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<div class="headertitle"><div class="title">inverse_fast_fourier_transform.cpp File Reference</div></div>
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<p><a href="https://www.geeksforgeeks.org/python-inverse-fast-fourier-transformation/" target="_blank">An inverse fast Fourier transform (IFFT)</a> is an algorithm that computes the inverse fourier transform.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;complex&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for inverse_fast_fourier_transform.cpp:</div>
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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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a> container <br /></td></tr>
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Functions</h2></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">numerical_methods::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. <a href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">More...</a><br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:abf9e6b7e6f15df4b525a2e7705ba3089"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#abf9e6b7e6f15df4b525a2e7705ba3089">main</a> (int argc, char const *argv[])</td></tr>
<tr class="memdesc:abf9e6b7e6f15df4b525a2e7705ba3089"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#abf9e6b7e6f15df4b525a2e7705ba3089">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://www.geeksforgeeks.org/python-inverse-fast-fourier-transformation/" target="_blank">An inverse fast Fourier transform (IFFT)</a> is an algorithm that computes the inverse fourier transform. </p>
<p >This algorithm has an application in use case scenario where a user wants find coefficients of a function in a short time by just using points generated by DFT. Time complexity this algorithm computes the IDFT in O(nlogn) time in comparison to traditional O(n^2). </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/ameyachawlaggsipu" target="_blank">Ameya Chawla</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abf9e6b7e6f15df4b525a2e7705ba3089" name="abf9e6b7e6f15df4b525a2e7705ba3089"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abf9e6b7e6f15df4b525a2e7705ba3089">&#9670;&nbsp;</a></span>main()</h2>
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<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
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<td class="paramtype">char const *&#160;</td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>commandline argument count (ignored) </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments (ignored) calls automated test function to test the working of fast fourier transform. </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <a class="code hl_function" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span>}</div>
<div class="ttc" id="ainverse__fast__fourier__transform_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> inverse_fast_fourier_transform.cpp:100</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<p>Self-test implementations. </p>
<p >Declaring two test cases and checking for the error in predicted and true value is less than 0.000000000001. </p><dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >Test case 1</p>
<p >Test case 2</p>
<p >True Answer for test case 1</p>
<p >True Answer for test case 2</p>
<p >Comparing for both real and imaginary values for test case 1</p>
<p >Comparing for both real and imaginary values for test case 2</p>
<div class="fragment"><div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keyword">auto</span> *t1 = <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>[2]; <span class="comment">/// Test case 1</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">auto</span> *t2 = <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>[4]; <span class="comment">/// Test case 2</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> t1[0] = {3, 0};</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> t1[1] = {-1, 0};</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> t2[0] = {10, 0};</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> t2[1] = {-2, -2};</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> t2[2] = {-2, 0};</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> t2[3] = {-2, 2};</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> uint8_t n1 = 2;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> uint8_t n2 = 4;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r1 = {</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> {1, 0}, {2, 0}}; <span class="comment">/// True Answer for test case 1</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r2 = {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> {1, 0}, {2, 0}, {3, 0}, {4, 0}}; <span class="comment">/// True Answer for test case 2</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> </div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o1 = <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t1, n1);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o2 = <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t2, n2);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> assert((r1[i].real() - o1[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> (r1[i].imag() - o1[i].imag() &lt;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="comment"> /// values for test case 1</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment"></span> </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="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> assert((r2[i].real() - o2[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> (r2[i].imag() - o2[i].imag() &lt;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment"> /// values for test case 2</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment"></span> </div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> }</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keyword">delete</span>[] t1;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keyword">delete</span>[] t2;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">delete</span>[] o1;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">delete</span>[] o2;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span>}</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="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_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="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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