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 3136 2013-11-28 00:18:22Z 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 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/VectorBase.h" |
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39 | #include "yat/utility/yat_assert.h" |
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40 | |
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41 | #include <boost/concept_check.hpp> |
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42 | |
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43 | #include <algorithm> |
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44 | #include <cmath> |
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45 | #include <iterator> |
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46 | #include <stdexcept> |
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47 | #include <vector> |
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48 | |
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49 | #include <gsl/gsl_statistics_double.h> |
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50 | |
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51 | namespace theplu { |
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52 | namespace yat { |
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53 | namespace statistics { |
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54 | |
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55 | /** |
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56 | Adding a range [\a first, \a last) into an object of type T. The |
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57 | requirements for the type T is to have an add(double, bool, double) |
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58 | function. |
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59 | */ |
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60 | template <typename T, typename ForwardIterator> |
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61 | void add(T& o, ForwardIterator first, ForwardIterator last, |
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62 | const classifier::Target& target); |
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63 | |
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64 | /** |
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65 | \brief Benjamini Hochberg multiple test correction |
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66 | |
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67 | Given a sorted range of p-values such that |
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68 | \f$ p_1 \le p_2 \le ... \le p_N \f$ a Benjamnini-Hochberg corrected |
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69 | p-value, \c q, is calculated recursively as |
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70 | \f$ q_i = \f$ min \f$(p_i \frac{N}{i}, q_{i+1})\f$ with the anchor |
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71 | constraint that \f$ q_m = p_m \f$. |
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72 | |
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73 | Requirements: \c BidirectionalIterator1 should be a |
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74 | \bidirectional_iterator and \c BidirectionalIterator2 should be a |
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75 | mutable \bidirectional_iterator |
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76 | |
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77 | \since New in yat 0.8 |
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78 | */ |
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79 | template<typename BidirectionalIterator1, typename BidirectionalIterator2> |
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80 | void benjamini_hochberg(BidirectionalIterator1 first, |
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81 | BidirectionalIterator1 last, |
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82 | BidirectionalIterator2 result); |
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83 | |
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84 | |
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85 | /// |
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86 | /// Calculates the probability to get \a k or smaller from a |
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87 | /// hypergeometric distribution with parameters \a n1 \a n2 \a |
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88 | /// t. Hypergeomtric situation you get in the following situation: |
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89 | /// Let there be \a n1 ways for a "good" selection and \a n2 ways |
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90 | /// for a "bad" selection out of a total of possibilities. Take \a |
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91 | /// t samples without replacement and \a k of those are "good" |
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92 | /// samples. \a k will follow a hypergeomtric distribution. |
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93 | /// |
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94 | /// @return cumulative hypergeomtric distribution functions P(k). |
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95 | /// |
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96 | double cdf_hypergeometric_P(unsigned int k, unsigned int n1, |
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97 | unsigned int n2, unsigned int t); |
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98 | |
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99 | |
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100 | /** |
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101 | The entropy is calculated as \f$ - \sum_i p_i \log p_i \f$ where |
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102 | \f$p_i = \frac{n_i}{\sum_j n_j} \f$ |
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103 | |
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104 | Requirements: |
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105 | - \c InputIterator should be an \input_iterator |
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106 | - \c InputIterator::value_type must be convertible to \c double |
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107 | |
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108 | \since New in yat 0.12 |
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109 | */ |
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110 | template<typename InputIterator> |
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111 | double entropy(InputIterator first, InputIterator last); |
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112 | |
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113 | /** |
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114 | \brief one-sided p-value |
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115 | |
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116 | This function uses the t-distribution to calculate the one-sided |
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117 | p-value. Given that the true correlation is zero (Null |
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118 | hypothesis) the estimated correlation, r, after a transformation |
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119 | is t-distributed: |
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120 | |
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121 | \f$ \sqrt{(n-2)} \frac{r}{\sqrt{(1-r^2)}} \in t(n-2) \f$ |
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122 | |
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123 | \return Probability that correlation is larger than \a r by |
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124 | chance when having \a n samples. For \a r larger or equal to 1.0, |
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125 | 0.0 is returned. For \a r smaller or equal to -1.0, 1.0 is |
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126 | returned. |
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127 | */ |
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128 | double pearson_p_value(double r, unsigned int n); |
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129 | |
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130 | /// |
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131 | /// @brief Computes the kurtosis of the data in a vector. |
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132 | /// |
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133 | /// The kurtosis measures how sharply peaked a distribution is, |
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134 | /// relative to its width. The kurtosis is normalized to zero for a |
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135 | /// gaussian distribution. |
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136 | /// |
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137 | double kurtosis(const utility::VectorBase&); |
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138 | |
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139 | |
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140 | /// |
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141 | /// @brief Median absolute deviation from median |
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142 | /// |
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143 | /// Function is non-mutable function |
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144 | /// |
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145 | /// Requirements: \c RandomAccessIterator should be a \ref |
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146 | /// concept_data_iterator and \random_access_iterator |
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147 | /// |
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148 | /// Since 0.6 function also work with a \ref |
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149 | /// concept_weighted_iterator |
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150 | /// |
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151 | template <class RandomAccessIterator> |
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152 | double mad(RandomAccessIterator first, RandomAccessIterator last, |
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153 | bool sorted=false); |
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154 | |
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155 | |
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156 | /// |
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157 | /// Median is defined to be value in the middle. If number of values |
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158 | /// is even median is the average of the two middle values. the |
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159 | /// median value is given by p equal to 50. If \a sorted is false |
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160 | /// (default), the range is copied, the copy is sorted, and then |
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161 | /// used to calculate the median. |
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162 | /// |
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163 | /// Function is a non-mutable function, i.e., \a first and \a last |
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164 | /// can be const_iterators. |
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165 | /// |
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166 | /// Requirements: \c RandomAccessIterator should be a \ref |
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167 | /// concept_data_iterator and \random_access_iterator |
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168 | /// |
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169 | /// @return median of range |
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170 | /// |
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171 | template <class RandomAccessIterator> |
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172 | double median(RandomAccessIterator first, RandomAccessIterator last, |
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173 | bool sorted=false); |
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174 | |
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175 | |
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176 | /** |
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177 | The percentile is determined by the \a p, a number between 0 and |
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178 | 100. The percentile is found by interpolation, using the formula |
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179 | \f$ percentile = (1 - \delta) x_i + \delta x_{i+1} \f$ where \a |
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180 | p is floor\f$((n - 1)p/100)\f$ and \f$ \delta \f$ is \f$ |
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181 | (n-1)p/100 - i \f$.Thus the minimum value of the vector is given |
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182 | by p equal to zero, the maximum is given by p equal to 100 and |
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183 | the median value is given by p equal to 50. If @a sorted |
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184 | is false (default), the vector is copied, the copy is sorted, |
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185 | and then used to calculate the median. |
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186 | |
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187 | Function is a non-mutable function, i.e., \a first and \a last |
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188 | can be const_iterators. |
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189 | |
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190 | Requirements: RandomAccessIterator is an iterator over a range of |
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191 | doubles (or any type being convertable to double). |
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192 | |
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193 | @return \a p'th percentile of range |
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194 | |
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195 | \deprecated percentile2 will replace this function in the future |
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196 | |
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197 | \note the definition of percentile used here is not identical to |
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198 | that one used in percentile2 and Percentile. The difference is |
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199 | smaller for large ranges. |
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200 | */ |
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201 | template <class RandomAccessIterator> |
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202 | double percentile(RandomAccessIterator first, RandomAccessIterator last, |
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203 | double p, bool sorted=false) YAT_DEPRECATE; |
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204 | |
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205 | /** |
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206 | \see Percentiler |
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207 | |
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208 | \since new in yat 0.5 |
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209 | */ |
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210 | template <class RandomAccessIterator> |
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211 | double percentile2(RandomAccessIterator first, RandomAccessIterator last, |
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212 | double p, bool sorted=false) |
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213 | { |
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214 | Percentiler percentiler(p, sorted); |
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215 | return percentiler(first, last); |
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216 | } |
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217 | |
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218 | /// |
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219 | /// @brief Computes the skewness of the data in a vector. |
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220 | /// |
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221 | /// The skewness measures the asymmetry of the tails of a |
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222 | /// distribution. |
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223 | /// |
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224 | double skewness(const utility::VectorBase&); |
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225 | |
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226 | |
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227 | //////// template implementations /////////// |
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228 | |
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229 | template <typename T, typename ForwardIterator> |
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230 | void add(T& o, ForwardIterator first, ForwardIterator last, |
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231 | const classifier::Target& target) |
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232 | { |
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233 | utility::iterator_traits<ForwardIterator> traits; |
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234 | for (size_t i=0; first!=last; ++i, ++first) |
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235 | o.add(traits.data(first), target.binary(i), traits.weight(first)); |
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236 | } |
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237 | |
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238 | |
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239 | template<typename BidirectionalIterator1, typename BidirectionalIterator2> |
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240 | void benjamini_hochberg(BidirectionalIterator1 first, |
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241 | BidirectionalIterator1 last, |
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242 | BidirectionalIterator2 result) |
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243 | { |
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244 | using boost::Mutable_BidirectionalIterator; |
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245 | BOOST_CONCEPT_ASSERT((boost::BidirectionalIterator<BidirectionalIterator1>)); |
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246 | BOOST_CONCEPT_ASSERT((Mutable_BidirectionalIterator<BidirectionalIterator2>)); |
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247 | size_t n = std::distance(first, last); |
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248 | if (!n) |
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249 | return; |
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250 | std::advance(result, n-1); |
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251 | first = last; |
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252 | --first; |
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253 | size_t rank = n; |
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254 | |
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255 | double prev = 1.0; |
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256 | while (rank) { |
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257 | *result = std::min(*first * n/static_cast<double>(rank), prev); |
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258 | prev = *result; |
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259 | --rank; |
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260 | --first; |
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261 | --result; |
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262 | } |
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263 | } |
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264 | |
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265 | |
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266 | template<typename InputIterator> |
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267 | double entropy(InputIterator first, InputIterator last) |
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268 | { |
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269 | BOOST_CONCEPT_ASSERT((boost::InputIterator<InputIterator>)); |
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270 | using boost::Convertible; |
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271 | typedef typename InputIterator::value_type T; |
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272 | BOOST_CONCEPT_ASSERT((Convertible<T,double>)); |
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273 | double sum = 0; |
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274 | double N = 0; |
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275 | for (; first != last; ++first) { |
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276 | if (*first) { |
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277 | N += *first; |
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278 | sum += *first * std::log(static_cast<double>(*first)); |
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279 | } |
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280 | } |
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281 | return -sum / N + log(N); |
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282 | } |
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283 | |
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284 | |
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285 | template <class RandomAccessIterator> |
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286 | double mad(RandomAccessIterator first, RandomAccessIterator last, |
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287 | bool sorted) |
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288 | { |
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289 | BOOST_CONCEPT_ASSERT((boost::RandomAccessIterator<RandomAccessIterator>)); |
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290 | BOOST_CONCEPT_ASSERT((utility::DataIteratorConcept<RandomAccessIterator>)); |
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291 | double m = median(first, last, sorted); |
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292 | typedef typename std::iterator_traits<RandomAccessIterator>::value_type T; |
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293 | std::vector<T> ad(std::distance(first, last)); |
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294 | // copy weights if needed |
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295 | normalizer::detail::copy_weight_if_weighted(first, last, ad.begin()); |
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296 | // assign data (absolute deviation from median) |
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297 | utility::iterator_traits<RandomAccessIterator> traits; |
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298 | utility::DataIterator<typename std::vector<T>::iterator> first2(ad.begin()); |
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299 | while (first!=last) { |
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300 | *first2 = std::abs(traits.data(first)-m); |
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301 | ++first; |
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302 | ++first2; |
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303 | } |
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304 | std::sort(ad.begin(), ad.end()); |
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305 | return median(ad.begin(), ad.end(), true); |
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306 | } |
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307 | |
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308 | |
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309 | template <class RandomAccessIterator> |
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310 | double median(RandomAccessIterator first, RandomAccessIterator last, |
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311 | bool sorted) |
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312 | { |
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313 | return percentile2(first, last, 50.0, sorted); |
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314 | } |
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315 | |
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316 | |
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317 | template <class RandomAccessIterator> |
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318 | double percentile(RandomAccessIterator first, RandomAccessIterator last, |
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319 | double p, bool sorted) |
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320 | { |
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321 | BOOST_CONCEPT_ASSERT((boost::RandomAccessIterator<RandomAccessIterator>)); |
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322 | BOOST_CONCEPT_ASSERT((utility::DataIteratorConcept<RandomAccessIterator>)); |
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323 | // range is one value only is a special case |
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324 | if (first+1 == last) |
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325 | return utility::iterator_traits<RandomAccessIterator>().data(first); |
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326 | if (sorted) { |
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327 | // have to take care of this special case |
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328 | if (p>=100) |
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329 | return utility::iterator_traits<RandomAccessIterator>().data(--last); |
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330 | double j = p/100 * (std::distance(first,last)-1); |
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331 | int i = static_cast<int>(j); |
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332 | return (1-j+floor(j))*first[i] + (j-floor(j))*first[i+1]; |
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333 | } |
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334 | using std::iterator_traits; |
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335 | typedef typename iterator_traits<RandomAccessIterator>::value_type value_t; |
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336 | std::vector<value_t> v_copy; |
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337 | v_copy.reserve(std::distance(first,last)); |
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338 | std::copy(first, last, std::back_inserter(v_copy)); |
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339 | size_t i = static_cast<size_t>(p/100 * (v_copy.size()-1)); |
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340 | if (i+2 < v_copy.size()) { |
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341 | std::partial_sort(v_copy.begin(), v_copy.begin()+i+2, v_copy.end()); |
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342 | } |
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343 | else |
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344 | std::sort(v_copy.begin(), v_copy.end()); |
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345 | return percentile(v_copy.begin(), v_copy.end(), p, true); |
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346 | } |
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347 | |
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348 | |
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349 | }}} // of namespace statistics, yat, and theplu |
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350 | |
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351 | #endif |
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