source: trunk/yat/regression/LinearWeighted.h @ 1000

Last change on this file since 1000 was 1000, checked in by Jari Häkkinen, 15 years ago

trac moved to new location.

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1#ifndef _theplu_yat_regression_linearweighted_
2#define _theplu_yat_regression_linearweighted_
3
4// $Id: LinearWeighted.h 1000 2007-12-23 20:09:15Z jari $
5
6/*
7  Copyright (C) 2005 Peter Johansson
8  Copyright (C) 2006 Jari Häkkinen, Markus Ringnér, Peter Johansson
9  Copyright (C) 2007 Peter Johansson
10
11  This file is part of the yat library, http://trac.thep.lu.se/yat
12
13  The yat library is free software; you can redistribute it and/or
14  modify it under the terms of the GNU General Public License as
15  published by the Free Software Foundation; either version 2 of the
16  License, or (at your option) any later version.
17
18  The yat library is distributed in the hope that it will be useful,
19  but WITHOUT ANY WARRANTY; without even the implied warranty of
20  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
21  General Public License for more details.
22
23  You should have received a copy of the GNU General Public License
24  along with this program; if not, write to the Free Software
25  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
26  02111-1307, USA.
27*/
28
29#include "OneDimensionalWeighted.h"
30
31namespace theplu {
32namespace yat {
33  namespace utility {
34    class vector;
35  }
36namespace regression {
37
38  ///
39  /// @brief linear regression.   
40  ///
41  /// @todo document
42  ///
43  class LinearWeighted : public OneDimensionalWeighted
44  {
45 
46  public:
47    ///
48    /// @brief The default constructor.
49    ///
50    LinearWeighted(void);
51
52    ///
53    /// @brief The destructor
54    ///
55    virtual ~LinearWeighted(void);
56         
57    /**
58       \f$ alpha \f$ is estimated as \f$ \frac{\sum w_iy_i}{\sum w_i} \f$
59   
60       @return the parameter \f$ \alpha \f$
61    */
62    double alpha(void) const;
63
64    /**
65       Variance is estimated as \f$ \frac{s^2}{\sum w_i} \f$
66
67       @see s2()
68
69       @return variance of parameter \f$ \alpha \f$
70    */
71    double alpha_var(void) const;
72
73    /**
74       \f$ beta \f$ is estimated as \f$ \frac{\sum
75       w_i(y_i-m_y)(x_i-m_x)}{\sum w_i(x_i-m_x)^2} \f$
76   
77       @return the parameter \f$ \beta \f$
78    */
79    double beta(void) const;
80
81    /**
82       Variance is estimated as \f$ \frac{s^2}{\sum w_i(x_i-m_x)^2} \f$
83
84       @see s2()
85
86       @return variance of parameter \f$ \beta \f$
87    */
88    double beta_var(void) const;
89   
90    /**
91       This function computes the best-fit linear regression
92       coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y =
93       \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by
94       minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$,
95       where \f$ m_x \f$ is the weighted average. By construction \f$
96       \alpha \f$ and \f$ \beta \f$ are independent.
97    **/
98    /// @todo calculate mse
99    void fit(const utility::vector& x, const utility::vector& y,
100             const utility::vector& w);
101   
102    ///
103    ///  Function predicting value using the linear model:
104    /// \f$ y =\alpha + \beta (x - m) \f$
105    ///
106    double predict(const double x) const;
107
108    /**
109       Noise level for points with weight @a w.
110    */
111    double s2(double w=1) const;
112
113    /**
114       estimated error \f$ y_{err} = \sqrt{ Var(\alpha) +
115       Var(\beta)*(x-m)} \f$.
116    */
117    double standard_error2(const double x) const;
118
119  private:
120    ///
121    /// Copy Constructor. (not implemented)
122    ///
123    LinearWeighted(const LinearWeighted&);
124
125    double m_x(void) const;
126    double m_y(void) const;
127    double sxx(void) const;
128    double syy(void) const;
129    double sxy(void) const;
130   
131    double alpha_;
132    double alpha_var_;
133    double beta_;
134    double beta_var_;
135  };
136
137}}} // of namespaces regression, yat, and theplu
138
139#endif
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