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

#ifndef _theplu_yat_regression_linear_
#define _theplu_yat_regression_linear_

// $Id: Linear.h 703 2006-12-18 00:47:44Z 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 "OneDimensional.h"

#include <cmath>

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

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

    ///
    /// @brief The destructor 
    ///
    virtual ~Linear(void);
         
    ///
    /// @return the parameter \f$ \alpha \f$
    ///
    inline double alpha(void) const { return alpha_; }

    ///
    /// @return standard deviation of parameter \f$ \alpha \f$
    ///
    inline double alpha_err(void) const { return sqrt(alpha_var_); }

    ///
    /// @return the parameter \f$ \beta \f$
    ///
    inline double beta(void) const { return beta_; }

    ///
    /// @return standard deviation of parameter \f$ \beta \f$
    ///
    inline double beta_err(void) const { return sqrt(beta_var_); }
    
    ///
    /// 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{(y_i - \alpha - \beta (x-m_x))^2} \f$. By
    /// construction \f$ \alpha \f$ and \f$ \beta \f$ are independent.
    ///
    void fit(const utility::vector& x, const utility::vector& y) ;
    
    ///
    /// @brief Mean Squared Error
    ///
    inline double mse(void) const { return mse_; }

    ///
    /// @return value in @a x of model 
    ///
    double predict(const double x) const;

    ///
    /// @return error of model value in @a x
    ///
    double standard_error(const double x) const;

    ///
    /// Function returning the coefficient of determination,
    /// i.e. fraction of variance explained by the linear model.
    ///
    inline double r2(void) const { return r2_; }

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

    double alpha_;
    double alpha_var_;
    double beta_;
    double beta_var_;
    double mse_;
    double m_x_; // average of x values
    double r2_; // coefficient of determination
  };

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

#endif