source: trunk/yat/regression/LinearWeighted.h @ 718

#ifndef _theplu_yat_regression_linearweighted_
#define _theplu_yat_regression_linearweighted_

// $Id: LinearWeighted.h 718 2006-12-26 09:56:26Z jari $

/*
  Copyright (C) The authors contributing to this file.

  This file is part of the yat library, http://lev.thep.lu.se/trac/yat

  The yat library is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 2 of the
  License, or (at your option) any later version.

  The yat library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
  02111-1307, USA.
*/

#include "OneDimensionalWeighted.h"

#include <cmath>

namespace theplu {
namespace yat {
  namespace utility {
    class vector;
  }
namespace regression {

  ///
  /// @brief linear regression.   
  ///
  /// @todo document
  ///
  class LinearWeighted : public OneDimensionalWeighted 
  {
  
  public:
    ///
    /// @brief The default constructor.
    ///
    LinearWeighted(void);

    ///
    /// @brief The destructor
    ///
    virtual ~LinearWeighted(void);
         
    ///
    /// @return the parameter \f$ \alpha \f$
    ///
    double alpha(void) const;

    ///
    /// @return standard deviation of parameter \f$ \alpha \f$
    ///
    double alpha_err(void) const;

    ///
    /// @return the parameter \f$ \beta \f$
    ///
    double beta(void) const;

    ///
    /// @return standard deviation of parameter \f$ \beta \f$
    ///
    double beta_err(void) const;
    
    /**
       This function computes the best-fit linear regression
       coefficients \f$ (\alpha, \beta)\f$ of the model \f$ y =
       \alpha + \beta (x-m_x) \f$ from vectors \a x and \a y, by
       minimizing \f$ \sum{w_i(y_i - \alpha - \beta (x-m_x))^2} \f$,
       where \f$ m_x \f$ is the weighted average. By construction \f$
       \alpha \f$ and \f$ \beta \f$ are independent.
    **/
    /// @todo calculate mse
    void fit(const utility::vector& x, const utility::vector& y,
             const utility::vector& w);
    
    ///
    /// @brief Mean Squared Error
    ///
    double mse(void) const;

    ///
    ///  Function predicting value using the linear model: 
    /// \f$ y =\alpha + \beta (x - m) \f$
    ///
    double predict(const double x) const { return alpha_ + beta_ * (x-m_x_); }

    ///
    /// estimated deviation from predicted value for a new data point
    /// in @a x with weight @a w
    ///
    double prediction_error(const double x, const double w=1) const;

    /**
       Noise level for points with weight @a w.
    */
    double s2(double w=1) const;

    /**
       estimated error \f$ y_{err} = \sqrt{ Var(\alpha) +
       Var(\beta)*(x-m)} \f$.
    */
    double standard_error(const double x) const;

  private:
    ///
    /// Copy Constructor. (not implemented)
    ///
    LinearWeighted(const LinearWeighted&);

    double m_x(void) const;
    double m_y(void) const;
    double sxx(void) const;
    double syy(void) const;
    double sxy(void) const;
    
    double alpha_;
    double alpha_var_;
    double beta_;
    double beta_var_;
    double m_x_; // average of x values
    double r2_; // coefficient of determination
    double s2_;
    double mse_;
  };

}}} // of namespaces regression, yat, and theplu

#endif