Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.8/doc/html/Advanced-Complex-DFTs.html @ 167:bd3cc4d1df30

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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
parents
children
rev   line source
cannam@167 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
cannam@167 2 <html>
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.
cannam@167 9
cannam@167 10 Permission is granted to make and distribute verbatim copies of this
cannam@167 11 manual provided the copyright notice and this permission notice are
cannam@167 12 preserved on all copies.
cannam@167 13
cannam@167 14 Permission is granted to copy and distribute modified versions of this
cannam@167 15 manual under the conditions for verbatim copying, provided that the
cannam@167 16 entire resulting derived work is distributed under the terms of a
cannam@167 17 permission notice identical to this one.
cannam@167 18
cannam@167 19 Permission is granted to copy and distribute translations of this manual
cannam@167 20 into another language, under the above conditions for modified versions,
cannam@167 21 except that this permission notice may be stated in a translation
cannam@167 22 approved by the Free Software Foundation. -->
cannam@167 23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
cannam@167 24 <head>
cannam@167 25 <title>FFTW 3.3.8: Advanced Complex DFTs</title>
cannam@167 26
cannam@167 27 <meta name="description" content="FFTW 3.3.8: Advanced Complex DFTs">
cannam@167 28 <meta name="keywords" content="FFTW 3.3.8: Advanced Complex DFTs">
cannam@167 29 <meta name="resource-type" content="document">
cannam@167 30 <meta name="distribution" content="global">
cannam@167 31 <meta name="Generator" content="makeinfo">
cannam@167 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
cannam@167 33 <link href="index.html#Top" rel="start" title="Top">
cannam@167 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
cannam@167 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
cannam@167 36 <link href="Advanced-Interface.html#Advanced-Interface" rel="up" title="Advanced Interface">
cannam@167 37 <link href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" rel="next" title="Advanced Real-data DFTs">
cannam@167 38 <link href="Advanced-Interface.html#Advanced-Interface" rel="prev" title="Advanced Interface">
cannam@167 39 <style type="text/css">
cannam@167 40 <!--
cannam@167 41 a.summary-letter {text-decoration: none}
cannam@167 42 blockquote.indentedblock {margin-right: 0em}
cannam@167 43 blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
cannam@167 44 blockquote.smallquotation {font-size: smaller}
cannam@167 45 div.display {margin-left: 3.2em}
cannam@167 46 div.example {margin-left: 3.2em}
cannam@167 47 div.lisp {margin-left: 3.2em}
cannam@167 48 div.smalldisplay {margin-left: 3.2em}
cannam@167 49 div.smallexample {margin-left: 3.2em}
cannam@167 50 div.smalllisp {margin-left: 3.2em}
cannam@167 51 kbd {font-style: oblique}
cannam@167 52 pre.display {font-family: inherit}
cannam@167 53 pre.format {font-family: inherit}
cannam@167 54 pre.menu-comment {font-family: serif}
cannam@167 55 pre.menu-preformatted {font-family: serif}
cannam@167 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
cannam@167 57 pre.smallexample {font-size: smaller}
cannam@167 58 pre.smallformat {font-family: inherit; font-size: smaller}
cannam@167 59 pre.smalllisp {font-size: smaller}
cannam@167 60 span.nolinebreak {white-space: nowrap}
cannam@167 61 span.roman {font-family: initial; font-weight: normal}
cannam@167 62 span.sansserif {font-family: sans-serif; font-weight: normal}
cannam@167 63 ul.no-bullet {list-style: none}
cannam@167 64 -->
cannam@167 65 </style>
cannam@167 66
cannam@167 67
cannam@167 68 </head>
cannam@167 69
cannam@167 70 <body lang="en">
cannam@167 71 <a name="Advanced-Complex-DFTs"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 74 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced 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="Advanced-Complex-DFTs-1"></a>
cannam@167 78 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
cannam@167 79
cannam@167 80 <div class="example">
cannam@167 81 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
cannam@167 82 fftw_complex *in, const int *inembed,
cannam@167 83 int istride, int idist,
cannam@167 84 fftw_complex *out, const int *onembed,
cannam@167 85 int ostride, int odist,
cannam@167 86 int sign, unsigned flags);
cannam@167 87 </pre></div>
cannam@167 88 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
cannam@167 89
cannam@167 90 <p>This routine plans multiple multidimensional complex DFTs, and it
cannam@167 91 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
cannam@167 92 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
cannam@167 93 <code>n</code>. In addition, the transform data need not be contiguous, but
cannam@167 94 it may be laid out in memory with an arbitrary stride. To account for
cannam@167 95 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
cannam@167 96 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
cannam@167 97 {<code>i</code>,<code>o</code>}<code>stride</code>, and
cannam@167 98 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
cannam@167 99 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
cannam@167 100 and&nbsp;3, but the advanced interface handles only the general-rank
cannam@167 101 case.
cannam@167 102 </p>
cannam@167 103 <p><code>howmany</code> is the (nonnegative) number of transforms to compute. The resulting
cannam@167 104 plan computes <code>howmany</code> transforms, where the input of the
cannam@167 105 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
cannam@167 106 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
cannam@167 107 obtained in this way can often be faster than calling FFTW multiple
cannam@167 108 times for the individual transforms. The basic <code>fftw_plan_dft</code>
cannam@167 109 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
cannam@167 110 parameters are ignored).
cannam@167 111 <a name="index-howmany-parameter"></a>
cannam@167 112 <a name="index-dist"></a>
cannam@167 113 </p>
cannam@167 114
cannam@167 115 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
cannam@167 116 <code>n</code>, as in the basic interface. In addition, the advanced
cannam@167 117 interface allows the input and output arrays of each transform to be
cannam@167 118 row-major subarrays of larger rank-<code>rank</code> arrays, described by
cannam@167 119 <code>inembed</code> and <code>onembed</code> parameters, respectively.
cannam@167 120 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
cannam@167 121 and <code>n</code> should be elementwise less than or equal to
cannam@167 122 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
cannam@167 123 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
cannam@167 124 physical and logical dimensions, as in the basic interface.)
cannam@167 125 </p>
cannam@167 126 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
cannam@167 127 the input or output arrays is located at <code>j*istride</code> or
cannam@167 128 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
cannam@167 129 <code>j</code> is the ordinary row-major index.) When combined with the
cannam@167 130 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
cannam@167 131 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
cannam@167 132 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
cannam@167 133 <a name="index-stride-1"></a>
cannam@167 134 </p>
cannam@167 135
cannam@167 136 <p>For in-place transforms, the input and output <code>stride</code> and
cannam@167 137 <code>dist</code> parameters should be the same; otherwise, the planner may
cannam@167 138 return <code>NULL</code>.
cannam@167 139 </p>
cannam@167 140 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
cannam@167 141 this function returns. You can safely free or reuse them.
cannam@167 142 </p>
cannam@167 143 <p><strong>Examples</strong>:
cannam@167 144 One transform of one 5 by 6 array contiguous in memory:
cannam@167 145 </p><div class="example">
cannam@167 146 <pre class="example"> int rank = 2;
cannam@167 147 int n[] = {5, 6};
cannam@167 148 int howmany = 1;
cannam@167 149 int idist = odist = 0; /* unused because howmany = 1 */
cannam@167 150 int istride = ostride = 1; /* array is contiguous in memory */
cannam@167 151 int *inembed = n, *onembed = n;
cannam@167 152 </pre></div>
cannam@167 153
cannam@167 154 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
cannam@167 155 stored in memory one after another:
cannam@167 156 </p><div class="example">
cannam@167 157 <pre class="example"> int rank = 2;
cannam@167 158 int n[] = {5, 6};
cannam@167 159 int howmany = 3;
cannam@167 160 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
cannam@167 161 between the first element
cannam@167 162 of the first array and the
cannam@167 163 first element of the second array */
cannam@167 164 int istride = ostride = 1; /* array is contiguous in memory */
cannam@167 165 int *inembed = n, *onembed = n;
cannam@167 166 </pre></div>
cannam@167 167
cannam@167 168 <p>Transform each column of a 2d array with 10 rows and 3 columns:
cannam@167 169 </p><div class="example">
cannam@167 170 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
cannam@167 171 int n[] = {10}; /* 1d transforms of length 10 */
cannam@167 172 int howmany = 3;
cannam@167 173 int idist = odist = 1;
cannam@167 174 int istride = ostride = 3; /* distance between two elements in
cannam@167 175 the same column */
cannam@167 176 int *inembed = n, *onembed = n;
cannam@167 177 </pre></div>
cannam@167 178
cannam@167 179 <hr>
cannam@167 180 <div class="header">
cannam@167 181 <p>
cannam@167 182 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced 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@167 183 </div>
cannam@167 184
cannam@167 185
cannam@167 186
cannam@167 187 </body>
cannam@167 188 </html>