class ROOT::Math::Chebyshev


   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

Function Members (Methods)

public:

virtual	~Chebyshev()
ROOT::Math::Chebyshev	Chebyshev(const ROOT::Math::IGenFunction& f, double a, double b, size_t n)
ROOT::Math::Chebyshev	Chebyshev(ROOT::Math::GSLFuncPointer f, void* p, double a, double b, size_t n)
ROOT::Math::Chebyshev*	Deriv()
pair<double,double>	EvalErr(double x) const
pair<double,double>	EvalErr(double x, size_t n) const
ROOT::Math::Chebyshev*	Integral()
double	operator()(double x) const
double	operator()(double x, size_t n) const

protected:

void	Initialize(ROOT::Math::GSLFuncPointer f, void* params, double a, double b)

private:

ROOT::Math::Chebyshev	Chebyshev(size_t n)
ROOT::Math::Chebyshev	Chebyshev(const ROOT::Math::Chebyshev&)
ROOT::Math::Chebyshev&	operator=(const ROOT::Math::Chebyshev&)

Data Members

private:

ROOT::Math::GSLFunctionWrapper*	fFunction	pointer to function
size_t	fOrder
ROOT::Math::GSLChebSeries*	fSeries

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

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 functions of type IGenFunction

Chebyshev(ROOT::Math::GSLFuncPointer f, void* p, 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

virtual ~Chebyshev()

 destructor

Chebyshev(size_t n)

      construct a Chebyshev series or order n
      The series must be initialized from a function

Chebyshev(const Chebyshev &)

 usually copying is non trivial, so we make this unaccessible

double operator()(double x) const

       Evaluate the series at a given point x

std::pair<double, double> EvalErr(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

double operator()(double x, size_t n) const

      Evaluate the series at a given point, to (at most) the given order n

std::pair<double, double> EvalErr(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

Chebyshev * Deriv()

      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 * Integral()

      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

void Initialize(ROOT::Math::GSLFuncPointer f, void* params, double a, double b)

       Initialize series passing function and range