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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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<title>Complex Multi-Dimensional DFTs (FFTW 3.3.10)</title>
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Tutorial.html" rel="up" title="Tutorial">
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<link href="One_002dDimensional-DFTs-of-Real-Data.html" rel="next" title="One-Dimensional DFTs of Real Data">
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<link href="Complex-One_002dDimensional-DFTs.html" rel="prev" title="Complex One-Dimensional DFTs">
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</head>
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<body lang="en">
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<span id="Complex-Multi_002dDimensional-DFTs"></span><div class="header">
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<p>
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Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html" accesskey="u" rel="up">Tutorial</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Complex-Multi_002dDimensional-DFTs-1"></span><h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>
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<p>Multi-dimensional transforms work much the same way as one-dimensional
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transforms: you allocate arrays of <code>fftw_complex</code> (preferably
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using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
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many times as you want with <code>fftw_execute(plan)</code>, and clean up
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with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>).
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</p>
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<p>FFTW provides two routines for creating plans for 2d and 3d transforms,
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and one routine for creating plans of arbitrary dimensionality.
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The 2d and 3d routines have the following signature:
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</p><div class="example">
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<pre class="example">fftw_plan fftw_plan_dft_2d(int n0, int n1,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fdft_005f2d"></span>
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<span id="index-fftw_005fplan_005fdft_005f3d"></span>
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<p>These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
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(2d) transforms and <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
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respectively. All of these transforms operate on contiguous arrays in
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the C-standard <em>row-major</em> order, so that the last dimension has the
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fastest-varying index in the array. This layout is described further in
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<a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>.
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</p>
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<p>FFTW can also compute transforms of higher dimensionality. In order to
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avoid confusion between the various meanings of the the word
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“dimension”, we use the term <em>rank</em>
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<span id="index-rank"></span>
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to denote the number of independent indices in an array.<a id="DOCF2" href="#FOOT2"><sup>2</sup></a> For
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example, we say that a 2d transform has rank 2, a 3d transform has
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rank 3, and so on. You can plan transforms of arbitrary rank by
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means of the following function:
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</p>
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<div class="example">
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<pre class="example">fftw_plan fftw_plan_dft(int rank, const int *n,
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fftw_complex *in, fftw_complex *out,
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int sign, unsigned flags);
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</pre></div>
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<span id="index-fftw_005fplan_005fdft"></span>
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<p>Here, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting an
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<code>n[0]</code> by <code>n[1]</code> by … by <code>n[rank-1]</code> transform.
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Thus, for example, the call
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</p><div class="example">
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<pre class="example">fftw_plan_dft_2d(n0, n1, in, out, sign, flags);
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</pre></div>
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<p>is equivalent to the following code fragment:
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</p><div class="example">
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<pre class="example">int n[2];
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n[0] = n0;
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n[1] = n1;
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fftw_plan_dft(2, n, in, out, sign, flags);
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</pre></div>
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<p><code>fftw_plan_dft</code> is not restricted to 2d and 3d transforms,
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however, but it can plan transforms of arbitrary rank.
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</p>
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<p>You may have noticed that all the planner routines described so far
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have overlapping functionality. For example, you can plan a 1d or 2d
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transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
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or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
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and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This
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pattern continues, and FFTW’s planning routines in general form a
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“partial order,” sequences of
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<span id="index-partial-order"></span>
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interfaces with strictly increasing generality but correspondingly
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greater complexity.
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</p>
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<p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
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describe in this tutorial, but there are also the advanced and guru interfaces,
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<span id="index-advanced-interface-1"></span>
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<span id="index-guru-interface-1"></span>
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which allow one to efficiently combine multiple/strided transforms
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into a single FFTW plan, transform a subset of a larger
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multi-dimensional array, and/or to handle more general complex-number
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formats. For more information, see <a href="FFTW-Reference.html">FFTW Reference</a>.
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</p>
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<div class="footnote">
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<hr>
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<h4 class="footnotes-heading">Footnotes</h4>
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<h5><a id="FOOT2" href="#DOCF2">(2)</a></h3>
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<p>The
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term “rank” is commonly used in the APL, FORTRAN, and Common Lisp
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traditions, although it is not so common in the C world.</p>
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</div>
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<hr>
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<div class="header">
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<p>
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Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html" accesskey="u" rel="up">Tutorial</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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