1 | #ifndef _theplu_yat_regression_linear_ |
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2 | #define _theplu_yat_regression_linear_ |
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3 | |
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4 | // $Id: Linear.h 1437 2008-08-25 17:55:00Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2004, 2005, 2006, 2007 Jari Häkkinen, Peter Johansson |
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8 | Copyright (C) 2008 Peter Johansson |
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9 | |
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10 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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11 | |
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12 | The yat library is free software; you can redistribute it and/or |
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13 | modify it under the terms of the GNU General Public License as |
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14 | published by the Free Software Foundation; either version 2 of the |
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15 | License, or (at your option) any later version. |
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16 | |
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17 | The yat library is distributed in the hope that it will be useful, |
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18 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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19 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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20 | General Public License for more details. |
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21 | |
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22 | You should have received a copy of the GNU General Public License |
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23 | along with this program; if not, write to the Free Software |
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24 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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25 | 02111-1307, USA. |
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26 | */ |
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27 | |
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28 | #include "OneDimensional.h" |
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29 | |
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30 | #include <cmath> |
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31 | |
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32 | namespace theplu { |
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33 | namespace yat { |
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34 | namespace utility { |
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35 | class VectorBase; |
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36 | } |
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37 | namespace regression { |
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38 | |
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39 | /** |
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40 | @brief linear regression. |
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41 | |
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42 | Data are modeled as \f$ y_i = \alpha + \beta (x_i-m_x) + |
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43 | \epsilon_i \f$. |
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44 | */ |
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45 | class Linear : public OneDimensional |
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46 | { |
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47 | |
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48 | public: |
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49 | /// |
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50 | /// @brief The default constructor |
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51 | /// |
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52 | Linear(void); |
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53 | |
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54 | /// |
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55 | /// @brief The destructor |
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56 | /// |
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57 | virtual ~Linear(void); |
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58 | |
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59 | /** |
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60 | The parameter \f$ \alpha \f$ is estimated as \f$ |
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61 | \frac{1}{n}\sum y_i \f$ |
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62 | |
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63 | @return the parameter \f$ \alpha \f$ |
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64 | */ |
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65 | double alpha(void) const; |
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66 | |
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67 | /** |
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68 | The standard deviation is estimated as \f$ \sqrt{\frac{s^2}{n}} |
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69 | \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$ |
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70 | |
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71 | @return standard deviation of parameter \f$ \alpha \f$ |
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72 | */ |
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73 | double alpha_var(void) const; |
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74 | |
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75 | /** |
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76 | The parameter \f$ \beta \f$ is estimated as \f$ |
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77 | \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$ |
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78 | |
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79 | @return the parameter \f$ \beta \f$ |
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80 | */ |
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81 | double beta(void) const; |
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82 | |
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83 | /** |
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84 | The standard deviation is estimated as \f$ \frac{s^2}{\sum |
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85 | (x-m_x)^2} \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$ |
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86 | |
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87 | @return standard deviation of parameter \f$ \beta \f$ |
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88 | */ |
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89 | double beta_var(void) const; |
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90 | |
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91 | /** |
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92 | Model is fitted by minimizing \f$ \sum{(y_i - \alpha - \beta |
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93 | (x-m_x))^2} \f$. By construction \f$ \alpha \f$ and \f$ \beta \f$ |
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94 | are independent. |
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95 | */ |
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96 | void fit(const utility::VectorBase& x, const utility::VectorBase& y) ; |
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97 | |
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98 | /// |
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99 | /// @return \f$ \alpha + \beta x \f$ |
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100 | /// |
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101 | double predict(const double x) const; |
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102 | |
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103 | /// |
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104 | /// Function returning the coefficient of determination, |
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105 | /// i.e. fraction of variance explained by the linear model. |
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106 | /// |
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107 | double r2(void) const; |
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108 | |
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109 | /** |
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110 | \f$ \frac{\sum \epsilon_i^2}{N-2} \f$ |
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111 | |
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112 | @return variance of residuals |
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113 | */ |
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114 | double s2(void) const; |
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115 | |
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116 | /** |
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117 | The error of the model is estimated as \f$ |
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118 | \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)\f$ |
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119 | |
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120 | @return estimated error of model in @a x |
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121 | */ |
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122 | double standard_error2(const double x) const; |
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123 | |
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124 | |
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125 | private: |
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126 | /// |
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127 | /// Copy Constructor. (not implemented) |
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128 | /// |
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129 | Linear(const Linear&); |
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130 | |
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131 | double alpha_; |
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132 | double alpha_var_; |
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133 | double beta_; |
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134 | double beta_var_; |
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135 | }; |
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136 | |
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137 | }}} // of namespaces regression, yat, and theplu |
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138 | |
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139 | #endif |
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