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<title>FFTW 3.3.8: Reversing array dimensions</title>

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<a name="Reversing-array-dimensions"></a>
<div class="header">
<p>
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>
</div>
<hr>
<a name="Reversing-array-dimensions-1"></a>
<h3 class="section">7.2 Reversing array dimensions</h3>

<a name="index-row_002dmajor-6"></a>
<a name="index-column_002dmajor-1"></a>
<p>A minor annoyance in calling FFTW from Fortran is that FFTW&rsquo;s array
dimensions are defined in the C convention (row-major order), while
Fortran&rsquo;s array dimensions are the opposite convention (column-major
order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>.  This is just a
bookkeeping difference, with no effect on performance.  The only
consequence of this is that, whenever you create an FFTW plan for a
multi-dimensional transform, you must always <em>reverse the
ordering of the dimensions</em>.
</p>
<p>For example, consider the three-dimensional (L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
) arrays:
</p>
<div class="example">
<pre class="example">  complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
</pre></div>

<p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
</p>
<a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
<div class="example">
<pre class="example">  plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
</pre></div>

<p>That is, from FFTW&rsquo;s perspective this is a N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L
 array.
<em>No data transposition need occur</em>, as this is <em>only
notation</em>.  Similarly, to use the more generic routine
<code>fftw_plan_dft</code> with the same arrays, you could do:
</p>
<div class="example">
<pre class="example">  integer(C_INT), dimension(3) :: n = [N,M,L]
  plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
</pre></div>

<p>Note, by the way, that this is different from the legacy Fortran
interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
reverses the order of the array dimension for you.  Here, you are
calling the C interface directly, so there is no &ldquo;translation&rdquo; layer.
</p>
<a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
<p>An important thing to keep in mind is the implication of this for
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
chops the last dimension roughly in half (N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L
 real input
goes to N&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;L/2+1
 complex output).  In Fortran, because
the array dimension notation is reversed, the <em>first</em> dimension of
the complex data is chopped roughly in half.  For example consider the
&lsquo;<samp>r2c</samp>&rsquo; transform of L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
 real input in Fortran:
</p>
<a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
<a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
<div class="example">
<pre class="example">  type(C_PTR) :: plan
  real(C_DOUBLE), dimension(L,M,N) :: in
  complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
  plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
  ...
  call fftw_execute_dft_r2c(plan, in, out)
</pre></div>

<a name="index-in_002dplace-9"></a>
<a name="index-padding-5"></a>
<p>Alternatively, for an in-place r2c transform, as described in the C
documentation we must <em>pad</em> the <em>first</em> dimension of the
real input with an extra two entries (which are ignored by FFTW) so as
to leave enough space for the complex output. The input is
<em>allocated</em> as a 2[L/2+1]&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
 array, even though only
L&nbsp;&times;&nbsp;M&nbsp;&times;&nbsp;N
 of it is actually used.  In this example, we will
allocate the array as a pointer type, using &lsquo;<samp>fftw_alloc</samp>&rsquo; to
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
same memory as both a real array and a complex array.
</p>
<a name="index-fftw_005falloc_005fcomplex-4"></a>
<a name="index-c_005ff_005fpointer"></a>
<div class="example">
<pre class="example">  real(C_DOUBLE), pointer :: in(:,:,:)
  complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
  type(C_PTR) :: plan, data
  data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
  call c_f_pointer(data, in, [2*(L/2+1),M,N])
  call c_f_pointer(data, out, [L/2+1,M,N])
  plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
  ...
  call fftw_execute_dft_r2c(plan, in, out)
  ...
  call fftw_destroy_plan(plan)
  call fftw_free(data)
</pre></div>

<hr>
<div class="header">
<p>
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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author	Chris Cannam <cannam@all-day-breakfast.com>
date	Tue, 19 Nov 2019 14:52:55 +0000
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