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3 <title>Complex Multi-Dimensional DFTs - FFTW 3.2.1</title>
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5 <meta name="description" content="FFTW 3.2.1">
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9 <link rel="prev" href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" title="Complex One-Dimensional DFTs">
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10 <link rel="next" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" title="One-Dimensional DFTs of Real Data">
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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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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="Complex-Multi-Dimensional-DFTs"></a>
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51 <a name="Complex-Multi_002dDimensional-DFTs"></a>
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52 Next: <a rel="next" accesskey="n" href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data">One-Dimensional DFTs of Real Data</a>,
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53 Previous: <a rel="previous" accesskey="p" href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs">Complex One-Dimensional DFTs</a>,
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54 Up: <a rel="up" accesskey="u" href="Tutorial.html#Tutorial">Tutorial</a>
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55 <hr>
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56 </div>
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57
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58 <h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>
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59
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60 <p>Multi-dimensional transforms work much the same way as one-dimensional
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61 transforms: you allocate arrays of <code>fftw_complex</code> (preferably
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62 using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
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63 many times as you want with <code>fftw_execute(plan)</code>, and clean up
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64 with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>). The only
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65 difference is the routine you use to create the plan:
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66
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67 <pre class="example"> fftw_plan fftw_plan_dft_2d(int n0, int n1,
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68 fftw_complex *in, fftw_complex *out,
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69 int sign, unsigned flags);
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70 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
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71 fftw_complex *in, fftw_complex *out,
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72 int sign, unsigned flags);
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73 fftw_plan fftw_plan_dft(int rank, const int *n,
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74 fftw_complex *in, fftw_complex *out,
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75 int sign, unsigned flags);
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76 </pre>
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77 <p><a name="index-fftw_005fplan_005fdft_005f2d-38"></a><a name="index-fftw_005fplan_005fdft_005f3d-39"></a><a name="index-fftw_005fplan_005fdft-40"></a>
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78 These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
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79 (2d) transforms, <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
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80 and arbitrary <code>rank</code>-dimensional transforms, respectively. In the
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81 <a name="index-rank-41"></a>third case, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting
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82 an <code>n[0]</code> by <code>n[1]</code> by <small class="dots">...</small> by <code>n[rank-1]</code>
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83 transform. All of these transforms operate on contiguous arrays in
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84 the C-standard <dfn>row-major</dfn> order, so that the last dimension has
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85 the fastest-varying index in the array. This layout is described
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86 further in <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
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87
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88 <p>You may have noticed that all the planner routines described so far
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89 have overlapping functionality. For example, you can plan a 1d or 2d
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90 transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
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91 or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
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92 and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This
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93 pattern continues, and FFTW's planning routines in general form a
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94 “partial order,” sequences of
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95 <a name="index-partial-order-42"></a>interfaces with strictly increasing generality but correspondingly
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96 greater complexity.
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97
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98 <p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
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99 describe in this tutorial, but there are also the advanced and guru interfaces,
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100 <a name="index-advanced-interface-43"></a><a name="index-guru-interface-44"></a>which allow one to efficiently combine multiple/strided transforms
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101 into a single FFTW plan, transform a subset of a larger
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102 multi-dimensional array, and/or to handle more general complex-number
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103 formats. For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>.
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104
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105 <!-- -->
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106 </body></html>
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107
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