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d1/d2a/knight__tour_8cpp.html
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@@ -344,7 +344,7 @@ template&lt;size_t V&gt; </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>}</div>
<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:115</div></div>
<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>
<div class="ttc" id="atower__of__hanoi_8cpp_html_af4cfc41e546f1f8d25f01e0804e8b61d"><div class="ttname"><a href="../../db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">mov</a></div><div class="ttdeci">void mov(tower *From, tower *To)</div><div class="ttdef"><b>Definition:</b> tower_of_hanoi.cpp:39</div></div>
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d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html
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@@ -407,7 +407,7 @@ template&lt;typename X &gt; </div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> }</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
<div class="ttc" id="aclassrange__queries_1_1heavy__light__decomposition_1_1_tree_html_ae8de7aefcb6635d3dacdd174cd4890c4"><div class="ttname"><a href="../../d1/d51/classrange__queries_1_1heavy__light__decomposition_1_1_tree.html#ae8de7aefcb6635d3dacdd174cd4890c4">range_queries::heavy_light_decomposition::Tree::dfs_lca</a></div><div class="ttdeci">void dfs_lca(int u, int p=-1)</div><div class="ttdoc">Utility function to populate the t_par vector.</div><div class="ttdef"><b>Definition:</b> heavy_light_decomposition.cpp:116</div></div>
<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:115</div></div>
<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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@@ -847,7 +847,7 @@ Here is the call graph for this function:</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> tmp &lt;&lt;= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">left</a>;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> quotient(0);</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0);</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keywordflow">while</span> (left &gt;= 0 &amp;&amp; tmp2 &gt;= p) {</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keywordflow">while</span> (tmp2 &gt;= p) {</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> uint16_t shf = tmp2._lez() - tmp.<a class="code hl_function" href="../../d1/d83/classuint256__t.html#a033d66c965e8d1fbc5bafb59ad60e163">_lez</a>();</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <span class="keywordflow">if</span> (shf) {</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> tmp &gt;&gt;= shf;</div>

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@@ -197,7 +197,7 @@ Algorithm</h3>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<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>
<div class="ttc" id="aclassgraph_1_1_h_k_graph_html"><div class="ttname"><a href="../../d8/d69/classgraph_1_1_h_k_graph.html">graph::HKGraph</a></div><div class="ttdoc">Represents Bipartite graph for Hopcroft Karp implementation.</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:67</div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:113</div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:115</div></div>
<div class="ttc" id="ahopcroft__karp_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d1/d9a/hopcroft__karp_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> hopcroft_karp.cpp:255</div></div>
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@@ -112,7 +112,7 @@ Include dependency graph for rungekutta.cpp:</div>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:d1/de0/namespacenumerical__methods"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d2/de7/namespacerunge__kutta"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a></td></tr>
<tr class="memdesc:d2/de7/namespacerunge__kutta"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method. <br /></td></tr>
@@ -307,7 +307,7 @@ Here is the call graph for this function:</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
<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:115</div></div>
<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>
<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:45</div></div>
<div class="ttc" id="arungekutta_8cpp_html_a450497475f5607333f9aca8f88901579"><div class="ttname"><a href="../../d1/da6/rungekutta_8cpp.html#a450497475f5607333f9aca8f88901579">change</a></div><div class="ttdeci">static double change(double x, double y)</div><div class="ttdoc">for using the vector container</div><div class="ttdef"><b>Definition:</b> rungekutta.cpp:33</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>

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@@ -139,7 +139,7 @@ Public Member Functions</h2></td></tr>
<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">return</span> (<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a>-&gt;freq &gt; r-&gt;freq);</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> }</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:119</div></div>
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</div>
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@@ -96,7 +96,7 @@ $(document).ready(function(){initNavTree('d1/de0/namespacenumerical__methods.htm
</div><!--header-->
<div class="contents">
<p>for IO operations
<p>for assert
<a href="../../d1/de0/namespacenumerical__methods.html#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
@@ -112,18 +112,21 @@ Functions</h2></td></tr>
<tr class="separator:aee56dc85997b8cd42bad71a5d6bd2d93"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >for IO operations </p>
<div class="textblock"><p >for assert </p>
<p >Numerical Methods.</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a> container</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p >for io operations</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a> container</p>
<p >for assert</p>
<p >for math functions</p>
<p >for IO operations</p>
<p >Numerical algorithms/methods</p>
<p >for assert for math functions for integer allocation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a> for IO operations</p>
<p >for assert for integer allocation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a> for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a> container</p>
<p >Numerical algorithms/methods</p>
<p >for math operations</p>
<p >Numerical methods</p>
<p >for assert for mathematical-related functions for storing points and coefficents for IO operations</p>
<p >Numerical algorithms/methods</p>
<p >for assert for math functions for integer allocation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a> for IO operations</p>
<p >Numerical algorithms/methods </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a28e67885f8606564cc8335f483f63309" name="a28e67885f8606564cc8335f483f63309"></a>
@@ -157,28 +160,28 @@ Functions</h2></td></tr>
<p >Temp variable to x0 and x1</p>
<p >Newly calculated root</p>
<p >Returning final root</p>
<div class="fragment"><div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordtype">int</span> i = 1; <span class="comment">/// To find initial root or rough approximation</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">while</span> (i * i &lt;= radicand) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> i++;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> }</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> i--; <span class="comment">/// Real Initial value will be i-1 as loop stops on +1 value</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordtype">double</span> x0 = i; <span class="comment">/// Storing previous value for comparison</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">double</span> x1 =</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> (radicand / x0 + x0) / 2; <span class="comment">/// Storing calculated value for comparison</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordtype">double</span> temp = NAN; <span class="comment">/// Temp variable to x0 and x1</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(x0, x1) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(x0, x1) &lt; 0.0001) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> temp = (radicand / x1 + x1) / 2; <span class="comment">/// Newly calculated root</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> x0 = x1;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> x1 = temp;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">return</span> x1; <span class="comment">/// Returning final root</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span>}</div>
<div class="fragment"><div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordtype">int</span> i = 1; <span class="comment">/// To find initial root or rough approximation</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">while</span> (i * i &lt;= radicand) {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> i++;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> }</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> i--; <span class="comment">/// Real Initial value will be i-1 as loop stops on +1 value</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">double</span> x0 = i; <span class="comment">/// Storing previous value for comparison</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordtype">double</span> x1 =</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> (radicand / x0 + x0) / 2; <span class="comment">/// Storing calculated value for comparison</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordtype">double</span> temp = NAN; <span class="comment">/// Temp variable to x0 and x1</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">while</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(x0, x1) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(x0, x1) &lt; 0.0001) {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> temp = (radicand / x1 + x1) / 2; <span class="comment">/// Newly calculated root</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> x0 = x1;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> x1 = temp;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">return</span> x1; <span class="comment">/// Returning final root</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span>}</div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
</div><!-- fragment --><div class="dynheader">
@@ -241,54 +244,53 @@ y if n!=1 </dd></dl>
<p >Updating the last n/2 elements</p>
<p >Deleting dynamic array ye</p>
<p >Deleting dynamic array yo</p>
<div class="fragment"><div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> }</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> } <span class="keywordflow">else</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="fragment"><div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> {</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> }</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> y[i] =</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> y[i + n / 2] =</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> k1++;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> k2++;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">if</span>(n!=2){</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> y[i] =</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> y[i + n / 2] =</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> k1++;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> k2++;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> }</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
@@ -296,7 +298,7 @@ y if n!=1 </dd></dl>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
<div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * FastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">FastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition:</b> fast_fourier_transform.cpp:40</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * FastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">FastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition:</b> fast_fourier_transform.cpp:41</div></div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
@@ -360,57 +362,56 @@ y if n!=1 </dd></dl>
<p >Updating the last n/2 elements</p>
<p >Deleting dynamic array ye</p>
<p >Deleting dynamic array yo</p>
<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> }</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>()/n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>()/n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> } <span class="keywordflow">else</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="fragment"><div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> }</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> y[i] =</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> y[i + n / 2] =</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> k1++;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> k2++;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">if</span>(n!=2){</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> y[i] =</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> y[i + n / 2] =</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> k1++;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> k2++;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>

51
d1/def/classdata__structures_1_1linked__list_1_1list.html
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@@ -584,19 +584,17 @@ Here is the call graph for this function:</div>
<p>Utility function to find the top element of the list. </p>
<dl class="section return"><dt>Returns</dt><dd>the top element of the list </dd></dl>
<div class="fragment"><div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">try</span> {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">return</span> head-&gt;val;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> } <span class="keywordflow">catch</span> (<span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/exception.html">std::exception</a> &amp;e) {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;List is empty&quot;</span> &lt;&lt; e.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/exception/what.html">what</a>() &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> }</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span>}</div>
<div class="ttc" id="aexception_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/exception.html">std::exception</a></div></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../d1/def/classdata__structures_1_1linked__list_1_1list.html#ae8424a4fce3d483f7c85d6f6a5c79a1a">isEmpty</a>()) {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">return</span> head-&gt;val;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/logic_error.html">std::logic_error</a>(<span class="stringliteral">&quot;List is empty&quot;</span>);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span>}</div>
<div class="ttc" id="alogic_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/logic_error.html">std::logic_error</a></div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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@@ -620,22 +618,23 @@ Here is the call graph for this function:</div>
<p>Utility function to find the i th element of the list. </p>
<dl class="section return"><dt>Returns</dt><dd>the i th element of the list </dd></dl>
<div class="fragment"><div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = head;</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">if</span> (count == index) {</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">return</span> (current-&gt;val);</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> }</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> count++;</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> current = current-&gt;next;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="comment">/* if we get to this line,the caller was asking for a non-existent element</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="comment"> so we assert fail */</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> assert(0);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span>}</div>
<div class="fragment"><div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> {</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <a class="code hl_class" href="../../db/d8b/struct_node.html">Node</a> *current = head;</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">while</span> (current != <span class="keyword">nullptr</span>) {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">if</span> (count == index) {</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordflow">return</span> (current-&gt;val);</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> count++;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> current = current-&gt;next;</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> }</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="comment">/* if we get to this line,the caller was asking for a non-existent element</span></div>
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