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2 <head>
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3 <title>Real-to-Real Transforms - 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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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="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" title="Real-data DFT Array Format">
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10 <link rel="next" href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" title="Real-to-Real Transform Kinds">
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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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35 <style type="text/css"><!--
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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-to-Real-Transforms"></a>
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51 <a name="Real_002dto_002dReal-Transforms"></a>
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52 Next: <a rel="next" accesskey="n" href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>,
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53 Previous: <a rel="previous" accesskey="p" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</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">4.3.5 Real-to-Real Transforms</h4>
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59
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60 <p><a name="index-r2r-194"></a>
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61 <pre class="example"> fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
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62 fftw_r2r_kind kind, unsigned flags);
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63 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
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64 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
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65 unsigned flags);
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66 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
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67 double *in, double *out,
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68 fftw_r2r_kind kind0,
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69 fftw_r2r_kind kind1,
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70 fftw_r2r_kind kind2,
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71 unsigned flags);
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72 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
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73 const fftw_r2r_kind *kind, unsigned flags);
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74 </pre>
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75 <p><a name="index-fftw_005fplan_005fr2r_005f1d-195"></a><a name="index-fftw_005fplan_005fr2r_005f2d-196"></a><a name="index-fftw_005fplan_005fr2r_005f3d-197"></a><a name="index-fftw_005fplan_005fr2r-198"></a>
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76 Plan a real input/output (r2r) transform of various kinds in zero or
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77 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
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78
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79 <p>Once you have created a plan for a certain transform type and
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80 parameters, then creating another plan of the same type and parameters,
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81 but for different arrays, is fast and shares constant data with the
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82 first plan (if it still exists).
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83
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84 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
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85 non-<code>NULL</code> plan is always returned by the basic interface unless
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86 you are using a customized FFTW configuration supporting a restricted
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87 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
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88 not defined).
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89 <a name="index-FFTW_005fREDFT00-199"></a>
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90
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91 <h5 class="subsubheading">Arguments</h5>
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92
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93 <ul>
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94 <li><code>rank</code> is the dimensionality of the transform (it should be the
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95 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
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96 non-negative integer. The `<samp><span class="samp">_1d</span></samp>', `<samp><span class="samp">_2d</span></samp>', and `<samp><span class="samp">_3d</span></samp>'
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97 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
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98 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
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99 of one number from input to output.
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100
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101 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
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102 respectively, gives the (physical) size of the transform dimensions.
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103 They can be any positive integer.
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104
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105 <ul>
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106 <li><a name="index-row_002dmajor-200"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
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107 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
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108 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
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109 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
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110 <li>FFTW is generally best at handling sizes of the form
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111 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
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112 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
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113 are arbitrary. Other sizes are computed by means of a slow,
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114 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>)
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115
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116 <p>performance even for prime sizes). (It is possible to customize FFTW
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117 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
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118 Transforms whose sizes are powers of 2 are especially fast.
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119 <li>For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
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120 size n, it is n-1 or n+1, respectively, that
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121 should be factorizable in the above form.
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122 </ul>
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123
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124 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
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125 transform, which may be the same (yielding an in-place transform).
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126 <a name="index-in_002dplace-201"></a>These arrays are overwritten during planning, unless
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127 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
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128 initialized, but they must be allocated.)
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129
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130 <li><code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
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131 <code>kind[rank]</code>, is the kind of r2r transform used for the
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132 corresponding dimension. The valid kind constants are described in
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133 <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
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134 what is computed is the separable product formed by taking each
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135 transform kind along the corresponding dimension, one dimension after
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136 another.
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137
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138 <li><a name="index-flags-202"></a><code>flags</code> is a bitwise OR (`<samp><span class="samp">|</span></samp>') of zero or more planner flags,
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139 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
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140
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141 </ul>
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142
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143 <!-- =========> -->
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144 </body></html>
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145
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