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2 <head>
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3 <title>Multi-dimensional MPI DFTs of Real Data - FFTW 3.3.3</title>
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4 <meta http-equiv="Content-Type" content="text/html">
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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="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" title="Distributed-memory FFTW with MPI">
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9 <link rel="prev" href="MPI-Data-Distribution.html#MPI-Data-Distribution" title="MPI Data Distribution">
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10 <link rel="next" href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" title="Other Multi-dimensional Real-data MPI Transforms">
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11 <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
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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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19
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20 Permission is granted to make and distribute verbatim copies of
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21 this manual provided the copyright notice and this permission
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22 notice are preserved on all copies.
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23
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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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28
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29 Permission is granted to copy and distribute translations of this
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30 manual into another language, under the above conditions for
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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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33 -->
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35 <style type="text/css"><!--
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44 span.sansserif { font-family:sans-serif; font-weight:normal; }
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45 --></style>
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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="Multi-dimensional-MPI-DFTs-of-Real-Data"></a>
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50 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
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51 <p>
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52 Next: <a rel="next" accesskey="n" href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms">Other Multi-dimensional Real-data MPI Transforms</a>,
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53 Previous: <a rel="previous" accesskey="p" href="MPI-Data-Distribution.html#MPI-Data-Distribution">MPI Data Distribution</a>,
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54 Up: <a rel="up" accesskey="u" href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI">Distributed-memory FFTW with MPI</a>
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55 <hr>
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56 </div>
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57
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58 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
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59
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60 <p>FFTW's MPI interface also supports multi-dimensional DFTs of real
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61 data, similar to the serial r2c and c2r interfaces. (Parallel
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62 one-dimensional real-data DFTs are not currently supported; you must
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63 use a complex transform and set the imaginary parts of the inputs to
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64 zero.)
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65
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66 <p>The key points to understand for r2c and c2r MPI transforms (compared
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67 to the MPI complex DFTs or the serial r2c/c2r transforms), are:
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68
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69 <ul>
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70 <li>Just as for serial transforms, r2c/c2r DFTs transform n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> real
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71 data to/from n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1) complex data: the last dimension of the
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72 complex data is cut in half (rounded down), plus one. As for the
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73 serial transforms, the sizes you pass to the ‘<samp><span class="samp">plan_dft_r2c</span></samp>’ and
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74 ‘<samp><span class="samp">plan_dft_c2r</span></samp>’ are the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub> dimensions of the real data.
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75
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76 <li><a name="index-padding-386"></a>Although the real data is <em>conceptually</em> n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>, it is
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77 <em>physically</em> stored as an n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × [2 (n<sub>d-1</sub>/2 + 1)] array, where the last
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78 dimension has been <em>padded</em> to make it the same size as the
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79 complex output. This is much like the in-place serial r2c/c2r
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80 interface (see <a href="Multi_002dDimensional-DFTs-of-Real-Data.html#Multi_002dDimensional-DFTs-of-Real-Data">Multi-Dimensional DFTs of Real Data</a>), except that
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81 in MPI the padding is required even for out-of-place data. The extra
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82 padding numbers are ignored by FFTW (they are <em>not</em> like
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83 zero-padding the transform to a larger size); they are only used to
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84 determine the data layout.
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85
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86 <li><a name="index-data-distribution-387"></a>The data distribution in MPI for <em>both</em> the real and complex data
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87 is determined by the shape of the <em>complex</em> data. That is, you
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88 call the appropriate ‘<samp><span class="samp">local size</span></samp>’ function for the n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × (n<sub>d-1</sub>/2 + 1)
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89
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90 <p>complex data, and then use the <em>same</em> distribution for the real
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91 data except that the last complex dimension is replaced by a (padded)
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92 real dimension of twice the length.
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93
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94 </ul>
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95
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96 <p>For example suppose we are performing an out-of-place r2c transform of
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97 L × M × N real data [padded to L × M × 2(N/2+1)],
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98 resulting in L × M × N/2+1 complex data. Similar to the
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99 example in <a href="2d-MPI-example.html#g_t2d-MPI-example">2d MPI example</a>, we might do something like:
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100
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101 <pre class="example"> #include <fftw3-mpi.h>
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102
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103 int main(int argc, char **argv)
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104 {
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105 const ptrdiff_t L = ..., M = ..., N = ...;
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106 fftw_plan plan;
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107 double *rin;
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108 fftw_complex *cout;
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109 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
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110
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111 MPI_Init(&argc, &argv);
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112 fftw_mpi_init();
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113
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114 /* <span class="roman">get local data size and allocate</span> */
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115 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
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116 &local_n0, &local_0_start);
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117 rin = fftw_alloc_real(2 * alloc_local);
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118 cout = fftw_alloc_complex(alloc_local);
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119
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120 /* <span class="roman">create plan for out-of-place r2c DFT</span> */
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121 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
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122 FFTW_MEASURE);
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123
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124 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
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125 for (i = 0; i < local_n0; ++i)
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126 for (j = 0; j < M; ++j)
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127 for (k = 0; k < N; ++k)
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128 rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
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129
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130 /* <span class="roman">compute transforms as many times as desired</span> */
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131 fftw_execute(plan);
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132
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133 fftw_destroy_plan(plan);
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134
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135 MPI_Finalize();
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136 }
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137 </pre>
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138 <p><a name="index-fftw_005falloc_005freal-388"></a><a name="index-row_002dmajor-389"></a>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
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139 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
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140 number of <em>complex</em> values to allocate, the number of <em>real</em>
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141 values is twice as many. The <code>rin</code> array is then
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142 local_n0 × M × 2(N/2+1) in row-major order, so its
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143 <code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) +
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144 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
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145
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146 <p><a name="index-transpose-390"></a><a name="index-FFTW_005fTRANSPOSED_005fOUT-391"></a><a name="index-FFTW_005fTRANSPOSED_005fIN-392"></a>As for the complex transforms, improved performance can be obtained by
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147 specifying that the output is the transpose of the input or vice versa
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148 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c
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149 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
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150 the input would be a padded L × M × 2(N/2+1) real array
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151 distributed over the <code>L</code> dimension, while the output would be a
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152 M × L × N/2+1 complex array distributed over the <code>M</code>
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153 dimension. To perform the inverse c2r transform with the same data
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154 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
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155
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156 <!-- -->
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157 </body></html>
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158
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