source: trunk/yat/regression/Polynomial.h @ 729

#ifndef _theplu_yat_regression_polynomial_
#define _theplu_yat_regression_polynomial_

// $Id: Polynomial.h 729 2007-01-05 16:00:15Z peter $

/*
  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 "MultiDimensional.h"
#include "yat/utility/vector.h"

namespace theplu {
namespace yat {
namespace regression {

  /**
     @brief Polynomial regression
     
     Data are modeled as \f$ y = \alpha + \beta x + \gamma x^2 +
     ... + \delta x_i^{\textrm{power}} + \epsilon_i \f$ 
  */
  class Polynomial : public OneDimensional
  {
  public:

    ///
    /// @param power degree of polynomial, e.g. 1 for a linear model
    ///
    explicit Polynomial(size_t power);

    ///
    /// @brief Destructor
    ///
    ~Polynomial(void);

    ///
    /// @brief covariance of parameters
    ///
    const utility::matrix& covariance(void) const;

    ///
    /// Fit the model by minimizing the mean squared deviation between
    /// model and data.
    ///
    void fit(const utility::vector& x, const utility::vector& y);

    ///
    /// @return parameters of the model
    ///
    /// @see MultiDimensional
    ///
    const utility::vector& fit_parameters(void) const;

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

    /**
       \f$ \frac{\sum \epsilon_i^2}{N-\textrm{DF}} \f$
       where DF is number of parameters in model.

       @return variance of residuals
    */
    double s2(void) const;

    ///
    /// @return squared error of model value in @a x
    ///
    double standard_error2(const double x) const;

  private:
    MultiDimensional md_;
    size_t power_;

  };

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

#endif