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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
cannam@127 5
cannam@127 6 Copyright (C) 2003 Matteo Frigo.
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cannam@127 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@127 24 <head>
cannam@127 25 <title>FFTW 3.3.5: Guru vector and transform sizes</title>
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cannam@127 69 </head>
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cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Guru-vector-and-transform-sizes"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 75 Next: <a href="Guru-Complex-DFTs.html#Guru-Complex-DFTs" accesskey="n" rel="next">Guru Complex DFTs</a>, Previous: <a href="Interleaved-and-split-arrays.html#Interleaved-and-split-arrays" accesskey="p" rel="prev">Interleaved and split arrays</a>, Up: <a href="Guru-Interface.html#Guru-Interface" accesskey="u" rel="up">Guru Interface</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>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Guru-vector-and-transform-sizes-1"></a>
cannam@127 79 <h4 class="subsection">4.5.2 Guru vector and transform sizes</h4>
cannam@127 80
cannam@127 81 <p>The guru interface introduces one basic new data structure,
cannam@127 82 <code>fftw_iodim</code>, that is used to specify sizes and strides for
cannam@127 83 multi-dimensional transforms and vectors:
cannam@127 84 </p>
cannam@127 85 <div class="example">
cannam@127 86 <pre class="example">typedef struct {
cannam@127 87 int n;
cannam@127 88 int is;
cannam@127 89 int os;
cannam@127 90 } fftw_iodim;
cannam@127 91 </pre></div>
cannam@127 92 <a name="index-fftw_005fiodim"></a>
cannam@127 93
cannam@127 94 <p>Here, <code>n</code> is the size of the dimension, and <code>is</code> and <code>os</code>
cannam@127 95 are the strides of that dimension for the input and output arrays. (The
cannam@127 96 stride is the separation of consecutive elements along this dimension.)
cannam@127 97 </p>
cannam@127 98 <p>The meaning of the stride parameter depends on the type of the array
cannam@127 99 that the stride refers to. <em>If the array is interleaved complex,
cannam@127 100 strides are expressed in units of complex numbers
cannam@127 101 (<code>fftw_complex</code>). If the array is split complex or real, strides
cannam@127 102 are expressed in units of real numbers (<code>double</code>).</em> This
cannam@127 103 convention is consistent with the usual pointer arithmetic in the C
cannam@127 104 language. An interleaved array is denoted by a pointer <code>p</code> to
cannam@127 105 <code>fftw_complex</code>, so that <code>p+1</code> points to the next complex
cannam@127 106 number. Split arrays are denoted by pointers to <code>double</code>, in
cannam@127 107 which case pointer arithmetic operates in units of
cannam@127 108 <code>sizeof(double)</code>.
cannam@127 109 <a name="index-stride-2"></a>
cannam@127 110 </p>
cannam@127 111
cannam@127 112 <p>The guru planner interfaces all take a (<code>rank</code>, <code>dims[rank]</code>)
cannam@127 113 pair describing the transform size, and a (<code>howmany_rank</code>,
cannam@127 114 <code>howmany_dims[howmany_rank]</code>) pair describing the &ldquo;vector&rdquo; size (a
cannam@127 115 multi-dimensional loop of transforms to perform), where <code>dims</code> and
cannam@127 116 <code>howmany_dims</code> are arrays of <code>fftw_iodim</code>.
cannam@127 117 </p>
cannam@127 118 <p>For example, the <code>howmany</code> parameter in the advanced complex-DFT
cannam@127 119 interface corresponds to <code>howmany_rank</code> = 1,
cannam@127 120 <code>howmany_dims[0].n</code> = <code>howmany</code>, <code>howmany_dims[0].is</code> =
cannam@127 121 <code>idist</code>, and <code>howmany_dims[0].os</code> = <code>odist</code>.
cannam@127 122 <a name="index-howmany-loop"></a>
cannam@127 123 <a name="index-dist-1"></a>
cannam@127 124 (To compute a single transform, you can just use <code>howmany_rank</code> = 0.)
cannam@127 125 </p>
cannam@127 126
cannam@127 127 <p>A row-major multidimensional array with dimensions <code>n[rank]</code>
cannam@127 128 (see <a href="Row_002dmajor-Format.html#Row_002dmajor-Format">Row-major Format</a>) corresponds to <code>dims[i].n</code> =
cannam@127 129 <code>n[i]</code> and the recurrence <code>dims[i].is</code> = <code>n[i+1] *
cannam@127 130 dims[i+1].is</code> (similarly for <code>os</code>). The stride of the last
cannam@127 131 (<code>i=rank-1</code>) dimension is the overall stride of the array.
cannam@127 132 e.g. to be equivalent to the advanced complex-DFT interface, you would
cannam@127 133 have <code>dims[rank-1].is</code> = <code>istride</code> and
cannam@127 134 <code>dims[rank-1].os</code> = <code>ostride</code>.
cannam@127 135 <a name="index-row_002dmajor-3"></a>
cannam@127 136 </p>
cannam@127 137
cannam@127 138 <p>In general, we only guarantee FFTW to return a non-<code>NULL</code> plan if
cannam@127 139 the vector and transform dimensions correspond to a set of distinct
cannam@127 140 indices, and for in-place transforms the input/output strides should
cannam@127 141 be the same.
cannam@127 142 </p>
cannam@127 143 <hr>
cannam@127 144 <div class="header">
cannam@127 145 <p>
cannam@127 146 Next: <a href="Guru-Complex-DFTs.html#Guru-Complex-DFTs" accesskey="n" rel="next">Guru Complex DFTs</a>, Previous: <a href="Interleaved-and-split-arrays.html#Interleaved-and-split-arrays" accesskey="p" rel="prev">Interleaved and split arrays</a>, Up: <a href="Guru-Interface.html#Guru-Interface" accesskey="u" rel="up">Guru Interface</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>
cannam@127 147 </div>
cannam@127 148
cannam@127 149
cannam@127 150
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cannam@127 152 </html>