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1 <html lang="en">
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2 <head>
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3 <title>Advanced Complex 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="Advanced-Interface.html#Advanced-Interface" title="Advanced Interface">
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9 <link rel="prev" href="Advanced-Interface.html#Advanced-Interface" title="Advanced Interface">
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10 <link rel="next" href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" title="Advanced Real-data DFTs">
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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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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="Advanced-Complex-DFTs"></a>
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50 <p>
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51 Next: <a rel="next" accesskey="n" href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs">Advanced Real-data DFTs</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>,
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53 Up: <a rel="up" accesskey="u" href="Advanced-Interface.html#Advanced-Interface">Advanced Interface</a>
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54 <hr>
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55 </div>
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56
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57 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
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58
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59 <pre class="example"> fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
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60 fftw_complex *in, const int *inembed,
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61 int istride, int idist,
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62 fftw_complex *out, const int *onembed,
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63 int ostride, int odist,
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64 int sign, unsigned flags);
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65 </pre>
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66 <p><a name="index-fftw_005fplan_005fmany_005fdft-232"></a>
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67 This routine plans multiple multidimensional complex DFTs, and it
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68 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
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69 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
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70 <code>n</code>. In addition, the transform data need not be contiguous, but
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71 it may be laid out in memory with an arbitrary stride. To account for
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72 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
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73 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
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74 {<code>i</code>,<code>o</code>}<code>stride</code>, and
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75 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
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76 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
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77 and 3, but the advanced interface handles only the general-rank
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78 case.
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79
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80 <p><code>howmany</code> is the number of transforms to compute. The resulting
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81 plan computes <code>howmany</code> transforms, where the input of the
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82 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
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83 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
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84 obtained in this way can often be faster than calling FFTW multiple
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85 times for the individual transforms. The basic <code>fftw_plan_dft</code>
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86 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
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87 parameters are ignored).
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88 <a name="index-howmany-parameter-233"></a><a name="index-dist-234"></a>
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89
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90 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
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91 <code>n</code>, as in the basic interface. In addition, the advanced
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92 interface allows the input and output arrays of each transform to be
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93 row-major subarrays of larger rank-<code>rank</code> arrays, described by
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94 <code>inembed</code> and <code>onembed</code> parameters, respectively.
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95 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
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96 and <code>n</code> should be elementwise less than or equal to
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97 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
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98 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
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99 physical and logical dimensions, as in the basic interface.)
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100
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101 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
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102 the input or output arrays is located at <code>j*istride</code> or
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103 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
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104 <code>j</code> is the ordinary row-major index.) When combined with the
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105 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
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106 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
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107 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
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108 <a name="index-stride-235"></a>
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109
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110 <p>For in-place transforms, the input and output <code>stride</code> and
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111 <code>dist</code> parameters should be the same; otherwise, the planner may
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112 return <code>NULL</code>.
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113
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114 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
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115 this function returns. You can safely free or reuse them.
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116
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117 <p><strong>Examples</strong>:
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118 One transform of one 5 by 6 array contiguous in memory:
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119 <pre class="example"> int rank = 2;
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120 int n[] = {5, 6};
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121 int howmany = 1;
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122 int idist = odist = 0; /* unused because howmany = 1 */
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123 int istride = ostride = 1; /* array is contiguous in memory */
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124 int *inembed = n, *onembed = n;
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125 </pre>
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126 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
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127 stored in memory one after another:
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128 <pre class="example"> int rank = 2;
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129 int n[] = {5, 6};
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130 int howmany = 3;
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131 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
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132 between the first element
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133 of the first array and the
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134 first element of the second array */
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135 int istride = ostride = 1; /* array is contiguous in memory */
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136 int *inembed = n, *onembed = n;
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137 </pre>
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138 <p>Transform each column of a 2d array with 10 rows and 3 columns:
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139 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
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140 int n[] = {10}; /* 1d transforms of length 10 */
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141 int howmany = 3;
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142 int idist = odist = 1;
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143 int istride = ostride = 3; /* distance between two elements in
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144 the same column */
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145 int *inembed = n, *onembed = n;
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146 </pre>
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147 <!-- =========> -->
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148 </body></html>
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149
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