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author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Thu, 09 Jul 2015 01:12:16 +0100
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1 <html lang="en">
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3 <title>Complex Multi-Dimensional DFTs - FFTW 3.2.1</title>
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52 Next:&nbsp;<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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57
58 <h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>
59
60 <p>Multi-dimensional transforms work much the same way as one-dimensional
61 transforms: you allocate arrays of <code>fftw_complex</code> (preferably
62 using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
63 many times as you want with <code>fftw_execute(plan)</code>, and clean up
64 with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>). The only
65 difference is the routine you use to create the plan:
66
67 <pre class="example"> fftw_plan fftw_plan_dft_2d(int n0, int n1,
68 fftw_complex *in, fftw_complex *out,
69 int sign, unsigned flags);
70 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
71 fftw_complex *in, fftw_complex *out,
72 int sign, unsigned flags);
73 fftw_plan fftw_plan_dft(int rank, const int *n,
74 fftw_complex *in, fftw_complex *out,
75 int sign, unsigned flags);
76 </pre>
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>
78 These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
79 (2d) transforms, <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
80 and arbitrary <code>rank</code>-dimensional transforms, respectively. In the
81 <a name="index-rank-41"></a>third case, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting
82 an <code>n[0]</code> by <code>n[1]</code> by <small class="dots">...</small> by <code>n[rank-1]</code>
83 transform. All of these transforms operate on contiguous arrays in
84 the C-standard <dfn>row-major</dfn> order, so that the last dimension has
85 the fastest-varying index in the array. This layout is described
86 further in <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
87
88 <p>You may have noticed that all the planner routines described so far
89 have overlapping functionality. For example, you can plan a 1d or 2d
90 transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
91 or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
92 and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This
93 pattern continues, and FFTW's planning routines in general form a
94 &ldquo;partial order,&rdquo; sequences of
95 <a name="index-partial-order-42"></a>interfaces with strictly increasing generality but correspondingly
96 greater complexity.
97
98 <p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
99 describe in this tutorial, but there are also the advanced and guru interfaces,
100 <a name="index-advanced-interface-43"></a><a name="index-guru-interface-44"></a>which allow one to efficiently combine multiple/strided transforms
101 into a single FFTW plan, transform a subset of a larger
102 multi-dimensional array, and/or to handle more general complex-number
103 formats. For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>.
104
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