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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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13
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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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21 except that this permission notice may be stated in a translation
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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: Transposed distributions</title>
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26
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27 <meta name="description" content="FFTW 3.3.8: Transposed distributions">
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28 <meta name="keywords" content="FFTW 3.3.8: Transposed distributions">
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33 <link href="index.html#Top" rel="start" title="Top">
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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="MPI-Data-Distribution.html#MPI-Data-Distribution" rel="up" title="MPI Data Distribution">
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37 <link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="next" title="One-dimensional distributions">
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38 <link href="Load-balancing.html#Load-balancing" rel="prev" title="Load balancing">
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64 -->
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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="Transposed-distributions"></a>
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72 <div class="header">
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73 <p>
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74 Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</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="Transposed-distributions-1"></a>
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78 <h4 class="subsection">6.4.3 Transposed distributions</h4>
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79
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80 <p>Internally, FFTW’s MPI transform algorithms work by first computing
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81 transforms of the data local to each process, then by globally
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82 <em>transposing</em> the data in some fashion to redistribute the data
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83 among the processes, transforming the new data local to each process,
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84 and transposing back. For example, a two-dimensional <code>n0</code> by
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85 <code>n1</code> array, distributed across the <code>n0</code> dimension, is
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86 transformd by: (i) transforming the <code>n1</code> dimension, which are
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87 local to each process; (ii) transposing to an <code>n1</code> by <code>n0</code>
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88 array, distributed across the <code>n1</code> dimension; (iii) transforming
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89 the <code>n0</code> dimension, which is now local to each process; (iv)
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90 transposing back.
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91 <a name="index-transpose"></a>
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92 </p>
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93
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94 <p>However, in many applications it is acceptable to compute a
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95 multidimensional DFT whose results are produced in transposed order
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96 (e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a
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97 significant performance advantage, because it means that the final
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98 transposition step can be omitted. FFTW supports this optimization,
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99 which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code>
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100 to the planner routines. To compute the inverse transform of
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101 transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell
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102 it that the input is transposed. In this section, we explain how to
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103 interpret the output format of such a transform.
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104 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT"></a>
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105 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN"></a>
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106 </p>
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107
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108 <p>Suppose you have are transforming multi-dimensional data with (at
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109 least two) dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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110 . As always, it is distributed along
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111 the first dimension n<sub>0</sub>
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112 . Now, if we compute its DFT with the
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113 <code>FFTW_MPI_TRANSPOSED_OUT</code> flag, the resulting output data are stored
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114 with the first <em>two</em> dimensions transposed: n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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115 ,
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116 distributed along the n<sub>1</sub>
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117 dimension. Conversely, if we take the
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118 n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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119 data and transform it with the
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120 <code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the
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121 original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>
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122 array.
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123 </p>
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124 <p>There are two ways to find the portion of the transposed array that
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125 resides on the current process. First, you can simply call the
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126 appropriate ‘<samp>local_size</samp>’ function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>
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127 (the
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128 transposed dimensions). This would mean calling the ‘<samp>local_size</samp>’
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129 function twice, once for the transposed and once for the
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130 non-transposed dimensions. Alternatively, you can call one of the
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131 ‘<samp>local_size_transposed</samp>’ functions, which returns both the
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132 non-transposed and transposed data distribution from a single call.
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133 For example, for a 3d transform with transposed output (or input), you
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134 might call:
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135 </p>
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136 <div class="example">
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137 <pre class="example">ptrdiff_t fftw_mpi_local_size_3d_transposed(
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138 ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
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139 ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
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140 ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
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141 </pre></div>
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142 <a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed"></a>
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143
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144 <p>Here, <code>local_n0</code> and <code>local_0_start</code> give the size and
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145 starting index of the <code>n0</code> dimension for the
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146 <em>non</em>-transposed data, as in the previous sections. For
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147 <em>transposed</em> data (e.g. the output for
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148 <code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and
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149 <code>local_1_start</code> give the size and starting index of the <code>n1</code>
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150 dimension, which is the first dimension of the transposed data
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151 (<code>n1</code> by <code>n0</code> by <code>n2</code>).
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152 </p>
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153 <p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to
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154 performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two
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155 dimensions to the planner in reverse order, or vice versa. If you
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156 pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and
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157 <code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the
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158 first two dimensions passed to the planner and passing <em>neither</em>
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159 flag.)
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160 </p>
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161 <hr>
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162 <div class="header">
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163 <p>
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164 Next: <a href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" accesskey="n" rel="next">One-dimensional distributions</a>, Previous: <a href="Load-balancing.html#Load-balancing" accesskey="p" rel="prev">Load balancing</a>, Up: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="u" rel="up">MPI Data Distribution</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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165 </div>
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166
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167
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168
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169 </body>
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170 </html>
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