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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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71 <a name="Complex-Multi_002dDimensional-DFTs"></a>
72 <div class="header">
73 <p>
74 Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html#Tutorial" accesskey="u" rel="up">Tutorial</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
75 </div>
76 <hr>
77 <a name="Complex-Multi_002dDimensional-DFTs-1"></a>
78 <h3 class="section">2.2 Complex Multi-Dimensional DFTs</h3>
79
80 <p>Multi-dimensional transforms work much the same way as one-dimensional
81 transforms: you allocate arrays of <code>fftw_complex</code> (preferably
82 using <code>fftw_malloc</code>), create an <code>fftw_plan</code>, execute it as
83 many times as you want with <code>fftw_execute(plan)</code>, and clean up
84 with <code>fftw_destroy_plan(plan)</code> (and <code>fftw_free</code>).
85 </p>
86 <p>FFTW provides two routines for creating plans for 2d and 3d transforms,
87 and one routine for creating plans of arbitrary dimensionality.
88 The 2d and 3d routines have the following signature:
89 </p><div class="example">
90 <pre class="example">fftw_plan fftw_plan_dft_2d(int n0, int n1,
91 fftw_complex *in, fftw_complex *out,
92 int sign, unsigned flags);
93 fftw_plan fftw_plan_dft_3d(int n0, int n1, int n2,
94 fftw_complex *in, fftw_complex *out,
95 int sign, unsigned flags);
96 </pre></div>
97 <a name="index-fftw_005fplan_005fdft_005f2d"></a>
98 <a name="index-fftw_005fplan_005fdft_005f3d"></a>
99
100 <p>These routines create plans for <code>n0</code> by <code>n1</code> two-dimensional
101 (2d) transforms and <code>n0</code> by <code>n1</code> by <code>n2</code> 3d transforms,
102 respectively. All of these transforms operate on contiguous arrays in
103 the C-standard <em>row-major</em> order, so that the last dimension has the
104 fastest-varying index in the array. This layout is described further in
105 <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
106 </p>
107 <p>FFTW can also compute transforms of higher dimensionality. In order to
108 avoid confusion between the various meanings of the the word
109 &ldquo;dimension&rdquo;, we use the term <em>rank</em>
110 <a name="index-rank"></a>
111 to denote the number of independent indices in an array.<a name="DOCF2" href="#FOOT2"><sup>2</sup></a> For
112 example, we say that a 2d transform has rank&nbsp;2, a 3d transform has
113 rank&nbsp;3, and so on. You can plan transforms of arbitrary rank by
114 means of the following function:
115 </p>
116 <div class="example">
117 <pre class="example">fftw_plan fftw_plan_dft(int rank, const int *n,
118 fftw_complex *in, fftw_complex *out,
119 int sign, unsigned flags);
120 </pre></div>
121 <a name="index-fftw_005fplan_005fdft"></a>
122
123 <p>Here, <code>n</code> is a pointer to an array <code>n[rank]</code> denoting an
124 <code>n[0]</code> by <code>n[1]</code> by &hellip; by <code>n[rank-1]</code> transform.
125 Thus, for example, the call
126 </p><div class="example">
127 <pre class="example">fftw_plan_dft_2d(n0, n1, in, out, sign, flags);
128 </pre></div>
129 <p>is equivalent to the following code fragment:
130 </p><div class="example">
131 <pre class="example">int n[2];
132 n[0] = n0;
133 n[1] = n1;
134 fftw_plan_dft(2, n, in, out, sign, flags);
135 </pre></div>
136 <p><code>fftw_plan_dft</code> is not restricted to 2d and 3d transforms,
137 however, but it can plan transforms of arbitrary rank.
138 </p>
139 <p>You may have noticed that all the planner routines described so far
140 have overlapping functionality. For example, you can plan a 1d or 2d
141 transform by using <code>fftw_plan_dft</code> with a <code>rank</code> of <code>1</code>
142 or <code>2</code>, or even by calling <code>fftw_plan_dft_3d</code> with <code>n0</code>
143 and/or <code>n1</code> equal to <code>1</code> (with no loss in efficiency). This
144 pattern continues, and FFTW&rsquo;s planning routines in general form a
145 &ldquo;partial order,&rdquo; sequences of
146 <a name="index-partial-order"></a>
147 interfaces with strictly increasing generality but correspondingly
148 greater complexity.
149 </p>
150 <p><code>fftw_plan_dft</code> is the most general complex-DFT routine that we
151 describe in this tutorial, but there are also the advanced and guru interfaces,
152 <a name="index-advanced-interface-1"></a>
153 <a name="index-guru-interface-1"></a>
154 which allow one to efficiently combine multiple/strided transforms
155 into a single FFTW plan, transform a subset of a larger
156 multi-dimensional array, and/or to handle more general complex-number
157 formats. For more information, see <a href="FFTW-Reference.html#FFTW-Reference">FFTW Reference</a>.
158 </p>
159 <div class="footnote">
160 <hr>
161 <h4 class="footnotes-heading">Footnotes</h4>
162
163 <h3><a name="FOOT2" href="#DOCF2">(2)</a></h3>
164 <p>The
165 term &ldquo;rank&rdquo; is commonly used in the APL, FORTRAN, and Common Lisp
166 traditions, although it is not so common in the C&nbsp;world.</p>
167 </div>
168 <hr>
169 <div class="header">
170 <p>
171 Next: <a href="One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data" accesskey="n" rel="next">One-Dimensional DFTs of Real Data</a>, Previous: <a href="Complex-One_002dDimensional-DFTs.html#Complex-One_002dDimensional-DFTs" accesskey="p" rel="prev">Complex One-Dimensional DFTs</a>, Up: <a href="Tutorial.html#Tutorial" accesskey="u" rel="up">Tutorial</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
172 </div>
173
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