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