Chebyshev.h

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// @(#)root/mathmore:$Id: Chebyshev.h 38027 2011-02-10 11:47:00Z rdm $
// Authors: L. Moneta, A. Zsenei   08/2005 

 /**********************************************************************
  *                                                                    *
  * Copyright (c) 2004 ROOT Foundation,  CERN/PH-SFT                   *
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  * This library is free software; you can redistribute it and/or      *
  * modify it under the terms of the GNU General Public License        *
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// Header file for class Chebyshev
// 
// Created by: moneta  at Thu Dec  2 14:51:15 2004
// 
// Last update: Thu Dec  2 14:51:15 2004
// 
#ifndef ROOT_Math_Chebyshev
#define ROOT_Math_Chebyshev

/**
   @defgroup NumAlgo Numerical Algorithms
   Numerical Algorithm mainly from the \ref MathMore and implemented using the 
   <A HREF="http://www.gnu.org/software/gsl/manual/html_node/">GSL</A> library
 */


/**
   @defgroup FuncApprox Function Approximation (Chebyshev)
   @ingroup NumAlgo
 */


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

#ifndef ROOT_Math_GSLFunctionAdapter
#include "Math/GSLFunctionAdapter.h"
#endif

#include <memory>
#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 Chebyshev {

public: 


   /**
      Construct a Chebyshev series approximation to a Function f in range [a,b];
      constructor based on functions of type IGenFunction
   */

  Chebyshev(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
   */
   Chebyshev(GSLFuncPointer f, void *p, double a, double b, size_t n); 

   // destructor
   virtual ~Chebyshev(); 


private:

   /**
      construct a Chebyshev series or order n
      The series must be initialized from a function 
   */
   Chebyshev(size_t n); 

// usually copying is non trivial, so we make this unaccessible
   Chebyshev(const Chebyshev &); 
   Chebyshev & operator = (const Chebyshev &); 

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
   Chebyshev * 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
   Chebyshev * 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_Chebyshev */

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