Mercurial > hg > sv-dependency-builds

annotate src/fftw-3.3.5/doc/html/Real_002dto_002dReal-Transforms.html @ 83:ae30d91d2ffe

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Replace these with versions built using an older toolset (so as to avoid ABI compatibilities when linking on Ubuntu 14.04 for packaging purposes)
author Chris Cannam
date Fri, 07 Feb 2020 11:51:13 +0000
parents 2cd0e3b3e1fd
children
rev   line source
Chris@42 1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
Chris@42 2 <html>
Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
Chris@42 5
Chris@42 6 Copyright (C) 2003 Matteo Frigo.
Chris@42 7
Chris@42 8 Copyright (C) 2003 Massachusetts Institute of Technology.
Chris@42 9
Chris@42 10 Permission is granted to make and distribute verbatim copies of this
Chris@42 11 manual provided the copyright notice and this permission notice are
Chris@42 12 preserved on all copies.
Chris@42 13
Chris@42 14 Permission is granted to copy and distribute modified versions of this
Chris@42 15 manual under the conditions for verbatim copying, provided that the
Chris@42 16 entire resulting derived work is distributed under the terms of a
Chris@42 17 permission notice identical to this one.
Chris@42 18
Chris@42 19 Permission is granted to copy and distribute translations of this manual
Chris@42 20 into another language, under the above conditions for modified versions,
Chris@42 21 except that this permission notice may be stated in a translation
Chris@42 22 approved by the Free Software Foundation. -->
Chris@42 23 <!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
Chris@42 24 <head>
Chris@42 25 <title>FFTW 3.3.5: Real-to-Real Transforms</title>
Chris@42 26
Chris@42 27 <meta name="description" content="FFTW 3.3.5: Real-to-Real Transforms">
Chris@42 28 <meta name="keywords" content="FFTW 3.3.5: Real-to-Real Transforms">
Chris@42 29 <meta name="resource-type" content="document">
Chris@42 30 <meta name="distribution" content="global">
Chris@42 31 <meta name="Generator" content="makeinfo">
Chris@42 32 <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
Chris@42 33 <link href="index.html#Top" rel="start" title="Top">
Chris@42 34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
Chris@42 35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
Chris@42 36 <link href="Basic-Interface.html#Basic-Interface" rel="up" title="Basic Interface">
Chris@42 37 <link href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" rel="next" title="Real-to-Real Transform Kinds">
Chris@42 38 <link href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" rel="prev" title="Real-data DFT Array Format">
Chris@42 39 <style type="text/css">
Chris@42 40 <!--
Chris@42 41 a.summary-letter {text-decoration: none}
Chris@42 42 blockquote.smallquotation {font-size: smaller}
Chris@42 43 div.display {margin-left: 3.2em}
Chris@42 44 div.example {margin-left: 3.2em}
Chris@42 45 div.indentedblock {margin-left: 3.2em}
Chris@42 46 div.lisp {margin-left: 3.2em}
Chris@42 47 div.smalldisplay {margin-left: 3.2em}
Chris@42 48 div.smallexample {margin-left: 3.2em}
Chris@42 49 div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
Chris@42 50 div.smalllisp {margin-left: 3.2em}
Chris@42 51 kbd {font-style:oblique}
Chris@42 52 pre.display {font-family: inherit}
Chris@42 53 pre.format {font-family: inherit}
Chris@42 54 pre.menu-comment {font-family: serif}
Chris@42 55 pre.menu-preformatted {font-family: serif}
Chris@42 56 pre.smalldisplay {font-family: inherit; font-size: smaller}
Chris@42 57 pre.smallexample {font-size: smaller}
Chris@42 58 pre.smallformat {font-family: inherit; font-size: smaller}
Chris@42 59 pre.smalllisp {font-size: smaller}
Chris@42 60 span.nocodebreak {white-space:nowrap}
Chris@42 61 span.nolinebreak {white-space:nowrap}
Chris@42 62 span.roman {font-family:serif; font-weight:normal}
Chris@42 63 span.sansserif {font-family:sans-serif; font-weight:normal}
Chris@42 64 ul.no-bullet {list-style: none}
Chris@42 65 -->
Chris@42 66 </style>
Chris@42 67
Chris@42 68
Chris@42 69 </head>
Chris@42 70
Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Real_002dto_002dReal-Transforms"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 75 Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic 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>
Chris@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Real_002dto_002dReal-Transforms-1"></a>
Chris@42 79 <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
Chris@42 80 <a name="index-r2r-1"></a>
Chris@42 81
Chris@42 82 <div class="example">
Chris@42 83 <pre class="example">fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
Chris@42 84 fftw_r2r_kind kind, unsigned flags);
Chris@42 85 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
Chris@42 86 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
Chris@42 87 unsigned flags);
Chris@42 88 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
Chris@42 89 double *in, double *out,
Chris@42 90 fftw_r2r_kind kind0,
Chris@42 91 fftw_r2r_kind kind1,
Chris@42 92 fftw_r2r_kind kind2,
Chris@42 93 unsigned flags);
Chris@42 94 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
Chris@42 95 const fftw_r2r_kind *kind, unsigned flags);
Chris@42 96 </pre></div>
Chris@42 97 <a name="index-fftw_005fplan_005fr2r_005f1d-1"></a>
Chris@42 98 <a name="index-fftw_005fplan_005fr2r_005f2d-1"></a>
Chris@42 99 <a name="index-fftw_005fplan_005fr2r_005f3d-1"></a>
Chris@42 100 <a name="index-fftw_005fplan_005fr2r-1"></a>
Chris@42 101
Chris@42 102 <p>Plan a real input/output (r2r) transform of various kinds in zero or
Chris@42 103 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@42 104 </p>
Chris@42 105 <p>Once you have created a plan for a certain transform type and
Chris@42 106 parameters, then creating another plan of the same type and parameters,
Chris@42 107 but for different arrays, is fast and shares constant data with the
Chris@42 108 first plan (if it still exists).
Chris@42 109 </p>
Chris@42 110 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@42 111 non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@42 112 you are using a customized FFTW configuration supporting a restricted
Chris@42 113 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
Chris@42 114 not defined).
Chris@42 115 <a name="index-FFTW_005fREDFT00-1"></a>
Chris@42 116 </p>
Chris@42 117 <a name="Arguments-2"></a>
Chris@42 118 <h4 class="subsubheading">Arguments</h4>
Chris@42 119 <ul>
Chris@42 120 <li> <code>rank</code> is the dimensionality of the transform (it should be the
Chris@42 121 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
Chris@42 122 non-negative integer. The &lsquo;<samp>_1d</samp>&rsquo;, &lsquo;<samp>_2d</samp>&rsquo;, and &lsquo;<samp>_3d</samp>&rsquo;
Chris@42 123 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
Chris@42 124 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
Chris@42 125 of one number from input to output.
Chris@42 126
Chris@42 127 </li><li> <code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
Chris@42 128 respectively, gives the (physical) size of the transform dimensions.
Chris@42 129 They can be any positive integer.
Chris@42 130
Chris@42 131 <ul class="no-bullet">
Chris@42 132 <li>- <a name="index-row_002dmajor-2"></a>
Chris@42 133 Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@42 134 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@42 135 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@42 136 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@42 137 </li><li>- FFTW is generally best at handling sizes of the form
Chris@42 138 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@42 139 11<sup>e</sup> 13<sup>f</sup>,where <em>e+f</em> is either <em>0</em> or <em>1</em>, and the other exponents
Chris@42 140 are arbitrary. Other sizes are computed by means of a slow,
Chris@42 141 general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>) performance even for prime sizes). (It is possible to customize FFTW
Chris@42 142 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@42 143 Transforms whose sizes are powers of <em>2</em> are especially fast.
Chris@42 144 </li><li>- For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
Chris@42 145 size <em>n</em>, it is <em>n-1</em> or <em>n+1</em>, respectively, that
Chris@42 146 should be factorizable in the above form.
Chris@42 147 </li></ul>
Chris@42 148
Chris@42 149 </li><li> <code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@42 150 transform, which may be the same (yielding an in-place transform).
Chris@42 151 <a name="index-in_002dplace-5"></a>
Chris@42 152 These arrays are overwritten during planning, unless
Chris@42 153 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@42 154 initialized, but they must be allocated.)
Chris@42 155
Chris@42 156 </li><li> <code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
Chris@42 157 <code>kind[rank]</code>, is the kind of r2r transform used for the
Chris@42 158 corresponding dimension. The valid kind constants are described in
Chris@42 159 <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform,
Chris@42 160 what is computed is the separable product formed by taking each
Chris@42 161 transform kind along the corresponding dimension, one dimension after
Chris@42 162 another.
Chris@42 163
Chris@42 164 </li><li> <a name="index-flags-4"></a>
Chris@42 165 <code>flags</code> is a bitwise OR (&lsquo;<samp>|</samp>&rsquo;) of zero or more planner flags,
Chris@42 166 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@42 167
Chris@42 168 </li></ul>
Chris@42 169
Chris@42 170 <hr>
Chris@42 171 <div class="header">
Chris@42 172 <p>
Chris@42 173 Next: <a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" accesskey="n" rel="next">Real-to-Real Transform Kinds</a>, Previous: <a href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" accesskey="p" rel="prev">Real-data DFT Array Format</a>, Up: <a href="Basic-Interface.html#Basic-Interface" accesskey="u" rel="up">Basic 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>
Chris@42 174 </div>
Chris@42 175
Chris@42 176
Chris@42 177
Chris@42 178 </body>
Chris@42 179 </html>