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diff src/fftw-3.3.3/doc/html/Real_002dto_002dReal-Transforms.html @ 95:89f5e221ed7b
Add FFTW3
| author | Chris Cannam <cannam@all-day-breakfast.com> |
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| date | Wed, 20 Mar 2013 15:35:50 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.3/doc/html/Real_002dto_002dReal-Transforms.html Wed Mar 20 15:35:50 2013 +0000 @@ -0,0 +1,143 @@ +<html lang="en"> +<head> +<title>Real-to-Real Transforms - FFTW 3.3.3</title> +<meta http-equiv="Content-Type" content="text/html"> +<meta name="description" content="FFTW 3.3.3"> +<meta name="generator" content="makeinfo 4.13"> +<link title="Top" rel="start" href="index.html#Top"> +<link rel="up" href="Basic-Interface.html#Basic-Interface" title="Basic Interface"> +<link rel="prev" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format" title="Real-data DFT Array Format"> +<link rel="next" href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds" title="Real-to-Real Transform Kinds"> +<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> +<!-- +This manual is for FFTW +(version 3.3.3, 25 November 2012). + +Copyright (C) 2003 Matteo Frigo. + +Copyright (C) 2003 Massachusetts Institute of Technology. + + Permission is granted to make and distribute verbatim copies of + this manual provided the copyright notice and this permission + notice are preserved on all copies. + + Permission is granted to copy and distribute modified versions of + this manual under the conditions for verbatim copying, provided + that the entire resulting derived work is distributed under the + terms of a permission notice identical to this one. + + Permission is granted to copy and distribute translations of this + manual into another language, under the above conditions for + modified versions, except that this permission notice may be + stated in a translation approved by the Free Software Foundation. + --> +<meta http-equiv="Content-Style-Type" content="text/css"> +<style type="text/css"><!-- + pre.display { font-family:inherit } + pre.format { font-family:inherit } + pre.smalldisplay { font-family:inherit; font-size:smaller } + pre.smallformat { font-family:inherit; font-size:smaller } + pre.smallexample { font-size:smaller } + pre.smalllisp { font-size:smaller } + span.sc { font-variant:small-caps } + span.roman { font-family:serif; font-weight:normal; } + span.sansserif { font-family:sans-serif; font-weight:normal; } +--></style> +</head> +<body> +<div class="node"> +<a name="Real-to-Real-Transforms"></a> +<a name="Real_002dto_002dReal-Transforms"></a> +<p> +Next: <a rel="next" accesskey="n" href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>, +Previous: <a rel="previous" accesskey="p" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>, +Up: <a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a> +<hr> +</div> + +<h4 class="subsection">4.3.5 Real-to-Real Transforms</h4> + +<p><a name="index-r2r-203"></a> +<pre class="example"> fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out, + fftw_r2r_kind kind, unsigned flags); + fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out, + fftw_r2r_kind kind0, fftw_r2r_kind kind1, + unsigned flags); + fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2, + double *in, double *out, + fftw_r2r_kind kind0, + fftw_r2r_kind kind1, + fftw_r2r_kind kind2, + unsigned flags); + fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out, + const fftw_r2r_kind *kind, unsigned flags); +</pre> + <p><a name="index-fftw_005fplan_005fr2r_005f1d-204"></a><a name="index-fftw_005fplan_005fr2r_005f2d-205"></a><a name="index-fftw_005fplan_005fr2r_005f3d-206"></a><a name="index-fftw_005fplan_005fr2r-207"></a> +Plan a real input/output (r2r) transform of various kinds in zero or +more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>). + + <p>Once you have created a plan for a certain transform type and +parameters, then creating another plan of the same type and parameters, +but for different arrays, is fast and shares constant data with the +first plan (if it still exists). + + <p>The planner returns <code>NULL</code> if the plan cannot be created. A +non-<code>NULL</code> plan is always returned by the basic interface unless +you are using a customized FFTW configuration supporting a restricted +set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are +not defined). +<a name="index-FFTW_005fREDFT00-208"></a> + +<h5 class="subsubheading">Arguments</h5> + + <ul> +<li><code>rank</code> is the dimensionality of the transform (it should be the +size of the arrays <code>*n</code> and <code>*kind</code>), and can be any +non-negative integer. The ‘<samp><span class="samp">_1d</span></samp>’, ‘<samp><span class="samp">_2d</span></samp>’, and ‘<samp><span class="samp">_3d</span></samp>’ +planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and +<code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy +of one number from input to output. + + <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>, +respectively, gives the (physical) size of the transform dimensions. +They can be any positive integer. + + <ul> +<li><a name="index-row_002dmajor-209"></a>Multi-dimensional arrays are stored in row-major order with dimensions: +<code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or +<code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>. +See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. +<li>FFTW is generally best at handling sizes of the form +2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup> + 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents +are arbitrary. Other sizes are computed by means of a slow, +general-purpose algorithm (which nevertheless retains <i>O</i>(<i>n</i> log <i>n</i>) performance even for prime sizes). (It is possible to customize FFTW +for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.) +Transforms whose sizes are powers of 2 are especially fast. +<li>For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of +size n, it is n-1 or n+1, respectively, that +should be factorizable in the above form. +</ul> + + <li><code>in</code> and <code>out</code> point to the input and output arrays of the +transform, which may be the same (yielding an in-place transform). +<a name="index-in_002dplace-210"></a>These arrays are overwritten during planning, unless +<code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be +initialized, but they must be allocated.) + + <li><code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or +<code>kind[rank]</code>, is the kind of r2r transform used for the +corresponding dimension. The valid kind constants are described in +<a href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>. In a multi-dimensional transform, +what is computed is the separable product formed by taking each +transform kind along the corresponding dimension, one dimension after +another. + + <li><a name="index-flags-211"></a><code>flags</code> is a bitwise OR (‘<samp><span class="samp">|</span></samp>’) of zero or more planner flags, +as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>. + +</ul> + +<!-- =========> --> + </body></html> +