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1 <html lang="en">
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2 <head>
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3 <title>Reversing array dimensions - FFTW 3.3.3</title>
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5 <meta name="description" content="FFTW 3.3.3">
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7 <link title="Top" rel="start" href="index.html#Top">
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8 <link rel="up" href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" title="Calling FFTW from Modern Fortran">
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9 <link rel="prev" href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface" title="Overview of Fortran interface">
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12 <!--
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13 This manual is for FFTW
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14 (version 3.3.3, 25 November 2012).
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15
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16 Copyright (C) 2003 Matteo Frigo.
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17
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18 Copyright (C) 2003 Massachusetts Institute of Technology.
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20 Permission is granted to make and distribute verbatim copies of
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24 Permission is granted to copy and distribute modified versions of
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25 this manual under the conditions for verbatim copying, provided
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26 that the entire resulting derived work is distributed under the
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27 terms of a permission notice identical to this one.
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29 Permission is granted to copy and distribute translations of this
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31 modified versions, except that this permission notice may be
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32 stated in a translation approved by the Free Software Foundation.
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46 </head>
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47 <body>
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48 <div class="node">
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49 <a name="Reversing-array-dimensions"></a>
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50 <p>
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51 Next: <a rel="next" accesskey="n" href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference">FFTW Fortran type reference</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Overview-of-Fortran-interface.html#Overview-of-Fortran-interface">Overview of Fortran interface</a>,
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53 Up: <a rel="up" accesskey="u" href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran">Calling FFTW from Modern Fortran</a>
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54 <hr>
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55 </div>
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56
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57 <h3 class="section">7.2 Reversing array dimensions</h3>
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58
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59 <p><a name="index-row_002dmajor-517"></a><a name="index-column_002dmajor-518"></a>A minor annoyance in calling FFTW from Fortran is that FFTW's array
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60 dimensions are defined in the C convention (row-major order), while
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61 Fortran's array dimensions are the opposite convention (column-major
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62 order). See <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>. This is just a
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63 bookkeeping difference, with no effect on performance. The only
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64 consequence of this is that, whenever you create an FFTW plan for a
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65 multi-dimensional transform, you must always <em>reverse the
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66 ordering of the dimensions</em>.
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67
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68 <p>For example, consider the three-dimensional (L × M × N) arrays:
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69
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70 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
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71 </pre>
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72 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
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73
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74 <p><a name="index-fftw_005fplan_005fdft_005f3d-519"></a>
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75 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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76 </pre>
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77 <p>That is, from FFTW's perspective this is a N × M × L array.
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78 <em>No data transposition need occur</em>, as this is <em>only
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79 notation</em>. Similarly, to use the more generic routine
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80 <code>fftw_plan_dft</code> with the same arrays, you could do:
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81
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82 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
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83 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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84 </pre>
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85 <p>Note, by the way, that this is different from the legacy Fortran
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86 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
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87 reverses the order of the array dimension for you. Here, you are
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88 calling the C interface directly, so there is no “translation” layer.
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89
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90 <p><a name="index-r2c_002fc2r-multi_002ddimensional-array-format-520"></a>An important thing to keep in mind is the implication of this for
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91 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
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92 chops the last dimension roughly in half (N × M × L real input
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93 goes to N × M × L/2+1 complex output). In Fortran, because
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94 the array dimension notation is reversed, the <em>first</em> dimension of
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95 the complex data is chopped roughly in half. For example consider the
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96 ‘<samp><span class="samp">r2c</span></samp>’ transform of L × M × N real input in Fortran:
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97
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98 <p><a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-521"></a><a name="index-fftw_005fexecute_005fdft_005fr2c-522"></a>
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99 <pre class="example"> type(C_PTR) :: plan
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100 real(C_DOUBLE), dimension(L,M,N) :: in
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101 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
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102 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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103 ...
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104 call fftw_execute_dft_r2c(plan, in, out)
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105 </pre>
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106 <p><a name="index-in_002dplace-523"></a><a name="index-padding-524"></a>Alternatively, for an in-place r2c transform, as described in the C
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107 documentation we must <em>pad</em> the <em>first</em> dimension of the
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108 real input with an extra two entries (which are ignored by FFTW) so as
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109 to leave enough space for the complex output. The input is
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110 <em>allocated</em> as a 2[L/2+1] × M × N array, even though only
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111 L × M × N of it is actually used. In this example, we will
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112 allocate the array as a pointer type, using ‘<samp><span class="samp">fftw_alloc</span></samp>’ to
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113 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
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114 same memory as both a real array and a complex array.
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115
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116 <p><a name="index-fftw_005falloc_005fcomplex-525"></a><a name="index-c_005ff_005fpointer-526"></a>
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117 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
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118 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
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119 type(C_PTR) :: plan, data
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120 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
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121 call c_f_pointer(data, in, [2*(L/2+1),M,N])
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122 call c_f_pointer(data, out, [L/2+1,M,N])
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123 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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124 ...
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125 call fftw_execute_dft_r2c(plan, in, out)
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126 ...
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127 call fftw_destroy_plan(plan)
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128 call fftw_free(data)
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129 </pre>
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130 <!-- -->
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131 </body></html>
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132
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