RootFinder.h

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// @(#)root/mathmore:$Id$
// Authors: L. Moneta, A. Zsenei   08/2005
 
 /**********************************************************************
  *                                                                    *
  * 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
 
 
#include "Math/IFunctionfwd.h"
 
#include "Math/IRootFinderMethod.h"
 
 
/**
   @defgroup RootFinders One-dimensional Root-Finding
   Classes implementing algorithms for finding the roots of a one-dimensional function.
   Various implementation esists in MathCore and MathMore
   The user interacts with a proxy class ROOT::Math::RootFinder which creates behing
   the chosen 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
 
 
#include "Math/WrappedFunction.h"
 
#include "Math/Functor.h"
 
/**
 * Solve `f(x) = 0`, given a derivative `d`.
 * @param f Function whose root should be found.
 * @param d Derivative of the function.
 * @param start Starting point for iteration.
 * @param maxIter Maximum number of iterations, passed to Solve(int,double,double)
 * @param absTol Absolute tolerance, as in Solve(int,double,double)
 * @param relTol Relative tolerance, passed to Solve(int,double,double)
 * @return true if a root was found. Retrieve the result using Root().
 */
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);
}
 
/**
 * Solve `f(x) = 0` numerically.
 * @param f Function whose root should be found.
 * @param min Minimum allowed value of `x`.
 * @param max Maximum allowed value of `x`.
 * @param maxIter Maximum number of iterations, passed to Solve(int,double,double)
 * @param absTol Absolute tolerance, as in Solve(int,double,double)
 * @param relTol Relative tolerance, passed to Solve(int,double,double)
 * @return true if a root was found. Retrieve the result using Root().
 */
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 */