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1 <html lang="en">
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2 <head>
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3 <title>Real-data DFTs - FFTW 3.2.1</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.2.1">
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6 <meta name="generator" content="makeinfo 4.8">
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7 <link title="Top" rel="start" href="index.html#Top">
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8 <link rel="up" href="Basic-Interface.html#Basic-Interface" title="Basic Interface">
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9 <link rel="prev" href="Planner-Flags.html#Planner-Flags" title="Planner Flags">
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10 <link rel="next" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" title="Real-data DFT Array Format">
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11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.2.1, 5 February 2009).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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19
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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33 -->
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34 <meta http-equiv="Content-Style-Type" content="text/css">
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35 <style type="text/css"><!--
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44 span.sansserif { font-family:sans-serif; font-weight:normal; }
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45 --></style>
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46 </head>
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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="Real-data-DFTs"></a>
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51 <a name="Real_002ddata-DFTs"></a>
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52 Next: <a rel="next" accesskey="n" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>,
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53 Previous: <a rel="previous" accesskey="p" href="Planner-Flags.html#Planner-Flags">Planner Flags</a>,
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54 Up: <a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
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55 <hr>
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56 </div>
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57
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58 <h4 class="subsection">4.3.3 Real-data DFTs</h4>
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59
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60 <pre class="example"> fftw_plan fftw_plan_dft_r2c_1d(int n,
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61 double *in, fftw_complex *out,
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62 unsigned flags);
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63 fftw_plan fftw_plan_dft_r2c_2d(int n0, int n1,
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64 double *in, fftw_complex *out,
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65 unsigned flags);
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66 fftw_plan fftw_plan_dft_r2c_3d(int n0, int n1, int n2,
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67 double *in, fftw_complex *out,
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68 unsigned flags);
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69 fftw_plan fftw_plan_dft_r2c(int rank, const int *n,
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70 double *in, fftw_complex *out,
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71 unsigned flags);
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72 </pre>
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73 <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f1d-176"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-177"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-178"></a><a name="index-fftw_005fplan_005fdft_005fr2c-179"></a><a name="index-r2c-180"></a>
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74 Plan a real-input/complex-output discrete Fourier transform (DFT) in
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75 zero or more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
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76
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77 <p>Once you have created a plan for a certain transform type and
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78 parameters, then creating another plan of the same type and parameters,
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79 but for different arrays, is fast and shares constant data with the
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80 first plan (if it still exists).
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81
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82 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
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83 non-<code>NULL</code> plan is always returned by the basic interface unless
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84 you are using a customized FFTW configuration supporting a restricted
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85 set of transforms, or if you use the <code>FFTW_PRESERVE_INPUT</code> flag
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86 with a multi-dimensional out-of-place c2r transform (see below).
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87
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88 <h5 class="subsubheading">Arguments</h5>
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89
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90 <ul>
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91 <li><code>rank</code> is the dimensionality of the transform (it should be the
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92 size of the array <code>*n</code>), and can be any non-negative integer. The
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93 `<samp><span class="samp">_1d</span></samp>', `<samp><span class="samp">_2d</span></samp>', and `<samp><span class="samp">_3d</span></samp>' planners correspond to a
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94 <code>rank</code> of <code>1</code>, <code>2</code>, and <code>3</code>, respectively. A
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95 <code>rank</code> of zero is equivalent to a transform of size 1, i.e. a copy
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96 of one number (with zero imaginary part) from input to output.
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97
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98 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
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99 respectively, gives the size of the <em>logical</em> transform dimensions.
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100 They can be any positive integer. This is different in general from the
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101 <em>physical</em> array dimensions, which are described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
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102
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103 <ul>
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104 <li>FFTW is best at handling sizes of the form
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105 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
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106 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
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107 are arbitrary. Other sizes are computed by means of a slow,
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108 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
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109
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110 <p>performance even for prime sizes). (It is possible to customize FFTW
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111 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
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112 Transforms whose sizes are powers of 2 are especially fast, and
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113 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
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114 transform to be <em>even</em>.
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115 </ul>
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116
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117 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
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118 transform, which may be the same (yielding an in-place transform).
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119 <a name="index-in_002dplace-181"></a>These arrays are overwritten during planning, unless
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120 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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121 initialized, but they must be allocated.) For an in-place transform, it
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122 is important to remember that the real array will require padding,
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123 described in <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>.
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124 <a name="index-padding-182"></a>
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125 <li><a name="index-flags-183"></a><code>flags</code> is a bitwise OR (`<samp><span class="samp">|</span></samp>') of zero or more planner flags,
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126 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
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127
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128 </ul>
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129
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130 <p>The inverse transforms, taking complex input (storing the non-redundant
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131 half of a logically Hermitian array) to real output, are given by:
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132
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133 <pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n,
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134 fftw_complex *in, double *out,
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135 unsigned flags);
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136 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
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137 fftw_complex *in, double *out,
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138 unsigned flags);
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139 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
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140 fftw_complex *in, double *out,
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141 unsigned flags);
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142 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
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143 fftw_complex *in, double *out,
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144 unsigned flags);
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145 </pre>
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146 <p><a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-184"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f2d-185"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f3d-186"></a><a name="index-fftw_005fplan_005fdft_005fc2r-187"></a><a name="index-c2r-188"></a>
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147 The arguments are the same as for the r2c transforms, except that the
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148 input and output data formats are reversed.
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149
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150 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
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151 c2r transform (or vice versa) will result in the original data
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152 multiplied by the size of the transform (the product of the logical
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153 dimensions).
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154 <a name="index-normalization-189"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
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155 complex DFT of the same input, and a c2r transform is correspondingly
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156 equivalent to <code>FFTW_BACKWARD</code>. For more information, see <a href="What-FFTW-Really-Computes.html#What-FFTW-Really-Computes">What FFTW Really Computes</a>.
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157
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158 <!-- =========> -->
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159 </body></html>
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160
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