source: trunk/yat/regression/LinearWeighted.h @ 1275

Last change on this file since 1275 was 1275, checked in by Jari Häkkinen, 13 years ago

Updating copyright statements.

  • Property svn:eol-style set to native
  • Property svn:keywords set to Id
File size: 3.4 KB
Line 
1#ifndef _theplu_yat_regression_linearweighted_
2#define _theplu_yat_regression_linearweighted_
3
4// $Id: LinearWeighted.h 1275 2008-04-11 06:10:12Z jari $
5
6/*
7  Copyright (C) 2005 Peter Johansson
8  Copyright (C) 2006 Jari Häkkinen, Peter Johansson, Markus Ringnér
9  Copyright (C) 2007 Jari Häkkinen, Peter Johansson
10  Copyright (C) 2008 Peter Johansson
11
12  This file is part of the yat library, http://trac.thep.lu.se/yat
13
14  The yat library is free software; you can redistribute it and/or
15  modify it under the terms of the GNU General Public License as
16  published by the Free Software Foundation; either version 2 of the
17  License, or (at your option) any later version.
18
19  The yat library is distributed in the hope that it will be useful,
20  but WITHOUT ANY WARRANTY; without even the implied warranty of
21  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
22  General Public License for more details.
23
24  You should have received a copy of the GNU General Public License
25  along with this program; if not, write to the Free Software
26  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
27  02111-1307, USA.
28*/
29
30#include "OneDimensionalWeighted.h"
31
32namespace theplu {
33namespace yat {
34  namespace utility {
35    class VectorBase;
36  }
37namespace regression {
38
39  ///
40  /// @brief linear regression.   
41  ///
42  /// @todo document
43  ///
44  class LinearWeighted : public OneDimensionalWeighted
45  {
46 
47  public:
48    ///
49    /// @brief The default constructor.
50    ///
51    LinearWeighted(void);
52
53    ///
54    /// @brief The destructor
55    ///
56    virtual ~LinearWeighted(void);
57         
58    /**
59       \f$ alpha \f$ is estimated as \f$ \frac{\sum w_iy_i}{\sum w_i} \f$
60   
61       @return the parameter \f$ \alpha \f$
62    */
63    double alpha(void) const;
64
65    /**
66       Variance is estimated as \f$ \frac{s^2}{\sum w_i} \f$
67
68       @see s2()
69
70       @return variance of parameter \f$ \alpha \f$
71    */
72    double alpha_var(void) const;
73
74    /**
75       \f$ beta \f$ is estimated as \f$ \frac{\sum
76       w_i(y_i-m_y)(x_i-m_x)}{\sum w_i(x_i-m_x)^2} \f$
77   
78       @return the parameter \f$ \beta \f$
79    */
80    double beta(void) const;
81
82    /**
83       Variance is estimated as \f$ \frac{s^2}{\sum w_i(x_i-m_x)^2} \f$
84
85       @see s2()
86
87       @return variance of parameter \f$ \beta \f$
88    */
89    double beta_var(void) const;
90   
91    /**
92       This function computes the best-fit linear regression
93       coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y =
94       \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by
95       minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$,
96       where \f$ m_x \f$ is the weighted average. By construction \f$
97       \alpha \f$ and \f$ \beta \f$ are independent.
98    **/
99    /// @todo calculate mse
100    void fit(const utility::VectorBase& x, const utility::VectorBase& y,
101             const utility::VectorBase& w);
102   
103    ///
104    ///  Function predicting value using the linear model:
105    /// \f$ y =\alpha + \beta (x - m) \f$
106    ///
107    double predict(const double x) const;
108
109    /**
110       Noise level for points with weight @a w.
111    */
112    double s2(double w=1) const;
113
114    /**
115       estimated error \f$ y_{err} = \sqrt{ Var(\alpha) +
116       Var(\beta)*(x-m)} \f$.
117    */
118    double standard_error2(const double x) const;
119
120  private:
121    ///
122    /// Copy Constructor. (not implemented)
123    ///
124    LinearWeighted(const LinearWeighted&);
125
126    double m_x(void) const;
127    double m_y(void) const;
128    double sxx(void) const;
129    double syy(void) const;
130    double sxy(void) const;
131   
132    double alpha_;
133    double alpha_var_;
134    double beta_;
135    double beta_var_;
136  };
137
138}}} // of namespaces regression, yat, and theplu
139
140#endif
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