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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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2 <html>
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3 <!-- This manual is for FFTW
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4 (version 3.3.8, 24 May 2018).
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5
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6 Copyright (C) 2003 Matteo Frigo.
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7
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8 Copyright (C) 2003 Massachusetts Institute of Technology.
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9
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10 Permission is granted to make and distribute verbatim copies of this
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11 manual provided the copyright notice and this permission notice are
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12 preserved on all copies.
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14 Permission is granted to copy and distribute modified versions of this
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15 manual under the conditions for verbatim copying, provided that the
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16 entire resulting derived work is distributed under the terms of a
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17 permission notice identical to this one.
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18
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19 Permission is granted to copy and distribute translations of this manual
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20 into another language, under the above conditions for modified versions,
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22 approved by the Free Software Foundation. -->
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23 <!-- Created by GNU Texinfo 6.3, http://www.gnu.org/software/texinfo/ -->
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24 <head>
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25 <title>FFTW 3.3.8: Reversing array dimensions</title>
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26
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27 <meta name="description" content="FFTW 3.3.8: Reversing array dimensions">
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34 <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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35 <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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36 <link href="Calling-FFTW-from-Modern-Fortran.html#Calling-FFTW-from-Modern-Fortran" rel="up" title="Calling FFTW from Modern Fortran">
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37 <link href="FFTW-Fortran-type-reference.html#FFTW-Fortran-type-reference" rel="next" title="FFTW Fortran type reference">
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38 <link href="Extended-and-quadruple-precision-in-Fortran.html#Extended-and-quadruple-precision-in-Fortran" rel="prev" title="Extended and quadruple precision in Fortran">
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65 </style>
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66
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67
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68 </head>
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69
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70 <body lang="en">
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71 <a name="Reversing-array-dimensions"></a>
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72 <div class="header">
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73 <p>
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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> [<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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75 </div>
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76 <hr>
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77 <a name="Reversing-array-dimensions-1"></a>
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78 <h3 class="section">7.2 Reversing array dimensions</h3>
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79
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80 <a name="index-row_002dmajor-6"></a>
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81 <a name="index-column_002dmajor-1"></a>
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82 <p>A minor annoyance in calling FFTW from Fortran is that FFTW’s array
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83 dimensions are defined in the C convention (row-major order), while
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84 Fortran’s array dimensions are the opposite convention (column-major
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85 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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86 bookkeeping difference, with no effect on performance. The only
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87 consequence of this is that, whenever you create an FFTW plan for a
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88 multi-dimensional transform, you must always <em>reverse the
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89 ordering of the dimensions</em>.
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90 </p>
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91 <p>For example, consider the three-dimensional (L × M × N
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92 ) arrays:
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93 </p>
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94 <div class="example">
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95 <pre class="example"> complex(C_DOUBLE_COMPLEX), dimension(L,M,N) :: in, out
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96 </pre></div>
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97
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98 <p>To plan a DFT for these arrays using <code>fftw_plan_dft_3d</code>, you could do:
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99 </p>
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100 <a name="index-fftw_005fplan_005fdft_005f3d-2"></a>
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101 <div class="example">
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102 <pre class="example"> plan = fftw_plan_dft_3d(N,M,L, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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103 </pre></div>
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104
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105 <p>That is, from FFTW’s perspective this is a N × M × L
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106 array.
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107 <em>No data transposition need occur</em>, as this is <em>only
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108 notation</em>. Similarly, to use the more generic routine
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109 <code>fftw_plan_dft</code> with the same arrays, you could do:
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110 </p>
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111 <div class="example">
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112 <pre class="example"> integer(C_INT), dimension(3) :: n = [N,M,L]
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113 plan = fftw_plan_dft_3d(3, n, in,out, FFTW_FORWARD,FFTW_ESTIMATE)
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114 </pre></div>
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115
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116 <p>Note, by the way, that this is different from the legacy Fortran
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117 interface (see <a href="Fortran_002dinterface-routines.html#Fortran_002dinterface-routines">Fortran-interface routines</a>), which automatically
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118 reverses the order of the array dimension for you. Here, you are
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119 calling the C interface directly, so there is no “translation” layer.
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120 </p>
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121 <a name="index-r2c_002fc2r-multi_002ddimensional-array-format-2"></a>
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122 <p>An important thing to keep in mind is the implication of this for
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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
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124 chops the last dimension roughly in half (N × M × L
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125 real input
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126 goes to N × M × L/2+1
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127 complex output). In Fortran, because
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128 the array dimension notation is reversed, the <em>first</em> dimension of
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129 the complex data is chopped roughly in half. For example consider the
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130 ‘<samp>r2c</samp>’ transform of L × M × N
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131 real input in Fortran:
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132 </p>
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133 <a name="index-fftw_005fplan_005fdft_005fr2c_005f3d-2"></a>
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134 <a name="index-fftw_005fexecute_005fdft_005fr2c-1"></a>
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135 <div class="example">
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136 <pre class="example"> type(C_PTR) :: plan
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137 real(C_DOUBLE), dimension(L,M,N) :: in
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138 complex(C_DOUBLE_COMPLEX), dimension(L/2+1,M,N) :: out
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139 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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140 ...
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141 call fftw_execute_dft_r2c(plan, in, out)
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142 </pre></div>
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143
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144 <a name="index-in_002dplace-9"></a>
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145 <a name="index-padding-5"></a>
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146 <p>Alternatively, for an in-place r2c transform, as described in the C
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147 documentation we must <em>pad</em> the <em>first</em> dimension of the
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148 real input with an extra two entries (which are ignored by FFTW) so as
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149 to leave enough space for the complex output. The input is
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150 <em>allocated</em> as a 2[L/2+1] × M × N
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151 array, even though only
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152 L × M × N
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153 of it is actually used. In this example, we will
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154 allocate the array as a pointer type, using ‘<samp>fftw_alloc</samp>’ to
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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
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156 same memory as both a real array and a complex array.
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157 </p>
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158 <a name="index-fftw_005falloc_005fcomplex-4"></a>
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159 <a name="index-c_005ff_005fpointer"></a>
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160 <div class="example">
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161 <pre class="example"> real(C_DOUBLE), pointer :: in(:,:,:)
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162 complex(C_DOUBLE_COMPLEX), pointer :: out(:,:,:)
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163 type(C_PTR) :: plan, data
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164 data = fftw_alloc_complex(int((L/2+1) * M * N, C_SIZE_T))
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165 call c_f_pointer(data, in, [2*(L/2+1),M,N])
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166 call c_f_pointer(data, out, [L/2+1,M,N])
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167 plan = fftw_plan_dft_r2c_3d(N,M,L, in,out, FFTW_ESTIMATE)
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168 ...
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169 call fftw_execute_dft_r2c(plan, in, out)
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170 ...
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171 call fftw_destroy_plan(plan)
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172 call fftw_free(data)
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173 </pre></div>
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174
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175 <hr>
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176 <div class="header">
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177 <p>
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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> [<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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179 </div>
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180
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181
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182
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183 </body>
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184 </html>
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