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date Tue, 18 Oct 2016 13:40:26 +0100
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72 <a name="Advanced-Complex-DFTs"></a>
73 <div class="header">
74 <p>
75 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>
76 </div>
77 <hr>
78 <a name="Advanced-Complex-DFTs-1"></a>
79 <h4 class="subsection">4.4.1 Advanced Complex DFTs</h4>
80
81 <div class="example">
82 <pre class="example">fftw_plan fftw_plan_many_dft(int rank, const int *n, int howmany,
83 fftw_complex *in, const int *inembed,
84 int istride, int idist,
85 fftw_complex *out, const int *onembed,
86 int ostride, int odist,
87 int sign, unsigned flags);
88 </pre></div>
89 <a name="index-fftw_005fplan_005fmany_005fdft"></a>
90
91 <p>This routine plans multiple multidimensional complex DFTs, and it
92 extends the <code>fftw_plan_dft</code> routine (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) to
93 compute <code>howmany</code> transforms, each having rank <code>rank</code> and size
94 <code>n</code>. In addition, the transform data need not be contiguous, but
95 it may be laid out in memory with an arbitrary stride. To account for
96 these possibilities, <code>fftw_plan_many_dft</code> adds the new parameters
97 <code>howmany</code>, {<code>i</code>,<code>o</code>}<code>nembed</code>,
98 {<code>i</code>,<code>o</code>}<code>stride</code>, and
99 {<code>i</code>,<code>o</code>}<code>dist</code>. The FFTW basic interface
100 (see <a href="Complex-DFTs.html#Complex-DFTs">Complex DFTs</a>) provides routines specialized for ranks 1, 2,
101 and&nbsp;3, but the advanced interface handles only the general-rank
102 case.
103 </p>
104 <p><code>howmany</code> is the number of transforms to compute. The resulting
105 plan computes <code>howmany</code> transforms, where the input of the
106 <code>k</code>-th transform is at location <code>in+k*idist</code> (in C pointer
107 arithmetic), and its output is at location <code>out+k*odist</code>. Plans
108 obtained in this way can often be faster than calling FFTW multiple
109 times for the individual transforms. The basic <code>fftw_plan_dft</code>
110 interface corresponds to <code>howmany=1</code> (in which case the <code>dist</code>
111 parameters are ignored).
112 <a name="index-howmany-parameter"></a>
113 <a name="index-dist"></a>
114 </p>
115
116 <p>Each of the <code>howmany</code> transforms has rank <code>rank</code> and size
117 <code>n</code>, as in the basic interface. In addition, the advanced
118 interface allows the input and output arrays of each transform to be
119 row-major subarrays of larger rank-<code>rank</code> arrays, described by
120 <code>inembed</code> and <code>onembed</code> parameters, respectively.
121 {<code>i</code>,<code>o</code>}<code>nembed</code> must be arrays of length <code>rank</code>,
122 and <code>n</code> should be elementwise less than or equal to
123 {<code>i</code>,<code>o</code>}<code>nembed</code>. Passing <code>NULL</code> for an
124 <code>nembed</code> parameter is equivalent to passing <code>n</code> (i.e. same
125 physical and logical dimensions, as in the basic interface.)
126 </p>
127 <p>The <code>stride</code> parameters indicate that the <code>j</code>-th element of
128 the input or output arrays is located at <code>j*istride</code> or
129 <code>j*ostride</code>, respectively. (For a multi-dimensional array,
130 <code>j</code> is the ordinary row-major index.) When combined with the
131 <code>k</code>-th transform in a <code>howmany</code> loop, from above, this means
132 that the (<code>j</code>,<code>k</code>)-th element is at <code>j*stride+k*dist</code>.
133 (The basic <code>fftw_plan_dft</code> interface corresponds to a stride of 1.)
134 <a name="index-stride-1"></a>
135 </p>
136
137 <p>For in-place transforms, the input and output <code>stride</code> and
138 <code>dist</code> parameters should be the same; otherwise, the planner may
139 return <code>NULL</code>.
140 </p>
141 <p>Arrays <code>n</code>, <code>inembed</code>, and <code>onembed</code> are not used after
142 this function returns. You can safely free or reuse them.
143 </p>
144 <p><strong>Examples</strong>:
145 One transform of one 5 by 6 array contiguous in memory:
146 </p><div class="example">
147 <pre class="example"> int rank = 2;
148 int n[] = {5, 6};
149 int howmany = 1;
150 int idist = odist = 0; /* unused because howmany = 1 */
151 int istride = ostride = 1; /* array is contiguous in memory */
152 int *inembed = n, *onembed = n;
153 </pre></div>
154
155 <p>Transform of three 5 by 6 arrays, each contiguous in memory,
156 stored in memory one after another:
157 </p><div class="example">
158 <pre class="example"> int rank = 2;
159 int n[] = {5, 6};
160 int howmany = 3;
161 int idist = odist = n[0]*n[1]; /* = 30, the distance in memory
162 between the first element
163 of the first array and the
164 first element of the second array */
165 int istride = ostride = 1; /* array is contiguous in memory */
166 int *inembed = n, *onembed = n;
167 </pre></div>
168
169 <p>Transform each column of a 2d array with 10 rows and 3 columns:
170 </p><div class="example">
171 <pre class="example"> int rank = 1; /* not 2: we are computing 1d transforms */
172 int n[] = {10}; /* 1d transforms of length 10 */
173 int howmany = 3;
174 int idist = odist = 1;
175 int istride = ostride = 3; /* distance between two elements in
176 the same column */
177 int *inembed = n, *onembed = n;
178 </pre></div>
179
180 <hr>
181 <div class="header">
182 <p>
183 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>
184 </div>
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