Genfun::GaudiMathImplementation::NumericalDefiniteIntegral Class Reference

This class allows the numerical evaluation of the following functions: More...

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

Inheritance diagram for Genfun::GaudiMathImplementation::NumericalDefiniteIntegral:

Collaboration diagram for Genfun::GaudiMathImplementation::NumericalDefiniteIntegral:

Classes
struct	_Function
struct	_Workspace
struct	gsl_ws_deleter

Public Types
typedef std::vector< double >	Points
	typedef for vector of singular points More...
typedef std::vector< double >	Points
	typedef for vector of singular points More...

Public Member Functions
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const double b, const GaudiMath::Integration::Type type=GaudiMath::Integration::Adaptive, const GaudiMath::Integration::KronrodRule rule=GaudiMath::Integration::Default, const double epsabs=1.e-10, const double epsrel=1.e-7, const size_t size=1000)
	From CLHEP/GenericFunctions. More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const double b, const Points &points, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const GaudiMath::Integration::Inf b=GaudiMath::Integration::Infinity, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const GaudiMath::Integration::Inf a, const double b, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const float epsabs=1e-9, const float epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const NumericalDefiniteIntegral &)
	copy constructor More...
virtual	~NumericalDefiniteIntegral ()=default
	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 Genfun::Derivative	partial (unsigned int index) const
	Derivatives. More...
const AbsFunction &	function () const
	accessor to the function itself More...
double	a () const
	integration limit More...
double	b () const
const Points &	points () const
	known singularities More...
double	epsabs () const
	absolute precision More...
double	epsrel () const
	relatiove precision More...
double	result () const
	previous result More...
double	error () const
	evaluate of previous error More...
size_t	size () const
GaudiMath::Integration::Type	type () const
	integration type More...
GaudiMath::Integration::Category	category () const
	integration category More...
GaudiMath::Integration::KronrodRule	rule () const
	integration rule More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const double b, const GaudiMath::Integration::Type type=GaudiMath::Integration::Adaptive, const GaudiMath::Integration::KronrodRule rule=GaudiMath::Integration::Default, const double epsabs=1.e-10, const double epsrel=1.e-7, const size_t size=1000)
	From CLHEP/GenericFunctions. More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const double b, const Points &points, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const GaudiMath::Integration::Inf b=GaudiMath::Integration::Infinity, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const GaudiMath::Integration::Inf a, const double b, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const AbsFunction &function, const size_t index, const float epsabs=1e-9, const float epsrel=1.e-6, const size_t size=1000)
	Standard constructor The function created with this constructor compute the following integral: More...
	NumericalDefiniteIntegral (const NumericalDefiniteIntegral &)
	copy constructor More...
virtual	~NumericalDefiniteIntegral ()=default
	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 Genfun::Derivative	partial (unsigned int index) const
	Derivatives. More...
const AbsFunction &	function () const
	accessor to the function itself More...
double	a () const
	integration limit More...
double	b () const
const Points &	points () const
	known singularities More...
double	epsabs () const
	absolute precision More...
double	epsrel () const
	relatiove precision More...
double	result () const
	previous result More...
double	error () const
	evaluate of previous error More...
size_t	size () const
GaudiMath::Integration::Type	type () const
	integration type More...
GaudiMath::Integration::Category	category () const
	integration category More...
GaudiMath::Integration::KronrodRule	rule () const
	integration rule More...

Protected Member Functions
double	QAGI (_Function *fun) const
double	QAGP (_Function *fun) const
double	QNG (_Function *fun) const
double	QAG (_Function *fun) const
double	QAGS (_Function *fun) const
_Workspace *	allocate () const
	allocate the integration workspace More...
_Workspace *	ws () const
StatusCode	Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const
double	QAGI (_Function *fun) const
double	QAGP (_Function *fun) const
double	QNG (_Function *fun) const
double	QAG (_Function *fun) const
double	QAGS (_Function *fun) const
_Workspace *	allocate () const
_Workspace *	ws () const
StatusCode	Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const

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

Private Attributes
std::unique_ptr< const AbsFunction >	m_function
size_t	m_DIM
size_t	m_index
double	m_a
double	m_b
bool	m_ia
bool	m_ib
GaudiMath::Integration::Type	m_type
GaudiMath::Integration::Category	m_category
GaudiMath::Integration::KronrodRule	m_rule
Points	m_points
std::unique_ptr< double[]>	m_pdata
double	m_epsabs
double	m_epsrel
double	m_result
double	m_error
size_t	m_size
std::unique_ptr< _Workspace, gsl_ws_deleter >	m_ws
Argument	m_argument
Argument	m_argF

Detailed Description

This class allows the numerical evaluation of the following functions:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

Author

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

Date

2003-08-31

Definition at line 71 of file NumericalDefiniteIntegral.h.

Member Typedef Documentation

typedef std::vector<double> Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::Points

typedef for vector of singular points

Definition at line 75 of file NumericalDefiniteIntegral.h.

typedef std::vector<double> Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::Points

typedef for vector of singular points

Definition at line 75 of file NumericalDefiniteIntegral.h.

Constructor & Destructor Documentation

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const double	b,
		const GaudiMath::Integration::Type	type = GaudiMath::Integration::Adaptive,
		const GaudiMath::Integration::KronrodRule	rule = GaudiMath::Integration::Default,
		const double	epsabs = 1.e-10,
		const double	epsrel = 1.e-7,
		const size_t	size = 1000
	)

From CLHEP/GenericFunctions.

from CLHEP/GenericFunctions

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

If function contains singularities, the type = Type::AdaptiveSingular need to be used

For faster integration of smooth function non-adaptive integration can be used: type = Type::NonAdaptive need to be used

For adaptive integration type = Type>>Adaptive one can specify the order of Gauss-Kronrad integration rule rule = KronrodRule::Gauss15 The higher-order rules give better accuracy for smooth functions, while lower-order rules save the time when the function contains local difficulties, such as discontinuites.

• The GSL routine gsl_integration_qng is used for type = Type:NonAdaptive :

The GSL routine gsl_integration_qag is used for type = Type:Adaptive :

• The GSL routine gsl_integration_qags is used for type = Type:AdaptiveSingular :

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	high integration limit
type	integration type
rule	integration rule (for adaptive integration)
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Definition at line 107 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction ()
      , m_function  ( function.clone          ()    )
      , m_DIM       ( 0                             )
      , m_index     ( index                         )
      , m_a         ( a      )
      , m_b         ( b      )
      , m_ia        ( false  )
      , m_ib        ( false  )
      , m_type      ( type   )
      , m_category  ( GaudiMath::Integration::Finite )
      , m_rule      ( rule       )
      , m_points    (            )
      , m_epsabs    ( epsabs     )
      , m_epsrel    ( epsrel     )
      , m_result    ( GSL_NEGINF )
      , m_error     ( GSL_POSINF )
      , m_size      ( size       )
      , m_argument  ()
      , m_argF      ()
    {
      if ( GaudiMath::Integration::Fixed == m_rule )
        { m_rule = GaudiMath::Integration::Default ; }
      if ( function.dimensionality() < 2          )
        { Exception("::constructor: invalid dimensionality ") ; }
      if ( m_index >= function.dimensionality()   )
        { Exception("::constructor: invalid variable index") ; }

      m_DIM = function.dimensionality() - 1 ;
      m_argument = Argument( m_DIM      ) ;
      m_argF     = Argument( m_DIM + 1  ) ;

    }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const double	b,
		const Points &	points,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

standard constructor

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

where function have known singulatities

• The GSL routine gsl_integration_qagp is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	high integration limit
pointns	vector of know singular points
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration
function	the base function
index	the variable index
a	integration limit
b	integration limit
points	list of known function singularities
epsabs	absolute precision for integration
epsrel	relative precision for integration

Definition at line 160 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction ()
      , m_function  ( function.clone()             )
      , m_DIM       ( 0                            )
      , m_index     ( index                        )
      , m_a         ( a                            )
      , m_b         ( b                            )
      , m_ia        ( false  )
      , m_ib        ( false  )
      , m_type      ( GaudiMath::Integration::    Other )
      , m_category  ( GaudiMath::Integration:: Singular )
      , m_rule      ( GaudiMath::Integration::    Fixed )
      , m_points    ( points  )
      , m_epsabs    ( epsabs  )
      , m_epsrel    ( epsrel  )
      //
      , m_result    ( GSL_NEGINF                          )
      , m_error     ( GSL_POSINF                          )
      //
      , m_size      ( size                                )
      , m_argument  ()
      , m_argF      ()
    {
      if ( function.dimensionality() < 2          )
        { Exception("::constructor: invalid dimensionality ") ; }
      if ( m_index >= function.dimensionality()   )
        { Exception("::constructor: invalid variable index") ; }

      m_DIM = function.dimensionality() - 1 ;
      m_argument = Argument( m_DIM      ) ;
      m_argF     = Argument( m_DIM + 1  ) ;

      const double l1 = std::min ( a , b ) ;
      const double l2 = std::max ( a , b ) ;
      m_points.push_back ( l1 ) ;
      m_points.push_back ( l2 ) ;
      std::sort ( m_points.begin() , m_points.end() ) ;
      m_points.erase( std::unique( m_points.begin () ,
                                   m_points.end   () ) ,
                      m_points.end() );

      Points::iterator lower =
        std::lower_bound ( m_points.begin () , m_points.end () , l1 ) ;
      m_points.erase     ( m_points.begin () , lower                ) ;
      Points::iterator upper =
        std::upper_bound ( m_points.begin () , m_points.end () , l2 ) ;
      m_points.erase     ( upper             , m_points.end ()      ) ;

      m_pdata.reset( new double[ m_points.size() ]  );
      std::copy( m_points.begin() , m_points.end() , m_pdata.get() );
    }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const GaudiMath::Integration::Inf	b = GaudiMath::Integration::Infinity,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagiu is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	indication for infinity
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Definition at line 245 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction()
      , m_function  ( function.clone()             )
      , m_DIM       ( 0                            )
      , m_index     ( index                        )
      , m_a         ( a                            )
      , m_b         ( GSL_POSINF                   )
      , m_ia        ( false  )
      , m_ib        ( true   )
      , m_type      ( GaudiMath::Integration::    Other )
      , m_category  ( GaudiMath::Integration:: Infinite )
      , m_rule      ( GaudiMath::Integration::    Fixed )
      , m_points    (         )
      , m_epsabs    ( epsabs  )
      , m_epsrel    ( epsrel  )
      //
      , m_result    ( GSL_NEGINF                          )
      , m_error     ( GSL_POSINF                          )
      //
      , m_size      ( size                                )
      , m_argument  ()
      , m_argF      ()
    {
      if ( function.dimensionality() < 2          )
        { Exception("::constructor: invalid dimensionality ") ; }
      if ( m_index >= function.dimensionality()   )
        { Exception("::constructor: invalid variable index") ; }

      m_DIM = function.dimensionality() - 1 ;
      m_argument = Argument( m_DIM      ) ;
      m_argF     = Argument( m_DIM + 1  ) ;

    }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const GaudiMath::Integration::Inf	a,
		const double	b,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagiu is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	indication for infinity
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Definition at line 312 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction()
      , m_function  ( function.clone()             )
      , m_DIM       ( 0                            )
      , m_index     ( index                        )
      , m_a         ( GSL_NEGINF                   )
      , m_b         ( b                            )
      , m_ia        ( true   )
      , m_ib        ( false  )
      , m_type      ( GaudiMath::Integration::    Other )
      , m_category  ( GaudiMath::Integration:: Infinite )
      , m_rule      ( GaudiMath::Integration::    Fixed )
      , m_points    (         )
      , m_epsabs    ( epsabs  )
      , m_epsrel    ( epsrel  )
      //
      , m_result    ( GSL_NEGINF                          )
      , m_error     ( GSL_POSINF                          )
      //
      , m_size      ( size                                )
      , m_argument  ()
      , m_argF      ()
    {
      if ( function.dimensionality() < 2          )
        { Exception("::constructor: invalid dimensionality ") ; }
      if ( m_index >= function.dimensionality()   )
        { Exception("::constructor: invalid variable index") ; }

      m_DIM = function.dimensionality() - 1 ;
      m_argument = Argument( m_DIM      ) ;
      m_argF     = Argument( m_DIM + 1  ) ;
    }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const float	epsabs = 1e-9,
		const float	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagi is used for integration

Parameters

function	funtion to be integrated
index	variable index
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Definition at line 375 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction()
      , m_function  ( function.clone()             )
      , m_DIM       ( 0      )
      , m_index     ( index                        )
      , m_a         ( GSL_NEGINF                   )
      , m_b         ( GSL_POSINF                   )
      , m_ia        ( true   )
      , m_ib        ( true   )
      , m_type      ( GaudiMath::Integration::    Other )
      , m_category  ( GaudiMath::Integration:: Infinite )
      , m_rule      ( GaudiMath::Integration::    Fixed )
      , m_points    (         )
      , m_epsabs    ( epsabs  )
      , m_epsrel    ( epsrel  )
      //
      , m_result    ( GSL_NEGINF                          )
      , m_error     ( GSL_POSINF                          )
      //
      , m_size      ( size                                )
      , m_argument  ()
      , m_argF      ()
    {
      if ( function.dimensionality() < 2          )
        { Exception("::constructor: invalid dimensionality ") ; }
      if ( m_index >= function.dimensionality()   )
        { Exception("::constructor: invalid variable index") ; }

      m_DIM = function.dimensionality() - 1 ;
      m_argument = Argument( m_DIM      ) ;
      m_argF     = Argument( m_DIM + 1  ) ;

    }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral

(

const NumericalDefiniteIntegral &

right

)

copy constructor

Definition at line 415 of file NumericalDefiniteIntegral.cpp.

      : AbsFunction ()
      , m_function  ( right.m_function->clone() )
      , m_DIM       ( right.m_DIM      )
      , m_index     ( right.m_index    )
      , m_a         ( right.m_a        )
      , m_b         ( right.m_b        )
      , m_ia        ( right.m_ia       )
      , m_ib        ( right.m_ib       )
      , m_type      ( right.m_type     )
      , m_category  ( right.m_category )
      , m_rule      ( right.m_rule     )
      , m_points    ( right.m_points   )
      , m_epsabs    ( right.m_epsabs   )
      , m_epsrel    ( right.m_epsrel   )
      , m_result    ( GSL_NEGINF       )
      , m_error     ( GSL_POSINF       )
      , m_size      ( right.m_size     )
      , m_argument  ( right.m_argument )
      , m_argF      ( right.m_argF     )
    {
      if( right.m_pdata )
        {
          m_pdata.reset( new double[m_points.size()] );
          std::copy( m_points.begin() , m_points.end() , m_pdata.get() );
        }
    }

virtual Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::~NumericalDefiniteIntegral ( )

virtualdefault

destructor

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral ( )

private

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const double	b,
		const GaudiMath::Integration::Type	type = GaudiMath::Integration::Adaptive,
		const GaudiMath::Integration::KronrodRule	rule = GaudiMath::Integration::Default,
		const double	epsabs = 1.e-10,
		const double	epsrel = 1.e-7,
		const size_t	size = 1000
	)

From CLHEP/GenericFunctions.

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

If function contains singularities, the type = Type::AdaptiveSingular need to be used

For faster integration of smooth function non-adaptive integration can be used: type = Type::NonAdaptive need to be used

For adaptive integration type = Type>>Adaptive one can specify the order of Gauss-Kronrad integration rule rule = KronrodRule::Gauss15 The higher-order rules give better accuracy for smooth functions, while lower-order rules save the time when the function contains local difficulties, such as discontinuites.

• The GSL routine gsl_integration_qng is used for type = Type:NonAdaptive :

The GSL routine gsl_integration_qag is used for type = Type:Adaptive :

• The GSL routine gsl_integration_qags is used for type = Type:AdaptiveSingular :

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	high integration limit
type	integration type
rule	integration rule (for adaptive integration)
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const double	b,
		const Points &	points,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

where function have known singulatities

• The GSL routine gsl_integration_qagp is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	high integration limit
pointns	vector of know singular points
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const GaudiMath::Integration::Inf	b = GaudiMath::Integration::Infinity,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{a}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagiu is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	indication for infinity
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const GaudiMath::Integration::Inf	a,
		const double	b,
		const double	epsabs = 1e-9,
		const double	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{b} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagiu is used for integration

Parameters

function	funtion to be integrated
index	variable index
a	lower intgeration limit
b	indication for infinity
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const float	epsabs = 1e-9,
		const float	epsrel = 1.e-6,
		const size_t	size = 1000
	)

Standard constructor The function created with this constructor compute the following integral:

\[ {\mathcal{F}}_i \left(x_1, \dots , x_{i-1}, x_{i+1}, \dots , x_n \right) = \int\limits_{-\infty}^{+\infty} f \left(x_1, \dots , x_{i-1}, \hat{x}_i , x_{i+1}, \dots , x_n \right) \, {\mathrm{d}} \hat{x}_i \]

• The GSL routine gsl_integration_qagi is used for integration

Parameters

function	funtion to be integrated
index	variable index
epsabs	required absolute precision
epsrel	required relative precision
size	maximal number of bisections for adaptive integration

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral

(

const NumericalDefiniteIntegral &

)

copy constructor

virtual Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::~NumericalDefiniteIntegral ( )

virtualdefault

destructor

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral ( )

private

Member Function Documentation

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::a ( ) const

inline

integration limit

Definition at line 321 of file NumericalDefiniteIntegral.h.

{ return         m_a ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::a ( ) const

inline

integration limit

Definition at line 321 of file NumericalDefiniteIntegral.h.

{ return         m_a ; }

NumericalDefiniteIntegral::_Workspace * Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::allocate ( ) const

protected

allocate the integration workspace

Definition at line 553 of file NumericalDefiniteIntegral.cpp.

    {
      if ( !m_ws ) {
        m_ws.reset(  new _Workspace() );
        m_ws->ws = gsl_integration_workspace_alloc( size () );
        if ( !m_ws->ws ) { Exception ( "allocate()::invalid workspace" ) ; };
      }
      return m_ws.get() ;
    }

_Workspace* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::allocate ( ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::b ( ) const

inline

Definition at line 322 of file NumericalDefiniteIntegral.h.

{ return         m_b ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::b ( ) const

inline

Definition at line 322 of file NumericalDefiniteIntegral.h.

{ return         m_b ; }

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::category ( ) const

inline

integration category

Definition at line 343 of file NumericalDefiniteIntegral.h.

{ return  m_category ; }

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::category ( ) const

inline

integration category

Definition at line 343 of file NumericalDefiniteIntegral.h.

{ return  m_category ; }

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

inlinevirtual

dimensionality of the problem

Definition at line 303 of file NumericalDefiniteIntegral.h.

{ return m_DIM ; }

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

inlinevirtual

dimensionality of the problem

Definition at line 303 of file NumericalDefiniteIntegral.h.

{ return m_DIM ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsabs ( ) const

inline

absolute precision

Definition at line 326 of file NumericalDefiniteIntegral.h.

{ return    m_epsabs ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsabs ( ) const

inline

absolute precision

Definition at line 326 of file NumericalDefiniteIntegral.h.

{ return    m_epsabs ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsrel ( ) const

inline

relatiove precision

Definition at line 328 of file NumericalDefiniteIntegral.h.

{ return    m_epsrel ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsrel ( ) const

inline

relatiove precision

Definition at line 328 of file NumericalDefiniteIntegral.h.

{ return    m_epsrel ; }

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

inline

evaluate of previous error

Definition at line 333 of file NumericalDefiniteIntegral.h.

{ return     m_error ; }

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

inline

evaluate of previous error

Definition at line 333 of file NumericalDefiniteIntegral.h.

{ return     m_error ; }

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

protected

Definition at line 447 of file NumericalDefiniteIntegral.cpp.

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

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

protected

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

inline

accessor to the function itself

Definition at line 319 of file NumericalDefiniteIntegral.h.

{ return *m_function ; }

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

inline

accessor to the function itself

Definition at line 319 of file NumericalDefiniteIntegral.h.

{ return *m_function ; }

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

inlinevirtual

Does this function have an analytic derivative?

Definition at line 311 of file NumericalDefiniteIntegral.h.

{ return true ;}

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

inlinevirtual

Does this function have an analytic derivative?

Definition at line 311 of file NumericalDefiniteIntegral.h.

{ return true ;}

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

virtual

Function value.

evaluate the function

Definition at line 460 of file NumericalDefiniteIntegral.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 " ) ; };

      m_argument[0] = argument ;
      return (*this) ( m_argument );
    }

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

virtual

Function value.

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

virtual

Function value.

evaluate the function

Definition at line 493 of file NumericalDefiniteIntegral.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 " ) ; };

      // copy the argument

      for( size_t i  = 0 ; i < m_DIM ; ++i )
        {
          m_argument [i] = argument [i] ;
          const size_t j =  i < m_index ? i : i + 1 ;
          m_argF     [j] = argument [i] ;
        };

      // create the helper object
      GSL_Helper helper( *m_function , m_argF , m_index );

      // use GSL to evaluate the numerical derivative
      gsl_function F ;
      F.function = &GSL_Adaptor ;
      F.params   = &helper                 ;
      _Function F1    ;
      F1.fn      = &F ;

      if        (  GaudiMath::Integration::Infinite         == category () )
        { return   QAGI ( &F1 ) ; }                                // RETURN

      if ( m_a == m_b )
        {
          m_result = 0    ; m_error  = 0    ;                      // EXACT
          return m_result ;                                       // RETURN
        }

      if        (  GaudiMath::Integration::Singular         == category () )
         { return   QAGP ( &F1 ) ; }                                // RETURN
      else if   (  GaudiMath::Integration::Finite           == category () )
        if      (  GaudiMath::Integration::NonAdaptive      == type     () )
          { return QNG  ( &F1 ) ; }                                // RETURN
        else if (  GaudiMath::Integration::Adaptive         == type     () )
          { return QAG  ( &F1 ) ; }                                // RETURN
        else if (  GaudiMath::Integration::AdaptiveSingular == type     () )
          { return QAGS ( &F1 ) ; }                                // RETURN
        else
          { Exception ( "::operator(): invalid type "  ); }
      else
        { Exception ( "::operator(): invalid category "  ); }

      return 0 ;
    }

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

virtual

Function value.

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

private

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

private

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

virtual

Derivatives.

Definition at line 478 of file NumericalDefiniteIntegral.cpp.

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

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

virtual

Derivatives.

const Points& Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::points ( ) const

inline

known singularities

Definition at line 324 of file NumericalDefiniteIntegral.h.

{ return    m_points ; }

const Points& Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::points ( ) const

inline

known singularities

Definition at line 324 of file NumericalDefiniteIntegral.h.

{ return    m_points ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAG ( _Function *  fun ) const

protected

Definition at line 670 of file NumericalDefiniteIntegral.cpp.

    {
      if( 0 == F ) { Exception("QAG::invalid function") ; }

      // allocate workspace
      allocate () ;

      // integration limits
      const double low  = std::min ( m_a , m_b ) ;
      const double high = std::max ( m_a , m_b ) ;

      int ierror =
        gsl_integration_qag ( F->fn                    ,
                              low       ,         high ,
                              m_epsabs  ,     m_epsrel ,
                              size   () , (int) rule() , ws ()->ws ,
                              &m_result ,     &m_error             );

      if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAG " ,
                                __FILE__ , __LINE__ , ierror ) ; }

      // sign
      if ( m_a > m_b ) { m_result *= -1 ; }

      return m_result ;
    }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAG ( _Function *  fun ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGI ( _Function *  fun ) const

protected

Definition at line 567 of file NumericalDefiniteIntegral.cpp.

    {
      // check the argument
      if ( 0 == F    ) { Exception("::QAGI: invalid function"); }

      // allocate workspace
      allocate() ;

      int ierror = 0 ;

      if ( m_ia && m_ib )
        {
          ierror = gsl_integration_qagi  ( F->fn                ,
                                           m_epsabs  , m_epsrel ,
                                           size ()   , ws()->ws ,
                                           &m_result , &m_error ) ;
        }
      else if ( m_ia )
        {
          ierror = gsl_integration_qagil ( F->fn     , m_b      ,
                                           m_epsabs  , m_epsrel ,
                                           size ()   , ws()->ws ,
                                           &m_result , &m_error ) ;
        }
      else if ( m_ib )
        {
          ierror = gsl_integration_qagiu ( F->fn     , m_a      ,
                                           m_epsabs  , m_epsrel ,
                                           size ()   , ws()->ws ,
                                           &m_result , &m_error ) ;
        }
      else
        { Exception ( "::QAGI: invalid mode" ) ; };

      if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGI" ,
                                __FILE__ , __LINE__ , ierror ) ;}

      return m_result ;
    }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGI ( _Function *  fun ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGP ( _Function *  fun ) const

protected

Definition at line 611 of file NumericalDefiniteIntegral.cpp.

    {
      if( 0 == F ) { Exception("QAGP::invalid function") ; }

      // no known singular points ?
      if( points().empty() || !m_pdata ) { return QAGS( F ) ; }

      const size_t npts = points().size();

      // use GSL
      int ierror =
        gsl_integration_qagp ( F->fn                ,
                               m_pdata.get() , npts ,
                               m_epsabs  , m_epsrel ,
                               size ()   , ws()->ws ,
                               &m_result , &m_error ) ;

      if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGI " ,
                                __FILE__ , __LINE__ , ierror ) ; }

      // the sign
      if ( m_a > m_b ) { m_result *= -1 ; }

      return m_result ;
    }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGP ( _Function *  fun ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGS ( _Function *  fun ) const

protected

Definition at line 701 of file NumericalDefiniteIntegral.cpp.

    {
      if( 0 == F ) { Exception("QAG::invalid function") ; }

      if ( m_a == m_b )
        {
          m_result = 0    ;
          m_error  = 0    ;   // EXACT !
          return m_result ;
        }

      // allocate workspace
      allocate () ;

      // integration limits
      const double low  = std::min ( m_a , m_b ) ;
      const double high = std::max ( m_a , m_b ) ;

      int ierror =
        gsl_integration_qags ( F->fn                ,
                               low       , high     ,
                               m_epsabs  , m_epsrel ,
                               size   () , ws()->ws ,
                               &m_result , &m_error );

      if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGS " ,
                                __FILE__ , __LINE__ , ierror ) ; }

      // sign
      if ( m_a > m_b ) { m_result *= -1 ; }

      return m_result ;
    }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGS ( _Function *  fun ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QNG ( _Function *  fun ) const

protected

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QNG ( _Function *  fun ) const

protected

Definition at line 641 of file NumericalDefiniteIntegral.cpp.

    {
      if( 0 == F ) { Exception("QNG::invalid function") ; }

      // integration limits
      const double low  = std::min ( m_a , m_b ) ;
      const double high = std::max ( m_a , m_b ) ;

      size_t neval = 0 ;
      int ierror =
        gsl_integration_qng ( F->fn                 ,
                              low       ,      high ,
                              m_epsabs  ,  m_epsrel ,
                              &m_result , &m_error  , &neval  ) ;

      if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QNG " ,
                                __FILE__ , __LINE__ , ierror ) ; }

      // sign
      if ( m_a > m_b ) { m_result *= -1 ; }

      return m_result ;
    }

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

inline

previous result

Definition at line 331 of file NumericalDefiniteIntegral.h.

{ return    m_result ; }

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

inline

previous result

Definition at line 331 of file NumericalDefiniteIntegral.h.

{ return    m_result ; }

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::rule ( ) const

inline

integration rule

Definition at line 346 of file NumericalDefiniteIntegral.h.

{ return      m_rule ; }

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::rule ( ) const

inline

integration rule

Definition at line 346 of file NumericalDefiniteIntegral.h.

{ return      m_rule ; }

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::size ( ) const

inline

Definition at line 336 of file NumericalDefiniteIntegral.h.

{ return      m_size ; }

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::size ( ) const

inline

Definition at line 336 of file NumericalDefiniteIntegral.h.

{ return      m_size ; }

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::type ( ) const

inline

integration type

Definition at line 340 of file NumericalDefiniteIntegral.h.

{ return      m_type ; }

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::type ( ) const

inline

integration type

Definition at line 340 of file NumericalDefiniteIntegral.h.

{ return      m_type ; }

_Workspace* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::ws ( ) const

inlineprotected

Definition at line 364 of file NumericalDefiniteIntegral.h.

      { return m_ws.get() ; };

_Workspace* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::ws ( ) const

inlineprotected

Definition at line 364 of file NumericalDefiniteIntegral.h.

      { return m_ws.get() ; };

Member Data Documentation

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_a

private

Definition at line 392 of file NumericalDefiniteIntegral.h.

Argument Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_argF

mutableprivate

Definition at line 414 of file NumericalDefiniteIntegral.h.

Argument Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_argument

mutableprivate

Definition at line 413 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_b

private

Definition at line 393 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_category

private

Definition at line 398 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_DIM

private

Definition at line 389 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_epsabs

private

Definition at line 404 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_epsrel

private

Definition at line 405 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_error

mutableprivate

Definition at line 408 of file NumericalDefiniteIntegral.h.

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

private

Definition at line 388 of file NumericalDefiniteIntegral.h.

bool Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ia

private

Definition at line 394 of file NumericalDefiniteIntegral.h.

bool Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ib

private

Definition at line 395 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_index

private

Definition at line 390 of file NumericalDefiniteIntegral.h.

std::unique_ptr< double[]> Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_pdata

private

Definition at line 402 of file NumericalDefiniteIntegral.h.

Points Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_points

private

Definition at line 401 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_result

mutableprivate

Definition at line 407 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_rule

private

Definition at line 399 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_size

private

Definition at line 410 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_type

private

Definition at line 397 of file NumericalDefiniteIntegral.h.

std::unique_ptr< _Workspace, gsl_ws_deleter > Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ws

mutableprivate

Definition at line 411 of file NumericalDefiniteIntegral.h.

---

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

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