Genfun::GaudiMathImplementation::NumericalDerivative Class Reference

Numerical derivative (using GSL adaptive numerical differentiation) More...

#include </scratch/z5/marcocle/GaudiDocs/lhcb-release/996/GAUDI/GAUDI_v26r4/InstallArea/x86_64-slc6-gcc48-opt/include/GaudiMath/NumericalDerivative.h>

Inheritance diagram for Genfun::GaudiMathImplementation::NumericalDerivative:

Collaboration diagram for Genfun::GaudiMathImplementation::NumericalDerivative:

Public Types
enum	Type {   Central, Forward, Backward, Central,   Forward, Backward }
	the type of numerical differentiation More...
enum	Type {   Central, Forward, Backward, Central,   Forward, Backward }
	the type of numerical differentiation More...

Public Member Functions
	NumericalDerivative (const AbsFunction &function, const size_t index, const Type &type=Central)
	From CLHEP/GenericFunctions. More...
	NumericalDerivative (const NumericalDerivative &right)
	copy constructor More...
virtual	~NumericalDerivative ()=default
	virtual destructor More...
virtual unsigned int	dimensionality () const
	dimensionality of the problem More...
virtual double	operator() (double argument) const
	Function value. More...
virtual double	operator() (const Argument &argument) const
	Function value. More...
virtual bool	hasAnalyticDerivative () const
	Does this function have an analytic derivative? More...
virtual Derivative	partial (unsigned int index) const
	Derivatives. More...
const AbsFunction &	function () const
	access to the function itself More...
size_t	index () const
	index More...
const Type &	type () const
	type More...
const Type &	setType (const Type &value)
	change the type of the adaptive differentiation More...
double	result () const
	the result of the last call More...
double	error () const
	the absolute error estimate for the last call More...
	NumericalDerivative (const AbsFunction &function, const size_t index, const Type &type=Central)
	From CLHEP/GenericFunctions. More...
	NumericalDerivative (const NumericalDerivative &right)
	copy constructor More...
virtual	~NumericalDerivative ()=default
	virtual destructor More...
virtual unsigned int	dimensionality () const
	dimensionality of the problem More...
virtual double	operator() (double argument) const
	Function value. More...
virtual double	operator() (const Argument &argument) const
	Function value. More...
virtual bool	hasAnalyticDerivative () const
	Does this function have an analytic derivative? More...
virtual Derivative	partial (unsigned int index) const
	Derivatives. More...
const AbsFunction &	function () const
	access to the function itself More...
size_t	index () const
	index More...
const Type &	type () const
	type More...
const Type &	setType (const Type &value)
	change the type of the adaptive differentiation More...
double	result () const
	the result of the last call More...
double	error () const
	the absolute error estimate for the last call More...

Protected Member Functions
StatusCode	Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const
	Exception. More...
StatusCode	Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const

Private Member Functions
	NumericalDerivative ()
NumericalDerivative &	operator= (const NumericalDerivative &)
	NumericalDerivative ()
NumericalDerivative &	operator= (const NumericalDerivative &)

Private Attributes
std::unique_ptr< const AbsFunction >	m_function
size_t	m_index
size_t	m_DIM
Type	m_type
Argument	m_argument
double	m_result
double	m_error

Detailed Description

Numerical derivative (using GSL adaptive numerical differentiation)

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) = \frac{\partial}{\partial x_i} f \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) \]

Author

Vanya BELYAEV Ivan..nosp@m.Bely.nosp@m.aev@i.nosp@m.tep..nosp@m.ru

Date

2003-08-27

Definition at line 34 of file NumericalDerivative.h.

Member Enumeration Documentation

enum Genfun::GaudiMathImplementation::NumericalDerivative::Type

the type of numerical differentiation

Enumerator
Central
Forward
Backward
Central
Forward
Backward

Definition at line 38 of file NumericalDerivative.h.

        { Central  ,
          Forward  ,
          Backward } ;

enum Genfun::GaudiMathImplementation::NumericalDerivative::Type

the type of numerical differentiation

Enumerator
Central
Forward
Backward
Central
Forward
Backward

Definition at line 38 of file NumericalDerivative.h.

        { Central  ,
          Forward  ,
          Backward } ;

Constructor & Destructor Documentation

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative	(	const AbsFunction &	function,
		const size_t	index,
		const Type &	type = Central
	)

From CLHEP/GenericFunctions.

from CLHEP/GenericFunctions

The standard constructor from AbsFunction and the index of the variable

The function, created with this constructor compute the numerical derivatived by finite differencing,. An adaptive algorithm is used to find teh best choice of finite difference and to estimate the error in derivative

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) = \frac{\partial}{\partial x_i} f \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) \]

• The central difference algorithm gsl_diff_central is used for type = Type::Central
• The forward difference algorithm gsl_diff_forward is used for type = Type::Forward. The function is evaluated only at points greater than x_i and x_i itself. This function should be used if f(x) has a singularity or if it is undefined for values less than x_i
• The backward difference algorithm gsl_diff_backward is used for type = Type::Backward. The function is evaluated only at points smaller than x_i and x_i itself. This function should be used if f(x) has a singularity or if it is undefined for values greater than x_i

The adaptime numerical differentiation is used

Parameters

function	the function
index	the variable index

The standard constructor from AbsFunction and the index of the variable

Parameters

function	the function
index	the variable index

Definition at line 52 of file NumericalDerivative.cpp.

      : AbsFunction () 
      , m_function  ( function.clone()          )  
      , m_index     ( index                     ) 
      , m_DIM       ( function.dimensionality() )
      , m_type      ( type                      )
      , m_argument  ( function.dimensionality() )
      , m_result    ( GSL_NEGINF                )
      , m_error     ( GSL_POSINF                )
    {
      if( m_index >= m_DIM ) 
        { Exception ( "::constructor invalid variable index " ) ; };
    }

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative

(

const NumericalDerivative &

right

)

copy constructor

Definition at line 73 of file NumericalDerivative.cpp.

      : AbsFunction () 
      , m_function  ( right.m_function->clone() )  
      , m_index     ( right.m_index             ) 
      , m_DIM       ( right.m_DIM               )
      , m_type      ( right.m_type              ) 
      , m_argument  ( right.m_DIM               )
      , m_result    ( GSL_NEGINF                )
      , m_error     ( GSL_POSINF                )
    {}

virtual Genfun::GaudiMathImplementation::NumericalDerivative::~NumericalDerivative ( )

virtualdefault

virtual destructor

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative ( )

private

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative	(	const AbsFunction &	function,
		const size_t	index,
		const Type &	type = Central
	)

From CLHEP/GenericFunctions.

The standard constructor from AbsFunction and the index of the variable

The function, created with this constructor compute the numerical derivatived by finite differencing,. An adaptive algorithm is used to find teh best choice of finite difference and to estimate the error in derivative

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) = \frac{\partial}{\partial x_i} f \left(x_1, \dots , x_{i-1}, x_i , x_{i+1}, \dots , x_n \right) \]

• The central difference algorithm gsl_diff_central is used for type = Type::Central
• The forward difference algorithm gsl_diff_forward is used for type = Type::Forward. The function is evaluated only at points greater than x_i and x_i itself. This function should be used if f(x) has a singularity or if it is undefined for values less than x_i
• The backward difference algorithm gsl_diff_backward is used for type = Type::Backward. The function is evaluated only at points smaller than x_i and x_i itself. This function should be used if f(x) has a singularity or if it is undefined for values greater than x_i

The adaptime numerical differentiation is used

Parameters

function	the function
index	the variable index

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative

(

const NumericalDerivative &

right

)

copy constructor

virtual Genfun::GaudiMathImplementation::NumericalDerivative::~NumericalDerivative ( )

virtualdefault

virtual destructor

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative ( )

private

Member Function Documentation

virtual unsigned int Genfun::GaudiMathImplementation::NumericalDerivative::dimensionality ( ) const

inlinevirtual

dimensionality of the problem

Definition at line 96 of file NumericalDerivative.h.

{ return m_DIM ; }

virtual unsigned int Genfun::GaudiMathImplementation::NumericalDerivative::dimensionality ( ) const

inlinevirtual

dimensionality of the problem

Definition at line 96 of file NumericalDerivative.h.

{ return m_DIM ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::error ( ) const

inline

the absolute error estimate for the last call

Definition at line 124 of file NumericalDerivative.h.

{ return m_error     ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::error ( ) const

inline

the absolute error estimate for the last call

Definition at line 124 of file NumericalDerivative.h.

{ return m_error     ; }

StatusCode Genfun::GaudiMathImplementation::NumericalDerivative::Exception ( const std::string &  message, const StatusCode &  sc = StatusCode::FAILURE  ) const

protected

StatusCode Genfun::GaudiMathImplementation::NumericalDerivative::Exception ( const std::string &  message, const StatusCode &  sc = StatusCode::FAILURE  ) const

protected

Exception.

Definition at line 175 of file NumericalDerivative.cpp.

    {
      throw GaudiException( "NumericalDerivative" + message , 
                            "*GaudiMath*"         , sc      ) ;
      return sc ;
    }

const AbsFunction& Genfun::GaudiMathImplementation::NumericalDerivative::function ( ) const

inline

access to the function itself

Definition at line 112 of file NumericalDerivative.h.

{ return *m_function ; }

const AbsFunction& Genfun::GaudiMathImplementation::NumericalDerivative::function ( ) const

inline

access to the function itself

Definition at line 112 of file NumericalDerivative.h.

{ return *m_function ; }

virtual bool Genfun::GaudiMathImplementation::NumericalDerivative::hasAnalyticDerivative ( ) const

inlinevirtual

Does this function have an analytic derivative?

Definition at line 104 of file NumericalDerivative.h.

{ return true ;}

virtual bool Genfun::GaudiMathImplementation::NumericalDerivative::hasAnalyticDerivative ( ) const

inlinevirtual

Does this function have an analytic derivative?

Definition at line 104 of file NumericalDerivative.h.

{ return true ;}

size_t Genfun::GaudiMathImplementation::NumericalDerivative::index ( ) const

inline

index

Definition at line 114 of file NumericalDerivative.h.

{ return  m_index    ; }

size_t Genfun::GaudiMathImplementation::NumericalDerivative::index ( ) const

inline

index

Definition at line 114 of file NumericalDerivative.h.

{ return  m_index    ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::operator() ( double  argument ) const

virtual

Function value.

Definition at line 156 of file NumericalDerivative.cpp.

    {
      // reset the result and the error  
      m_result = GSL_NEGINF ;
      m_error  = GSL_POSINF ;
      
      // check the argument 
      if( 1 != m_DIM ) { Exception ( "operator(): invalid argument size " ); }

      Argument arg(1) ;
      arg[0] = argument ;
      return (*this)( arg ) ;
    }

virtual double Genfun::GaudiMathImplementation::NumericalDerivative::operator() ( double  argument ) const

virtual

Function value.

virtual double Genfun::GaudiMathImplementation::NumericalDerivative::operator() ( const Argument &  argument ) const

virtual

Function value.

double Genfun::GaudiMathImplementation::NumericalDerivative::operator() ( const Argument &  argument ) const

virtual

Function value.

copy the argument

use GSL to evaluate the numerical derivative

Definition at line 110 of file NumericalDerivative.cpp.

    {
      // reset the result and the error  
      m_result = GSL_NEGINF ;
      m_error  = GSL_POSINF ;
      
      // check the argument 
      if( argument.dimension() != m_DIM ) 
        { Exception ( "::operator():invalid argument size" ) ; };
      
      {for( size_t i  = 0 ; i < m_DIM ; ++i ){ m_argument[i] = argument[i];}}
      
      // create the helper object 
      GSL_Helper helper( *m_function , m_argument , m_index );
      
      gsl_function F ;
      F.function = &GSL_Adaptor ;
      F.params   = &helper                 ;
      
      double x       = argument[m_index];
      int    ierrno  = 0                   ;
      switch ( type() ) 
        {
        case Central  : 
          ierrno = gsl_diff_central  ( &F , x , &m_result , &m_error ) ; break ;
        case Forward  : 
          ierrno = gsl_diff_forward  ( &F , x , &m_result , &m_error ) ; break ;
        case Backward :
          ierrno = gsl_diff_backward ( &F , x , &m_result , &m_error ) ; break ;
        default:
          Exception ( "::operator(): invalid diffrentiation type " ) ;          
        }
      
      if( ierrno ) 
        { gsl_error ( " NumericalDerivative:: the error from gsl_diff_XXXX" ,
                      __FILE__ , __LINE__ , ierrno ) ; }
      
      return result() ;
    }

NumericalDerivative& Genfun::GaudiMathImplementation::NumericalDerivative::operator= ( const NumericalDerivative &  )

private

NumericalDerivative& Genfun::GaudiMathImplementation::NumericalDerivative::operator= ( const NumericalDerivative &  )

private

Genfun::Derivative Genfun::GaudiMathImplementation::NumericalDerivative::partial ( unsigned int  index ) const

virtual

Derivatives.

Definition at line 96 of file NumericalDerivative.cpp.

    {
      if( idx >= m_DIM ) 
        { Exception ( "::partial(i): invalid variable index" ) ; }
      const  AbsFunction& aux = 
        NumericalDerivative( *this , idx , type() ) ;
      return FunctionNoop( &aux ) ;
    }

virtual Derivative Genfun::GaudiMathImplementation::NumericalDerivative::partial ( unsigned int  index ) const

virtual

Derivatives.

double Genfun::GaudiMathImplementation::NumericalDerivative::result ( ) const

inline

the result of the last call

Definition at line 122 of file NumericalDerivative.h.

{ return m_result    ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::result ( ) const

inline

the result of the last call

Definition at line 122 of file NumericalDerivative.h.

{ return m_result    ; }

const NumericalDerivative::Type & Genfun::GaudiMathImplementation::NumericalDerivative::setType

(

const Type &

value

)

change the type of the adaptive differentiation

Definition at line 89 of file NumericalDerivative.cpp.

    { m_type = value ; return type() ; }

const Type& Genfun::GaudiMathImplementation::NumericalDerivative::setType

(

const Type &

value

)

change the type of the adaptive differentiation

const Type& Genfun::GaudiMathImplementation::NumericalDerivative::type ( ) const

inline

type

Definition at line 116 of file NumericalDerivative.h.

{ return  m_type     ; }

const Type& Genfun::GaudiMathImplementation::NumericalDerivative::type ( ) const

inline

type

Definition at line 116 of file NumericalDerivative.h.

{ return  m_type     ; }

Member Data Documentation

Argument Genfun::GaudiMathImplementation::NumericalDerivative::m_argument

mutableprivate

Definition at line 145 of file NumericalDerivative.h.

size_t Genfun::GaudiMathImplementation::NumericalDerivative::m_DIM

private

Definition at line 142 of file NumericalDerivative.h.

double Genfun::GaudiMathImplementation::NumericalDerivative::m_error

mutableprivate

Definition at line 147 of file NumericalDerivative.h.

std::unique_ptr< const AbsFunction > Genfun::GaudiMathImplementation::NumericalDerivative::m_function

private

Definition at line 140 of file NumericalDerivative.h.

size_t Genfun::GaudiMathImplementation::NumericalDerivative::m_index

private

Definition at line 141 of file NumericalDerivative.h.

double Genfun::GaudiMathImplementation::NumericalDerivative::m_result

mutableprivate

Definition at line 146 of file NumericalDerivative.h.

Type Genfun::GaudiMathImplementation::NumericalDerivative::m_type

private

Definition at line 143 of file NumericalDerivative.h.

---

The documentation for this class was generated from the following files:

• InstallArea/x86_64-slc6-gcc48-opt/include/GaudiMath/NumericalDerivative.h
• GaudiGSL/src/Lib/NumericalDerivative.cpp