source: trunk/yat/regression/LinearWeighted.h @ 703

Last change on this file since 703 was 703, checked in by Jari Häkkinen, 16 years ago

Addresses #65 and #170.

  • Property svn:eol-style set to native
  • Property svn:keywords set to Id
File size: 3.9 KB
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1#ifndef _theplu_yat_regression_linearweighted_
2#define _theplu_yat_regression_linearweighted_
3
4// $Id: LinearWeighted.h 703 2006-12-18 00:47:44Z jari $
5
6/*
7  Copyright (C) The authors contributing to this file.
8
9  This file is part of the yat library, http://lev.thep.lu.se/trac/yat
10
11  The yat library is free software; you can redistribute it and/or
12  modify it under the terms of the GNU General Public License as
13  published by the Free Software Foundation; either version 2 of the
14  License, or (at your option) any later version.
15
16  The yat library is distributed in the hope that it will be useful,
17  but WITHOUT ANY WARRANTY; without even the implied warranty of
18  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
19  General Public License for more details.
20
21  You should have received a copy of the GNU General Public License
22  along with this program; if not, write to the Free Software
23  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
24  02111-1307, USA.
25*/
26
27#include "OneDimensionalWeighted.h"
28
29#include <cmath>
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    /// @return the parameter \f$ \alpha \f$
59    ///
60    inline double alpha(void) const { return alpha_; }
61
62    ///
63    /// @return standard deviation of parameter \f$ \alpha \f$
64    ///
65    inline double alpha_err(void) const { return sqrt(alpha_var_); }
66
67    ///
68    /// @return the parameter \f$ \beta \f$
69    ///
70    inline double beta(void) const { return beta_; }
71
72    ///
73    /// @return standard deviation of parameter \f$ \beta \f$
74    ///
75    inline double beta_err(void) const { return sqrt(beta_var_); }
76   
77    /**
78       This function computes the best-fit linear regression
79       coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y =
80       \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by
81       minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$,
82       where \f$ m_x \f$ is the weighted average. By construction \f$
83       \alpha \f$ and \f$ \beta \f$ are independent.
84    **/
85    /// @todo calculate mse
86    void fit(const utility::vector& x, const utility::vector& y,
87             const utility::vector& w);
88   
89    ///
90    /// @brief Mean Squared Error
91    ///
92    inline double mse(void) const { return mse_; }
93
94    ///
95    ///  Function predicting value using the linear model:
96    /// \f$ y =\alpha + \beta (x - m) \f$
97    ///
98    double predict(const double x) const { return alpha_ + beta_ * (x-m_x_); }
99
100    ///
101    /// estimated deviation from predicted value for a new data point
102    /// in @a x with weight @a w
103    ///
104    inline double prediction_error(const double x, const double w=1) const
105    { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_)+s2(w)); }
106
107    /**
108       estimated error \f$ y_{err} = \sqrt{ Var(\alpha) +
109       Var(\beta)*(x-m)} \f$.
110    */
111    inline double standard_error(const double x) const
112    { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_) ); }
113
114    /**
115       Noise level for points with weight @a w.
116    */
117    inline double s2(double w=1) const { return s2_/w; }
118
119  private:
120    ///
121    /// Copy Constructor. (not implemented)
122    ///
123    LinearWeighted(const LinearWeighted&);
124
125    inline double m_x(void) const {return ap_.x_averager().mean(); }
126    inline double m_y(void) const {return ap_.y_averager().mean(); }
127    inline double sxx(void) const {return ap_.x_averager().sum_xx_centered(); }
128    inline double syy(void) const {return ap_.y_averager().sum_xx_centered(); }
129    inline double sxy(void) const {return ap_.sum_xy_centered(); }
130   
131    double alpha_;
132    double alpha_var_;
133    double beta_;
134    double beta_var_;
135    double m_x_; // average of x values
136    double r2_; // coefficient of determination
137    double s2_;
138    double mse_;
139  };
140
141}}} // of namespaces regression, yat, and theplu
142
143#endif
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