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<div class="headertitle"><div class="title">inverse_fast_fourier_transform.cpp</div></div>
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<a href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;cmath&gt;</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;complex&gt;</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a> {</div>
<div class="foldopen" id="foldopen00034" data-start="{" data-end="}">
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93"> 34</a></span>std::complex&lt;double&gt; *<a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(std::complex&lt;double&gt; *p,</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> uint8_t n) {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">return</span> p; </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> }</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> std::complex&lt;double&gt; om = std::complex&lt;double&gt;(</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> cos(2 * pi / n), sin(2 * pi / n)); </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> om.real(om.real() / n); </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> om.imag(om.imag() / n); </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><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"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><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"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00053" name="l00053"></a><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"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> pe[k1++] = p[j]; </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> po[k2++] = p[j]; </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> }</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> std::complex&lt;double&gt; *ye =</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> std::complex&lt;double&gt; *yo =</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><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"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> k1 = 0, k2 = 0;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><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"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> y[i] =</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> ye[k1] + pow(om, i) * yo[k2]; </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> y[i + n / 2] =</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> ye[k1] - pow(om, i) * yo[k2]; </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> k1++;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> k2++;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">delete</span>[] ye; </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">delete</span>[] yo; </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>} <span class="comment">// namespace numerical_methods</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span></div>
<div class="foldopen" id="foldopen00101" data-start="{" data-end="}">
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 101</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> std::complex&lt;double&gt;[2]; </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> std::complex&lt;double&gt;[4]; </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> t1[0] = {3, 0};</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> t1[1] = {-1, 0};</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> t2[0] = {10, 0};</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> t2[1] = {-2, -2};</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> t2[2] = {-2, 0};</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> t2[3] = {-2, 2};</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> uint8_t n1 = 2;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> uint8_t n2 = 4;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> std::vector&lt;std::complex&lt;double&gt;&gt; r1 = {</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> {1, 0}, {2, 0}}; </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> std::vector&lt;std::complex&lt;double&gt;&gt; r2 = {</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> {1, 0}, {2, 0}, {3, 0}, {4, 0}}; </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> std::complex&lt;double&gt; *o1 =</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t1, n1);</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> std::complex&lt;double&gt; *o2 =</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t2, n2);</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> assert((r1[i].real() - o1[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> (r1[i].imag() - o1[i].imag() &lt;</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> 0.000000000001)); </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> assert((r2[i].real() - o2[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> (r2[i].imag() - o2[i].imag() &lt;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> 0.000000000001)); </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> std::cout &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>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="foldopen" id="foldopen00155" data-start="{" data-end="}">
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"><a class="line" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 155</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</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="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span>}</div>
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<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> <a href="#l00101">inverse_fast_fourier_transform.cpp:101</a></div></div>
<div class="ttc" id="ainverse__fast__fourier__transform_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d9/d37/inverse__fast__fourier__transform_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function calls automated test function to test the working of fast fourier transform.</div><div class="ttdef"><b>Definition</b> <a href="#l00155">inverse_fast_fourier_transform.cpp:155</a></div></div>
<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for assert</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> <a href="#l00034">inverse_fast_fourier_transform.cpp:34</a></div></div>
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