1 | #ifndef _theplu_yat_statistics_averagerweighted_ |
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2 | #define _theplu_yat_statistics_averagerweighted_ |
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3 | |
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4 | // $Id: AveragerWeighted.h 914 2007-09-29 02:18:52Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2004 Cecilia Ritz, Jari Häkkinen, Peter Johansson |
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8 | Copyright (C) 2005, 2006 Jari Häkkinen, Markus Ringnér, Peter Johansson |
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9 | Copyright (C) 2007 Jari Häkkinen, Peter Johansson |
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10 | |
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11 | This file is part of the yat library, http://trac.thep.lu.se/trac/yat |
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12 | |
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13 | The yat library is free software; you can redistribute it and/or |
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14 | modify it under the terms of the GNU General Public License as |
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15 | published by the Free Software Foundation; either version 2 of the |
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16 | License, or (at your option) any later version. |
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17 | |
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18 | The yat library is distributed in the hope that it will be useful, |
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19 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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20 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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21 | General Public License for more details. |
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22 | |
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23 | You should have received a copy of the GNU General Public License |
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24 | along with this program; if not, write to the Free Software |
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25 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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26 | 02111-1307, USA. |
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27 | */ |
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28 | |
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29 | #include "Averager.h" |
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30 | #include "yat/utility/IteratorTraits.h" |
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31 | |
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32 | #include <cmath> |
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33 | |
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34 | namespace theplu{ |
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35 | namespace yat{ |
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36 | namespace statistics{ |
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37 | |
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38 | /// |
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39 | /// @brief Class to calulate averages with weights. |
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40 | /// |
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41 | /// There are several different reasons why a statistical analysis |
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42 | /// needs to adjust for weighting. In the litterature reasons are |
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43 | /// mainly divided into two kinds of weights - probablity weights |
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44 | /// and analytical weights. 1) Analytical weights are appropriate |
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45 | /// for scientific experiments where some measurements are known to |
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46 | /// be more precise than others. The larger weight a measurement has |
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47 | /// the more precise is is assumed to be, or more formally the |
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48 | /// weight is proportional to the reciprocal variance |
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49 | /// \f$ \sigma_i^2 = \frac{\sigma^2}{w_i} \f$. 2) Probability weights |
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50 | /// are used for the situation when calculating averages over a |
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51 | /// distribution \f$ f \f$ , but sampling from a distribution \f$ f' \f$. |
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52 | /// Compensating for this discrepancy averages of observables |
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53 | /// are taken to be \f$ \sum \frac{f}{f'}X \f$ For further discussion: |
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54 | /// <a href="Statistics/index.html">Weighted Statistics document</a><br> |
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55 | /// |
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56 | /// If nothing else stated, each function fulfills the |
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57 | /// following:<br> <ul><li>Setting a weight to zero corresponds to |
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58 | /// removing the data point from the dataset.</li><li> Setting all |
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59 | /// weights to unity, the yields the same result as from |
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60 | /// corresponding function in Averager.</li><li> Rescaling weights |
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61 | /// does not change the performance of the object.</li></ul> |
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62 | /// |
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63 | /// @see Averager AveragerPair AveragerPairWeighted |
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64 | /// |
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65 | class AveragerWeighted |
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66 | { |
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67 | public: |
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68 | |
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69 | /// |
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70 | /// @brief The default constructor |
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71 | /// |
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72 | AveragerWeighted(void); |
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73 | |
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74 | /// |
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75 | /// @brief The copy constructor |
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76 | /// |
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77 | AveragerWeighted(const AveragerWeighted&); |
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78 | |
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79 | /// |
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80 | /// Adding a data point \a d, with weight \a w (default is 1) |
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81 | /// |
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82 | void add(const double d,const double w=1); |
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83 | |
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84 | /// |
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85 | /// Adding each value in an array \a x and corresponding value in |
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86 | /// weight array \a w. |
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87 | /// |
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88 | /// The requirements for the types T1 and T2 of the arrays \a x |
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89 | /// and \a w are: operator[] returning an element and function |
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90 | /// size() returning the number of elements. |
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91 | /// |
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92 | template <typename T1, typename T2> |
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93 | void add_values(const T1& x, const T2& w); |
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94 | |
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95 | /// |
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96 | /// @brief Calculate the weighted mean |
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97 | /// |
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98 | /// @return \f$ \frac{\sum w_ix_i}{\sum w_i} \f$ |
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99 | /// |
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100 | double mean(void) const; |
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101 | |
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102 | /// |
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103 | /// @brief Weighted version of number of data points. |
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104 | /// |
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105 | /// If all |
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106 | /// weights are equal, the unweighted version is identical to the |
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107 | /// non-weighted version. Adding a data point with zero weight |
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108 | /// does not change n(). The calculated value is always smaller |
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109 | /// than the actual number of data points added to object. |
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110 | /// |
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111 | /// @return \f$ \frac{\left(\sum w_i\right)^2}{\sum w_i^2} \f$ |
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112 | /// |
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113 | double n(void) const; |
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114 | |
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115 | /// |
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116 | /// @brief Rescale object. |
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117 | /// |
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118 | /// Each data point is rescaled as \f$ x = a * x \f$ |
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119 | /// |
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120 | void rescale(double a); |
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121 | |
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122 | /// |
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123 | /// @brief Reset everything to zero. |
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124 | /// |
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125 | void reset(void); |
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126 | |
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127 | /// |
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128 | /// @brief The standard deviation is defined as the square root of |
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129 | /// the variance(). |
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130 | /// |
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131 | /// @return The standard deviation, root of the variance(). |
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132 | /// |
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133 | double std(void) const; |
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134 | |
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135 | /// |
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136 | /// @brief Calculates standard deviation of the mean(). |
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137 | /// |
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138 | /// Variance from the |
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139 | /// weights are here neglected. This is true when the weight is |
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140 | /// known before the measurement. In case this is not a good |
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141 | /// approximation, use bootstrapping to estimate the error. |
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142 | /// |
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143 | /// @return \f$ \frac{\sum w^2}{\left(\sum w\right)^3}\sum w(x-m)^2 \f$ |
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144 | /// where \f$ m \f$ is the mean() |
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145 | /// |
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146 | double standard_error(void) const; |
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147 | |
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148 | /// |
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149 | /// Calculating the sum of weights |
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150 | /// |
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151 | /// @return \f$ \sum w_i \f$ |
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152 | /// |
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153 | double sum_w(void) const; |
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154 | |
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155 | /// |
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156 | /// @return \f$ \sum w_i^2 \f$ |
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157 | /// |
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158 | double sum_ww(void) const; |
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159 | |
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160 | /// |
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161 | /// \f$ \sum w_ix_i \f$ |
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162 | /// |
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163 | /// @return weighted sum of x |
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164 | /// |
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165 | double sum_wx(void) const; |
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166 | |
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167 | /// |
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168 | /// @return \f$ \sum w_i x_i^2 \f$ |
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169 | /// |
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170 | double sum_wxx(void) const; |
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171 | |
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172 | /// |
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173 | /// @return \f$ \sum_i w_i (x_i-m)^2\f$ |
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174 | /// |
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175 | double sum_xx_centered(void) const; |
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176 | |
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177 | /** |
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178 | The variance is calculated as \f$ \frac{\sum w_i (x_i - m)^2 |
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179 | }{\sum w_i} \f$, where \a m is the known mean. |
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180 | |
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181 | @return Variance when the mean is known to be \a m. |
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182 | */ |
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183 | double variance(const double m) const; |
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184 | |
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185 | /** |
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186 | The variance is calculated as \f$ \frac{\sum w_i (x_i - m)^2 |
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187 | }{\sum w_i} \f$, where \a m is the mean(). Here the weight are |
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188 | interpreted as probability weights. For analytical weights the |
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189 | variance has no meaning as each data point has its own |
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190 | variance. |
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191 | |
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192 | @return The variance. |
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193 | */ |
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194 | double variance(void) const; |
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195 | |
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196 | |
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197 | private: |
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198 | /// |
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199 | /// @return \f$ \sum w_i^2x_i \f$ |
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200 | /// |
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201 | double sum_wwx(void) const; |
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202 | |
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203 | /// |
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204 | /// @return \f$ \sum w_i^2x_i^2 \f$ |
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205 | /// |
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206 | double sum_wwxx(void) const; |
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207 | |
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208 | const Averager& wx(void) const; |
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209 | const Averager& w(void) const; |
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210 | |
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211 | /// |
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212 | /// operator to add a AveragerWeighted |
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213 | /// |
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214 | const AveragerWeighted& operator+=(const AveragerWeighted&); |
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215 | |
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216 | Averager w_; |
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217 | Averager wx_; |
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218 | double wwx_; |
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219 | double wxx_; |
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220 | }; |
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221 | |
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222 | /** |
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223 | \brief adding a ranges of values to Averager \a a |
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224 | */ |
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225 | template <typename Iter> |
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226 | void add(AveragerWeighted& a, Iter first, Iter last) |
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227 | { |
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228 | for ( ; first != last; ++first) |
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229 | a.add(utility::iterator_traits_data(first)); |
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230 | } |
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231 | |
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232 | // Template implementations |
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233 | template <typename T1, typename T2> |
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234 | void AveragerWeighted::add_values(const T1& x, const T2& w) |
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235 | { |
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236 | for (size_t i=0; i<x.size(); i++) |
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237 | add(x[i],w[i]); |
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238 | } |
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239 | |
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240 | /// |
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241 | /// The AveragerWeighted output operator |
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242 | /// |
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243 | ///std::ostream& operator<<(std::ostream& s,const AveragerWeighted&); |
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244 | |
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245 | }}} // of namespace statistics, yat, and theplu |
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246 | |
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247 | #endif |
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