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1 <html lang="en">
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2 <head>
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3 <title>Real-data DFTs - FFTW 3.3.3</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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5 <meta name="description" content="FFTW 3.3.3">
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6 <meta name="generator" content="makeinfo 4.13">
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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 3.3.3, 25 November 2012).
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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 <a name="Real-data-DFTs"></a>
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50 <a name="Real_002ddata-DFTs"></a>
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51 <p>
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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 n0,
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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-185"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f2d-186"></a><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-187"></a><a name="index-fftw_005fplan_005fdft_005fr2c-188"></a><a name="index-r2c-189"></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 rank of the transform (it should be the size of the
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92 array <code>*n</code>), and can be any non-negative integer. (See <a href="Complex-Multi_002dDimensional-DFTs.html#Complex-Multi_002dDimensional-DFTs">Complex Multi-Dimensional DFTs</a>, for the definition of “rank”.) 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. The rank
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95 may be zero, which is equivalent to a rank-1 transform of size 1, i.e. a
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96 copy of one real number (with zero imaginary part) from input to output.
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97
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98 <li><code>n0</code>, <code>n1</code>, <code>n2</code>, or <code>n[0..rank-1]</code>, (as appropriate
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99 for each routine) specify the size of the transform dimensions. They
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100 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>) performance even for prime sizes). (It is possible to customize FFTW
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109 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
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110 Transforms whose sizes are powers of 2 are especially fast, and
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111 it is generally beneficial for the <em>last</em> dimension of an r2c/c2r
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112 transform to be <em>even</em>.
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113 </ul>
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114
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115 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
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116 transform, which may be the same (yielding an in-place transform).
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117 <a name="index-in_002dplace-190"></a>These arrays are overwritten during planning, unless
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118 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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119 initialized, but they must be allocated.) For an in-place transform, it
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120 is important to remember that the real array will require padding,
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121 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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122 <a name="index-padding-191"></a>
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123 <li><a name="index-flags-192"></a><code>flags</code> is a bitwise OR (‘<samp><span class="samp">|</span></samp>’) of zero or more planner flags,
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124 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
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125
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126 </ul>
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127
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128 <p>The inverse transforms, taking complex input (storing the non-redundant
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129 half of a logically Hermitian array) to real output, are given by:
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130
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131 <pre class="example"> fftw_plan fftw_plan_dft_c2r_1d(int n0,
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132 fftw_complex *in, double *out,
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133 unsigned flags);
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134 fftw_plan fftw_plan_dft_c2r_2d(int n0, int n1,
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135 fftw_complex *in, double *out,
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136 unsigned flags);
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137 fftw_plan fftw_plan_dft_c2r_3d(int n0, int n1, int n2,
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138 fftw_complex *in, double *out,
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139 unsigned flags);
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140 fftw_plan fftw_plan_dft_c2r(int rank, const int *n,
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141 fftw_complex *in, double *out,
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142 unsigned flags);
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143 </pre>
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144 <p><a name="index-fftw_005fplan_005fdft_005fc2r_005f1d-193"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f2d-194"></a><a name="index-fftw_005fplan_005fdft_005fc2r_005f3d-195"></a><a name="index-fftw_005fplan_005fdft_005fc2r-196"></a><a name="index-c2r-197"></a>
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145 The arguments are the same as for the r2c transforms, except that the
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146 input and output data formats are reversed.
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147
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148 <p>FFTW computes an unnormalized transform: computing an r2c followed by a
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149 c2r transform (or vice versa) will result in the original data
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150 multiplied by the size of the transform (the product of the logical
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151 dimensions).
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152 <a name="index-normalization-198"></a>An r2c transform produces the same output as a <code>FFTW_FORWARD</code>
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153 complex DFT of the same input, and a c2r transform is correspondingly
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154 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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155
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156 <!-- =========> -->
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157 </body></html>
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158
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