1 | #ifndef _theplu_yat_statistics_percentiler_ |
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2 | #define _theplu_yat_statistics_percentiler_ |
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3 | |
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4 | // $Id: Percentiler.h 1487 2008-09-10 08:41:36Z jari $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2008 Peter Johansson |
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8 | |
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9 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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10 | |
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11 | The yat library is free software; you can redistribute it and/or |
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12 | modify it under the terms of the GNU General Public License as |
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13 | published by the Free Software Foundation; either version 3 of the |
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14 | License, or (at your option) any later version. |
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15 | |
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16 | The yat library is distributed in the hope that it will be useful, |
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17 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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19 | General Public License for more details. |
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20 | |
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21 | You should have received a copy of the GNU General Public License |
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22 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
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23 | */ |
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24 | |
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25 | #include "yat/utility/DataWeight.h" |
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26 | #include "yat/utility/iterator_traits.h" |
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27 | #include "yat/utility/yat_assert.h" |
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28 | #include "yat/utility/WeightIterator.h" |
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29 | |
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30 | #include <algorithm> |
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31 | #include <cassert> |
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32 | #include <cmath> |
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33 | #include <numeric> |
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34 | #include <stdexcept> |
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35 | #include <vector> |
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36 | |
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37 | #include <iostream> |
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38 | |
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39 | namespace theplu { |
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40 | namespace yat { |
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41 | namespace statistics { |
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42 | |
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43 | /** |
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44 | \brief Functor to calculate percentile of a range |
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45 | |
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46 | \since New in yat 0.5 |
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47 | */ |
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48 | class Percentiler |
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49 | { |
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50 | public: |
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51 | /** |
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52 | \param perc percentile to calculate [0,100]. Default value is |
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53 | 50, which implies class will calculate median. |
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54 | \param sorted if true class assumes that ranges are already |
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55 | sorted, if false the range will copied to a new range which is |
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56 | sorted. |
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57 | */ |
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58 | Percentiler(double perc=50, bool sorted=false); |
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59 | |
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60 | /** |
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61 | Function is a non-mutable function, i.e., \a first and \a last |
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62 | can be const_iterators. |
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63 | |
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64 | The \a Nth percentile is defined such that, for example, when |
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65 | having four numbers \f$ 0.69 < 1.41 < 3.14 < 28 \f$, the \a Nth |
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66 | percentile is: |
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67 | |
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68 | - \f$ 0.69 \f$ if \f$ N < 25 \f$ |
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69 | - \f$ (0.69+1.41)/2 \f$ if \f$ N=25 \f$ |
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70 | - \f$ 1.41 \f$ if \f$ 25 < N < 50 \f$ |
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71 | - \f$ (1.41+3.14)/2 \f$ if \f$ N=50 \f$ |
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72 | - \f$ 3.14 \f$ if \f$ 50 < N < 75 \f$ |
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73 | - \f$ (3.14+28)/2 \f$ if \f$ N=75 \f$ |
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74 | - \f$ 28 \f$ if \f$ 75 < N \f$ |
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75 | |
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76 | Similarily, if we have a weighted range \f$ x_0=0.69, w_0=1 ; |
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77 | x_1=1.41, w_1=0 ; x_2=3.14, w_2=0.5 ; x_3=28, w_3=0.5 \f$, we |
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78 | calculate the accumulated normalized weight \f$ S_k = \frac |
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79 | {100}{\sum w_i}\sum_{i=0}^k w_i \f$ and the percentile is |
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80 | |
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81 | - \f$ 0.69 \f$ if \f$ N < S_0 \f$ |
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82 | - \f$ (0.69+3.14)/2 \f$ if \f$ N=S_0 \f$ |
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83 | - \f$ 3.14 \f$ if \f$ S_0 < N < S_2 \f$ |
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84 | - \f$ (3.14+28)/2 \f$ if \f$ N=S_2 \f$ |
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85 | - \f$ 28 \f$ if \f$ S_2 < N \f$ |
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86 | |
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87 | Note, that data point with weight zero is completely ignored. |
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88 | |
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89 | \return percentile of range |
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90 | */ |
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91 | template<typename RandomAccessIterator> |
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92 | double operator()(RandomAccessIterator first, |
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93 | RandomAccessIterator last) const |
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94 | { |
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95 | return calculate(first, last, sorted_, |
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96 | typename utility::weighted_iterator_traits<RandomAccessIterator>::type()); |
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97 | } |
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98 | private: |
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99 | double perc_; |
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100 | bool sorted_; |
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101 | |
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102 | // unweighted version |
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103 | template<typename RandomAccessIterator> |
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104 | double calculate(RandomAccessIterator first, RandomAccessIterator last, |
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105 | bool sorted, utility::unweighted_iterator_tag tag) const; |
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106 | |
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107 | // weighted version |
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108 | template<typename RandomAccessIterator> |
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109 | double calculate(RandomAccessIterator first, RandomAccessIterator last, |
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110 | bool sorted, utility::weighted_iterator_tag tag) const; |
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111 | |
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112 | // using compiler generated copy |
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113 | //Percentiler(const Percentiler&); |
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114 | //Percentiler& operator=(const Percentiler&); |
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115 | |
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116 | }; |
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117 | |
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118 | // template implementations |
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119 | // ///////////////////////// |
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120 | |
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121 | // unweighted version |
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122 | template<typename RandomAccessIterator> |
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123 | double |
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124 | Percentiler::calculate(RandomAccessIterator first, |
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125 | RandomAccessIterator last, |
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126 | bool sorted, |
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127 | utility::unweighted_iterator_tag tag) const |
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128 | { |
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129 | // range is one value only is a special case |
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130 | if (first+1 == last) |
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131 | *first; |
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132 | if (sorted) { |
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133 | size_t n = last - first; |
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134 | // have to take care of this special case |
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135 | if (perc_>= 100.0) |
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136 | return *(--last); |
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137 | if (perc_<= 0.0) |
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138 | return *first; |
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139 | double j = n * perc_ / 100.0; |
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140 | size_t i = static_cast<size_t>(j); |
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141 | if (i==j) |
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142 | return (first[i]+first[i-1])/2; |
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143 | return first[i]; |
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144 | } |
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145 | |
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146 | std::vector<double> v_copy; |
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147 | v_copy.reserve(std::distance(first,last)); |
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148 | std::copy(first, last, std::back_inserter(v_copy)); |
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149 | std::sort(v_copy.begin(), v_copy.end()); |
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150 | return calculate(v_copy.begin(), v_copy.end(), true, tag); |
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151 | } |
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152 | |
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153 | |
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154 | // weighted version |
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155 | template<typename RandomAccessIterator> |
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156 | double Percentiler::calculate(RandomAccessIterator first, |
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157 | RandomAccessIterator last, |
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158 | bool sorted, |
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159 | utility::weighted_iterator_tag tag) const |
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160 | { |
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161 | if (sorted) { |
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162 | utility::iterator_traits<RandomAccessIterator> trait; |
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163 | std::vector<double> accum_w; |
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164 | accum_w.reserve(last-first); |
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165 | std::partial_sum(weight_iterator(first), |
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166 | weight_iterator(last), |
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167 | std::back_inserter(accum_w)); |
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168 | |
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169 | double w_bound=perc_/100.0*accum_w.back(); |
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170 | std::vector<double>::const_iterator upper(accum_w.begin()); |
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171 | double margin=1e-10; |
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172 | while (*upper <= w_bound+margin && upper!=accum_w.end()) |
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173 | ++upper; |
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174 | if (upper==accum_w.end()) |
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175 | --upper; |
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176 | std::vector<double>::const_iterator lower(upper); |
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177 | while ( *(lower-1)>=w_bound-margin && lower>accum_w.begin()) |
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178 | --lower; |
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179 | |
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180 | return (trait.data(first+(upper-accum_w.begin()))+ |
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181 | trait.data(first+(lower-accum_w.begin())))/2; |
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182 | } |
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183 | |
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184 | std::vector<utility::DataWeight> v_copy; |
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185 | v_copy.reserve(last-first); |
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186 | std::copy(first, last, std::back_inserter(v_copy)); |
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187 | std::sort(v_copy.begin(), v_copy.end()); |
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188 | return calculate(v_copy.begin(), v_copy.end(), true, tag); |
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189 | } |
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190 | |
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191 | |
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192 | }}} // of namespace statistics, yat, and theplu |
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193 | |
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194 | #endif |
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