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174 lines
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<!-- This manual is for FFTW
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(version 3.3.10, 10 December 2020).
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Copyright (C) 2003 Matteo Frigo.
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Copyright (C) 2003 Massachusetts Institute of Technology.
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Permission is granted to make and distribute verbatim copies of this
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manual provided the copyright notice and this permission notice are
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<title>Reversing array dimensions (FFTW 3.3.10)</title>
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Calling-FFTW-from-Modern-Fortran.html" rel="up" title="Calling FFTW from Modern Fortran">
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<span id="Reversing-array-dimensions"></span><div class="header">
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<p>
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Next: <a href="FFTW-Fortran-type-reference.html" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html" accesskey="u" rel="up">Calling FFTW from Modern Fortran</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<span id="Reversing-array-dimensions-1"></span><h3 class="section">7.2 Reversing array dimensions</h3>
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<span id="index-row_002dmajor-6"></span>
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<span id="index-column_002dmajor-1"></span>
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<p>A minor annoyance in calling FFTW from Fortran is that FFTW’s array
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dimensions are defined in the C convention (row-major order), while
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Fortran’s array dimensions are the opposite convention (column-major
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order). See <a href="Multi_002ddimensional-Array-Format.html">Multi-dimensional Array Format</a>. This is just a
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bookkeeping difference, with no effect on performance. The only
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consequence of this is that, whenever you create an FFTW plan for a
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multi-dimensional transform, you must always <em>reverse the
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ordering of the dimensions</em>.
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</p>
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<p>For example, consider the three-dimensional (L × M × N
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) arrays:
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</p>
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<div class="example">
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<pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
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</pre></div>
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<p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
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</p>
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<span id="index-fftw_005fplan_005fdft_005f3d-2"></span>
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<div class="example">
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<pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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</pre></div>
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<p>That is, from FFTW’s perspective this is a N × M × L
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array.
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<em>No data transposition need occur</em>, as this is <em>only
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notation</em>. Similarly, to use the more generic routine
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<code>fftw_plan_dft</code> with the same arrays, you could do:
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</p>
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<div class="example">
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<pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
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plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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</pre></div>
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<p>Note, by the way, that this is different from the legacy Fortran
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interface (see <a href="Fortran_002dinterface-routines.html">Fortran-interface routines</a>), which automatically
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reverses the order of the array dimension for you. Here, you are
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calling the C interface directly, so there is no “translation” layer.
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</p>
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<span id="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></span>
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<p>An important thing to keep in mind is the implication of this for
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multidimensional real-to-complex transforms (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html">Multi-Dimensional DFTs of Real Data</a>). In C, a multidimensional real-to-complex DFT
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chops the last dimension roughly in half (N × M × L
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real input
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goes to N × M × L/2+1
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complex output). In Fortran, because
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the array dimension notation is reversed, the <em>first</em> dimension of
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the complex data is chopped roughly in half. For example consider the
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‘<samp>r2c</samp>’ transform of L × M × N
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real input in Fortran:
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</p>
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<span id="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></span>
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<span id="index-fftw_005fexecute_005fdft_005fr2c-1"></span>
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<div class="example">
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<pre class="example"> type(C_PTR) :: plan
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real(C_DOUBLE), dimension(L,M,N) :: in
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complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
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plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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...
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call fftw_execute_dft_r2c(plan, in, out)
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</pre></div>
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<span id="index-in_002dplace-9"></span>
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<span id="index-padding-5"></span>
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<p>Alternatively, for an in-place r2c transform, as described in the C
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documentation we must <em>pad</em> the <em>first</em> dimension of the
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real input with an extra two entries (which are ignored by FFTW) so as
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to leave enough space for the complex output. The input is
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<em>allocated</em> as a 2[L/2+1] × M × N
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array, even though only
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L × M × N
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of it is actually used. In this example, we will
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allocate the array as a pointer type, using ‘<samp>fftw_alloc</samp>’ to
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ensure aligned memory for maximum performance (see <a href="Allocating-aligned-memory-in-Fortran.html">Allocating aligned memory in Fortran</a>); this also makes it easy to reference the
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same memory as both a real array and a complex array.
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</p>
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<span id="index-fftw_005falloc_005fcomplex-4"></span>
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<span id="index-c_005ff_005fpointer"></span>
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<div class="example">
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<pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
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complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
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type(C_PTR) :: plan, data
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data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
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call c_f_pointer(data, in, [2*(L/2+1),M,N])
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call c_f_pointer(data, out, [L/2+1,M,N])
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plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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...
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call fftw_execute_dft_r2c(plan, in, out)
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...
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call fftw_destroy_plan(plan)
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call fftw_free(data)
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</pre></div>
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<hr>
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<div class="header">
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<p>
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Next: <a href="FFTW-Fortran-type-reference.html" accesskey="n" rel="next">FFTW Fortran type reference</a>, Previous: <a href="Overview-of-Fortran-interface.html" accesskey="p" rel="prev">Overview of Fortran interface</a>, Up: <a href="Calling-FFTW-from-Modern-Fortran.html" accesskey="u" rel="up">Calling FFTW from Modern Fortran</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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