Genfun::GaudiMathImplementation::NumericalDerivative Class Reference

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

#include <NumericalDerivative.h>

List of all members.

Public Types

enum Type { Central, Forward, Backward }

the type of numerical differentiation More...

Public Member Functions

FUNCTION_OBJECT_DEF (NumericalDerivative)

From CLHEP/GenericFunctions.

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

The standard constructor from AbsFunction and the index of the variable.

NumericalDerivative (const NumericalDerivative &right)

copy constructor

virtual ~NumericalDerivative ()

virtual destructor

virtual unsigned int dimensionality () const

dimensionality of the problem

virtual double operator() (double argument) const

Function value.

virtual double operator() (const Argument &argument) const

Function value.

virtual bool hasAnalyticDerivative () const

Does this function have an analytic derivative?

virtual Derivative partial (unsigned int index) const

Derivatives.

const AbsFunction & function () const

access to the function itself

size_t index () const

index

const Type & type () const

type

const Type & setType (const Type &value)

change the type of the adaptive differentiation

double result () const

the result of the last call

double error () const

the absolute error estimate for the last call

Protected Member Functions

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

Exception.

Private Member Functions

NumericalDerivative ()

NumericalDerivative & operator= (const NumericalDerivative &)

Private Attributes

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.Belyaev@itep.ru

Date:: 2003-08-27

Definition at line 36 of file NumericalDerivative.h.

Member Enumeration Documentation

enum Genfun::GaudiMathImplementation::NumericalDerivative::Type

the type of numerical differentiation

Enumerator:

Central
Forward
Backward

Definition at line 40 of file NumericalDerivative.h.

00041         { Central  ,
00042           Forward  ,
00043           Backward } ;

Constructor & Destructor Documentation

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

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
	function	the function
	index	the variable index

Definition at line 53 of file NumericalDerivative.cpp.

00056       : AbsFunction () 
00057       , m_function  ( function.clone()          )  
00058       , m_index     ( index                     ) 
00059       , m_DIM       ( function.dimensionality() )
00060       , m_type      ( type                      )
00061       , m_argument  ( function.dimensionality() )
00062       , m_result    ( GSL_NEGINF                )
00063       , m_error     ( GSL_POSINF                )
00064     {
00065       if( m_index >= m_DIM ) 
00066         { Exception ( "::constructor invalid variable index " ) ; };
00067     } ;

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative ( const NumericalDerivative & right )

copy constructor

Definition at line 74 of file NumericalDerivative.cpp.

00075       : AbsFunction () 
00076       , m_function  ( right.m_function->clone() )  
00077       , m_index     ( right.m_index             ) 
00078       , m_DIM       ( right.m_DIM               )
00079       , m_type      ( right.m_type              ) 
00080       , m_argument  ( right.m_DIM               )
00081       , m_result    ( GSL_NEGINF                )
00082       , m_error     ( GSL_POSINF                )
00083     {} ;

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

virtual destructor

destructor

Definition at line 89 of file NumericalDerivative.cpp.

00090     { if( 0 != m_function ) { delete m_function ; m_function = 0 ; } };

Genfun::GaudiMathImplementation::NumericalDerivative::NumericalDerivative ( ) [private]

Member Function Documentation

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

From CLHEP/GenericFunctions.

virtual unsigned int Genfun::GaudiMathImplementation::NumericalDerivative::dimensionality ( ) const [inline, virtual]

dimensionality of the problem

Definition at line 98 of file NumericalDerivative.h.

00098 { return m_DIM ; }

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

Function value.

Definition at line 164 of file NumericalDerivative.cpp.

00165     {
00166       // reset the result and the error  
00167       m_result = GSL_NEGINF ;
00168       m_error  = GSL_POSINF ;
00169       
00170       // check the argument 
00171       if( 1 != m_DIM ) { Exception ( "operator(): invalid argument size " ); }
00172 
00173       Argument arg(1) ;
00174       arg[0] = argument ;
00175       return (*this)( arg ) ;
00176     };

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 118 of file NumericalDerivative.cpp.

00119     {
00120       // reset the result and the error  
00121       m_result = GSL_NEGINF ;
00122       m_error  = GSL_POSINF ;
00123       
00124       // check the argument 
00125       if( argument.dimension() != m_DIM ) 
00126         { Exception ( "::operator():invalid argument size" ) ; };
00127       
00129       {for( size_t i  = 0 ; i < m_DIM ; ++i ){ m_argument[i] = argument[i];}}
00130       
00131       // create the helper object 
00132       GSL_Helper helper( *m_function , m_argument , m_index );
00133       
00135       gsl_function F ;
00136       F.function = &GSL_Adaptor ;
00137       F.params   = &helper                 ;
00138       
00139       double x       = argument[m_index];
00140       int    ierrno  = 0                   ;
00141       switch ( type() ) 
00142         {
00143         case Central  : 
00144           ierrno = gsl_diff_central  ( &F , x , &m_result , &m_error ) ; break ;
00145         case Forward  : 
00146           ierrno = gsl_diff_forward  ( &F , x , &m_result , &m_error ) ; break ;
00147         case Backward :
00148           ierrno = gsl_diff_backward ( &F , x , &m_result , &m_error ) ; break ;
00149         default:
00150           Exception ( "::operator(): invalid diffrentiation type " ) ;          
00151         }
00152       
00153       if( ierrno ) 
00154         { gsl_error ( " NumericalDerivative:: the error from gsl_diff_XXXX" ,
00155                       __FILE__ , __LINE__ , ierrno ) ; }
00156       
00157       return result() ;
00158     };

virtual bool Genfun::GaudiMathImplementation::NumericalDerivative::hasAnalyticDerivative ( ) const [inline, virtual]

Does this function have an analytic derivative?

Definition at line 106 of file NumericalDerivative.h.

00106 { return true ;}

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

Derivatives.

Definition at line 104 of file NumericalDerivative.cpp.

00105     {
00106       if( idx >= m_DIM ) 
00107         { Exception ( "::partial(i): invalid variable index" ) ; }
00108       const  AbsFunction& aux = 
00109         NumericalDerivative( *this , idx , type() ) ;
00110       return FunctionNoop( &aux ) ;
00111     };

const AbsFunction& Genfun::GaudiMathImplementation::NumericalDerivative::function ( ) const [inline]

access to the function itself

Definition at line 114 of file NumericalDerivative.h.

00114 { return *m_function ; }

size_t Genfun::GaudiMathImplementation::NumericalDerivative::index ( ) const [inline]

index

Definition at line 116 of file NumericalDerivative.h.

00116 { return  m_index    ; }

const Type& Genfun::GaudiMathImplementation::NumericalDerivative::type ( ) const [inline]

type

Definition at line 118 of file NumericalDerivative.h.

00118 { return  m_type     ; }

const NumericalDerivative::Type & Genfun::GaudiMathImplementation::NumericalDerivative::setType ( const Type & value )

change the type of the adaptive differentiation

Definition at line 97 of file NumericalDerivative.cpp.

00098     { m_type = value ; return type() ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::result ( ) const [inline]

the result of the last call

Definition at line 124 of file NumericalDerivative.h.

00124 { return m_result    ; }

double Genfun::GaudiMathImplementation::NumericalDerivative::error ( ) const [inline]

the absolute error estimate for the last call

Definition at line 126 of file NumericalDerivative.h.

00126 { return m_error     ; }

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

Exception.

Definition at line 183 of file NumericalDerivative.cpp.

00185     {
00186       throw GaudiException( "NumericalDerivative" + message , 
00187                             "*GaudiMath*"         , sc      ) ;
00188       return sc ;
00189     };

NumericalDerivative& Genfun::GaudiMathImplementation::NumericalDerivative::operator= ( const NumericalDerivative & ) [private]

Member Data Documentation

const AbsFunction* Genfun::GaudiMathImplementation::NumericalDerivative::m_function [private]

Definition at line 142 of file NumericalDerivative.h.

size_t Genfun::GaudiMathImplementation::NumericalDerivative::m_index [private]

Definition at line 143 of file NumericalDerivative.h.

size_t Genfun::GaudiMathImplementation::NumericalDerivative::m_DIM [private]

Definition at line 144 of file NumericalDerivative.h.

Type Genfun::GaudiMathImplementation::NumericalDerivative::m_type [private]

Definition at line 145 of file NumericalDerivative.h.

Argument Genfun::GaudiMathImplementation::NumericalDerivative::m_argument [mutable, private]

Definition at line 147 of file NumericalDerivative.h.

double Genfun::GaudiMathImplementation::NumericalDerivative::m_result [mutable, private]

Definition at line 148 of file NumericalDerivative.h.

double Genfun::GaudiMathImplementation::NumericalDerivative::m_error [mutable, private]

Definition at line 149 of file NumericalDerivative.h.

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

/afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v21r7/GaudiGSL/GaudiMath/NumericalDerivative.h
/afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v21r7/GaudiGSL/src/Lib/NumericalDerivative.cpp


Public Types
enum	Type { Central, Forward, Backward }
	the type of numerical differentiation More...
Public Member Functions
	FUNCTION_OBJECT_DEF (NumericalDerivative)
	From CLHEP/GenericFunctions.
	NumericalDerivative (const AbsFunction &function, const size_t index, const Type &type=Central)
	The standard constructor from AbsFunction and the index of the variable.
	NumericalDerivative (const NumericalDerivative &right)
	copy constructor
virtual	~NumericalDerivative ()
	virtual destructor
virtual unsigned int	dimensionality () const
	dimensionality of the problem
virtual double	operator() (double argument) const
	Function value.
virtual double	operator() (const Argument &argument) const
	Function value.
virtual bool	hasAnalyticDerivative () const
	Does this function have an analytic derivative?
virtual Derivative	partial (unsigned int index) const
	Derivatives.
const AbsFunction &	function () const
	access to the function itself
size_t	index () const
	index
const Type &	type () const
	type
const Type &	setType (const Type &value)
	change the type of the adaptive differentiation
double	result () const
	the result of the last call
double	error () const
	the absolute error estimate for the last call
Protected Member Functions
StatusCode	Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const
	Exception.
Private Member Functions
	NumericalDerivative ()
NumericalDerivative &	operator= (const NumericalDerivative &)
Private Attributes
const AbsFunction *	m_function
size_t	m_index
size_t	m_DIM
Type	m_type
Argument	m_argument
double	m_result
double	m_error

Gaudi Framework, version v21r7

Genfun::GaudiMathImplementation::NumericalDerivative Class Reference

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation