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author Geogaddi\David <d.m.ronan@qmul.ac.uk>
date Thu, 09 Jul 2015 01:12:16 +0100
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1 <html lang="en">
2 <head>
3 <title>Advanced Complex DFTs - FFTW 3.2.1</title>
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50 <a name="Advanced-Complex-DFTs"></a>
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55 </div>
56
57 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
58
59 <pre class="example"> fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
60 fftw_complex *in, const int *inembed,
61 int istride, int idist,
62 fftw_complex *out, const int *onembed,
63 int ostride, int odist,
64 int sign, unsigned flags);
65 </pre>
66 <p><a name="index-fftw_005fplan_005fmany_005fdft-223"></a>
67 This plans multidimensional complex DFTs, and is exactly the same as
68 <code>fftw_plan_dft</code> except for the new parameters <code>howmany</code>,
69 {<code>i</code>,<code>o</code>}<code>nembed</code>, {<code>i</code>,<code>o</code>}<code>stride</code>,
70 and {<code>i</code>,<code>o</code>}<code>dist</code>.
71
72 <p><code>howmany</code> is the number of transforms to compute, where the
73 <code>k</code>-th transform is of the arrays starting at <code>in+k*idist</code> and
74 <code>out+k*odist</code>. The resulting plans can often be faster than
75 calling FFTW multiple times for the individual transforms. The basic
76 <code>fftw_plan_dft</code> interface corresponds to <code>howmany=1</code> (in which
77 case the <code>dist</code> parameters are ignored).
78 <a name="index-howmany-parameter-224"></a><a name="index-dist-225"></a>
79 The two <code>nembed</code> parameters (which should be arrays of length
80 <code>rank</code>) indicate the sizes of the input and output array
81 dimensions, respectively, where the transform is of a subarray of size
82 <code>n</code>. (Each dimension of <code>n</code> should be <code>&lt;=</code> the
83 corresponding dimension of the <code>nembed</code> arrays.) That is, the
84 input and output arrays are stored in row-major order with size given by
85 <code>nembed</code> (not counting the strides and howmany multiplicities).
86 Passing <code>NULL</code> for an <code>nembed</code> parameter is equivalent to
87 passing <code>n</code> (i.e. same physical and logical dimensions, as in the
88 basic interface.)
89
90 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
91 the input or output arrays is located at <code>j*istride</code> or
92 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
93 <code>j</code> is the ordinary row-major index.) When combined with the
94 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
95 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
96 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
97 <a name="index-stride-226"></a>
98 For in-place transforms, the input and output <code>stride</code> and
99 <code>dist</code> parameters should be the same; otherwise, the planner may
100 return <code>NULL</code>.
101
102 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
103 this function returns. You can safely free or reuse them.
104
105 <p>So, for example, to transform a sequence of contiguous arrays, stored
106 one after another, one would use a <code>stride</code> of 1 and a <code>dist</code>
107 of N, where N is the product of the dimensions. In
108 another example, to transform an array of contiguous &ldquo;vectors&rdquo; of
109 length M, one would use a <code>howmany</code> of M, a
110 <code>stride</code> of M, and a <code>dist</code> of 1.
111 <a name="index-vector-227"></a>
112 <!-- =========> -->
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115