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 // @(#)root/mathmore:$Id$
 // Authors: L. Moneta, A. Zsenei   08/2005
 
  /**********************************************************************
   *                                                                    *
   * 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 ChebyshevApprox
 //
 // Created by: moneta  at Thu Dec  2 14:51:15 2004
 //
 // Last update: Thu Dec  2 14:51:15 2004
 //
 #ifndef ROOT_Math_ChebyshevApprox
 #define ROOT_Math_ChebyshevApprox
 
 
 
 /**
    @defgroup FuncApprox Function Approximation (ChebyshevApprox)
    Numerical algorithm from the \ref MathMore library and implemented using the
    <A HREF="http://www.gnu.org/software/gsl/manual/html_node/">GSL</A> library
  
    @ingroup NumAlgo
  */
 
 
 #include "Math/IFunctionfwd.h"
 
 #include "Math/GSLFunctionAdapter.h"
 
 #include <utility>
 #include <cstddef>
 
 
 namespace ROOT {
 namespace Math {
 
 class GSLChebSeries;
 class GSLFunctionWrapper;
 
 //____________________________________________________________________________
 /**
    Class describing a Chebyshev series which can be used to approximate a
    function in a defined range [a,b] using Chebyshev polynomials.
    It uses the algorithm from
    <A HREF="http://www.gnu.org/software/gsl/manual/html_node/Chebyshev-Approximations.html">GSL</A>
 
    This class does not support copying
    @ingroup FuncApprox
  */
 
 
 class ChebyshevApprox {
 
 public:
 
 
    /**
       Construct a Chebyshev series approximation to a Function f in range [a,b];
       constructor based on functions of type IGenFunction
    */
 
   ChebyshevApprox(const ROOT::Math::IGenFunction & f, double a, double b, size_t n);
 
    /**
       Construct a Chebyshev series approximation to a Function f in range [a,b];
       constructor based on free functions with gsl_function type signature
    */
    ChebyshevApprox(GSLFuncPointer f, void *p, double a, double b, size_t n);
 
    // destructor
    virtual ~ChebyshevApprox();
 
 
 private:
 
    /**
       construct a Chebyshev series or order n
       The series must be initialized from a function
    */
    ChebyshevApprox(size_t n);
 
 // usually copying is non trivial, so we make this unaccessible
    ChebyshevApprox(const ChebyshevApprox &);
    ChebyshevApprox & operator = (const ChebyshevApprox &);
 
 public:
 
    /**
        Evaluate the series at a given point x
    */
    double operator() ( double x) const;
 
    /**
       Evaluate the series at a given point x estimating both the series result and its absolute error.
       The error estimate is made from the first neglected term in the series.
       A pair containing result and error is returned
    */
    std::pair<double, double>  EvalErr( double x) const;
 
    /**
       Evaluate the series at a given point, to (at most) the given order n
    */
    double operator() ( double x, size_t n) const;
 
    /**
       evaluate the series at a given point x to the given order n,
       estimating both the series result and its absolute error.
       The error estimate is made from the first neglected term in the series.
       A pair containing result and error is returned
    */
    std::pair<double, double>  EvalErr( double x, size_t n) const;
 
    /**
       Compute the derivative of the series and return a pointer to a new Chebyshev series with the
       derivatives coefficients. The returned pointer must be managed by the user.
    */
    //TO DO: implement copying to return by value
    ChebyshevApprox * Deriv();
 
    /**
       Compute the integral of the series and return a pointer to a new Chebyshev series with the
       integral coefficients. The lower limit of the integration is the left range value a.
       The returned pointer must be managed by the user
    */
    //TO DO: implement copying to return by value
    ChebyshevApprox * Integral();
 
 protected:
 
    /**
        Initialize series passing function and range
    */
    void Initialize( GSLFuncPointer f, void * params, double a, double b);
 
 private:
 
    size_t fOrder;
 
    GSLChebSeries * fSeries;
    GSLFunctionWrapper * fFunction;     // pointer to function
 
 };
 
 } // namespace Math
 } // namespace ROOT
 
 #endif /* ROOT_Math_ChebyshevApprox */

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