class="lineno"> 205</span> }</div>
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<div class="line"><span class="lineno"> 206</span> }</div>
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<div class="line"><span class="lineno"> 207</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:117</div></div>
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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> vector_ops.hpp:232</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> qr_decompose.h:104</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> qr_decompose.h:92</div></div>
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<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</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> vector_cross_product.cpp:83</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d2/d3b/namespaceqr__algorithm_a73ce637634fc49e1d10d190eb388ebf1_cgraph.svg" width="622" height="86"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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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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@@ -494,12 +489,12 @@ template<typename T > </div>
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<tr>
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<td class="memname">double qr_algorithm::vector_dot </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<td class="paramtype">const std::valarray< T > &</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &</td> <td class="paramname"><span class="paramname"><em>b</em></span> )</td>
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<td class="paramtype">const std::valarray< T > &</td> <td class="paramname"><span class="paramname"><em>b</em></span> )</td>
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</tr>
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@@ -511,6 +506,8 @@ template<typename T > </div>
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||||
<p>Compute dot product of two vectors of equal lengths</p>
|
||||
<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) and \(\vec{b}=\left[b_0,b_1,b_1,...,b_L\right]\) then \(\vec{a}\cdot\vec{b}=\displaystyle\sum_{i=0}^L a_i\times b_i\)</p>
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||||
<dl class="section return"><dt>Returns</dt><dd>\(\vec{a}\cdot\vec{b}\) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00076">76</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
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||||
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">return</span> (a * b).sum();</div>
|
||||
<div class="line"><span class="lineno"> 78</span> <span class="comment">// could also use following</span></div>
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@@ -534,7 +531,7 @@ template<typename T > </div>
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||||
<tr>
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||||
<td class="memname">double qr_algorithm::vector_mag </td>
|
||||
<td>(</td>
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||||
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
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<td class="paramtype">const std::valarray< T > &</td> <td class="paramname"><span class="paramname"><em>a</em></span></td><td>)</td>
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@@ -547,18 +544,14 @@ template<typename T > </div>
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||||
<p>Compute magnitude of vector.</p>
|
||||
<p>If \(\vec{a}=\left[a_0,a_1,a_2,...,a_L\right]\) then \(\left|\vec{a}\right|=\sqrt{\displaystyle\sum_{i=0}^L a_i^2}\)</p>
|
||||
<dl class="section return"><dt>Returns</dt><dd>\(\left|\vec{a}\right|\) </dd></dl>
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||||
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||||
<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00092">92</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 92</span> {</div>
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<div class="line"><span class="lineno"> 93</span> <span class="keywordtype">double</span> dot = <a class="code hl_function" href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, a);</div>
|
||||
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(dot);</div>
|
||||
<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">return</span> std::sqrt(dot);</div>
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||||
<div class="line"><span class="lineno"> 95</span>}</div>
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||||
<div class="ttc" id="anamespaceqr__algorithm_html_a8ea313a1a1b5f9d0e3e332c29c6446ec"><div class="ttname"><a href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm::vector_dot</a></div><div class="ttdeci">double vector_dot(const std::valarray< T > &a, const std::valarray< T > &b)</div><div class="ttdef"><b>Definition</b> qr_decompose.h:76</div></div>
|
||||
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a8ea313a1a1b5f9d0e3e332c29c6446ec"><div class="ttname"><a href="#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm::vector_dot</a></div><div class="ttdeci">double vector_dot(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#l00076">qr_decompose.h:76</a></div></div>
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template<typename T > </div>
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<table class="memname">
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > qr_algorithm::vector_proj </td>
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<td class="memname">std::valarray< T > qr_algorithm::vector_proj </td>
|
||||
<td>(</td>
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||||
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< T > &</td> <td class="paramname"><span class="paramname"><em>b</em></span> )</td>
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<td class="paramtype">const std::valarray< T > &</td> <td class="paramname"><span class="paramname"><em>b</em></span> )</td>
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@@ -586,13 +579,14 @@ template<typename T > </div>
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</p>
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<dl class="section return"><dt>Returns</dt><dd>NULL if error, otherwise pointer to output </dd></dl>
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<p>check for division by zero using machine epsilon</p>
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<p class="definition">Definition at line <a class="el" href="../../d4/d68/qr__decompose_8h_source.html#l00104">104</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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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>
|
||||
<div class="line"><span class="lineno"> 108</span><span class="comment"></span> </div>
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<div class="line"><span class="lineno"> 109</span><span class="comment"> /*! check for division by zero using machine epsilon */</span></div>
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<div class="line"><span class="lineno"> 110</span> <span class="keywordflow">if</span> (deno <= <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits<double>::epsilon</a>()) {</div>
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<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> << <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"> 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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<div class="line"><span class="lineno"> 113</span> }</div>
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<div class="line"><span class="lineno"> 114</span> </div>
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@@ -600,12 +594,7 @@ template<typename T > </div>
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<div class="line"><span class="lineno"> 116</span> </div>
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<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> b * scalar;</div>
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<div class="line"><span class="lineno"> 118</span>}</div>
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