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2021-11-02 17:00:20 +00:00
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<div class="headertitle"><div class="title">fast_fourier_transform.cpp File Reference</div></div>
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<p><a href="https://medium.com/@aiswaryamathur/understanding-fast-fouriertransform-from-scratch-to-solve-polynomial-multiplication-8018d511162f" target="_blank">A fast Fourier transform (FFT)</a> is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT).
<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 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 io operations <br /></td></tr>
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Functions</h2></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">numerical_methods::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. <a href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">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="../../d8/d9a/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="../../d8/d9a/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="../../d8/d9a/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="../../d8/d9a/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://medium.com/@aiswaryamathur/understanding-fast-fouriertransform-from-scratch-to-solve-polynomial-multiplication-8018d511162f" target="_blank">A fast Fourier transform (FFT)</a> is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). </p>
<p >This algorithm has application in use case scenario where a user wants to find points of a function in a short time by just using the coefficients of the polynomial function. It can be also used to find inverse fourier transform by just switching the value of omega. Time complexity this algorithm computes the DFT 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>
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<h2 class="memtitle"><span class="permalink"><a href="#abf9e6b7e6f15df4b525a2e7705ba3089">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramname"><em>argc</em>, </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>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_function" href="../../d8/d9a/fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span>}</div>
<div class="ttc" id="afast__fourier__transform_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/d9a/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> fast_fourier_transform.cpp:104</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 >Temporary variable used to delete memory location of o1</p>
<p >Temporary variable used to delete memory location of o2</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="l00104" name="l00104"></a><span class="lineno"> 104</span> {</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</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="l00108" name="l00108"></a><span class="lineno"> 108</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="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> t1[0] = {1, 0};</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> t1[1] = {2, 0};</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> t2[0] = {1, 0};</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> t2[1] = {2, 0};</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> t2[2] = {3, 0};</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> t2[3] = {4, 0};</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> uint8_t n1 = 2;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> uint8_t n2 = 4;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</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="l00120" name="l00120"></a><span class="lineno"> 120</span> {3, 0}, {-1, 0}}; <span class="comment">/// True Answer for test case 1</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</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="l00123" name="l00123"></a><span class="lineno"> 123</span> {10, 0}, {-2, -2}, {-2, 0}, {-2, 2}}; <span class="comment">/// True Answer for test case 2</span></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> <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#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a>(t1, n1);</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *t3=o1; <span class="comment">/// Temporary variable used to delete memory location of o1</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</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#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a>(t2, n2);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *t4=o2; <span class="comment">/// Temporary variable used to delete memory location of o2</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> assert((r1[i].real() - o1-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> (r1[i].imag() - o1-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() &lt;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="comment"> /// values for test case 1</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="comment"></span> o1++;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> assert((r2[i].real() - o2-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> (r2[i].imag() - o2-&gt;<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() &lt;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment"> /// values for test case 2</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment"></span> o2++;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
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