source: trunk/c++_tools/statistics/LinearWeighted.h @ 616

#ifndef _theplu_statistics_regression_linear_weighted_
#define _theplu_statistics_regression_linear_weighted_

// $Id: LinearWeighted.h 616 2006-08-31 08:52:02Z jari $

#include <c++_tools/statistics/OneDimensionalWeighted.h>

#include <cmath>

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

  ///
  /// @brief linear regression.   
  ///
  /// @todo document
  ///
  class LinearWeighted : public OneDimensionalWeighted 
  {
  
  public:
    ///
    /// Default Constructor.
    ///
    inline LinearWeighted(void)
      : OneDimensionalWeighted(), alpha_(0), alpha_var_(0), beta_(0), 
        beta_var_(0),
        m_x_(0){}

    ///
    /// Destructor 
    ///
    inline virtual ~LinearWeighted(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{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.
    ///
    void fit(const utility::vector& x, const utility::vector& y,
             const utility::vector& w);
    
    ///
    /// Function predicting value using the linear model: \f$ y =
    /// \alpha + \beta (x - m) 
    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
    ///
    inline double prediction_error(const double x, const double w=1) const
    { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_)+s2_/w); }

    ///
    /// estimated error @a y_err \f$ y_err = \sqrt{ Var(\alpha) +
    /// Var(\beta)*(x-m)^2 }.
    ///
    inline double standard_error(const double x) const
    { return sqrt(alpha_var_ + beta_var_*(x-m_x_)*(x-m_x_) ); }

    ///
    /// 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)
    ///
    LinearWeighted(const LinearWeighted&);

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

}}} // of namespaces regression, statisitcs and thep

#endif