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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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cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
cannam@167 5
cannam@167 6 Copyright (C) 2003 Matteo Frigo.
cannam@167 7
cannam@167 8 Copyright (C) 2003 Massachusetts Institute of Technology.
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cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: Guru vector and transform sizes</title>
cannam@167 26
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cannam@167 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@167 36 <link href="Guru-Interface.html#Guru-Interface" rel="up" title="Guru Interface">
cannam@167 37 <link href="Guru-Complex-DFTs.html#Guru-Complex-DFTs" rel="next" title="Guru Complex DFTs">
cannam@167 38 <link href="Interleaved-and-split-arrays.html#Interleaved-and-split-arrays" rel="prev" title="Interleaved and split arrays">
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cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="Guru-vector-and-transform-sizes"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 74 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@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="Guru-vector-and-transform-sizes-1"></a>
cannam@167 78 <h4 class="subsection">4.5.2 Guru vector and transform sizes</h4>
cannam@167 79
cannam@167 80 <p>The guru interface introduces one basic new data structure,
cannam@167 81 <code>fftw_iodim</code>, that is used to specify sizes and strides for
cannam@167 82 multi-dimensional transforms and vectors:
cannam@167 83 </p>
cannam@167 84 <div class="example">
cannam@167 85 <pre class="example">typedef struct {
cannam@167 86 int n;
cannam@167 87 int is;
cannam@167 88 int os;
cannam@167 89 } fftw_iodim;
cannam@167 90 </pre></div>
cannam@167 91 <a name="index-fftw_005fiodim"></a>
cannam@167 92
cannam@167 93 <p>Here, <code>n</code> is the size of the dimension, and <code>is</code> and <code>os</code>
cannam@167 94 are the strides of that dimension for the input and output arrays. (The
cannam@167 95 stride is the separation of consecutive elements along this dimension.)
cannam@167 96 </p>
cannam@167 97 <p>The meaning of the stride parameter depends on the type of the array
cannam@167 98 that the stride refers to. <em>If the array is interleaved complex,
cannam@167 99 strides are expressed in units of complex numbers
cannam@167 100 (<code>fftw_complex</code>). If the array is split complex or real, strides
cannam@167 101 are expressed in units of real numbers (<code>double</code>).</em> This
cannam@167 102 convention is consistent with the usual pointer arithmetic in the C
cannam@167 103 language. An interleaved array is denoted by a pointer <code>p</code> to
cannam@167 104 <code>fftw_complex</code>, so that <code>p+1</code> points to the next complex
cannam@167 105 number. Split arrays are denoted by pointers to <code>double</code>, in
cannam@167 106 which case pointer arithmetic operates in units of
cannam@167 107 <code>sizeof(double)</code>.
cannam@167 108 <a name="index-stride-2"></a>
cannam@167 109 </p>
cannam@167 110
cannam@167 111 <p>The guru planner interfaces all take a (<code>rank</code>, <code>dims[rank]</code>)
cannam@167 112 pair describing the transform size, and a (<code>howmany_rank</code>,
cannam@167 113 <code>howmany_dims[howmany_rank]</code>) pair describing the &ldquo;vector&rdquo; size (a
cannam@167 114 multi-dimensional loop of transforms to perform), where <code>dims</code> and
cannam@167 115 <code>howmany_dims</code> are arrays of <code>fftw_iodim</code>. Each <code>n</code> field must
cannam@167 116 be positive for <code>dims</code> and nonnegative for <code>howmany_dims</code>, while both
cannam@167 117 <code>rank</code> and <code>howmany_rank</code> must be nonnegative.
cannam@167 118 </p>
cannam@167 119 <p>For example, the <code>howmany</code> parameter in the advanced complex-DFT
cannam@167 120 interface corresponds to <code>howmany_rank</code> = 1,
cannam@167 121 <code>howmany_dims[0].n</code> = <code>howmany</code>, <code>howmany_dims[0].is</code> =
cannam@167 122 <code>idist</code>, and <code>howmany_dims[0].os</code> = <code>odist</code>.
cannam@167 123 <a name="index-howmany-loop"></a>
cannam@167 124 <a name="index-dist-1"></a>
cannam@167 125 (To compute a single transform, you can just use <code>howmany_rank</code> = 0.)
cannam@167 126 </p>
cannam@167 127
cannam@167 128 <p>A row-major multidimensional array with dimensions <code>n[rank]</code>
cannam@167 129 (see <a href="Row_002dmajor-Format.html#Row_002dmajor-Format">Row-major Format</a>) corresponds to <code>dims[i].n</code> =
cannam@167 130 <code>n[i]</code> and the recurrence <code>dims[i].is</code> = <code>n[i+1] *
cannam@167 131 dims[i+1].is</code> (similarly for <code>os</code>). The stride of the last
cannam@167 132 (<code>i=rank-1</code>) dimension is the overall stride of the array.
cannam@167 133 e.g. to be equivalent to the advanced complex-DFT interface, you would
cannam@167 134 have <code>dims[rank-1].is</code> = <code>istride</code> and
cannam@167 135 <code>dims[rank-1].os</code> = <code>ostride</code>.
cannam@167 136 <a name="index-row_002dmajor-3"></a>
cannam@167 137 </p>
cannam@167 138
cannam@167 139 <p>In general, we only guarantee FFTW to return a non-<code>NULL</code> plan if
cannam@167 140 the vector and transform dimensions correspond to a set of distinct
cannam@167 141 indices, and for in-place transforms the input/output strides should
cannam@167 142 be the same.
cannam@167 143 </p>
cannam@167 144 <hr>
cannam@167 145 <div class="header">
cannam@167 146 <p>
cannam@167 147 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@167 148 </div>
cannam@167 149
cannam@167 150
cannam@167 151
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cannam@167 153 </html>