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3 <title>Transposed distributions - FFTW 3.2alpha3</title>
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12 <!--
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13 This manual is for FFTW
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14 (version 3.2alpha3, 14 August 2007).
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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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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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46 </head>
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47 <body>
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48 <div class="node">
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49 <p>
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50 <a name="Transposed-distributions"></a>
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51 Next: <a rel="next" accesskey="n" href="One_002ddimensional-distributions.html#One_002ddimensional-distributions">One-dimensional distributions</a>,
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52 Previous: <a rel="previous" accesskey="p" href="Load-balancing.html#Load-balancing">Load balancing</a>,
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53 Up: <a rel="up" accesskey="u" href="MPI-data-distribution.html#MPI-data-distribution">MPI data distribution</a>
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54 <hr>
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55 </div>
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56
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57 <h4 class="subsection">6.4.3 Transposed distributions</h4>
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58
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59 <p>Internally, FFTW's MPI transform algorithms work by first computing
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60 transforms of the data local to each process, then by globally
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61 <em>transposing</em> the data in some fashion to redistribute the data
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62 among the processes, transforming the new data local to each process,
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63 and transposing back. For example, a two-dimensional <code>n0</code> by
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64 <code>n1</code> array, distributed across the <code>n0</code> dimension, is
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65 transformd by: (i) transforming the <code>n1</code> dimension, which are
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66 local to each process; (ii) transposing to a <code>n1</code> by <code>n0</code>
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67 array, distributed across the <code>n1</code> dimension; (iii) transforming
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68 the <code>n0</code> dimension, which is now local to each process; (iv)
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69 transposing back.
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70 <a name="index-transpose-359"></a>
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71 However, in many applications it is acceptable to compute a
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72 multidimensional DFT whose results are produced in transposed order
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73 (e.g., <code>n1</code> by <code>n0</code> in two dimensions). This provides a
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74 significant performance advantage, because it means that the final
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75 transposition step can be omitted. FFTW supports this optimization,
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76 which you specify by passing the flag <code>FFTW_MPI_TRANSPOSED_OUT</code>
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77 to the planner routines. To compute the inverse transform of
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78 transposed output, you specify <code>FFTW_MPI_TRANSPOSED_IN</code> to tell
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79 it that the input is transposed. In this section, we explain how to
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80 interpret the output format of such a transform.
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81 <a name="index-FFTW_005fMPI_005fTRANSPOSED_005fOUT-360"></a><a name="index-FFTW_005fMPI_005fTRANSPOSED_005fIN-361"></a>
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82 Suppose you have are transforming multi-dimensional data with (at
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83 least two) dimensions n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>. As always, it is distributed along
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84 the first dimension n<sub>0</sub>. Now, if we compute its DFT with the
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85 <code>FFTW_MPI_TRANSPOSED_OUT</code>, the resulting output data are stored
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86 with the first <em>two</em> dimensions transosed: n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub>,
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87 distributed along the n<sub>0</sub> dimension. Conversely, if we take the
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88 n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> data and transform it with the
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89 <code>FFTW_MPI_TRANSPOSED_IN</code> flag, then the format goes back to the
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90 original n<sub>0</sub> × n<sub>1</sub> × n<sub>2</sub> × … × n<sub>d-1</sub>.
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91
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92 <p>There are two ways to find the portion of the transposed array that
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93 resides on the current process. First, you can simply call the
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94 appropriate `<samp><span class="samp">local_size</span></samp>' function, passing n<sub>1</sub> × n<sub>0</sub> × n<sub>2</sub> ×…× n<sub>d-1</sub> (the
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95 transposed dimensions). This would mean calling the `<samp><span class="samp">local_size</span></samp>'
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96 function twice, once for the transposed and once for the
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97 non-transposed dimensions. Alternatively, you can call one of the
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98 `<samp><span class="samp">local_size_transposed</span></samp>' functions, which returns both the
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99 non-transposed and transposed data distribution from a single call.
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100 For example, for a 3d transform with transposed output (or input), you
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101 might call:
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102
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103 <pre class="example"> ptrdiff_t fftw_mpi_local_size_3d_transposed(
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104 ptrdiff_t n0, ptrdiff_t n1, ptrdiff_t n2, MPI_Comm comm,
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105 ptrdiff_t *local_n0, ptrdiff_t *local_0_start,
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106 ptrdiff_t *local_n1, ptrdiff_t *local_1_start);
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107 </pre>
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108 <p><a name="index-fftw_005fmpi_005flocal_005fsize_005f3d_005ftransposed-362"></a>
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109 Here, <code>local_n0</code> and <code>local_0_start</code> give the size and
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110 starting index of the <code>n0</code> dimension, for the
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111 <em>non</em>-transposed data, as in the previous sections. For
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112 <em>transposed</em> data (e.g. the output for
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113 <code>FFTW_MPI_TRANSPOSED_OUT</code>), <code>local_n1</code> and
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114 <code>local_1_start</code> give the size and starting index of the <code>n1</code>
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115 dimension, which is the first dimension of the transposed data
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116 (<code>n1</code> by <code>n0</code> by <code>n2</code>).
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117
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118 <p>(Note that <code>FFTW_MPI_TRANSPOSED_IN</code> is completely equivalent to
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119 performing <code>FFTW_MPI_TRANSPOSED_OUT</code> and passing the first two
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120 dimensions to the planner in reverse order, or vice versa. If you
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121 pass <em>both</em> the <code>FFTW_MPI_TRANSPOSED_IN</code> and
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122 <code>FFTW_MPI_TRANSPOSED_OUT</code> flags, it is equivalent to swapping the
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123 first two dimensions passed to the planner and passing <em>neither</em>
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124 flag.)
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125
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126 </body></html>
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127
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