source: trunk/yat/regression/Linear.h @ 1655

Last change on this file since 1655 was 1487, checked in by Jari Häkkinen, 13 years ago

Addresses #436. GPL license copy reference should also be updated.

  • Property svn:eol-style set to native
  • Property svn:keywords set to Author Date Id Revision
File size: 3.0 KB
Line 
1#ifndef _theplu_yat_regression_linear_
2#define _theplu_yat_regression_linear_
3
4// $Id: Linear.h 1487 2008-09-10 08:41:36Z jari $
5
6/*
7  Copyright (C) 2004, 2005, 2006, 2007 Jari Häkkinen, Peter Johansson
8  Copyright (C) 2008 Peter Johansson
9
10  This file is part of the yat library, http://dev.thep.lu.se/yat
11
12  The yat library is free software; you can redistribute it and/or
13  modify it under the terms of the GNU General Public License as
14  published by the Free Software Foundation; either version 3 of the
15  License, or (at your option) any later version.
16
17  The yat library is distributed in the hope that it will be useful,
18  but WITHOUT ANY WARRANTY; without even the implied warranty of
19  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20  General Public License for more details.
21
22  You should have received a copy of the GNU General Public License
23  along with yat. If not, see <http://www.gnu.org/licenses/>.
24*/
25
26#include "OneDimensional.h"
27
28#include <cmath>
29
30namespace theplu {
31namespace yat {
32  namespace utility {
33    class VectorBase;
34  }
35namespace regression {
36
37  /**
38     @brief linear regression.   
39     
40     Data are modeled as \f$ y_i = \alpha + \beta (x_i-m_x) +
41     \epsilon_i \f$.
42  */
43  class Linear : public OneDimensional
44  {
45 
46  public:
47    ///
48    /// @brief The default constructor
49    ///
50    Linear(void);
51
52    ///
53    /// @brief The destructor
54    ///
55    virtual ~Linear(void);
56         
57    /**
58       The parameter \f$ \alpha \f$ is estimated as \f$
59       \frac{1}{n}\sum y_i \f$
60       
61       @return the parameter \f$ \alpha \f$
62    */
63    double alpha(void) const;
64
65    /**
66       The standard deviation is estimated as \f$ \sqrt{\frac{s^2}{n}}
67       \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$
68       
69       @return standard deviation of parameter \f$ \alpha \f$
70    */
71    double alpha_var(void) const;
72
73    /**
74       The parameter \f$ \beta \f$ is estimated as \f$
75       \frac{\textrm{Cov}(x,y)}{\textrm{Var}(x)} \f$
76       
77       @return the parameter \f$ \beta \f$
78    */
79    double beta(void) const;
80
81    /**
82       The standard deviation is estimated as \f$ \frac{s^2}{\sum
83       (x-m_x)^2} \f$ where \f$ s^2 = \frac{\sum \epsilon^2}{n-2} \f$
84
85       @return standard deviation of parameter \f$ \beta \f$
86    */
87    double beta_var(void) const;
88
89    /**
90       Model is fitted by minimizing \f$ \sum{(y_i - \alpha - \beta
91       (x-m_x))^2} \f$. By construction \f$ \alpha \f$ and \f$ \beta \f$
92       are independent.
93    */
94    void fit(const utility::VectorBase& x, const utility::VectorBase& y) ;
95   
96    ///
97    /// @return \f$ \alpha + \beta x \f$
98    ///
99    double predict(const double x) const;
100
101    /**
102       \f$ \frac{\sum \epsilon_i^2}{N-2} \f$
103
104       @return variance of residuals
105    */
106    double s2(void) const;
107
108    /**
109       The error of the model is estimated as \f$
110       \textrm{alpha\_err}^2+\textrm{beta\_err}^2*(x-m_x)*(x-m_x)\f$
111   
112       @return estimated error of model in @a x
113    */
114    double standard_error2(const double x) const;
115
116
117  private:
118    ///
119    /// Copy Constructor. (not implemented)
120    ///
121    Linear(const Linear&);
122
123    double alpha_;
124    double alpha_var_;
125    double beta_;
126    double beta_var_;
127  };
128
129}}} // of namespaces regression, yat, and theplu
130
131#endif
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