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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 37bf6b4a2645
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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
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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