backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-03-21 12:23:13 +08:00
Code Issues Projects Releases Wiki Activity
Files
a87e2fa7cb505dc2a80a54eb9eb3be99ddfd417f
C-Plus-Plus/d8/d9a/fast__fourier__transform_8cpp.html
github-actions b48f6e8671 Documentation for 0931d530ae
2023-01-22 19:44:10 +00:00

301 lines
22 KiB
HTML
Raw Blame History

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.9.6"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C++: numerical_methods/fast_fourier_transform.cpp File Reference</title>
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../resize.js"></script>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.js"></script>
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectalign">
<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">Set of algorithms implemented in C++.</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.6 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
/* @license-end */
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() {
initMenu('../../',true,false,'search.php','Search');
$(document).ready(function() { init_search(); });
});
/* @license-end */
</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(document).ready(function(){initNavTree('d8/d9a/fast__fourier__transform_8cpp.html','../../'); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="summary">
<a href="#namespaces">Namespaces</a> &#124;
<a href="#func-members">Functions</a> </div>
<div class="headertitle"><div class="title">fast_fourier_transform.cpp File Reference</div></div>
</div><!--header-->
<div class="contents">
<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 />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for fast_fourier_transform.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d15/fast__fourier__transform_8cpp__incl.svg" width="435" height="124"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div><table class="memberdecls">
<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 assert <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><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: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. <br /></td></tr>
<tr class="separator:a158fd271b9a53e8f3f60b08b18857150"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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. <br /></td></tr>
<tr class="separator:abf9e6b7e6f15df4b525a2e7705ba3089"><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><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>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abf9e6b7e6f15df4b525a2e7705ba3089" name="abf9e6b7e6f15df4b525a2e7705ba3089"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abf9e6b7e6f15df4b525a2e7705ba3089">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char const *&#160;</td>
<td class="paramname"><em>argv</em>[]&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<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"><span class="lineno"> 162</span> {</div>
<div class="line"><span class="lineno"> 163</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"><span class="lineno"> 164</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><span class="lineno"> 165</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 166</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>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d9a/fast__fourier__transform_8cpp_abf9e6b7e6f15df4b525a2e7705ba3089_cgraph.svg" width="348" height="175"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div>
</div>
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">static void test </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span> </td>
</tr>
</table>
</div><div class="memdoc">
<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"><span class="lineno"> 104</span> {</div>
<div class="line"><span class="lineno"> 105</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><span class="lineno"> 106</span> </div>
<div class="line"><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"><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"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> t1[0] = {1, 0};</div>
<div class="line"><span class="lineno"> 111</span> t1[1] = {2, 0};</div>
<div class="line"><span class="lineno"> 112</span> t2[0] = {1, 0};</div>
<div class="line"><span class="lineno"> 113</span> t2[1] = {2, 0};</div>
<div class="line"><span class="lineno"> 114</span> t2[2] = {3, 0};</div>
<div class="line"><span class="lineno"> 115</span> t2[3] = {4, 0};</div>
<div class="line"><span class="lineno"> 116</span> </div>
<div class="line"><span class="lineno"> 117</span> uint8_t n1 = 2;</div>
<div class="line"><span class="lineno"> 118</span> uint8_t n2 = 4;</div>
<div class="line"><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"><span class="lineno"> 120</span> {3, 0}, {-1, 0}}; <span class="comment">/// True Answer for test case 1</span></div>
<div class="line"><span class="lineno"> 121</span> </div>
<div class="line"><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"><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"><span class="lineno"> 124</span> </div>
<div class="line"><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"><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 =</div>
<div class="line"><span class="lineno"> 127</span> o1; <span class="comment">/// Temporary variable used to delete memory location of o1</span></div>
<div class="line"><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> *o2 = <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a>(t2, n2);</div>
<div class="line"><span class="lineno"> 129</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 =</div>
<div class="line"><span class="lineno"> 130</span> o2; <span class="comment">/// Temporary variable used to delete memory location of o2</span></div>
<div class="line"><span class="lineno"> 131</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><span class="lineno"> 132</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"><span class="lineno"> 133</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"><span class="lineno"> 134</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 135</span><span class="comment"> /// values for test case 1</span></div>
<div class="line"><span class="lineno"> 136</span><span class="comment"></span> o1++;</div>
<div class="line"><span class="lineno"> 137</span> }</div>
<div class="line"><span class="lineno"> 138</span> </div>
<div class="line"><span class="lineno"> 139</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><span class="lineno"> 140</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"><span class="lineno"> 141</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"><span class="lineno"> 142</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 143</span><span class="comment"> /// values for test case 2</span></div>
<div class="line"><span class="lineno"> 144</span><span class="comment"></span> o2++;</div>
<div class="line"><span class="lineno"> 145</span> }</div>
<div class="line"><span class="lineno"> 146</span> </div>
<div class="line"><span class="lineno"> 147</span> <span class="keyword">delete</span>[] t1;</div>
<div class="line"><span class="lineno"> 148</span> <span class="keyword">delete</span>[] t2;</div>
<div class="line"><span class="lineno"> 149</span> <span class="keyword">delete</span>[] t3;</div>
<div class="line"><span class="lineno"> 150</span> <span class="keyword">delete</span>[] t4;</div>
<div class="line"><span class="lineno"> 151</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"><span class="lineno"> 152</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="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_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="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>
<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>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d9a/fast__fourier__transform_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.svg" width="250" height="175"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d8/d9a/fast__fourier__transform_8cpp.html">fast_fourier_transform.cpp</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.6 </li>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink