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Add FFTW3
author Chris Cannam
date Wed, 20 Mar 2013 15:35:50 +0000
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Chris@10 1 <html lang="en">
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Chris@10 3 <title>Real-to-Real Transforms - FFTW 3.3.3</title>
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Chris@10 13 This manual is for FFTW
Chris@10 14 (version 3.3.3, 25 November 2012).
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Chris@10 48 <div class="node">
Chris@10 49 <a name="Real-to-Real-Transforms"></a>
Chris@10 50 <a name="Real_002dto_002dReal-Transforms"></a>
Chris@10 51 <p>
Chris@10 52 Next:&nbsp;<a rel="next" accesskey="n" href="Real_002dto_002dReal-Transform-Kinds.html#Real_002dto_002dReal-Transform-Kinds">Real-to-Real Transform Kinds</a>,
Chris@10 53 Previous:&nbsp;<a rel="previous" accesskey="p" href="Real_002ddata-DFT-Array-Format.html#Real_002ddata-DFT-Array-Format">Real-data DFT Array Format</a>,
Chris@10 54 Up:&nbsp;<a rel="up" accesskey="u" href="Basic-Interface.html#Basic-Interface">Basic Interface</a>
Chris@10 55 <hr>
Chris@10 56 </div>
Chris@10 57
Chris@10 58 <h4 class="subsection">4.3.5 Real-to-Real Transforms</h4>
Chris@10 59
Chris@10 60 <p><a name="index-r2r-203"></a>
Chris@10 61 <pre class="example"> fftw_plan fftw_plan_r2r_1d(int n, double *in, double *out,
Chris@10 62 fftw_r2r_kind kind, unsigned flags);
Chris@10 63 fftw_plan fftw_plan_r2r_2d(int n0, int n1, double *in, double *out,
Chris@10 64 fftw_r2r_kind kind0, fftw_r2r_kind kind1,
Chris@10 65 unsigned flags);
Chris@10 66 fftw_plan fftw_plan_r2r_3d(int n0, int n1, int n2,
Chris@10 67 double *in, double *out,
Chris@10 68 fftw_r2r_kind kind0,
Chris@10 69 fftw_r2r_kind kind1,
Chris@10 70 fftw_r2r_kind kind2,
Chris@10 71 unsigned flags);
Chris@10 72 fftw_plan fftw_plan_r2r(int rank, const int *n, double *in, double *out,
Chris@10 73 const fftw_r2r_kind *kind, unsigned flags);
Chris@10 74 </pre>
Chris@10 75 <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>
Chris@10 76 Plan a real input/output (r2r) transform of various kinds in zero or
Chris@10 77 more dimensions, returning an <code>fftw_plan</code> (see <a href="Using-Plans.html#Using-Plans">Using Plans</a>).
Chris@10 78
Chris@10 79 <p>Once you have created a plan for a certain transform type and
Chris@10 80 parameters, then creating another plan of the same type and parameters,
Chris@10 81 but for different arrays, is fast and shares constant data with the
Chris@10 82 first plan (if it still exists).
Chris@10 83
Chris@10 84 <p>The planner returns <code>NULL</code> if the plan cannot be created. A
Chris@10 85 non-<code>NULL</code> plan is always returned by the basic interface unless
Chris@10 86 you are using a customized FFTW configuration supporting a restricted
Chris@10 87 set of transforms, or for size-1 <code>FFTW_REDFT00</code> kinds (which are
Chris@10 88 not defined).
Chris@10 89 <a name="index-FFTW_005fREDFT00-208"></a>
Chris@10 90
Chris@10 91 <h5 class="subsubheading">Arguments</h5>
Chris@10 92
Chris@10 93 <ul>
Chris@10 94 <li><code>rank</code> is the dimensionality of the transform (it should be the
Chris@10 95 size of the arrays <code>*n</code> and <code>*kind</code>), and can be any
Chris@10 96 non-negative integer. The &lsquo;<samp><span class="samp">_1d</span></samp>&rsquo;, &lsquo;<samp><span class="samp">_2d</span></samp>&rsquo;, and &lsquo;<samp><span class="samp">_3d</span></samp>&rsquo;
Chris@10 97 planners correspond to a <code>rank</code> of <code>1</code>, <code>2</code>, and
Chris@10 98 <code>3</code>, respectively. A <code>rank</code> of zero is equivalent to a copy
Chris@10 99 of one number from input to output.
Chris@10 100
Chris@10 101 <li><code>n</code>, or <code>n0</code>/<code>n1</code>/<code>n2</code>, or <code>n[rank]</code>,
Chris@10 102 respectively, gives the (physical) size of the transform dimensions.
Chris@10 103 They can be any positive integer.
Chris@10 104
Chris@10 105 <ul>
Chris@10 106 <li><a name="index-row_002dmajor-209"></a>Multi-dimensional arrays are stored in row-major order with dimensions:
Chris@10 107 <code>n0</code> x <code>n1</code>; or <code>n0</code> x <code>n1</code> x <code>n2</code>; or
Chris@10 108 <code>n[0]</code> x <code>n[1]</code> x ... x <code>n[rank-1]</code>.
Chris@10 109 See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.
Chris@10 110 <li>FFTW is generally best at handling sizes of the form
Chris@10 111 2<sup>a</sup> 3<sup>b</sup> 5<sup>c</sup> 7<sup>d</sup>
Chris@10 112 11<sup>e</sup> 13<sup>f</sup>,where e+f is either 0 or 1, and the other exponents
Chris@10 113 are arbitrary. Other sizes are computed by means of a slow,
Chris@10 114 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@10 115 for different array sizes; see <a href="Installation-and-Customization.html#Installation-and-Customization">Installation and Customization</a>.)
Chris@10 116 Transforms whose sizes are powers of 2 are especially fast.
Chris@10 117 <li>For a <code>REDFT00</code> or <code>RODFT00</code> transform kind in a dimension of
Chris@10 118 size n, it is n-1 or n+1, respectively, that
Chris@10 119 should be factorizable in the above form.
Chris@10 120 </ul>
Chris@10 121
Chris@10 122 <li><code>in</code> and <code>out</code> point to the input and output arrays of the
Chris@10 123 transform, which may be the same (yielding an in-place transform).
Chris@10 124 <a name="index-in_002dplace-210"></a>These arrays are overwritten during planning, unless
Chris@10 125 <code>FFTW_ESTIMATE</code> is used in the flags. (The arrays need not be
Chris@10 126 initialized, but they must be allocated.)
Chris@10 127
Chris@10 128 <li><code>kind</code>, or <code>kind0</code>/<code>kind1</code>/<code>kind2</code>, or
Chris@10 129 <code>kind[rank]</code>, is the kind of r2r transform used for the
Chris@10 130 corresponding dimension. The valid kind constants are described in
Chris@10 131 <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@10 132 what is computed is the separable product formed by taking each
Chris@10 133 transform kind along the corresponding dimension, one dimension after
Chris@10 134 another.
Chris@10 135
Chris@10 136 <li><a name="index-flags-211"></a><code>flags</code> is a bitwise OR (&lsquo;<samp><span class="samp">|</span></samp>&rsquo;) of zero or more planner flags,
Chris@10 137 as defined in <a href="Planner-Flags.html#Planner-Flags">Planner Flags</a>.
Chris@10 138
Chris@10 139 </ul>
Chris@10 140
Chris@10 141 <!-- =========> -->
Chris@10 142 </body></html>
Chris@10 143