// @(#)root/mathmore:$Id$ // Author: L. Moneta 03/2011 /********************************************************************** * * * Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT * * * * This library is free software; you can redistribute it and/or * * modify it under the terms of the GNU General Public License * * as published by the Free Software Foundation; either version 2 * * of the License, or (at your option) any later version. * * * * This library is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * * General Public License for more details. * * * * You should have received a copy of the GNU General Public License * * along with this library (see file COPYING); if not, write * * to the Free Software Foundation, Inc., 59 Temple Place, Suite * * 330, Boston, MA 02111-1307 USA, or contact the author. * * * **********************************************************************/ // Header file for class GSLMultiRootFinder // #ifndef ROOT_Math_GSLMultiRootFinder #define ROOT_Math_GSLMultiRootFinder #include "Math/IFunction.h" #include "Math/WrappedFunction.h" #include #include #include namespace ROOT { namespace Math { class GSLMultiRootBaseSolver; /** @defgroup MultiRoot Multidimensional ROOT finding Classes for finding the roots of a multi-dimensional system. @ingroup NumAlgo */ /** Class for Multidimensional root finding algorithms bassed on GSL. This class is used to solve a non-linear system of equations: f1(x1,....xn) = 0 f2(x1,....xn) = 0 .................. fn(x1,....xn) = 0 See the GSL online manual for information on the GSL MultiRoot finding algorithms The available GSL algorithms require the derivatives of the supplied functions or not (they are computed internally by GSL). In the first case the user needs to provide a list of multidimensional functions implementing the gradient interface (ROOT::Math::IMultiGradFunction) while in the second case it is enough to supply a list of functions impelmenting the ROOT::Math::IMultiGenFunction interface. The available algorithms requiring derivatives (see also the GSL documentation ) are the followings:
  • ROOT::Math::GSLMultiRootFinder::kHybridSJ with name "HybridSJ": modified Powell's hybrid method as implemented in HYBRJ in MINPACK
  • ROOT::Math::GSLMultiRootFinder::kHybridJ with name "HybridJ": unscaled version of the previous algorithm
  • ROOT::Math::GSLMultiRootFinder::kNewton with name "Newton": Newton method
  • ROOT::Math::GSLMultiRootFinder::kGNewton with name "GNewton": modified Newton method
The algorithms without derivatives (see also the GSL documentation ) are the followings:
  • ROOT::Math::GSLMultiRootFinder::kHybridS with name "HybridS": same as HybridSJ but using finate difference approximation for the derivatives
  • ROOT::Math::GSLMultiRootFinder::kHybrid with name "Hybrid": unscaled version of the previous algorithm
  • ROOT::Math::GSLMultiRootFinder::kDNewton with name "DNewton": discrete Newton algorithm
  • ROOT::Math::GSLMultiRootFinder::kBroyden with name "Broyden": Broyden algorithm
@ingroup MultiRoot */ class GSLMultiRootFinder { public: /** enumeration specifying the types of GSL multi root finders requiring the derivatives */ enum EDerivType { kHybridSJ, kHybridJ, kNewton, kGNewton }; /** enumeration specifying the types of GSL multi root finders which do not require the derivatives */ enum EType { kHybridS, kHybrid, kDNewton, kBroyden }; /// create a multi-root finder based on an algorithm not requiring function derivative GSLMultiRootFinder(EType type); /// create a multi-root finder based on an algorithm requiring function derivative GSLMultiRootFinder(EDerivType type); /* create a multi-root finder using a string. The names are those defined in the GSL manuals after having remived the GSL prefix (gsl_multiroot_fsolver). Default algorithm is "hybrids" (without derivative). */ GSLMultiRootFinder(const char * name = nullptr); /// destructor virtual ~GSLMultiRootFinder(); // usually copying is non trivial, so we delete this GSLMultiRootFinder(const GSLMultiRootFinder &) = delete; GSLMultiRootFinder & operator = (const GSLMultiRootFinder &) = delete; GSLMultiRootFinder(GSLMultiRootFinder &&) = delete; GSLMultiRootFinder & operator = (GSLMultiRootFinder &&) = delete; /// set the type for an algorithm without derivatives void SetType(EType type) { fType = type; fUseDerivAlgo = false; } /// set the type of algorithm using derivatives void SetType(EDerivType type) { fType = type; fUseDerivAlgo = true; } /// set the type using a string void SetType(const char * name); /* add the list of functions f1(x1,..xn),...fn(x1,...xn). The list must contain pointers of ROOT::Math::IMultiGenFunctions. The method requires the the begin and end of the list iterator. The list can be any stl container or a simple array of ROOT::Math::IMultiGenFunctions* or whatever implementing an iterator. If using a derivative type algorithm the function pointers must implement the ROOT::Math::IMultiGradFunction interface */ template bool SetFunctionList( FuncIterator begin, FuncIterator end) { bool ret = true; for (FuncIterator itr = begin; itr != end; ++itr) { const ROOT::Math::IMultiGenFunction * f = *itr; // Using bitwise operator &= require the operand to be a bool // to have the intended effect here. ret &= (AddFunction( *f) != 0); } return ret; } /* add (set) a single function fi(x1,...xn) which is part of the system of specifying the begin and end of the iterator. If using a derivative type algorithm the function must implement the ROOT::Math::IMultiGradFunction interface Return the current number of function in the list and 0 if failed to add the function */ int AddFunction( const ROOT::Math::IMultiGenFunction & func); /// same method as before but using any function implementing /// the operator(), so can be wrapped in a IMultiGenFunction interface template int AddFunction( Function & f, int ndim) { // no need to care about lifetime of wfunc. It will be cloned inside AddFunction WrappedMultiFunction wfunc(f, ndim); return AddFunction(wfunc); } /** return the number of sunctions set in the class. The number must be equal to the dimension of the functions */ unsigned int Dim() const { return fFunctions.size(); } /// clear list of functions void Clear(); /// return the root X values solving the system const double * X() const; /// return the function values f(X) solving the system /// i.e. they must be close to zero at the solution const double * FVal() const; /// return the last step size const double * Dx() const; /** Find the root starting from the point X; Use the number of iteration and tolerance if given otherwise use default parameter values which can be defined by the static method SetDefault... */ bool Solve(const double * x, int maxIter = 0, double absTol = 0, double relTol = 0); /// Return number of iterations int Iterations() const { return fIter; } /// Return the status of last root finding int Status() const { return fStatus; } /// Return the algorithm name used for solving /// Note the name is available only after having called solved /// Otherwise an empyty string is returned const char * Name() const; /* set print level level = 0 quiet (no messages print) = 1 print only the result = 3 max debug. Print result at each iteration */ void SetPrintLevel(int level) { fPrintLevel = level; } /// return the print level int PrintLevel() const { return fPrintLevel; } //-- static methods to set configurations /// set tolerance (absolute and relative) /// relative tolerance is only use to verify the convergence /// do it is a minor parameter static void SetDefaultTolerance(double abstol, double reltol = 0 ); /// set maximum number of iterations static void SetDefaultMaxIterations(int maxiter); /// print iteration state void PrintState(std::ostream & os = std::cout); protected: // return type given a name std::pair GetType(const char * name); // clear list of functions void ClearFunctions(); private: int fIter; // current number of iterations int fStatus; // current status int fPrintLevel; // print level // int fMaxIter; // max number of iterations // double fAbsTolerance; // absolute tolerance // double fRelTolerance; // relative tolerance int fType; // type of algorithm bool fUseDerivAlgo; // algorithm using derivative GSLMultiRootBaseSolver * fSolver; std::vector fFunctions; ///