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 1487 2008-09-10 08:41:36Z jari $ |
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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 3 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 yat. If not, see <http://www.gnu.org/licenses/>. |
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24 | */ |
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25 | |
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26 | #include "OneDimensional.h" |
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27 | |
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28 | #include <cmath> |
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29 | |
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30 | namespace theplu { |
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31 | namespace yat { |
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32 | namespace utility { |
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33 | class VectorBase; |
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34 | } |
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35 | namespace regression { |
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36 | |
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37 | /** |
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38 | @brief linear regression. |
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39 | |
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40 | Data are modeled as \f$ y_i = \alpha + \beta (x_i-m_x) + |
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41 | \epsilon_i \f$. |
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42 | */ |
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43 | class Linear : public OneDimensional |
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44 | { |
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45 | |
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46 | public: |
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47 | /// |
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48 | /// @brief The default constructor |
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49 | /// |
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50 | Linear(void); |
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51 | |
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52 | /// |
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53 | /// @brief The destructor |
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54 | /// |
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55 | virtual ~Linear(void); |
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56 | |
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57 | /** |
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58 | The parameter \f$ \alpha \f$ is estimated as \f$ |
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59 | \frac{1}{n}\sum y_i \f$ |
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60 | |
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61 | @return the parameter \f$ \alpha \f$ |
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62 | */ |
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63 | double alpha(void) const; |
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64 | |
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65 | /** |
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66 | The standard deviation is estimated as \f$ \sqrt{\frac{s^2}{n}} |
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67 | \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$ |
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68 | |
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69 | @return standard deviation of parameter \f$ \alpha \f$ |
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70 | */ |
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71 | double alpha_var(void) const; |
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72 | |
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73 | /** |
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74 | The parameter \f$ \beta \f$ is estimated as \f$ |
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75 | \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$ |
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76 | |
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77 | @return the parameter \f$ \beta \f$ |
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78 | */ |
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79 | double beta(void) const; |
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80 | |
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81 | /** |
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82 | The standard deviation is estimated as \f$ \frac{s^2}{\sum |
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83 | (x-m_x)^2} \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$ |
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84 | |
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85 | @return standard deviation of parameter \f$ \beta \f$ |
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86 | */ |
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87 | double beta_var(void) const; |
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88 | |
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89 | /** |
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90 | Model is fitted by minimizing \f$ \sum{(y_i - \alpha - \beta |
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91 | (x-m_x))^2} \f$. By construction \f$ \alpha \f$ and \f$ \beta \f$ |
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92 | are independent. |
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93 | */ |
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94 | void fit(const utility::VectorBase& x, const utility::VectorBase& y) ; |
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95 | |
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96 | /// |
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97 | /// @return \f$ \alpha + \beta x \f$ |
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98 | /// |
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99 | double predict(const double x) const; |
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100 | |
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101 | /** |
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102 | \f$ \frac{\sum \epsilon_i^2}{N-2} \f$ |
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103 | |
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104 | @return variance of residuals |
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105 | */ |
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106 | double s2(void) const; |
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107 | |
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108 | /** |
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109 | The error of the model is estimated as \f$ |
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110 | \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)\f$ |
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111 | |
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112 | @return estimated error of model in @a x |
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113 | */ |
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114 | double standard_error2(const double x) const; |
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115 | |
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116 | |
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117 | private: |
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118 | /// |
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119 | /// Copy Constructor. (not implemented) |
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120 | /// |
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121 | Linear(const Linear&); |
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122 | |
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123 | double alpha_; |
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124 | double alpha_var_; |
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125 | double beta_; |
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126 | double beta_var_; |
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127 | }; |
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128 | |
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129 | }}} // of namespaces regression, yat, and theplu |
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130 | |
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131 | #endif |
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