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Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>Guru vector and transform sizes - FFTW 3.3.3</title>
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49 <a name="Guru-vector-and-transform-sizes"></a>
50 <p>
51 Next:&nbsp;<a rel="next" accesskey="n" href="Guru-Complex-DFTs.html#Guru-Complex-DFTs">Guru Complex DFTs</a>,
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56
57 <h4 class="subsection">4.5.2 Guru vector and transform sizes</h4>
58
59 <p>The guru interface introduces one basic new data structure,
60 <code>fftw_iodim</code>, that is used to specify sizes and strides for
61 multi-dimensional transforms and vectors:
62
63 <pre class="example"> typedef struct {
64 int n;
65 int is;
66 int os;
67 } fftw_iodim;
68 </pre>
69 <p><a name="index-fftw_005fiodim-243"></a>
70 Here, <code>n</code> is the size of the dimension, and <code>is</code> and <code>os</code>
71 are the strides of that dimension for the input and output arrays. (The
72 stride is the separation of consecutive elements along this dimension.)
73
74 <p>The meaning of the stride parameter depends on the type of the array
75 that the stride refers to. <em>If the array is interleaved complex,
76 strides are expressed in units of complex numbers
77 (</em><code>fftw_complex</code><em>). If the array is split complex or real, strides
78 are expressed in units of real numbers (</em><code>double</code><em>).</em> This
79 convention is consistent with the usual pointer arithmetic in the C
80 language. An interleaved array is denoted by a pointer <code>p</code> to
81 <code>fftw_complex</code>, so that <code>p+1</code> points to the next complex
82 number. Split arrays are denoted by pointers to <code>double</code>, in
83 which case pointer arithmetic operates in units of
84 <code>sizeof(double)</code>.
85 <a name="index-stride-244"></a>
86
87 <p>The guru planner interfaces all take a (<code>rank</code>, <code>dims[rank]</code>)
88 pair describing the transform size, and a (<code>howmany_rank</code>,
89 <code>howmany_dims[howmany_rank]</code>) pair describing the &ldquo;vector&rdquo; size (a
90 multi-dimensional loop of transforms to perform), where <code>dims</code> and
91 <code>howmany_dims</code> are arrays of <code>fftw_iodim</code>.
92
93 <p>For example, the <code>howmany</code> parameter in the advanced complex-DFT
94 interface corresponds to <code>howmany_rank</code> = 1,
95 <code>howmany_dims[0].n</code> = <code>howmany</code>, <code>howmany_dims[0].is</code> =
96 <code>idist</code>, and <code>howmany_dims[0].os</code> = <code>odist</code>.
97 <a name="index-howmany-loop-245"></a><a name="index-dist-246"></a>(To compute a single transform, you can just use <code>howmany_rank</code> = 0.)
98
99 <p>A row-major multidimensional array with dimensions <code>n[rank]</code>
100 (see <a href="Row_002dmajor-Format.html#Row_002dmajor-Format">Row-major Format</a>) corresponds to <code>dims[i].n</code> =
101 <code>n[i]</code> and the recurrence <code>dims[i].is</code> = <code>n[i+1] *
102 dims[i+1].is</code> (similarly for <code>os</code>). The stride of the last
103 (<code>i=rank-1</code>) dimension is the overall stride of the array.
104 e.g. to be equivalent to the advanced complex-DFT interface, you would
105 have <code>dims[rank-1].is</code> = <code>istride</code> and
106 <code>dims[rank-1].os</code> = <code>ostride</code>.
107 <a name="index-row_002dmajor-247"></a>
108
109 <p>In general, we only guarantee FFTW to return a non-<code>NULL</code> plan if
110 the vector and transform dimensions correspond to a set of distinct
111 indices, and for in-place transforms the input/output strides should
112 be the same.
113
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