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author Chris Cannam <cannam@all-day-breakfast.com>
date Wed, 20 Mar 2013 15:35:50 +0000
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3 <title>Advanced Complex DFTs - FFTW 3.3.3</title>
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49 <a name="Advanced-Complex-DFTs"></a>
50 <p>
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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-232"></a>
67 This routine plans multiple multidimensional complex DFTs, and it
68 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
69 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
70 <code>n</code>. In addition, the transform data need not be contiguous, but
71 it may be laid out in memory with an arbitrary stride. To account for
72 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
73 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
74 {<code>i</code>,<code>o</code>}<code>stride</code>, and
75 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
76 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
77 and&nbsp;3, but the advanced interface handles only the general-rank
78 case.
79
80 <p><code>howmany</code> is the number of transforms to compute. The resulting
81 plan computes <code>howmany</code> transforms, where the input of the
82 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
83 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
84 obtained in this way can often be faster than calling FFTW multiple
85 times for the individual transforms. The basic <code>fftw_plan_dft</code>
86 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
87 parameters are ignored).
88 <a name="index-howmany-parameter-233"></a><a name="index-dist-234"></a>
89
90 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
91 <code>n</code>, as in the basic interface. In addition, the advanced
92 interface allows the input and output arrays of each transform to be
93 row-major subarrays of larger rank-<code>rank</code> arrays, described by
94 <code>inembed</code> and <code>onembed</code> parameters, respectively.
95 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
96 and <code>n</code> should be elementwise less than or equal to
97 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
98 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
99 physical and logical dimensions, as in the basic interface.)
100
101 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
102 the input or output arrays is located at <code>j*istride</code> or
103 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
104 <code>j</code> is the ordinary row-major index.) When combined with the
105 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
106 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
107 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
108 <a name="index-stride-235"></a>
109
110 <p>For in-place transforms, the input and output <code>stride</code> and
111 <code>dist</code> parameters should be the same; otherwise, the planner may
112 return <code>NULL</code>.
113
114 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
115 this function returns. You can safely free or reuse them.
116
117 <p><strong>Examples</strong>:
118 One transform of one 5 by 6 array contiguous in memory:
119 <pre class="example"> int rank = 2;
120 int n[] = {5, 6};
121 int howmany = 1;
122 int idist = odist = 0; /* unused because howmany = 1 */
123 int istride = ostride = 1; /* array is contiguous in memory */
124 int *inembed = n, *onembed = n;
125 </pre>
126 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
127 stored in memory one after another:
128 <pre class="example"> int rank = 2;
129 int n[] = {5, 6};
130 int howmany = 3;
131 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
132 between the first element
133 of the first array and the
134 first element of the second array */
135 int istride = ostride = 1; /* array is contiguous in memory */
136 int *inembed = n, *onembed = n;
137 </pre>
138 <p>Transform each column of a 2d array with 10 rows and 3 columns:
139 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
140 int n[] = {10}; /* 1d transforms of length 10 */
141 int howmany = 3;
142 int idist = odist = 1;
143 int istride = ostride = 3; /* distance between two elements in
144 the same column */
145 int *inembed = n, *onembed = n;
146 </pre>
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