source: trunk/yat/regression/LinearWeighted.h

Last change on this file was 3076, checked in by Peter, 8 years ago

remove todo doxygen tag

  • Property svn:eol-style set to native
  • Property svn:keywords set to Id
File size: 3.3 KB
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1#ifndef _theplu_yat_regression_linearweighted_
2#define _theplu_yat_regression_linearweighted_
3
4// $Id: LinearWeighted.h 3076 2013-09-05 08:01:19Z peter $
5
6/*
7  Copyright (C) 2005 Peter Johansson
8  Copyright (C) 2006 Jari Häkkinen, Peter Johansson, Markus Ringnér
9  Copyright (C) 2007, 2008 Jari Häkkinen, Peter Johansson
10  Copyright (C) 2012 Peter Johansson
11
12  This file is part of the yat library, http://dev.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 3 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 yat. If not, see <http://www.gnu.org/licenses/>.
26*/
27
28#include "OneDimensionalWeighted.h"
29
30namespace theplu {
31namespace yat {
32  namespace utility {
33    class VectorBase;
34  }
35namespace regression {
36
37  ///
38  /// @brief linear regression.
39  ///
40  class LinearWeighted : public OneDimensionalWeighted
41  {
42
43  public:
44    ///
45    /// @brief The default constructor.
46    ///
47    LinearWeighted(void);
48
49    ///
50    /// @brief The destructor
51    ///
52    virtual ~LinearWeighted(void);
53
54    /**
55       \f$ alpha \f$ is estimated as \f$ \frac{\sum w_iy_i}{\sum w_i} \f$
56
57       @return the parameter \f$ \alpha \f$
58    */
59    double alpha(void) const;
60
61    /**
62       Variance is estimated as \f$ \frac{s^2}{\sum w_i} \f$
63
64       @see s2()
65
66       @return variance of parameter \f$ \alpha \f$
67    */
68    double alpha_var(void) const;
69
70    /**
71       \f$ beta \f$ is estimated as \f$ \frac{\sum
72       w_i(y_i-m_y)(x_i-m_x)}{\sum w_i(x_i-m_x)^2} \f$
73
74       @return the parameter \f$ \beta \f$
75    */
76    double beta(void) const;
77
78    /**
79       Variance is estimated as \f$ \frac{s^2}{\sum w_i(x_i-m_x)^2} \f$
80
81       @see s2()
82
83       @return variance of parameter \f$ \beta \f$
84    */
85    double beta_var(void) const;
86
87    /**
88       This function computes the best-fit linear regression
89       coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y =
90       \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by
91       minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$,
92       where \f$ m_x \f$ is the weighted average. By construction \f$
93       \alpha \f$ and \f$ \beta \f$ are independent.
94    **/
95    void fit(const utility::VectorBase& x, const utility::VectorBase& y,
96             const utility::VectorBase& w);
97
98    ///
99    ///  Function predicting value using the linear model:
100    /// \f$ y =\alpha + \beta (x - m) \f$
101    ///
102    double predict(const double x) const;
103
104    /**
105       Noise level for points with weight @a w.
106    */
107    double s2(double w=1) const;
108
109    /**
110       estimated error \f$ y_{err} = \sqrt{ Var(\alpha) +
111       Var(\beta)*(x-m)} \f$.
112    */
113    double standard_error2(const double x) const;
114
115  private:
116    ///
117    /// Copy Constructor. (not implemented)
118    ///
119    LinearWeighted(const LinearWeighted&);
120
121    double m_x(void) const;
122    double m_y(void) const;
123    double sxx(void) const;
124    double syy(void) const;
125    double sxy(void) const;
126
127    double alpha_;
128    double alpha_var_;
129    double beta_;
130    double beta_var_;
131  };
132
133}}} // of namespaces regression, yat, and theplu
134
135#endif
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