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2 <html>
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3 <!-- This manual is for FFTW
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4 (version 3.3.5, 30 July 2016).
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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 5.2, http://www.gnu.org/software/texinfo/ -->
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24 <head>
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25 <title>FFTW 3.3.5: Multi-dimensional MPI DFTs of Real Data</title>
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26
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27 <meta name="description" content="FFTW 3.3.5: Multi-dimensional MPI DFTs of Real Data">
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28 <meta name="keywords" content="FFTW 3.3.5: Multi-dimensional MPI DFTs of Real Data">
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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="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" rel="up" title="Distributed-memory FFTW with MPI">
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37 <link href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" rel="next" title="Other Multi-dimensional Real-data MPI Transforms">
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38 <link href="One_002ddimensional-distributions.html#One_002ddimensional-distributions" rel="prev" title="One-dimensional distributions">
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65 -->
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66 </style>
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68
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69 </head>
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70
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71 <body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
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72 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data"></a>
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73 <div class="header">
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74 <p>
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75 Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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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76 </div>
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77 <hr>
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78 <a name="Multi_002ddimensional-MPI-DFTs-of-Real-Data-1"></a>
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79 <h3 class="section">6.5 Multi-dimensional MPI DFTs of Real Data</h3>
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80
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81 <p>FFTW’s MPI interface also supports multi-dimensional DFTs of real
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82 data, similar to the serial r2c and c2r interfaces. (Parallel
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83 one-dimensional real-data DFTs are not currently supported; you must
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84 use a complex transform and set the imaginary parts of the inputs to
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85 zero.)
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86 </p>
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87 <p>The key points to understand for r2c and c2r MPI transforms (compared
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88 to the MPI complex DFTs or the serial r2c/c2r transforms), are:
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89 </p>
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90 <ul>
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91 <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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92 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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93 complex data is cut in half (rounded down), plus one. As for the
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94 serial transforms, the sizes you pass to the ‘<samp>plan_dft_r2c</samp>’ and
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95 ‘<samp>plan_dft_c2r</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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96
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97 </li><li> <a name="index-padding-4"></a>
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98 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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99 <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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100 dimension has been <em>padded</em> to make it the same size as the
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101 complex output. This is much like the in-place serial r2c/c2r
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102 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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103 in MPI the padding is required even for out-of-place data. The extra
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104 padding numbers are ignored by FFTW (they are <em>not</em> like
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105 zero-padding the transform to a larger size); they are only used to
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106 determine the data layout.
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107
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108 </li><li> <a name="index-data-distribution-3"></a>
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109 The data distribution in MPI for <em>both</em> the real and complex data
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110 is determined by the shape of the <em>complex</em> data. That is, you
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111 call the appropriate ‘<samp>local size</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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112 complex data, and then use the <em>same</em> distribution for the real
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113 data except that the last complex dimension is replaced by a (padded)
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114 real dimension of twice the length.
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115
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116 </li></ul>
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117
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118 <p>For example suppose we are performing an out-of-place r2c transform of
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119 L × M × N real data [padded to L × M × 2(N/2+1)],
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120 resulting in L × M × N/2+1 complex data. Similar to the
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121 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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122 </p>
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123 <div class="example">
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124 <pre class="example">#include <fftw3-mpi.h>
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125
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126 int main(int argc, char **argv)
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127 {
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128 const ptrdiff_t L = ..., M = ..., N = ...;
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129 fftw_plan plan;
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130 double *rin;
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131 fftw_complex *cout;
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132 ptrdiff_t alloc_local, local_n0, local_0_start, i, j, k;
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133
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134 MPI_Init(&argc, &argv);
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135 fftw_mpi_init();
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136
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137 /* <span class="roman">get local data size and allocate</span> */
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138 alloc_local = fftw_mpi_local_size_3d(L, M, N/2+1, MPI_COMM_WORLD,
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139 &local_n0, &local_0_start);
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140 rin = fftw_alloc_real(2 * alloc_local);
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141 cout = fftw_alloc_complex(alloc_local);
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142
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143 /* <span class="roman">create plan for out-of-place r2c DFT</span> */
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144 plan = fftw_mpi_plan_dft_r2c_3d(L, M, N, rin, cout, MPI_COMM_WORLD,
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145 FFTW_MEASURE);
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146
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147 /* <span class="roman">initialize rin to some function</span> my_func(x,y,z) */
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148 for (i = 0; i < local_n0; ++i)
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149 for (j = 0; j < M; ++j)
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150 for (k = 0; k < N; ++k)
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151 rin[(i*M + j) * (2*(N/2+1)) + k] = my_func(local_0_start+i, j, k);
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152
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153 /* <span class="roman">compute transforms as many times as desired</span> */
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154 fftw_execute(plan);
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155
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156 fftw_destroy_plan(plan);
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157
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158 MPI_Finalize();
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159 }
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160 </pre></div>
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161
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162 <a name="index-fftw_005falloc_005freal-2"></a>
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163 <a name="index-row_002dmajor-5"></a>
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164 <p>Note that we allocated <code>rin</code> using <code>fftw_alloc_real</code> with an
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165 argument of <code>2 * alloc_local</code>: since <code>alloc_local</code> is the
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166 number of <em>complex</em> values to allocate, the number of <em>real</em>
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167 values is twice as many. The <code>rin</code> array is then
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168 local_n0 × M × 2(N/2+1) in row-major order, so its
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169 <code>(i,j,k)</code> element is at the index <code>(i*M + j) * (2*(N/2+1)) +
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170 k</code> (see <a href="Multi_002ddimensional-Array-Format.html#Multi_002ddimensional-Array-Format">Multi-dimensional Array Format</a>).
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171 </p>
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172 <a name="index-transpose-1"></a>
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173 <a name="index-FFTW_005fTRANSPOSED_005fOUT"></a>
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174 <a name="index-FFTW_005fTRANSPOSED_005fIN"></a>
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175 <p>As for the complex transforms, improved performance can be obtained by
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176 specifying that the output is the transpose of the input or vice versa
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177 (see <a href="Transposed-distributions.html#Transposed-distributions">Transposed distributions</a>). In our L × M × N r2c
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178 example, including <code>FFTW_TRANSPOSED_OUT</code> in the flags means that
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179 the input would be a padded L × M × 2(N/2+1) real array
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180 distributed over the <code>L</code> dimension, while the output would be a
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181 M × L × N/2+1 complex array distributed over the <code>M</code>
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182 dimension. To perform the inverse c2r transform with the same data
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183 distributions, you would use the <code>FFTW_TRANSPOSED_IN</code> flag.
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184 </p>
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185 <hr>
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186 <div class="header">
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187 <p>
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188 Next: <a href="Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms.html#Other-Multi_002ddimensional-Real_002ddata-MPI-Transforms" accesskey="n" rel="next">Other Multi-dimensional Real-data MPI Transforms</a>, Previous: <a href="MPI-Data-Distribution.html#MPI-Data-Distribution" accesskey="p" rel="prev">MPI Data Distribution</a>, Up: <a href="Distributed_002dmemory-FFTW-with-MPI.html#Distributed_002dmemory-FFTW-with-MPI" accesskey="u" rel="up">Distributed-memory FFTW with MPI</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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189 </div>
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190
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191
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192
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193 </body>
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194 </html>
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