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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="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a28e67885f8606564cc8335f483f63309" id="r_a28e67885f8606564cc8335f483f63309"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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="memitem:a158fd271b9a53e8f3f60b08b18857150" id="r_a158fd271b9a53e8f3f60b08b18857150"><td class="memItemLeft" align="right" valign="top">std::complex&lt; double &gt; *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a> (std::complex&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="memitem:aee56dc85997b8cd42bad71a5d6bd2d93" id="r_aee56dc85997b8cd42bad71a5d6bd2d93"><td class="memItemLeft" align="right" valign="top">std::complex&lt; double &gt; *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a> (std::complex&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>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>for assert </p>
<p>Numerical Methods.</p>
<p>for std::map container</p>
<p>for storing points and coefficents</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 std::atof for std::function for IO operations for std::map container</p>
<p>Numerical algorithms/methods</p>
<p>for math operations</p>
<p>Numerical methods</p>
<p>for assert for mathematical-related functions for IO operations for std::vector</p>
<p>Numerical algorithms/methods</p>
<p>for std::array for assert for fabs</p>
<p>Numerical Methods algorithms</p>
<p>for assert for math functions for integer allocation for std::atof for std::function for IO operations</p>
<p>Numerical algorithms/methods </p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" 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>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">double numerical_methods::babylonian_method </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>radicand</em></span></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>
<p class="definition">Definition at line <a class="el" href="../../dc/d9c/babylonian__method_8cpp_source.html#l00030">30</a> of file <a class="el" href="../../dc/d9c/babylonian__method_8cpp_source.html">babylonian_method.cpp</a>.</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; </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--; </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; </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; </div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordtype">double</span> temp = NAN; </div>
<div class="line"><span class="lineno"> 43</span> </div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">while</span> (std::max(x0, x1) - std::min(x0, x1) &lt; 0.0001) {</div>
<div class="line"><span class="lineno"> 45</span> temp = (radicand / x1 + x1) / 2; </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; </div>
<div class="line"><span class="lineno"> 51</span>}</div>
</div><!-- fragment -->
</div>
</div>
<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">std::complex&lt; double &gt; * numerical_methods::FastFourierTransform </td>
<td>(</td>
<td class="paramtype">std::complex&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>p</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>n</em></span>&#160;)</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>
<p class="definition">Definition at line <a class="el" href="../../d8/d9a/fast__fourier__transform_8cpp_source.html#l00042">42</a> of file <a class="el" href="../../d8/d9a/fast__fourier__transform_8cpp_source.html">fast_fourier_transform.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> p; </div>
<div class="line"><span class="lineno"> 45</span> }</div>
<div class="line"><span class="lineno"> 46</span> </div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); </div>
<div class="line"><span class="lineno"> 48</span> </div>
<div class="line"><span class="lineno"> 49</span> std::complex&lt;double&gt; om = std::complex&lt;double&gt;(</div>
<div class="line"><span class="lineno"> 50</span> cos(2 * pi / n), sin(2 * pi / n)); </div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> std::complex&lt;double&gt;[n / 2]; </div>
<div class="line"><span class="lineno"> 53</span> </div>
<div class="line"><span class="lineno"> 54</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> std::complex&lt;double&gt;[n / 2]; </div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 59</span> pe[k1++] = p[j]; </div>
<div class="line"><span class="lineno"> 60</span> </div>
<div class="line"><span class="lineno"> 61</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 62</span> po[k2++] = p[j]; </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> </div>
<div class="line"><span class="lineno"> 66</span> std::complex&lt;double&gt; *ye =</div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2); </div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> std::complex&lt;double&gt; *yo =</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2); </div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> std::complex&lt;double&gt;[n]; </div>
<div class="line"><span class="lineno"> 73</span> </div>
<div class="line"><span class="lineno"> 74</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 75</span> </div>
<div class="line"><span class="lineno"> 76</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"> 77</span> y[i] =</div>
<div class="line"><span class="lineno"> 78</span> ye[k1] + pow(om, i) * yo[k2]; </div>
<div class="line"><span class="lineno"> 79</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 80</span> ye[k1] - pow(om, i) * yo[k2]; </div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> k1++;</div>
<div class="line"><span class="lineno"> 83</span> k2++;</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="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 88</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">delete</span>[] ye; </div>
<div class="line"><span class="lineno"> 92</span> <span class="keyword">delete</span>[] yo; </div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 94</span>}</div>
<div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="#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> <a href="../../d8/d9a/fast__fourier__transform_8cpp_source.html#l00042">fast_fourier_transform.cpp:42</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="aee56dc85997b8cd42bad71a5d6bd2d93" name="aee56dc85997b8cd42bad71a5d6bd2d93"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aee56dc85997b8cd42bad71a5d6bd2d93">&#9670;&#160;</a></span>InverseFastFourierTransform()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">std::complex&lt; double &gt; * numerical_methods::InverseFastFourierTransform </td>
<td>(</td>
<td class="paramtype">std::complex&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>p</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t</td> <td class="paramname"><span class="paramname"><em>n</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<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>
<p class="definition">Definition at line <a class="el" href="../../d9/d37/inverse__fast__fourier__transform_8cpp_source.html#l00034">34</a> of file <a class="el" href="../../d9/d37/inverse__fast__fourier__transform_8cpp_source.html">inverse_fast_fourier_transform.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">return</span> p; </div>
<div class="line"><span class="lineno"> 38</span> }</div>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); </div>
<div class="line"><span class="lineno"> 41</span> </div>
<div class="line"><span class="lineno"> 42</span> std::complex&lt;double&gt; om = std::complex&lt;double&gt;(</div>
<div class="line"><span class="lineno"> 43</span> cos(2 * pi / n), sin(2 * pi / n)); </div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> om.real(om.real() / n); </div>
<div class="line"><span class="lineno"> 46</span> om.imag(om.imag() / n); </div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> std::complex&lt;double&gt;[n / 2]; </div>
<div class="line"><span class="lineno"> 49</span> </div>
<div class="line"><span class="lineno"> 50</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> std::complex&lt;double&gt;[n / 2]; </div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 55</span> pe[k1++] = p[j]; </div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 58</span> po[k2++] = p[j]; </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> </div>
<div class="line"><span class="lineno"> 62</span> std::complex&lt;double&gt; *ye =</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); </div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> std::complex&lt;double&gt; *yo =</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); </div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> std::complex&lt;double&gt;[n]; </div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</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"> 73</span> y[i] =</div>
<div class="line"><span class="lineno"> 74</span> ye[k1] + pow(om, i) * yo[k2]; </div>
<div class="line"><span class="lineno"> 75</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 76</span> ye[k1] - pow(om, i) * yo[k2]; </div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> k1++;</div>
<div class="line"><span class="lineno"> 79</span> k2++;</div>
<div class="line"><span class="lineno"> 80</span> }</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] ye; </div>
<div class="line"><span class="lineno"> 88</span> <span class="keyword">delete</span>[] yo; </div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 90</span>}</div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="#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> <a href="../../d9/d37/inverse__fast__fourier__transform_8cpp_source.html#l00034">inverse_fast_fourier_transform.cpp:34</a></div></div>
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