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Current fftw source
author Chris Cannam
date Tue, 18 Oct 2016 13:40:26 +0100
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Chris@42 3 <!-- This manual is for FFTW
Chris@42 4 (version 3.3.5, 30 July 2016).
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Chris@42 6 Copyright (C) 2003 Matteo Frigo.
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Chris@42 25 <title>FFTW 3.3.5: Reversing array dimensions</title>
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Chris@42 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
Chris@42 72 <a name="Reversing-array-dimensions"></a>
Chris@42 73 <div class="header">
Chris@42 74 <p>
Chris@42 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>
Chris@42 76 </div>
Chris@42 77 <hr>
Chris@42 78 <a name="Reversing-array-dimensions-1"></a>
Chris@42 79 <h3 class="section">7.2 Reversing array dimensions</h3>
Chris@42 80
Chris@42 81 <a name="index-row_002dmajor-6"></a>
Chris@42 82 <a name="index-column_002dmajor-1"></a>
Chris@42 83 <p>A minor annoyance in calling FFTW from Fortran is that FFTW&rsquo;s array
Chris@42 84 dimensions are defined in the C convention (row-major order), while
Chris@42 85 Fortran&rsquo;s array dimensions are the opposite convention (column-major
Chris@42 86 order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. This is just a
Chris@42 87 bookkeeping difference, with no effect on performance. The only
Chris@42 88 consequence of this is that, whenever you create an FFTW plan for a
Chris@42 89 multi-dimensional transform, you must always <em>reverse the
Chris@42 90 ordering of the dimensions</em>.
Chris@42 91 </p>
Chris@42 92 <p>For example, consider the three-dimensional (L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N) arrays:
Chris@42 93 </p>
Chris@42 94 <div class="example">
Chris@42 95 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
Chris@42 96 </pre></div>
Chris@42 97
Chris@42 98 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
Chris@42 99 </p>
Chris@42 100 <a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
Chris@42 101 <div class="example">
Chris@42 102 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
Chris@42 103 </pre></div>
Chris@42 104
Chris@42 105 <p>That is, from FFTW&rsquo;s perspective this is a N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L array.
Chris@42 106 <em>No data transposition need occur</em>, as this is <em>only
Chris@42 107 notation</em>. Similarly, to use the more generic routine
Chris@42 108 <code>fftw_plan_dft</code> with the same arrays, you could do:
Chris@42 109 </p>
Chris@42 110 <div class="example">
Chris@42 111 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
Chris@42 112 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
Chris@42 113 </pre></div>
Chris@42 114
Chris@42 115 <p>Note, by the way, that this is different from the legacy Fortran
Chris@42 116 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
Chris@42 117 reverses the order of the array dimension for you. Here, you are
Chris@42 118 calling the C interface directly, so there is no &ldquo;translation&rdquo; layer.
Chris@42 119 </p>
Chris@42 120 <a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
Chris@42 121 <p>An important thing to keep in mind is the implication of this for
Chris@42 122 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
Chris@42 123 chops the last dimension roughly in half (N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L real input
Chris@42 124 goes to N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L/2+1 complex output). In Fortran, because
Chris@42 125 the array dimension notation is reversed, the <em>first</em> dimension of
Chris@42 126 the complex data is chopped roughly in half. For example consider the
Chris@42 127 &lsquo;<samp>r2c</samp>&rsquo; transform of L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N real input in Fortran:
Chris@42 128 </p>
Chris@42 129 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
Chris@42 130 <a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
Chris@42 131 <div class="example">
Chris@42 132 <pre class="example"> type(C_PTR) :: plan
Chris@42 133 real(C_DOUBLE), dimension(L,M,N) :: in
Chris@42 134 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
Chris@42 135 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
Chris@42 136 ...
Chris@42 137 call fftw_execute_dft_r2c(plan, in, out)
Chris@42 138 </pre></div>
Chris@42 139
Chris@42 140 <a name="index-in_002dplace-9"></a>
Chris@42 141 <a name="index-padding-5"></a>
Chris@42 142 <p>Alternatively, for an in-place r2c transform, as described in the C
Chris@42 143 documentation we must <em>pad</em> the <em>first</em> dimension of the
Chris@42 144 real input with an extra two entries (which are ignored by FFTW) so as
Chris@42 145 to leave enough space for the complex output. The input is
Chris@42 146 <em>allocated</em> as a 2[L/2+1]&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N array, even though only
Chris@42 147 L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N of it is actually used. In this example, we will
Chris@42 148 allocate the array as a pointer type, using &lsquo;<samp>fftw_alloc</samp>&rsquo; to
Chris@42 149 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
Chris@42 150 same memory as both a real array and a complex array.
Chris@42 151 </p>
Chris@42 152 <a name="index-fftw_005falloc_005fcomplex-4"></a>
Chris@42 153 <a name="index-c_005ff_005fpointer"></a>
Chris@42 154 <div class="example">
Chris@42 155 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
Chris@42 156 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
Chris@42 157 type(C_PTR) :: plan, data
Chris@42 158 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
Chris@42 159 call c_f_pointer(data, in, [2*(L/2+1),M,N])
Chris@42 160 call c_f_pointer(data, out, [L/2+1,M,N])
Chris@42 161 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
Chris@42 162 ...
Chris@42 163 call fftw_execute_dft_r2c(plan, in, out)
Chris@42 164 ...
Chris@42 165 call fftw_destroy_plan(plan)
Chris@42 166 call fftw_free(data)
Chris@42 167 </pre></div>
Chris@42 168
Chris@42 169 <hr>
Chris@42 170 <div class="header">
Chris@42 171 <p>
Chris@42 172 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>
Chris@42 173 </div>
Chris@42 174
Chris@42 175
Chris@42 176
Chris@42 177 </body>
Chris@42 178 </html>