BrentRootFinder.h

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// @(#)root/mathcore:$Id: BrentRootFinder.h 36905 2010-11-24 15:44:34Z moneta $
// Authors: David Gonzalez Maline    01/2008 

/**********************************************************************
 *                                                                    *
 * Copyright (c) 2006 , LCG ROOT MathLib Team                         *
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 * This library is free software; you can redistribute it and/or      *
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// Header for the RootFinder
// 
// Created by: David Gonzalez Maline  : Wed Jan 21 2008
// 

#ifndef ROOT_Math_BrentRootFinder
#define ROOT_Math_BrentRootFinder

#ifndef ROOT_Math_IFunctionfwd
#include "Math/IFunctionfwd.h"
#endif

#ifndef ROOT_Math_IRootFinderMethod
#include "Math/IRootFinderMethod.h"
#endif

namespace ROOT {
namespace Math {

//___________________________________________________________________________________________
/**
   Class for finding the root of a one dimensional function using the Brent algorithm.
   It will use the Brent Method for finding function roots in a given interval. 
   First, a grid search is used to bracket the root value
   with the a step size = (xmax-xmin)/npx. The step size
   can be controlled via the SetNpx() function. A default value of npx = 100 is used. 
   The default value con be changed using the static method SetDefaultNpx.
   If the function is unimodal or if its extrema are far apart, setting the fNpx to 
   a small value speeds the algorithm up many times.  
   Then, Brent's method is applied on the bracketed interval. 
   It will use the Brent Method for finding function roots in a given interval. 
   If the Brent method fails to converge the bracketing is repeted on the latest best estimate of the 
   interval. The procedure is repeted with a maximum value (default =10) which can be set for all
   BrentRootFinder classes with the method SetDefaultNSearch

   This class is implemented from TF1::GetX() method.

   @ingroup RootFinders
  
 */

   class BrentRootFinder: public IRootFinderMethod {
   public:


      /** Default Constructor. */
      BrentRootFinder();


      /** Default Destructor. */
      virtual ~BrentRootFinder() {}

      
      /** Set function to solve and the interval in where to look for the root. 

          \@param f Function to be minimized.
          \@param xlow Lower bound of the search interval.
          \@param xup Upper bound of the search interval.
      */
      using IRootFinderMethod::SetFunction;
      bool SetFunction(const ROOT::Math::IGenFunction& f, double xlow, double xup);
      

      /** Returns the X value corresponding to the function value fy for (xmin<x<xmax).
          Method:
          First, the grid search is used to bracket the maximum
          with the step size = (xmax-xmin)/fNpx. This way, the step size
          can be controlled via the SetNpx() function. If the function is
          unimodal or if its extrema are far apart, setting the fNpx to
          a small value speeds the algorithm up many times.
          Then, Brent's method is applied on the bracketed interval.

          \@param maxIter maximum number of iterations.
          \@param absTol desired absolute error in the minimum position.
          \@param absTol desired relative error in the minimum position.
      */
      bool Solve(int maxIter = 100, double absTol = 1E-8, double relTol = 1E-10);

      /** Set the number of point used to bracket root using a grid */
      void SetNpx(int npx) { fNpx = npx; }

      /** 
          Set a log grid scan (default is equidistant bins) 
          will work only if xlow > 0
      */ 
      void SetLogScan(bool on) { fLogScan = on; }

      /** Returns root value. Need to call first Solve(). */
      double Root() const { return fRoot; }

      /** Returns status of last estimate. If = 0 is OK */
      int Status() const { return fStatus; }

      /** Return number of iteration used to find minimum */
      int Iterations() const { return fNIter; }
      
      /** Return name of root finder algorithm ("BrentRootFinder"). */
      const char* Name() const;

      // static function used to modify the default parameters 

      /** set number of default Npx used at construction time (when SetNpx is not called) 
          Default value is 100
       */ 
      static void SetDefaultNpx(int npx); 

      /** set number of  times the bracketing search in combination with is done to find a good interval  
          Default value is 10
       */       
      static void SetDefaultNSearch(int n);

      
   private:

      const IGenFunction* fFunction; // Pointer to the function.
      bool fLogScan;                 // flag to control usage of a log scan      
      int fNIter;                    // Number of iterations needed for the last estimation.
      int fNpx;                      // Number of points to bracket root with initial grid (def is 100)
      int fStatus;                   // Status of code of the last estimate
      double fXMin;                  // Lower bound of the search interval.
      double fXMax;                  // Upper bound of the search interval
      double fRoot;                  // Current stimation of the function root.
   };
   
} // namespace Math
} // namespace ROOT

#endif /* ROOT_Math_BrentRootFinder */

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