1 | #ifndef _theplu_yat_statistics_utility_ |
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2 | #define _theplu_yat_statistics_utility_ |
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3 | |
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4 | // $Id: utility.h 3239 2014-05-24 13:30:49Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2004 Jari Häkkinen, Peter Johansson |
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8 | Copyright (C) 2005 Peter Johansson |
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9 | Copyright (C) 2006 Jari Häkkinen, Peter Johansson, Markus Ringnér |
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10 | Copyright (C) 2007, 2008 Jari Häkkinen, Peter Johansson |
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11 | Copyright (C) 2009, 2010, 2011, 2013, 2014 Peter Johansson |
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12 | |
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13 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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14 | |
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15 | The yat library is free software; you can redistribute it and/or |
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16 | modify it under the terms of the GNU General Public License as |
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17 | published by the Free Software Foundation; either version 3 of the |
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18 | License, or (at your option) any later version. |
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19 | |
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20 | The yat library is distributed in the hope that it will be useful, |
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21 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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22 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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23 | General Public License for more details. |
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24 | |
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25 | You should have received a copy of the GNU General Public License |
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26 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
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27 | */ |
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28 | |
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29 | #include "Percentiler.h" |
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30 | |
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31 | #include "yat/classifier/DataLookupWeighted1D.h" |
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32 | #include "yat/classifier/Target.h" |
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33 | #include "yat/normalizer/utility.h" |
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34 | #include "yat/utility/concept_check.h" |
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35 | #include "yat/utility/DataIterator.h" |
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36 | #include "yat/utility/deprecate.h" |
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37 | #include "yat/utility/iterator_traits.h" |
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38 | #include "yat/utility/sort_index.h" |
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39 | #include "yat/utility/Vector.h" |
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40 | #include "yat/utility/VectorBase.h" |
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41 | #include "yat/utility/yat_assert.h" |
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42 | |
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43 | #include <boost/concept_check.hpp> |
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44 | #include <boost/iterator/permutation_iterator.hpp> |
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45 | |
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46 | #include <gsl/gsl_math.h> |
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47 | #include <gsl/gsl_statistics_double.h> |
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48 | |
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49 | #include <algorithm> |
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50 | #include <cmath> |
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51 | #include <iterator> |
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52 | #include <stdexcept> |
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53 | #include <vector> |
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54 | |
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55 | namespace theplu { |
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56 | namespace yat { |
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57 | namespace statistics { |
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58 | |
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59 | /** |
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60 | Adding a range [\a first, \a last) into an object of type T. The |
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61 | requirements for the type T is to have an add(double, bool, double) |
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62 | function. |
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63 | */ |
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64 | template <typename T, typename ForwardIterator> |
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65 | void add(T& o, ForwardIterator first, ForwardIterator last, |
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66 | const classifier::Target& target); |
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67 | |
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68 | /** |
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69 | \brief Benjamini Hochberg multiple test correction |
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70 | |
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71 | Given a sorted range of p-values such that |
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72 | \f$ p_1 \le p_2 \le ... \le p_N \f$ a Benjamnini-Hochberg corrected |
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73 | p-value, \c q, is calculated recursively as |
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74 | \f$ q_i = \f$ min \f$(p_i \frac{N}{i}, q_{i+1})\f$ with the anchor |
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75 | constraint that \f$ q_m = p_m \f$. |
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76 | |
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77 | Type Requirements: |
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78 | - \c BidirectionalIterator1 is a \bidirectional_iterator |
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79 | - \c BidirectionalIterator1::value type is convertible to \c double |
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80 | - \c BidirectionalIterator2 is a mutable \bidirectional_iterator |
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81 | - \c double is convertible to \c BidirectionalIterator2::value_type |
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82 | |
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83 | \since New in yat 0.8 |
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84 | */ |
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85 | template<typename BidirectionalIterator1, typename BidirectionalIterator2> |
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86 | void benjamini_hochberg(BidirectionalIterator1 first, |
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87 | BidirectionalIterator1 last, |
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88 | BidirectionalIterator2 result); |
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89 | |
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90 | |
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91 | /** |
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92 | \brief Benjamini Hochberg multiple test correction |
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93 | |
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94 | Similar to benjamini_hochberg() but does not assume that input |
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95 | range, [first, last), is sorted. The resulting range is the same |
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96 | as if sorting input range, call benjamini_hochberg, and unsort |
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97 | the result range. |
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98 | |
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99 | Type Requirements: |
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100 | - \c RandomAccessIterator models a \random_access_iterator |
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101 | - \c RandomAccessIterator::value type is convertible to \c double |
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102 | - \c MutableRandomAccessIterator models a mutable \random_access_iterator |
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103 | - \c double is convertible to \c MutableRandomAccessIterator::value_type |
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104 | |
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105 | \since New in yat 0.13 |
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106 | */ |
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107 | template<typename RandomAccessIterator, typename MutableRandomAccessIterator> |
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108 | void benjamini_hochberg_unsorted(RandomAccessIterator first, |
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109 | RandomAccessIterator last, |
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110 | MutableRandomAccessIterator result); |
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111 | |
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112 | |
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113 | /// |
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114 | /// Calculates the probability to get \a k or smaller from a |
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115 | /// hypergeometric distribution with parameters \a n1 \a n2 \a |
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116 | /// t. Hypergeomtric situation you get in the following situation: |
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117 | /// Let there be \a n1 ways for a "good" selection and \a n2 ways |
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118 | /// for a "bad" selection out of a total of possibilities. Take \a |
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119 | /// t samples without replacement and \a k of those are "good" |
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120 | /// samples. \a k will follow a hypergeomtric distribution. |
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121 | /// |
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122 | /// @return cumulative hypergeomtric distribution functions P(k). |
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123 | /// |
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124 | double cdf_hypergeometric_P(unsigned int k, unsigned int n1, |
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125 | unsigned int n2, unsigned int t); |
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126 | |
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127 | |
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128 | /** |
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129 | The entropy is calculated as \f$ - \sum_i p_i \log p_i \f$ where |
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130 | \f$p_i = \frac{n_i}{\sum_j n_j} \f$ |
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131 | |
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132 | Requirements: |
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133 | - \c InputIterator should be an \input_iterator |
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134 | - \c InputIterator::value_type must be convertible to \c double |
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135 | |
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136 | \since New in yat 0.12 |
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137 | */ |
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138 | template<typename InputIterator> |
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139 | double entropy(InputIterator first, InputIterator last); |
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140 | |
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141 | /** |
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142 | \brief one-sided p-value |
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143 | |
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144 | This function uses the t-distribution to calculate the one-sided |
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145 | p-value. Given that the true correlation is zero (Null |
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146 | hypothesis) the estimated correlation, r, after a transformation |
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147 | is t-distributed: |
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148 | |
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149 | \f$ \sqrt{(n-2)} \frac{r}{\sqrt{(1-r^2)}} \in t(n-2) \f$ |
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150 | |
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151 | \return Probability that correlation is larger than \a r by |
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152 | chance when having \a n samples. For \a r larger or equal to 1.0, |
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153 | 0.0 is returned. For \a r smaller or equal to -1.0, 1.0 is |
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154 | returned. |
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155 | */ |
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156 | double pearson_p_value(double r, unsigned int n); |
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157 | |
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158 | /// |
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159 | /// @brief Computes the kurtosis of the data in a vector. |
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160 | /// |
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161 | /// The kurtosis measures how sharply peaked a distribution is, |
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162 | /// relative to its width. The kurtosis is normalized to zero for a |
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163 | /// gaussian distribution. |
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164 | /// |
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165 | double kurtosis(const utility::VectorBase&); |
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166 | |
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167 | |
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168 | /// |
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169 | /// @brief Median absolute deviation from median |
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170 | /// |
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171 | /// Function is non-mutable function |
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172 | /// |
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173 | /// Requirements: \c RandomAccessIterator should be a \ref |
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174 | /// concept_data_iterator and \random_access_iterator |
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175 | /// |
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176 | /// Since 0.6 function also work with a \ref |
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177 | /// concept_weighted_iterator |
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178 | /// |
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179 | template <class RandomAccessIterator> |
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180 | double mad(RandomAccessIterator first, RandomAccessIterator last, |
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181 | bool sorted=false); |
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182 | |
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183 | |
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184 | /// |
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185 | /// Median is defined to be value in the middle. If number of values |
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186 | /// is even median is the average of the two middle values. the |
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187 | /// median value is given by p equal to 50. If \a sorted is false |
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188 | /// (default), the range is copied, the copy is sorted, and then |
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189 | /// used to calculate the median. |
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190 | /// |
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191 | /// Function is a non-mutable function, i.e., \a first and \a last |
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192 | /// can be const_iterators. |
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193 | /// |
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194 | /// Requirements: \c RandomAccessIterator should be a \ref |
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195 | /// concept_data_iterator and \random_access_iterator |
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196 | /// |
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197 | /// @return median of range |
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198 | /// |
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199 | template <class RandomAccessIterator> |
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200 | double median(RandomAccessIterator first, RandomAccessIterator last, |
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201 | bool sorted=false); |
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202 | |
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203 | |
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204 | /** |
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205 | \brief Calculates the mutual information of \a A. |
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206 | |
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207 | The elements in A are unnormalized probabilies of the joint |
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208 | distribution. |
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209 | |
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210 | The mutual information is calculated as \f$ \sum \sum p(x,y) \log_2 |
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211 | \frac {p(x,y)} {p(x)p(y)} \f$ where |
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212 | \f$ p(x,y) = \frac {A_{xy}}{\sum_{x,y} A_{xy}} \f$; |
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213 | \f$ p(x) = \sum_y A_{xy} / \sum_{x,y} A_{xy} \f$; |
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214 | \f$ p(y) = \sum_x A_{xy} / \sum_{x,y} A_{xy} \f$ |
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215 | |
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216 | Requirements: |
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217 | - \c T must be a model of \ref concept_container_2d |
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218 | - \c T::value_type must be convertible to \c double |
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219 | |
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220 | \return mutual information in bits; if you want in natural base |
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221 | multiply with \c M_LN2 (defined in \c gsl/gsl_math.h ) |
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222 | |
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223 | \since New in yat 0.12 |
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224 | */ |
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225 | template<class T> |
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226 | double mutual_information(const T& A); |
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227 | |
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228 | /** |
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229 | The percentile is determined by the \a p, a number between 0 and |
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230 | 100. The percentile is found by interpolation, using the formula |
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231 | \f$ percentile = (1 - \delta) x_i + \delta x_{i+1} \f$ where \a |
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232 | p is floor\f$((n - 1)p/100)\f$ and \f$ \delta \f$ is \f$ |
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233 | (n-1)p/100 - i \f$.Thus the minimum value of the vector is given |
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234 | by p equal to zero, the maximum is given by p equal to 100 and |
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235 | the median value is given by p equal to 50. If @a sorted |
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236 | is false (default), the vector is copied, the copy is sorted, |
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237 | and then used to calculate the median. |
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238 | |
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239 | Function is a non-mutable function, i.e., \a first and \a last |
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240 | can be const_iterators. |
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241 | |
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242 | Requirements: RandomAccessIterator is an iterator over a range of |
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243 | doubles (or any type being convertable to double). |
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244 | |
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245 | @return \a p'th percentile of range |
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246 | |
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247 | \deprecated percentile2 will replace this function in the future |
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248 | |
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249 | \note the definition of percentile used here is not identical to |
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250 | that one used in percentile2 and Percentile. The difference is |
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251 | smaller for large ranges. |
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252 | */ |
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253 | template <class RandomAccessIterator> |
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254 | double percentile(RandomAccessIterator first, RandomAccessIterator last, |
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255 | double p, bool sorted=false) YAT_DEPRECATE; |
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256 | |
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257 | /** |
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258 | \see Percentiler |
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259 | |
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260 | \since new in yat 0.5 |
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261 | */ |
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262 | template <class RandomAccessIterator> |
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263 | double percentile2(RandomAccessIterator first, RandomAccessIterator last, |
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264 | double p, bool sorted=false) |
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265 | { |
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266 | Percentiler percentiler(p, sorted); |
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267 | return percentiler(first, last); |
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268 | } |
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269 | |
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270 | /// |
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271 | /// @brief Computes the skewness of the data in a vector. |
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272 | /// |
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273 | /// The skewness measures the asymmetry of the tails of a |
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274 | /// distribution. |
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275 | /// |
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276 | double skewness(const utility::VectorBase&); |
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277 | |
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278 | |
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279 | //////// template implementations /////////// |
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280 | |
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281 | template <typename T, typename ForwardIterator> |
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282 | void add(T& o, ForwardIterator first, ForwardIterator last, |
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283 | const classifier::Target& target) |
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284 | { |
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285 | utility::iterator_traits<ForwardIterator> traits; |
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286 | for (size_t i=0; first!=last; ++i, ++first) |
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287 | o.add(traits.data(first), target.binary(i), traits.weight(first)); |
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288 | } |
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289 | |
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290 | |
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291 | template<typename BidirectionalIterator1, typename BidirectionalIterator2> |
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292 | void benjamini_hochberg(BidirectionalIterator1 first, |
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293 | BidirectionalIterator1 last, |
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294 | BidirectionalIterator2 result) |
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295 | { |
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296 | using boost::Mutable_BidirectionalIterator; |
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297 | using boost::BidirectionalIterator; |
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298 | BOOST_CONCEPT_ASSERT((BidirectionalIterator<BidirectionalIterator1>)); |
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299 | BOOST_CONCEPT_ASSERT((Mutable_BidirectionalIterator<BidirectionalIterator2>)); |
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300 | typedef typename std::iterator_traits<BidirectionalIterator1> traits; |
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301 | typename traits::difference_type n = std::distance(first, last); |
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302 | if (!n) |
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303 | return; |
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304 | std::advance(result, n-1); |
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305 | first = last; |
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306 | --first; |
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307 | typename traits::difference_type rank = n; |
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308 | |
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309 | double prev = 1.0; |
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310 | while (rank) { |
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311 | *result = std::min(*first * n/static_cast<double>(rank), prev); |
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312 | prev = *result; |
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313 | --rank; |
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314 | --first; |
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315 | --result; |
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316 | } |
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317 | } |
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318 | |
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319 | |
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320 | template<typename RandomAccessIterator, typename MutableRandomAccessIterator> |
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321 | void benjamini_hochberg_unsorted(RandomAccessIterator first, |
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322 | RandomAccessIterator last, |
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323 | MutableRandomAccessIterator result) |
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324 | { |
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325 | BOOST_CONCEPT_ASSERT((boost::RandomAccessIterator<RandomAccessIterator>)); |
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326 | using boost::Mutable_RandomAccessIterator; |
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327 | BOOST_CONCEPT_ASSERT((Mutable_RandomAccessIterator<MutableRandomAccessIterator>)); |
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328 | |
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329 | std::vector<size_t> idx; |
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330 | utility::sort_index(first, last, idx); |
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331 | benjamini_hochberg(boost::make_permutation_iterator(first, idx.begin()), |
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332 | boost::make_permutation_iterator(first, idx.end()), |
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333 | boost::make_permutation_iterator(result, idx.begin())); |
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334 | } |
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335 | |
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336 | |
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337 | template<typename InputIterator> |
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338 | double entropy(InputIterator first, InputIterator last) |
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339 | { |
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340 | BOOST_CONCEPT_ASSERT((boost::InputIterator<InputIterator>)); |
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341 | using boost::Convertible; |
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342 | typedef typename InputIterator::value_type T; |
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343 | BOOST_CONCEPT_ASSERT((Convertible<T,double>)); |
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344 | double sum = 0; |
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345 | double N = 0; |
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346 | for (; first != last; ++first) { |
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347 | if (*first) { |
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348 | N += *first; |
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349 | sum += *first * std::log(static_cast<double>(*first)); |
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350 | } |
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351 | } |
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352 | return -sum / N + log(N); |
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353 | } |
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354 | |
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355 | |
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356 | template <class RandomAccessIterator> |
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357 | double mad(RandomAccessIterator first, RandomAccessIterator last, |
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358 | bool sorted) |
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359 | { |
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360 | BOOST_CONCEPT_ASSERT((boost::RandomAccessIterator<RandomAccessIterator>)); |
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361 | BOOST_CONCEPT_ASSERT((utility::DataIteratorConcept<RandomAccessIterator>)); |
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362 | double m = median(first, last, sorted); |
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363 | typedef typename std::iterator_traits<RandomAccessIterator>::value_type T; |
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364 | std::vector<T> ad(std::distance(first, last)); |
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365 | // copy weights if needed |
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366 | normalizer::detail::copy_weight_if_weighted(first, last, ad.begin()); |
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367 | // assign data (absolute deviation from median) |
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368 | utility::iterator_traits<RandomAccessIterator> traits; |
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369 | utility::DataIterator<typename std::vector<T>::iterator> first2(ad.begin()); |
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370 | while (first!=last) { |
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371 | *first2 = std::abs(traits.data(first)-m); |
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372 | ++first; |
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373 | ++first2; |
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374 | } |
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375 | std::sort(ad.begin(), ad.end()); |
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376 | return median(ad.begin(), ad.end(), true); |
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377 | } |
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378 | |
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379 | |
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380 | template <class RandomAccessIterator> |
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381 | double median(RandomAccessIterator first, RandomAccessIterator last, |
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382 | bool sorted) |
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383 | { |
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384 | return percentile2(first, last, 50.0, sorted); |
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385 | } |
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386 | |
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387 | |
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388 | template<class T> |
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389 | double mutual_information(const T& n) |
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390 | { |
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391 | BOOST_CONCEPT_ASSERT((utility::Container2D<T>)); |
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392 | using boost::Convertible; |
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393 | BOOST_CONCEPT_ASSERT((Convertible<typename T::value_type,double>)); |
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394 | |
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395 | // p_x = \sum_y p_xy |
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396 | |
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397 | // Mutual Information is defined as |
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398 | // \sum_xy p_xy * log (p_xy / (p_x p_y)) = |
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399 | // \sum_xy p_xy * [log p_xy - log p_x - log p_y] |
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400 | // \sum_xy p_xy log p_xy - p_xy log p_x - p_xy log p_y |
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401 | // \sum_xy p_xy log p_xy - \sum_x p_x log p_x - \sum_y p_y log p_y |
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402 | // - entropy_xy + entropy_x + entropy_y |
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403 | |
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404 | utility::Vector rowsum(n.columns(), 0); |
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405 | for (size_t c = 0; c<n.columns(); ++c) |
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406 | rowsum(c) = std::accumulate(n.begin_column(c), n.end_column(c), 0); |
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407 | |
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408 | utility::Vector colsum(n.rows(), 0); |
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409 | for (size_t r = 0; r<n.rows(); ++r) |
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410 | colsum(r) = std::accumulate(n.begin_row(r), n.end_row(r), 0); |
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411 | |
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412 | double mi = - entropy(n.begin(), n.end()); |
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413 | mi += entropy(rowsum.begin(), rowsum.end()); |
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414 | mi += entropy(colsum.begin(), colsum.end()); |
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415 | |
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416 | return mi/M_LN2; |
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417 | } |
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418 | |
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419 | |
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420 | template <class RandomAccessIterator> |
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421 | double percentile(RandomAccessIterator first, RandomAccessIterator last, |
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422 | double p, bool sorted) |
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423 | { |
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424 | BOOST_CONCEPT_ASSERT((boost::RandomAccessIterator<RandomAccessIterator>)); |
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425 | BOOST_CONCEPT_ASSERT((utility::DataIteratorConcept<RandomAccessIterator>)); |
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426 | // range is one value only is a special case |
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427 | if (first+1 == last) |
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428 | return utility::iterator_traits<RandomAccessIterator>().data(first); |
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429 | if (sorted) { |
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430 | // have to take care of this special case |
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431 | if (p>=100) |
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432 | return utility::iterator_traits<RandomAccessIterator>().data(--last); |
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433 | double j = p/100 * (std::distance(first,last)-1); |
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434 | int i = static_cast<int>(j); |
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435 | return (1-j+floor(j))*first[i] + (j-floor(j))*first[i+1]; |
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436 | } |
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437 | using std::iterator_traits; |
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438 | typedef typename iterator_traits<RandomAccessIterator>::value_type value_t; |
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439 | std::vector<value_t> v_copy(first, last); |
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440 | size_t i = static_cast<size_t>(p/100 * (v_copy.size()-1)); |
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441 | if (i+2 < v_copy.size()) { |
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442 | std::partial_sort(v_copy.begin(), v_copy.begin()+i+2, v_copy.end()); |
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443 | } |
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444 | else |
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445 | std::sort(v_copy.begin(), v_copy.end()); |
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446 | return percentile(v_copy.begin(), v_copy.end(), p, true); |
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447 | } |
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448 | |
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449 | |
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450 | }}} // of namespace statistics, yat, and theplu |
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451 | |
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452 | #endif |
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