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Add FFTW 3.3.8 source, and a Linux build
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 19 Nov 2019 14:52:55 +0000
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71 <a name="Advanced-Complex-DFTs"></a>
72 <div class="header">
73 <p>
74 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
75 </div>
76 <hr>
77 <a name="Advanced-Complex-DFTs-1"></a>
78 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
79
80 <div class="example">
81 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
82 fftw_complex *in, const int *inembed,
83 int istride, int idist,
84 fftw_complex *out, const int *onembed,
85 int ostride, int odist,
86 int sign, unsigned flags);
87 </pre></div>
88 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
89
90 <p>This routine plans multiple multidimensional complex DFTs, and it
91 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
92 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
93 <code>n</code>. In addition, the transform data need not be contiguous, but
94 it may be laid out in memory with an arbitrary stride. To account for
95 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
96 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
97 {<code>i</code>,<code>o</code>}<code>stride</code>, and
98 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
99 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
100 and&nbsp;3, but the advanced interface handles only the general-rank
101 case.
102 </p>
103 <p><code>howmany</code> is the (nonnegative) number of transforms to compute. The resulting
104 plan computes <code>howmany</code> transforms, where the input of the
105 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
106 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
107 obtained in this way can often be faster than calling FFTW multiple
108 times for the individual transforms. The basic <code>fftw_plan_dft</code>
109 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
110 parameters are ignored).
111 <a name="index-howmany-parameter"></a>
112 <a name="index-dist"></a>
113 </p>
114
115 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
116 <code>n</code>, as in the basic interface. In addition, the advanced
117 interface allows the input and output arrays of each transform to be
118 row-major subarrays of larger rank-<code>rank</code> arrays, described by
119 <code>inembed</code> and <code>onembed</code> parameters, respectively.
120 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
121 and <code>n</code> should be elementwise less than or equal to
122 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
123 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
124 physical and logical dimensions, as in the basic interface.)
125 </p>
126 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
127 the input or output arrays is located at <code>j*istride</code> or
128 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
129 <code>j</code> is the ordinary row-major index.) When combined with the
130 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
131 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
132 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
133 <a name="index-stride-1"></a>
134 </p>
135
136 <p>For in-place transforms, the input and output <code>stride</code> and
137 <code>dist</code> parameters should be the same; otherwise, the planner may
138 return <code>NULL</code>.
139 </p>
140 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
141 this function returns. You can safely free or reuse them.
142 </p>
143 <p><strong>Examples</strong>:
144 One transform of one 5 by 6 array contiguous in memory:
145 </p><div class="example">
146 <pre class="example"> int rank = 2;
147 int n[] = {5, 6};
148 int howmany = 1;
149 int idist = odist = 0; /* unused because howmany = 1 */
150 int istride = ostride = 1; /* array is contiguous in memory */
151 int *inembed = n, *onembed = n;
152 </pre></div>
153
154 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
155 stored in memory one after another:
156 </p><div class="example">
157 <pre class="example"> int rank = 2;
158 int n[] = {5, 6};
159 int howmany = 3;
160 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
161 between the first element
162 of the first array and the
163 first element of the second array */
164 int istride = ostride = 1; /* array is contiguous in memory */
165 int *inembed = n, *onembed = n;
166 </pre></div>
167
168 <p>Transform each column of a 2d array with 10 rows and 3 columns:
169 </p><div class="example">
170 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
171 int n[] = {10}; /* 1d transforms of length 10 */
172 int howmany = 3;
173 int idist = odist = 1;
174 int istride = ostride = 3; /* distance between two elements in
175 the same column */
176 int *inembed = n, *onembed = n;
177 </pre></div>
178
179 <hr>
180 <div class="header">
181 <p>
182 Next: <a href="Advanced-Real_002ddata-DFTs.html#Advanced-Real_002ddata-DFTs" accesskey="n" rel="next">Advanced Real-data DFTs</a>, Previous: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="p" rel="prev">Advanced Interface</a>, Up: <a href="Advanced-Interface.html#Advanced-Interface" accesskey="u" rel="up">Advanced Interface</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
183 </div>
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