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Add null config files
author Chris Cannam <cannam@all-day-breakfast.com>
date Mon, 02 Mar 2020 14:03:47 +0000
parents 7867fa7e1b6b
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cannam@127 3 <!-- This manual is for FFTW
cannam@127 4 (version 3.3.5, 30 July 2016).
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cannam@127 6 Copyright (C) 2003 Matteo Frigo.
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cannam@127 25 <title>FFTW 3.3.5: Reversing array dimensions</title>
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cannam@127 71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
cannam@127 72 <a name="Reversing-array-dimensions"></a>
cannam@127 73 <div class="header">
cannam@127 74 <p>
cannam@127 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>
cannam@127 76 </div>
cannam@127 77 <hr>
cannam@127 78 <a name="Reversing-array-dimensions-1"></a>
cannam@127 79 <h3 class="section">7.2 Reversing array dimensions</h3>
cannam@127 80
cannam@127 81 <a name="index-row_002dmajor-6"></a>
cannam@127 82 <a name="index-column_002dmajor-1"></a>
cannam@127 83 <p>A minor annoyance in calling FFTW from Fortran is that FFTW&rsquo;s array
cannam@127 84 dimensions are defined in the C convention (row-major order), while
cannam@127 85 Fortran&rsquo;s array dimensions are the opposite convention (column-major
cannam@127 86 order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. This is just a
cannam@127 87 bookkeeping difference, with no effect on performance. The only
cannam@127 88 consequence of this is that, whenever you create an FFTW plan for a
cannam@127 89 multi-dimensional transform, you must always <em>reverse the
cannam@127 90 ordering of the dimensions</em>.
cannam@127 91 </p>
cannam@127 92 <p>For example, consider the three-dimensional (L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N) arrays:
cannam@127 93 </p>
cannam@127 94 <div class="example">
cannam@127 95 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
cannam@127 96 </pre></div>
cannam@127 97
cannam@127 98 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
cannam@127 99 </p>
cannam@127 100 <a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
cannam@127 101 <div class="example">
cannam@127 102 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
cannam@127 103 </pre></div>
cannam@127 104
cannam@127 105 <p>That is, from FFTW&rsquo;s perspective this is a N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L array.
cannam@127 106 <em>No data transposition need occur</em>, as this is <em>only
cannam@127 107 notation</em>. Similarly, to use the more generic routine
cannam@127 108 <code>fftw_plan_dft</code> with the same arrays, you could do:
cannam@127 109 </p>
cannam@127 110 <div class="example">
cannam@127 111 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
cannam@127 112 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
cannam@127 113 </pre></div>
cannam@127 114
cannam@127 115 <p>Note, by the way, that this is different from the legacy Fortran
cannam@127 116 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
cannam@127 117 reverses the order of the array dimension for you. Here, you are
cannam@127 118 calling the C interface directly, so there is no &ldquo;translation&rdquo; layer.
cannam@127 119 </p>
cannam@127 120 <a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
cannam@127 121 <p>An important thing to keep in mind is the implication of this for
cannam@127 122 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
cannam@127 123 chops the last dimension roughly in half (N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L real input
cannam@127 124 goes to N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L/2+1 complex output). In Fortran, because
cannam@127 125 the array dimension notation is reversed, the <em>first</em> dimension of
cannam@127 126 the complex data is chopped roughly in half. For example consider the
cannam@127 127 &lsquo;<samp>r2c</samp>&rsquo; transform of L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N real input in Fortran:
cannam@127 128 </p>
cannam@127 129 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
cannam@127 130 <a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
cannam@127 131 <div class="example">
cannam@127 132 <pre class="example"> type(C_PTR) :: plan
cannam@127 133 real(C_DOUBLE), dimension(L,M,N) :: in
cannam@127 134 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
cannam@127 135 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
cannam@127 136 ...
cannam@127 137 call fftw_execute_dft_r2c(plan, in, out)
cannam@127 138 </pre></div>
cannam@127 139
cannam@127 140 <a name="index-in_002dplace-9"></a>
cannam@127 141 <a name="index-padding-5"></a>
cannam@127 142 <p>Alternatively, for an in-place r2c transform, as described in the C
cannam@127 143 documentation we must <em>pad</em> the <em>first</em> dimension of the
cannam@127 144 real input with an extra two entries (which are ignored by FFTW) so as
cannam@127 145 to leave enough space for the complex output. The input is
cannam@127 146 <em>allocated</em> as a 2[L/2+1]&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N array, even though only
cannam@127 147 L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N of it is actually used. In this example, we will
cannam@127 148 allocate the array as a pointer type, using &lsquo;<samp>fftw_alloc</samp>&rsquo; to
cannam@127 149 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
cannam@127 150 same memory as both a real array and a complex array.
cannam@127 151 </p>
cannam@127 152 <a name="index-fftw_005falloc_005fcomplex-4"></a>
cannam@127 153 <a name="index-c_005ff_005fpointer"></a>
cannam@127 154 <div class="example">
cannam@127 155 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
cannam@127 156 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
cannam@127 157 type(C_PTR) :: plan, data
cannam@127 158 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
cannam@127 159 call c_f_pointer(data, in, [2*(L/2+1),M,N])
cannam@127 160 call c_f_pointer(data, out, [L/2+1,M,N])
cannam@127 161 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
cannam@127 162 ...
cannam@127 163 call fftw_execute_dft_r2c(plan, in, out)
cannam@127 164 ...
cannam@127 165 call fftw_destroy_plan(plan)
cannam@127 166 call fftw_free(data)
cannam@127 167 </pre></div>
cannam@127 168
cannam@127 169 <hr>
cannam@127 170 <div class="header">
cannam@127 171 <p>
cannam@127 172 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>
cannam@127 173 </div>
cannam@127 174
cannam@127 175
cannam@127 176
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