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<div class="headertitle"><div class="title">numerical_methods Namespace Reference</div></div>
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<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>
Functions</h2></td></tr>
<tr class="memitem:a28e67885f8606564cc8335f483f63309"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html#a28e67885f8606564cc8335f483f63309">babylonian_method</a> (double radicand)</td></tr>
<tr class="memdesc:a28e67885f8606564cc8335f483f63309"><td class="mdescLeft">&#160;</td><td class="mdescRight">Babylonian methods is an iterative function which returns square root of radicand. <br /></td></tr>
<tr class="separator:a28e67885f8606564cc8335f483f63309"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a158fd271b9a53e8f3f60b08b18857150"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *p, uint8_t n)</td></tr>
<tr class="memdesc:a158fd271b9a53e8f3f60b08b18857150"><td class="mdescLeft">&#160;</td><td class="mdescRight">FastFourierTransform is a recursive function which returns list of complex numbers. <br /></td></tr>
<tr class="separator:a158fd271b9a53e8f3f60b08b18857150"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aee56dc85997b8cd42bad71a5d6bd2d93"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *p, uint8_t n)</td></tr>
<tr class="memdesc:aee56dc85997b8cd42bad71a5d6bd2d93"><td class="mdescLeft">&#160;</td><td class="mdescRight">InverseFastFourierTransform is a recursive function which returns list of complex numbers. <br /></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 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 math functions</p>
<p>for IO operations</p>
<p>Numerical algorithms/methods</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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a> for assert for fabs</p>
<p>Numerical Methods algorithms</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>
<h2 class="memtitle"><span class="permalink"><a href="#a28e67885f8606564cc8335f483f63309">&#9670;&#160;</a></span>babylonian_method()</h2>
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<td class="memname">double numerical_methods::babylonian_method </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>radicand</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Babylonian methods is an iterative function which returns square root of radicand. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">radicand</td><td>is the radicand </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>x1 the square root of radicand </dd></dl>
<p>To find initial root or rough approximation</p>
<p>Real Initial value will be i-1 as loop stops on +1 value</p>
<p>Storing previous value for comparison</p>
<p>Storing calculated value for comparison</p>
<p>Temp variable to x0 and x1</p>
<p>Newly calculated root</p>
<p>Returning final root</p>
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
<div class="line"><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"><span class="lineno"> 32</span> </div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">while</span> (i * i &lt;= radicand) {</div>
<div class="line"><span class="lineno"> 34</span> i++;</div>
<div class="line"><span class="lineno"> 35</span> }</div>
<div class="line"><span class="lineno"> 36</span> </div>
<div class="line"><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"><span class="lineno"> 38</span> </div>
<div class="line"><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"><span class="lineno"> 40</span> <span class="keywordtype">double</span> x1 =</div>
<div class="line"><span class="lineno"> 41</span> (radicand / x0 + x0) / 2; <span class="comment">/// Storing calculated value for comparison</span></div>
<div class="line"><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"><span class="lineno"> 43</span> </div>
<div class="line"><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"><span class="lineno"> 45</span> temp = (radicand / x1 + x1) / 2; <span class="comment">/// Newly calculated root</span></div>
<div class="line"><span class="lineno"> 46</span> x0 = x1;</div>
<div class="line"><span class="lineno"> 47</span> x1 = temp;</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> </div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> x1; <span class="comment">/// Returning final root</span></div>
<div class="line"><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">
Here is the call graph for this function:</div>
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<a id="a158fd271b9a53e8f3f60b08b18857150" name="a158fd271b9a53e8f3f60b08b18857150"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a158fd271b9a53e8f3f60b08b18857150">&#9670;&#160;</a></span>FastFourierTransform()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; * numerical_methods::FastFourierTransform </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>FastFourierTransform is a recursive function which returns list of complex numbers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>List of Coefficents in form of complex numbers </td></tr>
<tr><td class="paramname">n</td><td>Count of elements in list p </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>p if n==1 </dd>
<dd>
y if n!=1 </dd></dl>
<p>Base Case To return</p>
<p>Declaring value of pi</p>
<p>Calculating value of omega</p>
<p>Coefficients of even power</p>
<p>Coefficients of odd power</p>
<p>Assigning values of even Coefficients</p>
<p>Assigning value of odd Coefficients</p>
<p>Recursive Call</p>
<p>Recursive Call</p>
<p>Final value representation list</p>
<p>Updating the first n/2 elements</p>
<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"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 44</span> }</div>
<div class="line"><span class="lineno"> 45</span> </div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><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"><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"><span class="lineno"> 50</span> </div>
<div class="line"><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"><span class="lineno"> 52</span> </div>
<div class="line"><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"><span class="lineno"> 54</span> </div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><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"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 58</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 61</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 62</span> }</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><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"><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"><span class="lineno"> 67</span> </div>
<div class="line"><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"><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"><span class="lineno"> 70</span> </div>
<div class="line"><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"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><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"><span class="lineno"> 76</span> y[i] =</div>
<div class="line"><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"><span class="lineno"> 78</span> y[i + n / 2] =</div>
<div class="line"><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"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> k1++;</div>
<div class="line"><span class="lineno"> 82</span> k2++;</div>
<div class="line"><span class="lineno"> 83</span> }</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 86</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><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: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>
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<h2 class="memtitle"><span class="permalink"><a href="#aee56dc85997b8cd42bad71a5d6bd2d93">&#9670;&#160;</a></span>InverseFastFourierTransform()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; * numerical_methods::InverseFastFourierTransform </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>p</em>, </td>
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<td class="paramtype">uint8_t&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
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<td>)</td>
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<p>InverseFastFourierTransform is a recursive function which returns list of complex numbers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>List of Coefficents in form of complex numbers </td></tr>
<tr><td class="paramname">n</td><td>Count of elements in list p </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>p if n==1 </dd>
<dd>
y if n!=1 </dd></dl>
<p>Base Case To return</p>
<p>Declaring value of pi</p>
<p>Calculating value of omega</p>
<p>One change in comparison with DFT</p>
<p>One change in comparison with DFT</p>
<p>Coefficients of even power</p>
<p>Coefficients of odd power</p>
<p>Assigning values of even Coefficients</p>
<p>Assigning value of odd Coefficients</p>
<p>Recursive Call</p>
<p>Recursive Call</p>
<p>Final value representation list</p>
<p>Updating the first n/2 elements</p>
<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"><span class="lineno"> 34</span> {</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 37</span> }</div>
<div class="line"><span class="lineno"> 38</span> </div>
<div class="line"><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"><span class="lineno"> 40</span> </div>
<div class="line"><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"><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"><span class="lineno"> 43</span> </div>
<div class="line"><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"><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"><span class="lineno"> 46</span> </div>
<div class="line"><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"><span class="lineno"> 48</span> </div>
<div class="line"><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"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><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"><span class="lineno"> 53</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 54</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 57</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> }</div>
<div class="line"><span class="lineno"> 60</span> </div>
<div class="line"><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"><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"><span class="lineno"> 63</span> </div>
<div class="line"><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"><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"><span class="lineno"> 66</span> </div>
<div class="line"><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"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><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"><span class="lineno"> 72</span> y[i] =</div>
<div class="line"><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"><span class="lineno"> 74</span> y[i + n / 2] =</div>
<div class="line"><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"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> k1++;</div>
<div class="line"><span class="lineno"> 78</span> k2++;</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 82</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 83</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 84</span> }</div>
<div class="line"><span class="lineno"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 89</span>}</div>
<div class="ttc" id="aimag_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">std::complex::imag</a></div><div class="ttdeci">T imag(T... args)</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * InverseFastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">InverseFastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition:</b> inverse_fast_fourier_transform.cpp:33</div></div>
<div class="ttc" id="areal_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">std::complex::real</a></div><div class="ttdeci">T real(T... args)</div></div>
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