backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-07-27 08:51:41 +08:00
Code Issues Projects Releases Wiki Activity

Documentation for 8476290081

Browse Source
This commit is contained in:
github-actions
2020-06-24 22:53:44 +00:00
parent 49f2865ffd
commit 87398be5d8
547 changed files with 9502 additions and 7787 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
d4/d68/qr__decompose_8h.html
View File

@@ -137,13 +137,13 @@ Functions</h2></td></tr>
<tr class="memitem:a240edf2b6b5942c0e5f2c9d3e326797f"><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> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a240edf2b6b5942c0e5f2c9d3e326797f">qr_algorithm::operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; const &amp;v)</td></tr>
<tr class="separator:a240edf2b6b5942c0e5f2c9d3e326797f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8ea313a1a1b5f9d0e3e332c29c6446ec"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a8ea313a1a1b5f9d0e3e332c29c6446ec"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm::vector_dot</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;b)</td></tr>
<tr class="memitem:a8ea313a1a1b5f9d0e3e332c29c6446ec"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm::vector_dot</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;a, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;b)</td></tr>
<tr class="separator:a8ea313a1a1b5f9d0e3e332c29c6446ec"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad16da2183db22378435042f26af43d5f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ad16da2183db22378435042f26af43d5f"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>)</td></tr>
<tr class="memitem:ad16da2183db22378435042f26af43d5f"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;a)</td></tr>
<tr class="separator:ad16da2183db22378435042f26af43d5f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5422c76bfa322620de611083bd518d71"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a5422c76bfa322620de611083bd518d71"><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>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm::vector_proj</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;<a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;b)</td></tr>
<tr class="memitem:a5422c76bfa322620de611083bd518d71"><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>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm::vector_proj</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;a, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &amp;b)</td></tr>
<tr class="separator:a5422c76bfa322620de611083bd518d71"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab1ac74497ffb2101040cc1efe3546de8"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab1ac74497ffb2101040cc1efe3546de8"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_algorithm::qr_decompose</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; &amp;A, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *Q, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt;&gt; *R)</td></tr>
@@ -158,7 +158,7 @@ Functions</h2></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d4/d68/qr__decompose_8h.html">qr_decompose.h</a></li>
<li class="footer">Generated on Wed Jun 24 2020 22:45:08 for Algorithms_in_C++ by
<li class="footer">Generated on Wed Jun 24 2020 22:52:56 for Algorithms_in_C++ by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
</ul>

31
d4/d68/qr__decompose_8h_source.html
View File

@@ -169,8 +169,8 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment"> * \returns \f$\vec{a}\cdot\vec{b}\f$</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec"> 76</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <span class="keyword">const</span> <a class="codeRef" 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 name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a> * b).sum();</div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec"> 76</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<span class="keyword">const</span> <a class="codeRef" 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="codeRef" 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 name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> (a * b).sum();</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// could also use following</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="comment">// return std::inner_product(std::begin(a), std::end(a), std::begin(b),</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="comment">// 0.f);</span></div>
@@ -185,8 +185,8 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="comment"> * \returns \f$\left|\vec{a}\right|\f$</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f"> 92</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>) {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordtype">double</span> dot = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>);</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f"> 92</a></span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(<span class="keyword">const</span> <a class="codeRef" 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 name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordtype">double</span> dot = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, a);</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(dot);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160;}</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;<span class="comment"></span> </div>
@@ -197,15 +197,15 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160;<span class="comment"> * \returns NULL if error, otherwise pointer to output</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71"> 104</a></span>&#160;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> &amp;<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>,</div>
<div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71"> 104</a></span>&#160;<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;T&gt;</a> <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(<span class="keyword">const</span> <a class="codeRef" 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 name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keyword">const</span> <a class="codeRef" 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 name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="keywordtype">double</span> num = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>, b);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="keywordtype">double</span> num = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(a, b);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordtype">double</span> deno = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">vector_dot</a>(b, b);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160;<span class="comment"> /*! check for division by zero using machine epsilon */</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordflow">if</span> (deno &lt;= <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits&lt;double&gt;::epsilon</a>()) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; __func__ &lt;&lt; <span class="stringliteral">&quot;] Possible division by zero\n&quot;</span>;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a>; <span class="comment">// return vector a back</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <span class="keywordflow">return</span> a; <span class="comment">// return vector a back</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="keywordtype">double</span> scalar = num / deno;</div>
@@ -265,8 +265,8 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; col_vector[j] = A[j][i];</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; i; j++) {</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; ROWS; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; col_vector2[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = Q[0][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j];</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; ROWS; k++) {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; col_vector2[k] = Q[0][k][j];</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; }</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; col_vector2 = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">vector_proj</a>(col_vector, col_vector2);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; tmp_vector -= col_vector2;</div>
@@ -293,11 +293,11 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="comment">// parallelize on threads</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = i; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; COLUMNS; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i; k &lt; COLUMNS; k++) {</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> kk = 0; kk &lt; ROWS; kk++) {</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; col_vector2[kk] = A[kk][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>];</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; col_vector2[kk] = A[kk][k];</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; }</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; R[0][i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] = (col_vector * col_vector2).sum();</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; R[0][i][k] = (col_vector * col_vector2).sum();</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; }</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160;}</div>
@@ -319,6 +319,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="afalse__position_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:24</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_a7e7a1a2b0a03df0a70cac40d193421d2"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">statistics::stats_computer2::operator&gt;&gt;</a></div><div class="ttdeci">friend std::istream &amp; operator&gt;&gt;(std::istream &amp;input, stats_computer2 &amp;stat)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:97</div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:21</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">solution accuracy limit</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:17</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:188</div></div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
@@ -340,7 +341,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_aa141a7904f0c4668bac112d652a3acf9"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a></div><div class="ttdeci">int multiply(int x, int res[], int res_size)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:25</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_a0ddf1224851353fc92bfbff6f499fa97"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a></div><div class="ttdeci">int main(int argc, char *argv[])</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:188</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:94</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:59</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_af50a5c87d27cfd3462745b37fb9b0f46"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">print</a></div><div class="ttdeci">void print(uint32_t N)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:40</div></div>
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a3bada3e58ad8d1b00918db2ffe83a740"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a3bada3e58ad8d1b00918db2ffe83a740">complex_str</a></div><div class="ttdeci">const char * complex_str(const std::complex&lt; double &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:76</div></div>
@@ -383,7 +384,6 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="afalse__position_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> false_position.cpp:39</div></div>
<div class="ttc" id="aisinf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a></div><div class="ttdeci">T isinf(T... args)</div></div>
<div class="ttc" id="anamespaceqr__algorithm_html_ad16da2183db22378435042f26af43d5f"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a></div><div class="ttdeci">double vector_mag(const std::valarray&lt; T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:92</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_afcf0d19607cd0edd8ae333d2b9c220c0"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a></div><div class="ttdeci">ll k</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:48</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_af6198817084276113b3c064e87ce0555"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">statistics::stats_computer2::variance</a></div><div class="ttdeci">double variance() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:89</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a></div><div class="ttdeci">unsigned int gcd(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:16</div></div>
<div class="ttc" id="asqrt__double_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/d24/sqrt__double_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> sqrt_double.cpp:42</div></div>
@@ -407,7 +407,6 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div class="ttc" id="agroup__ode_html_gae0509f8843e2bc42de2abbd00a14b7b9"><div class="ttname"><a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a></div><div class="ttdeci">double forward_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the forward-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:102</div></div>
<div class="ttc" id="arealtime__stats_8cpp_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="../../d0/d08/realtime__stats_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:158</div></div>
<div class="ttc" id="afalse__position_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition:</b> false_position.cpp:34</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9ecd98ce0064e2f7f97bb6a92f58ee72"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9ecd98ce0064e2f7f97bb6a92f58ee72">a</a></div><div class="ttdeci">vector&lt; ll &gt; a</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:53</div></div>
<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
<div class="ttc" id="aode__semi__implicit__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:53</div></div>
@@ -495,7 +494,7 @@ $(document).ready(function(){initNavTree('d4/d68/qr__decompose_8h_source.html','
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d4/d68/qr__decompose_8h.html">qr_decompose.h</a></li>
<li class="footer">Generated on Wed Jun 24 2020 22:45:07 for Algorithms_in_C++ by
<li class="footer">Generated on Wed Jun 24 2020 22:52:56 for Algorithms_in_C++ by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="../../doxygen.png" alt="doxygen"/></a> 1.8.18 </li>
</ul>