1 | // $Id: AveragerWeighted.h 492 2006-01-09 09:38:12Z peter $ |
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2 | |
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3 | #ifndef _theplu_statistics_averager_weighted_ |
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4 | #define _theplu_statistics_averager_weighted_ |
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5 | |
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6 | #include <c++_tools/statistics/Averager.h> |
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7 | |
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8 | #include <cmath> |
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9 | //#include <ostream> |
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10 | |
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11 | namespace theplu{ |
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12 | class gslapi::vector; |
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13 | |
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14 | namespace statistics{ |
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15 | |
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16 | /// |
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17 | /// @brief Class to calulate averages with weights. |
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18 | /// |
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19 | /// There are several different reasons why a statistical analysis |
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20 | /// needs to adjust for weighting. In the litterature reasons are |
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21 | /// mainly divided into two kinds of weights - probablity weights |
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22 | /// and analytical weights. 1) Analytical weights are appropriate |
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23 | /// for scientific experiments where some measurements are known to |
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24 | /// be more precise than others. The larger weight a measurement has |
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25 | /// the more precise is is assumed to be, or more formally the |
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26 | /// weight is proportional to the reciprocal variance |
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27 | /// \f$ \sigma_i^2 = \frac{\sigma^2}{w_i} \f$. 2) Probablity weights |
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28 | /// are used for the situation when calculating averages over a |
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29 | /// distribution \f$ f \f$ , but sampling from a distribution \f$ f' |
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30 | /// \f$. Compensating for this discrepancy averages of observables |
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31 | /// are taken to be \f$ \sum \frac{f}{f'}X \f$ For further discussion: |
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32 | /// <a href="../Statistics/index.html">Weighted Statistics document</a><br> |
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33 | /// |
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34 | /// If nothing else stated, each function fulfills the |
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35 | /// following:<br> <ul><li>Setting a weight to zero corresponds to |
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36 | /// removing the data point from the dataset.</li><li> Setting all |
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37 | /// weights to unity, the yields the same result as from |
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38 | /// corresponding function in Averager.</li><li> Rescaling weights |
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39 | /// does not change the performance of the object.</li></ul> |
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40 | /// |
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41 | /// @see Averager AveragerPair AveragerPairWeighted |
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42 | /// |
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43 | class AveragerWeighted |
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44 | { |
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45 | public: |
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46 | |
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47 | /// |
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48 | /// Default constructor |
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49 | /// |
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50 | inline AveragerWeighted(void) |
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51 | : w_(Averager()), wx_(Averager()), wwx_(0), wxx_(0) {} |
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52 | |
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53 | /// |
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54 | /// Copy constructor |
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55 | /// |
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56 | inline AveragerWeighted(const AveragerWeighted& a) |
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57 | : w_(Averager(a.sum_w(),a.sum_ww(),1)), |
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58 | wx_(Averager(a.sum_wx(),a.sum_wwxx(),1)), wwx_(a.sum_wwx()), |
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59 | wxx_(a.sum_wxx()) {} |
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60 | |
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61 | /// |
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62 | /// adding a data point d, with weight w (default is 1) |
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63 | /// |
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64 | inline void add(const double d,const double w=1) |
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65 | { if(w==0) return; w_.add(w); wx_.add(w*d); wwx_+=w*w*d; wxx_+=w*d*d; } |
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66 | |
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67 | /// |
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68 | /// Adding each value in vector \a x and corresponding value in |
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69 | /// weight vector \a w. |
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70 | /// |
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71 | void add(const gslapi::vector& x, const gslapi::vector& w); |
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72 | |
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73 | /// |
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74 | /// Calculating the weighted mean |
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75 | /// |
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76 | /// @return \f$ \frac{\sum w_ix_i}{\sum w_i} \f$ |
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77 | /// |
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78 | inline double mean(void) const { return sum_w() ? |
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79 | sum_wx()/sum_w() : 0; } |
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80 | |
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81 | /// |
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82 | /// @return \f$ \frac{\left(\sum w_i\right)^2}{\sum w_i^2} \f$ |
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83 | /// |
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84 | inline double n(void) const { return sum_w()*sum_w()/sum_ww(); } |
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85 | |
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86 | /// |
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87 | /// rescale object, i.e. each data point is rescaled |
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88 | /// \f$ x = a * x \f$ |
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89 | /// |
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90 | inline void rescale(double a) { wx_.rescale(a); wwx_*=a; wxx_*=a*a; } |
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91 | |
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92 | /// |
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93 | /// resets everything to zero |
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94 | /// |
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95 | inline void reset(void) { wx_.reset(); w_.reset(); wwx_=0; wxx_=0; } |
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96 | |
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97 | /// |
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98 | /// The standard deviation is defined as the square root of the |
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99 | /// variance(). |
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100 | /// |
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101 | /// @return The standard deviation, root of the variance(). |
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102 | /// |
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103 | inline double std(void) const { return sqrt(variance()); } |
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104 | |
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105 | /// |
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106 | /// Calculates standard deviation of the mean(). Variance from the |
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107 | /// weights are here neglected. This is true when the weight is |
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108 | /// known before the measurement. In case this is not a good |
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109 | /// approximation, use bootstrapping to estimate the error. |
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110 | /// |
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111 | /// @return \f$ \frac{\sum w^2}{\left(\sum w\right)^3}\sum w(x-m)^2 \f$ |
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112 | /// where \f$ m \f$ is the mean() |
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113 | /// |
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114 | inline double standard_error(void) const |
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115 | { return sqrt(sum_ww()/(sum_w()*sum_w()*sum_w()) * |
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116 | sum_xx_centered()); } |
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117 | |
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118 | /// |
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119 | /// Calculating the sum of weights |
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120 | /// |
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121 | /// @return \f$ \sum w_i \f$ |
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122 | /// |
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123 | inline double sum_w(void) const |
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124 | { return w_.sum_x(); } |
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125 | |
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126 | /// |
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127 | /// @return \f$ \sum w_i^2 \f$ |
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128 | /// |
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129 | inline double sum_ww(void) const |
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130 | { return w_.sum_xx(); } |
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131 | |
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132 | /// |
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133 | /// \f$ \sum w_ix_i \f$ |
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134 | /// |
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135 | /// @return weighted sum of x |
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136 | /// |
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137 | inline double sum_wx(void) const |
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138 | { return wx_.sum_x(); } |
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139 | |
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140 | /// |
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141 | /// @return \f$ \sum_i w_i (x_i-m)^2\f$ |
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142 | /// |
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143 | inline double sum_xx_centered(void) const |
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144 | { return sum_wxx() - mean()*mean()*sum_w(); } |
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145 | |
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146 | /// |
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147 | /// The variance is calculated as \f$ \frac{\sum w_i (x_i - m)^2 |
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148 | /// }{\sum w_i} \f$, where \a m is the known mean. |
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149 | /// |
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150 | /// @return Variance when the mean is known to be \a m. |
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151 | /// |
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152 | inline double variance(const double m) const |
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153 | { return (sum_wxx()-2*m*sum_wx())/sum_w()+m*m; } |
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154 | |
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155 | /// |
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156 | /// The variance is calculated as \f$ \frac{\sum w_i (x_i - m)^2 |
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157 | /// }{\sum w_i} \f$, where \a m is the mean(). Here the weight are |
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158 | /// interpreted as probability weights. For analytical weights the |
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159 | /// variance has no meaning as each data point has its own |
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160 | /// variance. |
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161 | /// |
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162 | /// @return The variance. |
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163 | /// |
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164 | inline double variance(void) const |
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165 | { return sum_xx_centered()/sum_w(); } |
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166 | |
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167 | |
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168 | private: |
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169 | /// |
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170 | /// @return \f$ \sum w_i^2x_i^2 \f$ |
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171 | /// |
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172 | inline double sum_wwxx(void) const |
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173 | { return wx_.sum_xx(); } |
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174 | |
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175 | /// |
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176 | /// @return \f$ \sum w_i^2x_i \f$ |
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177 | /// |
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178 | inline double sum_wwx(void) const |
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179 | { return wwx_; } |
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180 | |
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181 | /// |
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182 | /// @return \f$ \sum w_i x_i^2 \f$ |
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183 | /// |
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184 | inline double sum_wxx(void) const { return wxx_; } |
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185 | |
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186 | /// |
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187 | /// operator to add a AveragerWeighted |
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188 | /// |
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189 | AveragerWeighted operator+=(const AveragerWeighted&); |
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190 | |
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191 | Averager w_; |
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192 | Averager wx_; |
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193 | double wwx_; |
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194 | double wxx_; |
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195 | |
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196 | inline Averager wx(void) const {return wx_;} |
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197 | inline Averager w(void) const {return w_;} |
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198 | |
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199 | |
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200 | }; |
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201 | |
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202 | /// |
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203 | /// The AveragerWeighted output operator |
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204 | /// |
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205 | ///std::ostream& operator<<(std::ostream& s,const AveragerWeighted&); |
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206 | |
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207 | }} // of namespace statistics and namespace theplu |
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208 | |
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209 | #endif |
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