MnParabola.h

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// @(#)root/minuit2:$Id$
// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
 *                                                                    *
 **********************************************************************/
 
#ifndef ROOT_Minuit2_MnParabola
#define ROOT_Minuit2_MnParabola
 
#include <cmath>
 
namespace ROOT {
 
namespace Minuit2 {
 
/**
 
This class defines a parabola of the form a*x*x + b*x + c
 
@author Fred James and Matthias Winkler; comments added by Andras Zsenei
and Lorenzo Moneta
 
@ingroup Minuit
 
 */
 
class MnParabola {
 
public:
   /**
 
   Constructor that initializes the parabola with its three parameters.
 
   @param a the coefficient of the quadratic term
   @param b the coefficient of the linear term
   @param c the constant
 
   */
 
   MnParabola(double a, double b, double c) : fA(a), fB(b), fC(c) {}
 
   /**
 
   Evaluates the parabola a the point x.
 
   @param x the coordinate where the parabola needs to be evaluated.
 
   @return the y coordinate of the parabola corresponding to x.
 
   */
 
   double Y(double x) const { return (fA * x * x + fB * x + fC); }
 
   /**
 
   Calculates the bigger of the two x values corresponding to the
   given y Value.
 
   <p>
 
   ???????!!!!!!!!! And when there is none?? it looks like it will
   crash?? what is sqrt (-1.0) ?
 
   @param y the y Value for which the x Value is to be calculated.
 
   @return the bigger one of the two corresponding values.
 
   */
 
   // ok, at first glance it does not look like the formula for the quadratic
   // equation, but it is!  ;-)
   double X_pos(double y) const { return (std::sqrt(y / fA + Min() * Min() - fC / fA) + Min()); }
   // maybe it is worth to check the performance improvement with the below formula??
   //   double X_pos(double y) const {return (std::sqrt(y/fA + fB*fB/(4.*fA*fA) - fC/fA)  - fB/(2.*fA));}
 
   /**
 
   Calculates the smaller of the two x values corresponding to the
   given y Value.
 
   <p>
 
   ???????!!!!!!!!! And when there is none?? it looks like it will
   crash?? what is sqrt (-1.0) ?
 
   @param y the y Value for which the x Value is to be calculated.
 
   @return the smaller one of the two corresponding values.
 
   */
 
   double X_neg(double y) const { return (-std::sqrt(y / fA + Min() * Min() - fC / fA) + Min()); }
 
   /**
 
   Calculates the x coordinate of the Minimum of the parabola.
 
   @return x coordinate of the Minimum.
 
   */
 
   double Min() const { return -fB / (2. * fA); }
 
   /**
 
   Calculates the y coordinate of the Minimum of the parabola.
 
   @return y coordinate of the Minimum.
 
   */
 
   double YMin() const { return (-fB * fB / (4. * fA) + fC); }
 
   /**
 
   Accessor to the coefficient of the quadratic term.
 
   @return the coefficient of the quadratic term.
 
    */
 
   double A() const { return fA; }
 
   /**
 
   Accessor to the coefficient of the linear term.
 
   @return the coefficient of the linear term.
 
   */
 
   double B() const { return fB; }
 
   /**
 
   Accessor to the coefficient of the constant term.
 
   @return the coefficient of the constant term.
 
   */
 
   double C() const { return fC; }
 
private:
   double fA;
   double fB;
   double fC;
};
 
} // namespace Minuit2
 
} // namespace ROOT
 
#endif // ROOT_Minuit2_MnParabola