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Current fftw source
author Chris Cannam <cannam@all-day-breakfast.com>
date Tue, 18 Oct 2016 13:40:26 +0100
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72 <a name="Reversing-array-dimensions"></a>
73 <div class="header">
74 <p>
75 Next: <a href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" accesskey="u" rel="up">Calling FFTW from Modern Fortran</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="Reversing-array-dimensions-1"></a>
79 <h3 class="section">7.2 Reversing array dimensions</h3>
80
81 <a name="index-row_002dmajor-6"></a>
82 <a name="index-column_002dmajor-1"></a>
83 <p>A minor annoyance in calling FFTW from Fortran is that FFTW&rsquo;s array
84 dimensions are defined in the C convention (row-major order), while
85 Fortran&rsquo;s array dimensions are the opposite convention (column-major
86 order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. This is just a
87 bookkeeping difference, with no effect on performance. The only
88 consequence of this is that, whenever you create an FFTW plan for a
89 multi-dimensional transform, you must always <em>reverse the
90 ordering of the dimensions</em>.
91 </p>
92 <p>For example, consider the three-dimensional (L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N) arrays:
93 </p>
94 <div class="example">
95 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
96 </pre></div>
97
98 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
99 </p>
100 <a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
101 <div class="example">
102 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
103 </pre></div>
104
105 <p>That is, from FFTW&rsquo;s perspective this is a N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L array.
106 <em>No data transposition need occur</em>, as this is <em>only
107 notation</em>. Similarly, to use the more generic routine
108 <code>fftw_plan_dft</code> with the same arrays, you could do:
109 </p>
110 <div class="example">
111 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
112 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
113 </pre></div>
114
115 <p>Note, by the way, that this is different from the legacy Fortran
116 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
117 reverses the order of the array dimension for you. Here, you are
118 calling the C interface directly, so there is no &ldquo;translation&rdquo; layer.
119 </p>
120 <a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
121 <p>An important thing to keep in mind is the implication of this for
122 multidimensional real-to-complex transforms (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data">Multi-Dimensional DFTs of Real Data</a>). In C, a multidimensional real-to-complex DFT
123 chops the last dimension roughly in half (N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L real input
124 goes to N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L/2+1 complex output). In Fortran, because
125 the array dimension notation is reversed, the <em>first</em> dimension of
126 the complex data is chopped roughly in half. For example consider the
127 &lsquo;<samp>r2c</samp>&rsquo; transform of L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N real input in Fortran:
128 </p>
129 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
130 <a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
131 <div class="example">
132 <pre class="example"> type(C_PTR) :: plan
133 real(C_DOUBLE), dimension(L,M,N) :: in
134 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
135 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
136 ...
137 call fftw_execute_dft_r2c(plan, in, out)
138 </pre></div>
139
140 <a name="index-in_002dplace-9"></a>
141 <a name="index-padding-5"></a>
142 <p>Alternatively, for an in-place r2c transform, as described in the C
143 documentation we must <em>pad</em> the <em>first</em> dimension of the
144 real input with an extra two entries (which are ignored by FFTW) so as
145 to leave enough space for the complex output. The input is
146 <em>allocated</em> as a 2[L/2+1]&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N array, even though only
147 L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N of it is actually used. In this example, we will
148 allocate the array as a pointer type, using &lsquo;<samp>fftw_alloc</samp>&rsquo; to
149 ensure aligned memory for maximum performance (see <a href="Allocating-aligned-memory-in-Fortran.html#Allocating-aligned-memory-in-Fortran">Allocating aligned memory in Fortran</a>); this also makes it easy to reference the
150 same memory as both a real array and a complex array.
151 </p>
152 <a name="index-fftw_005falloc_005fcomplex-4"></a>
153 <a name="index-c_005ff_005fpointer"></a>
154 <div class="example">
155 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
156 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
157 type(C_PTR) :: plan, data
158 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
159 call c_f_pointer(data, in, [2*(L/2+1),M,N])
160 call c_f_pointer(data, out, [L/2+1,M,N])
161 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
162 ...
163 call fftw_execute_dft_r2c(plan, in, out)
164 ...
165 call fftw_destroy_plan(plan)
166 call fftw_free(data)
167 </pre></div>
168
169 <hr>
170 <div class="header">
171 <p>
172 Next: <a href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" accesskey="u" rel="up">Calling FFTW from Modern Fortran</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>
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