RootFinder.h

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// @(#)root/mathmore:$Id: RootFinder.h 33942 2010-06-16 13:12:17Z moneta $
// Authors: L. Moneta, A. Zsenei   08/2005 

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  * Copyright (c) 2004 ROOT Foundation,  CERN/PH-SFT                   *
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// Header file for class RootFinder
// 
// Created by: moneta  at Sun Nov 14 16:59:55 2004
// 
// Last update: Sun Nov 14 16:59:55 2004
// 
#ifndef ROOT_Math_RootFinder
#define ROOT_Math_RootFinder


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

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


/**
   @defgroup RootFinders One-dimensional Root-Finding algorithms 
   Various implementation esists in MathCore and MathMore
   The user interacts with a proxy class ROOT::Math::RootFinder which creates behing 
   the choosen algorithms which are implemented using the ROOT::Math::IRootFinderMethod interface

   @ingroup NumAlgo
*/


namespace ROOT {
   namespace Math {


//_____________________________________________________________________________________
      /**
         User Class to find the Root of one dimensional functions. 
         The GSL Methods are implemented in MathMore and they are loaded automatically 
         via the plug-in manager

         The possible types of Root-finding algorithms are: 
         <ul>
         <li>Root Bracketing Algorithms which do not require function derivatives
         <ol>
         <li>RootFinder::kBRENT  (default method implemented in MathCore)
         <li>RootFinder::kGSL_BISECTION
         <li>RootFinder::kGSL_FALSE_POS
         <li>RootFinder::kGSL_BRENT
         </ol>
         <li>Root Finding Algorithms using Derivatives
         <ol>
         <li>RootFinder::kGSL_NEWTON
         <li>RootFinder::kGSL_SECANT
         <li>RootFinder::kGSL_STEFFENSON
         </ol>
         </ul>
         
         This class does not cupport copying
         
         @ingroup RootFinders
         
      */
      
      class RootFinder {
         
      public: 
         
         enum EType { kBRENT,                                   // Methods from MathCore
                     kGSL_BISECTION, kGSL_FALSE_POS, kGSL_BRENT, // GSL Normal
                     kGSL_NEWTON, kGSL_SECANT, kGSL_STEFFENSON   // GSL Derivatives
         }; 
         
         /**
            Construct a Root-Finder algorithm
         */
         RootFinder(RootFinder::EType type = RootFinder::kBRENT);
         virtual ~RootFinder();
         
      private:
         // usually copying is non trivial, so we make this unaccessible
         RootFinder(const RootFinder & ) {}
         RootFinder & operator = (const RootFinder & rhs) 
         {   
            if (this == &rhs) return *this;  // time saving self-test
            return *this;
         } 
         
      public: 
         
         bool SetMethod(RootFinder::EType type = RootFinder::kBRENT);

         /**
            Provide to the solver the function and the initial search interval [xlow, xup] 
            for algorithms not using derivatives (bracketing algorithms) 
            The templated function f must be of a type implementing the \a operator() method, 
            <em>  double  operator() (  double  x ) </em>
            Returns non zero if interval is not valid (i.e. does not contains a root)
         */
         
         bool SetFunction( const IGenFunction & f, double xlow, double xup) { 
            return fSolver->SetFunction( f, xlow, xup); 
         }   
         
         
         /**
            Provide to the solver the function and an initial estimate of the root, 
            for algorithms using derivatives. 
            The templated function f must be of a type implementing the \a operator()  
            and the \a Gradient() methods. 
            <em>  double  operator() (  double  x ) </em>
            Returns non zero if starting point is not valid 
         */
         
         bool  SetFunction( const IGradFunction & f, double xstart) { 
            return fSolver->SetFunction( f, xstart); 
         }   

         template<class Function, class Derivative> 
         bool Solve(Function &f, Derivative &d, double start,
                   int maxIter = 100, double absTol = 1E-8, double relTol = 1E-10);
         
         template<class Function> 
         bool Solve(Function &f, double min, double max, 
                   int maxIter = 100, double absTol = 1E-8, double relTol = 1E-10);

         /** 
             Compute the roots iterating until the estimate of the Root is within the required tolerance returning 
             the iteration Status
         */
         bool Solve( int maxIter = 100, double absTol = 1E-8, double relTol = 1E-10) { 
            return fSolver->Solve( maxIter, absTol, relTol ); 
         }
         
         /** 
             Return the number of iteration performed to find the Root. 
         */ 
         int Iterations() const {
            return fSolver->Iterations(); 
         }
         
         /**
            Perform a single iteration and return the Status
         */
         int Iterate() { 
            return fSolver->Iterate(); 
         }
         
         /**
            Return the current and latest estimate of the Root
         */ 
         double Root() const { 
            return fSolver->Root(); 
         }
         
         /**
            Return the status of the last estimate of the Root
            = 0 OK, not zero failure 
         */
         int Status() const { 
            return fSolver->Status(); 
         }

         
         /**
            Return the current and latest estimate of the lower value of the Root-finding interval (for bracketing algorithms)
         */
/*   double XLower() const {  */
/*     return fSolver->XLower();  */
/*   } */
         
         /**
            Return the current and latest estimate of the upper value of the Root-finding interval (for bracketing algorithms)
         */
/*   double XUpper() const {  */
/*     return  fSolver->XUpper();  */
/*   } */
         
         /**
            Get Name of the Root-finding solver algorithm
         */
         const char * Name() const { 
            return fSolver->Name(); 
         }
                  
         
      protected: 
         
         
      private: 
         
         IRootFinderMethod* fSolver;   // type of algorithm to be used 
         
         
      }; 
      
   } // namespace Math
} // namespace ROOT


#ifndef ROOT_Math_WrappedFunction
#include "Math/WrappedFunction.h"
#endif

#ifndef ROOT_Math_Functor
#include "Math/Functor.h"
#endif

template<class Function, class Derivative> 
bool ROOT::Math::RootFinder::Solve(Function &f, Derivative &d, double start,
                                  int maxIter, double absTol, double relTol)
{
   if (!fSolver) return false; 
   ROOT::Math::GradFunctor1D wf(f, d);
   bool ret = fSolver->SetFunction(wf, start);
   if (!ret) return false;
   return Solve(maxIter, absTol, relTol);
}
         
template<class Function> 
bool ROOT::Math::RootFinder::Solve(Function &f, double min, double max, 
                                  int maxIter, double absTol, double relTol)
{
   if (!fSolver) return false; 
   ROOT::Math::WrappedFunction<Function &> wf(f); 
   bool ret = fSolver->SetFunction(wf, min, max);
   if (!ret) return false;
   return Solve(maxIter, absTol, relTol);
}

#endif /* ROOT_Math_RootFinder */

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