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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 bd3cc4d1df30
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cannam@167 3 <!-- This manual is for FFTW
cannam@167 4 (version 3.3.8, 24 May 2018).
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cannam@167 6 Copyright (C) 2003 Matteo Frigo.
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cannam@167 25 <title>FFTW 3.3.8: Reversing array dimensions</title>
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cannam@167 70 <body lang="en">
cannam@167 71 <a name="Reversing-array-dimensions"></a>
cannam@167 72 <div class="header">
cannam@167 73 <p>
cannam@167 74 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@167 75 </div>
cannam@167 76 <hr>
cannam@167 77 <a name="Reversing-array-dimensions-1"></a>
cannam@167 78 <h3 class="section">7.2 Reversing array dimensions</h3>
cannam@167 79
cannam@167 80 <a name="index-row_002dmajor-6"></a>
cannam@167 81 <a name="index-column_002dmajor-1"></a>
cannam@167 82 <p>A minor annoyance in calling FFTW from Fortran is that FFTW&rsquo;s array
cannam@167 83 dimensions are defined in the C convention (row-major order), while
cannam@167 84 Fortran&rsquo;s array dimensions are the opposite convention (column-major
cannam@167 85 order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. This is just a
cannam@167 86 bookkeeping difference, with no effect on performance. The only
cannam@167 87 consequence of this is that, whenever you create an FFTW plan for a
cannam@167 88 multi-dimensional transform, you must always <em>reverse the
cannam@167 89 ordering of the dimensions</em>.
cannam@167 90 </p>
cannam@167 91 <p>For example, consider the three-dimensional (L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
cannam@167 92 ) arrays:
cannam@167 93 </p>
cannam@167 94 <div class="example">
cannam@167 95 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
cannam@167 96 </pre></div>
cannam@167 97
cannam@167 98 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
cannam@167 99 </p>
cannam@167 100 <a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
cannam@167 101 <div class="example">
cannam@167 102 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
cannam@167 103 </pre></div>
cannam@167 104
cannam@167 105 <p>That is, from FFTW&rsquo;s perspective this is a N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L
cannam@167 106 array.
cannam@167 107 <em>No data transposition need occur</em>, as this is <em>only
cannam@167 108 notation</em>. Similarly, to use the more generic routine
cannam@167 109 <code>fftw_plan_dft</code> with the same arrays, you could do:
cannam@167 110 </p>
cannam@167 111 <div class="example">
cannam@167 112 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
cannam@167 113 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
cannam@167 114 </pre></div>
cannam@167 115
cannam@167 116 <p>Note, by the way, that this is different from the legacy Fortran
cannam@167 117 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
cannam@167 118 reverses the order of the array dimension for you. Here, you are
cannam@167 119 calling the C interface directly, so there is no &ldquo;translation&rdquo; layer.
cannam@167 120 </p>
cannam@167 121 <a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
cannam@167 122 <p>An important thing to keep in mind is the implication of this for
cannam@167 123 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@167 124 chops the last dimension roughly in half (N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L
cannam@167 125 real input
cannam@167 126 goes to N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L/2+1
cannam@167 127 complex output). In Fortran, because
cannam@167 128 the array dimension notation is reversed, the <em>first</em> dimension of
cannam@167 129 the complex data is chopped roughly in half. For example consider the
cannam@167 130 &lsquo;<samp>r2c</samp>&rsquo; transform of L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
cannam@167 131 real input in Fortran:
cannam@167 132 </p>
cannam@167 133 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
cannam@167 134 <a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
cannam@167 135 <div class="example">
cannam@167 136 <pre class="example"> type(C_PTR) :: plan
cannam@167 137 real(C_DOUBLE), dimension(L,M,N) :: in
cannam@167 138 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
cannam@167 139 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
cannam@167 140 ...
cannam@167 141 call fftw_execute_dft_r2c(plan, in, out)
cannam@167 142 </pre></div>
cannam@167 143
cannam@167 144 <a name="index-in_002dplace-9"></a>
cannam@167 145 <a name="index-padding-5"></a>
cannam@167 146 <p>Alternatively, for an in-place r2c transform, as described in the C
cannam@167 147 documentation we must <em>pad</em> the <em>first</em> dimension of the
cannam@167 148 real input with an extra two entries (which are ignored by FFTW) so as
cannam@167 149 to leave enough space for the complex output. The input is
cannam@167 150 <em>allocated</em> as a 2[L/2+1]&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
cannam@167 151 array, even though only
cannam@167 152 L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
cannam@167 153 of it is actually used. In this example, we will
cannam@167 154 allocate the array as a pointer type, using &lsquo;<samp>fftw_alloc</samp>&rsquo; to
cannam@167 155 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@167 156 same memory as both a real array and a complex array.
cannam@167 157 </p>
cannam@167 158 <a name="index-fftw_005falloc_005fcomplex-4"></a>
cannam@167 159 <a name="index-c_005ff_005fpointer"></a>
cannam@167 160 <div class="example">
cannam@167 161 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
cannam@167 162 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
cannam@167 163 type(C_PTR) :: plan, data
cannam@167 164 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
cannam@167 165 call c_f_pointer(data, in, [2*(L/2+1),M,N])
cannam@167 166 call c_f_pointer(data, out, [L/2+1,M,N])
cannam@167 167 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
cannam@167 168 ...
cannam@167 169 call fftw_execute_dft_r2c(plan, in, out)
cannam@167 170 ...
cannam@167 171 call fftw_destroy_plan(plan)
cannam@167 172 call fftw_free(data)
cannam@167 173 </pre></div>
cannam@167 174
cannam@167 175 <hr>
cannam@167 176 <div class="header">
cannam@167 177 <p>
cannam@167 178 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@167 179 </div>
cannam@167 180
cannam@167 181
cannam@167 182
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