The simple class for numerical integrations. More...

#include </scratch/z5/marcocle/GaudiDocs/lhcb-release/825/GAUDI/GAUDI_v26r3/InstallArea/x86_64-slc6-gcc48-opt/include/GaudiMath/NumericalIndefiniteIntegral.h>

Inheritance diagram for Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral:

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Collaboration diagram for Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral:

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Classes
struct	_Function

struct	_Workspace

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
	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const GaudiMath::Integration::Type type=GaudiMath::Integration::Adaptive, const GaudiMath::Integration::KronrodRule rule=GaudiMath::Integration::Default, const double epsabs=1e-10, const double epsrel=1.e-7, const size_t size=1000)
	From CLHEP/GenericFunctions. More...

	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const Points &points, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	standard constructor More...

	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	standard constructor The function, created with this constructor evaluates following indefinite integral: More...

	NumericalIndefiniteIntegral (const NumericalIndefiniteIntegral &)
	copy constructor More...

virtual	~NumericalIndefiniteIntegral ()
	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...

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::Limit	limit () const
	integration limit More...

GaudiMath::Integration::Type	type () const
	integration type More...

GaudiMath::Integration::Category	category () const
	integration category More...

GaudiMath::Integration::KronrodRule	rule () const
	integration rule More...

	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const GaudiMath::Integration::Type type=GaudiMath::Integration::Adaptive, const GaudiMath::Integration::KronrodRule rule=GaudiMath::Integration::Default, const double epsabs=1e-10, const double epsrel=1.e-7, const size_t size=1000)
	From CLHEP/GenericFunctions. More...

	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const double a, const Points &points, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	standard constructor More...

	NumericalIndefiniteIntegral (const AbsFunction &function, const size_t index, const GaudiMath::Integration::Limit limit=GaudiMath::Integration::VariableHighLimit, const double epsabs=1e-9, const double epsrel=1.e-6, const size_t size=1000)
	standard constructor The function, created with this constructor evaluates following indefinite integral: More...

	NumericalIndefiniteIntegral (const NumericalIndefiniteIntegral &)
	copy constructor More...

virtual	~NumericalIndefiniteIntegral ()
	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...

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::Limit	limit () const
	integration limit More...

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
	NumericalIndefiniteIntegral ()

NumericalIndefiniteIntegral &	operator= (const NumericalIndefiniteIntegral &)

	NumericalIndefiniteIntegral ()

NumericalIndefiniteIntegral &	operator= (const NumericalIndefiniteIntegral &)

Private Attributes
const AbsFunction *	m_function

size_t	m_DIM

size_t	m_index

double	m_a

GaudiMath::Integration::Limit	m_limit

GaudiMath::Integration::Type	m_type

GaudiMath::Integration::Category	m_category

GaudiMath::Integration::KronrodRule	m_rule

Points	m_points

double *	m_pdata

double	m_epsabs

double	m_epsrel

double	m_result

double	m_error

size_t	m_size

_Workspace *	m_ws

Argument	m_argument

Detailed Description

The simple class for numerical integrations.

It allows to evaluate following indefinite integrals:

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

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

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

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

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

Date: 2003-08-31

Definition at line 76 of file NumericalIndefiniteIntegral.h.

Member Typedef Documentation

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

typedef for vector of singular points

Definition at line 80 of file NumericalIndefiniteIntegral.h.

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

typedef for vector of singular points

Definition at line 80 of file NumericalIndefiniteIntegral.h.

Constructor & Destructor Documentation

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const GaudiMath::Integration::Limit	limit = `GaudiMath::Integration::VariableHighLimit`,
		const GaudiMath::Integration::Type	type = `GaudiMath::Integration::Adaptive`,
		const GaudiMath::Integration::KronrodRule	rule = `GaudiMath::Integration::Default`,
		const double	epsabs = `1e-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 evaluates following indefinite integral:

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

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 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	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
type	the integration type (adaptive, non-adaptive or adaptive for singular functions
key	Gauss-Kronrad integration rule
epsabs	absolute precision for integration
epsrel	relative precision for integration
lim	bisection limit

Standard constructor

Parameters

function	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
type	the integration type (adaptive, non-adaptive or adaptive for singular functions
key	Gauss-Kronrad integration rule
epsabs	absolute precision for integration
epsrel	relative precision for integration
lim	bisection limit

Definition at line 83 of file NumericalIndefiniteIntegral.cpp.

       : AbsFunction ()
       , m_function  ( function.clone()                    )
       , m_DIM       ( function.dimensionality()           )
       , m_index     ( index                               )
       , m_a         ( a                                   )
       , m_limit     ( limit                               )
       , m_type      ( type                                )
       , m_category  ( GaudiMath::Integration::Finite      )
       , m_rule      ( rule                                )
       //
       , m_points    (                                     )
       , m_pdata     ( 0                                   )
       //
       , m_epsabs    ( epsabs                              )
       , m_epsrel    ( epsrel                              )
       //
       , m_result    ( GSL_NEGINF                          )
       , m_error     ( GSL_POSINF                          )
       //
       , m_size      ( size                                )
       , m_ws        ( 0                                   )
       , m_argument  ( function.dimensionality()           )
     {
       if ( GaudiMath::Integration::Fixed == m_rule )
         { m_rule = GaudiMath::Integration::Default ; }
       if ( m_index >= m_DIM  )
         { Exception("::constructor: invalid variable index") ; }
     }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const Points &	points,
		const GaudiMath::Integration::Limit	limit = `GaudiMath::Integration::VariableHighLimit`,
		const double	epsabs = `1e-9`,
		const double	epsrel = `1.e-6`,
		const size_t	size = `1000`
	)

standard constructor

The function, created with this constructor evaluates following indefinite integral:

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

The integrand is assumed to have a known discontinuities

The GSL routine gsl_integration_qagp is used for integration

Parameters

function	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
points	list of known function singularities
epsabs	absolute precision for integration
epsrel	relative precision for integration
function	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
points	list of known function singularities
epsabs	absolute precision for integration
epsrel	relative precision for integration

Definition at line 133 of file NumericalIndefiniteIntegral.cpp.

       : AbsFunction ()
       , m_function  ( function.clone()          )
       , m_DIM       ( function.dimensionality() )
       , m_index     ( index                     )
       , m_a         ( a                         )
       , m_limit     ( limit                     )
       , m_type      ( GaudiMath::Integration::    Other )
       , m_category  ( GaudiMath::Integration:: Singular )
       , m_rule      ( GaudiMath::Integration::    Fixed )
       , m_points    ( points  )
       , m_pdata     ( 0       )
       , m_epsabs    ( epsabs  )
       , m_epsrel    ( epsrel  )
       //
       , m_result    ( GSL_NEGINF                          )
       , m_error     ( GSL_POSINF                          )
       //
       , m_size      ( size                                )
       , m_ws        ( 0                                   )
       , m_argument  ( function.dimensionality()           )
     {
       if ( m_index >= m_DIM )
         { Exception("::constructor: invalid variable index") ; }
       m_pdata = new double[ 2 + m_points.size() ] ;
       m_points.push_back( a ) ;
       std::sort( m_points.begin() , m_points.end() ) ;
       m_points.erase ( std::unique( m_points.begin () ,
                                     m_points.end   () ) , m_points.end() );
     }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const GaudiMath::Integration::Limit	limit = `GaudiMath::Integration::VariableHighLimit`,
		const double	epsabs = `1e-9`,
		const double	epsrel = `1.e-6`,
		const size_t	size = `1000`
	)

standard constructor The function, created with this constructor evaluates following indefinite integral:

standard constructor the integral limt is assumed to be infinity

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

The GSL routines gsl_integration_qagil and gsl_integration_qagiu are used for adapive integration

Parameters

function	the base function
index	the variable index
limit	flag to distinguisch low variable limit from high variable limit
singularities	list of known function singularities
function	the base function
index	the variable index
limit	flag to distinguisch low variable limit from high variable limit

Definition at line 181 of file NumericalIndefiniteIntegral.cpp.

       : AbsFunction ()
       , m_function  ( function.clone() )
       , m_DIM       ( function.dimensionality() )
       , m_index     ( index            )
       , m_a         ( GSL_NEGINF       ) // should not be used!
       , m_limit     ( limit            )
       , m_type      ( GaudiMath::Integration::    Other )
       , m_category  ( GaudiMath::Integration:: Infinite )
       , m_rule      ( GaudiMath::Integration::    Fixed )
       , m_points    (            )
       , m_pdata     ( 0          )
       , m_epsabs    ( epsabs     )
       , m_epsrel    ( epsrel     )
       , m_result    ( GSL_NEGINF )
       , m_error     ( GSL_POSINF )
       , m_size      ( size       )
       , m_ws        ( 0          )
       , m_argument  ( function.dimensionality()           )
     {
       if ( m_index >= m_DIM )
         { Exception("::constructor: invalid variable index") ; }
     }

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

copy constructor

Definition at line 216 of file NumericalIndefiniteIntegral.cpp.

       : AbsFunction ()
       , m_function  ( right.m_function->clone() )
       , m_DIM       ( right.m_DIM      )
       , m_index     ( right.m_index    )
       , m_a         ( right.m_a        )
       , m_limit     ( right.m_limit    )
       , m_type      ( right.m_type     )
       , m_category  ( right.m_category )
       , m_rule      ( right.m_rule     )
       , m_points    ( right.m_points   )
       , m_pdata     ( 0 )           // attention
       , m_epsabs    ( right.m_epsabs   )
       , m_epsrel    ( right.m_epsrel   )
       , m_result    ( GSL_NEGINF       )
       , m_error     ( GSL_POSINF       )
       , m_size      ( right.m_size     )
       , m_ws        ( 0                )
       , m_argument  ( right.m_argument )
     {
       m_pdata = new double[ 2 + m_points.size() ] ; // attention!
     }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::~NumericalIndefiniteIntegral ( )

virtual

destructor

Definition at line 244 of file NumericalIndefiniteIntegral.cpp.

     {
       if( 0 != m_ws )
         {
           gsl_integration_workspace_free ( m_ws->ws ) ;
           delete m_ws ;
           m_ws = 0 ;
         }
       if ( 0 != m_pdata    ) { delete m_pdata    ; m_pdata    = 0 ; }
       if ( 0 != m_function ) { delete m_function ; m_function = 0 ; }
     }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral ( )

private

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

From CLHEP/GenericFunctions.

Standard constructor The function, created with this constructor evaluates following indefinite integral:

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

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 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	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
type	the integration type (adaptive, non-adaptive or adaptive for singular functions
key	Gauss-Kronrad integration rule
epsabs	absolute precision for integration
epsrel	relative precision for integration
lim	bisection limit

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const double	a,
		const Points &	points,
		const GaudiMath::Integration::Limit	limit = `GaudiMath::Integration::VariableHighLimit`,
		const double	epsabs = `1e-9`,
		const double	epsrel = `1.e-6`,
		const size_t	size = `1000`
	)

standard constructor

The function, created with this constructor evaluates following indefinite integral:

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

The integrand is assumed to have a known discontinuities

The GSL routine gsl_integration_qagp is used for integration

Parameters

function	the base function
index	the variable index
a	integration limit
limit	flag to distinguisch low variable limit from high variable limit
points	list of known function singularities
epsabs	absolute precision for integration
epsrel	relative precision for integration

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral	(	const AbsFunction &	function,
		const size_t	index,
		const GaudiMath::Integration::Limit	limit = `GaudiMath::Integration::VariableHighLimit`,
		const double	epsabs = `1e-9`,
		const double	epsrel = `1.e-6`,
		const size_t	size = `1000`
	)

standard constructor The function, created with this constructor evaluates following indefinite integral:

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

for value of limit = VariableHighLimit and the integral

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

for value of limit = VariableLowLimit

The GSL routines gsl_integration_qagil and gsl_integration_qagiu are used for adapive integration

Parameters

function	the base function
index	the variable index
limit	flag to distinguisch low variable limit from high variable limit
singularities	list of known function singularities

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral ( const NumericalIndefiniteIntegral & )

copy constructor

virtual Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::~NumericalIndefiniteIntegral ( )

virtual

destructor

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::NumericalIndefiniteIntegral ( )

private

Member Function Documentation

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

inline

integration limit

Definition at line 296 of file NumericalIndefiniteIntegral.h.

296 { return m_a ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_a

double m_a

Definition: NumericalIndefiniteIntegral.h:363

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

inline

integration limit

Definition at line 296 of file NumericalIndefiniteIntegral.h.

296 { return m_a ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_a

double m_a

Definition: NumericalIndefiniteIntegral.h:363

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

protected

allocate the integration workspace

Definition at line 361 of file NumericalIndefiniteIntegral.cpp.

     {
       if ( 0 != m_ws ) { return m_ws; }
       gsl_integration_workspace* aux =
         gsl_integration_workspace_alloc( size () );
       if ( 0 == aux ) { Exception ( "allocate()::invalid workspace" ) ; };
       m_ws = new _Workspace() ;
       m_ws->ws = aux ;
       return m_ws ;
     }

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

protected

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

inline

integration category

Definition at line 320 of file NumericalIndefiniteIntegral.h.

320 { return m_category ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_category

GaudiMath::Integration::Category m_category

Definition: NumericalIndefiniteIntegral.h:367

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

inline

integration category

Definition at line 320 of file NumericalIndefiniteIntegral.h.

320 { return m_category ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_category

GaudiMath::Integration::Category m_category

Definition: NumericalIndefiniteIntegral.h:367

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

inlinevirtual

dimensionality of the problem

Definition at line 278 of file NumericalIndefiniteIntegral.h.

278 { return m_DIM ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_DIM

size_t m_DIM

Definition: NumericalIndefiniteIntegral.h:360

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

inlinevirtual

dimensionality of the problem

Definition at line 278 of file NumericalIndefiniteIntegral.h.

278 { return m_DIM ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_DIM

size_t m_DIM

Definition: NumericalIndefiniteIntegral.h:360

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

inline

absolute precision

Definition at line 300 of file NumericalIndefiniteIntegral.h.

300 { return m_epsabs ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsabs

double m_epsabs

Definition: NumericalIndefiniteIntegral.h:373

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

inline

absolute precision

Definition at line 300 of file NumericalIndefiniteIntegral.h.

300 { return m_epsabs ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsabs

double m_epsabs

Definition: NumericalIndefiniteIntegral.h:373

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

inline

relatiove precision

Definition at line 302 of file NumericalIndefiniteIntegral.h.

302 { return m_epsrel ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsrel

double m_epsrel

Definition: NumericalIndefiniteIntegral.h:374

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

inline

relatiove precision

Definition at line 302 of file NumericalIndefiniteIntegral.h.

302 { return m_epsrel ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsrel

double m_epsrel

Definition: NumericalIndefiniteIntegral.h:374

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

inline

evaluate of previous error

Definition at line 307 of file NumericalIndefiniteIntegral.h.

307 { return m_error ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_error

double m_error

Definition: NumericalIndefiniteIntegral.h:377

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

inline

evaluate of previous error

Definition at line 307 of file NumericalIndefiniteIntegral.h.

307 { return m_error ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_error

double m_error

Definition: NumericalIndefiniteIntegral.h:377

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

protected

Definition at line 261 of file NumericalIndefiniteIntegral.cpp.

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

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

protected

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

inline

accessor to the function itself

Definition at line 294 of file NumericalIndefiniteIntegral.h.

294 { return *m_function ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_function

const AbsFunction * m_function

Definition: NumericalIndefiniteIntegral.h:359

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

inline

accessor to the function itself

Definition at line 294 of file NumericalIndefiniteIntegral.h.

294 { return *m_function ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_function

const AbsFunction * m_function

Definition: NumericalIndefiniteIntegral.h:359

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

inlinevirtual

Does this function have an analytic derivative?

Definition at line 286 of file NumericalIndefiniteIntegral.h.

286 { return true ;}

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

inlinevirtual

Does this function have an analytic derivative?

Definition at line 286 of file NumericalIndefiniteIntegral.h.

286 { return true ;}

GaudiMath::Integration::Limit Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::limit ( ) const

inline

integration limit

Definition at line 314 of file NumericalIndefiniteIntegral.h.

314 { return m_limit ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_limit

GaudiMath::Integration::Limit m_limit

Definition: NumericalIndefiniteIntegral.h:365

GaudiMath::Integration::Limit Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::limit ( ) const

inline

integration limit

Definition at line 314 of file NumericalIndefiniteIntegral.h.

314 { return m_limit ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_limit

GaudiMath::Integration::Limit m_limit

Definition: NumericalIndefiniteIntegral.h:365

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

virtual

Function value.

evaluate the function

Definition at line 274 of file NumericalIndefiniteIntegral.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::NumericalIndefiniteIntegral::operator() ( double argument ) const

virtual

Function value.

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

virtual

Function value.

evaluate the function

Definition at line 314 of file NumericalIndefiniteIntegral.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];}}
 
       // create the helper object
       GSL_Helper helper( *m_function , m_argument , 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
       else 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::NumericalIndefiniteIntegral::operator() ( const Argument & argument ) const

virtual

Function value.

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

private

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

private

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

virtual

Derivatives.

Definition at line 292 of file NumericalIndefiniteIntegral.cpp.

     {
       if      ( idx >= m_DIM   )
         { Exception ( "::partial(i): invalid variable index " ) ; };
       if      ( idx != m_index )
         {
           const AbsFunction& aux = NumericalDerivative( *this , idx ) ;
           return Genfun::FunctionNoop( &aux ) ;
         }
       else if ( GaudiMath::Integration::VariableLowLimit == limit () )
         {
           const AbsFunction& aux = -1 * function() ;
           return Genfun::FunctionNoop( &aux ) ;
         }
       const AbsFunction& aux = function() ;
       return Genfun::FunctionNoop( &aux ) ;
     }

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

virtual

Derivatives.

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

inline

known singularities

Definition at line 298 of file NumericalIndefiniteIntegral.h.

298 { return m_points ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_points

Points m_points

Definition: NumericalIndefiniteIntegral.h:370

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

inline

known singularities

Definition at line 298 of file NumericalIndefiniteIntegral.h.

298 { return m_points ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_points

Points m_points

Definition: NumericalIndefiniteIntegral.h:370

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

protected

Definition at line 507 of file NumericalIndefiniteIntegral.cpp.

     {
       if( 0 == F ) { Exception("QAG::invalid function") ; }
 
       const double x = m_argument[m_index] ;
       if ( m_a == x  )
         {
           m_result = 0    ;
           m_error  = 0    ;   // EXACT !
           return m_result ;
         }
 
       // allocate workspace
       if( 0 == ws () ) { allocate () ; }
 
       // integration limits
       const double a = std::min ( m_a , x ) ;
       const double b = std::max ( m_a , x ) ;
 
       int ierror =
         gsl_integration_qag ( F->fn                    ,
                               a         ,            b ,
                               m_epsabs  ,     m_epsrel ,
                               size   () , (int) rule() , ws ()->ws ,
                               &m_result ,     &m_error             );
 
       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QAG " ,
                                 __FILE__ , __LINE__ , ierror ) ; }
 
       // sign
       if      ( GaudiMath::Integration::VariableHighLimit == limit()
                 &&  x < m_a  ) { m_result *= -1 ; }
       else if ( GaudiMath::Integration::VariableLowLimit  == limit()
                 &&  x > m_a  ) { m_result *= -1 ; }
 
       return m_result ;
     }

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

protected

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

protected

Definition at line 376 of file NumericalIndefiniteIntegral.cpp.

     {
       // check the argument
       if( 0 == F ) { Exception("::QAGI: invalid function"); }
 
       const double x = m_argument[m_index] ;
 
       // allocate workspace
       if( 0 == ws() ) { allocate() ; }
 
       int ierror = 0 ;
       switch ( limit() )
         {
         case GaudiMath::Integration::VariableLowLimit  :
           ierror = gsl_integration_qagiu ( F->fn     , x        ,
                                            m_epsabs  , m_epsrel ,
                                            size ()   , ws()->ws ,
                                            &m_result , &m_error ) ; break ;
         case GaudiMath::Integration::VariableHighLimit :
           ierror = gsl_integration_qagil ( F->fn     , x        ,
                                            m_epsabs  , m_epsrel ,
                                            size ()   , ws()->ws ,
                                            &m_result , &m_error ) ; break ;
         default :
           Exception ( "::QAGI: invalid mode" ) ;
         };
 
       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QAGI" ,
                                 __FILE__ , __LINE__ , ierror ) ;}
 
       return m_result ;
     }

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

protected

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

protected

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

protected

Definition at line 413 of file NumericalIndefiniteIntegral.cpp.

     {
       if( 0 == F ) { Exception("QAGP::invalid function") ; }
 
       const double x = m_argument[m_index] ;
       if ( m_a == x  )
         {
           m_result = 0    ;
           m_error  = 0    ;   // EXACT !
           return m_result ;
         }
 
       // no known singular points ?
       if( points().empty() ) { return QAGS( F ) ; }
 
       // integration limits
       const double a = std::min ( m_a , x ) ;
       const double b = std::max ( m_a , x ) ;
 
       // "active" singular points
       Points::const_iterator lower =
         std::lower_bound ( points().begin() , points().end() , a ) ;
       Points::const_iterator upper =
         std::upper_bound ( points().begin() , points().end() , b ) ;
 
       Points pnts ( upper - lower ) ;
       std::copy( lower , upper , pnts.begin() );
       if ( *lower != a       ) { pnts.insert( pnts.begin () , a ) ; }
       if ( *upper != b       ) { pnts.insert( pnts.end   () , b ) ; }
       std::copy( pnts.begin() , pnts.end() , m_pdata );
       const size_t npts = pnts.size() ;
 
       // use GSL
       int ierror =
         gsl_integration_qagp ( F->fn                ,
                                m_pdata   , npts     ,
                                m_epsabs  , m_epsrel ,
                                size ()   , ws()->ws ,
                                &m_result , &m_error ) ;
 
       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QAGI " ,
                                 __FILE__ , __LINE__ , ierror ) ; }
 
       // sign
       if      ( GaudiMath::Integration::VariableHighLimit == limit()
                 &&  x < m_a  ) { m_result *= -1 ; }
       else if ( GaudiMath::Integration::VariableLowLimit  == limit()
                 &&  x > m_a  ) { m_result *= -1 ; }
 
       return m_result ;
     }

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

protected

Definition at line 549 of file NumericalIndefiniteIntegral.cpp.

     {
       if( 0 == F ) { Exception("QAG::invalid function") ; }
 
       const double x = m_argument[m_index] ;
       if ( m_a == x  )
         {
           m_result = 0    ;
           m_error  = 0    ;   // EXACT !
           return m_result ;
         }
 
       // allocate workspace
       if( 0 == ws () ) { allocate () ; }
 
       // integration limits
       const double a = std::min ( m_a , x ) ;
       const double b = std::max ( m_a , x ) ;
 
       int ierror =
         gsl_integration_qags ( F->fn                ,
                                a         , b        ,
                                m_epsabs  , m_epsrel ,
                                size   () , ws()->ws ,
                                &m_result , &m_error );
 
       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QAGS " ,
                                 __FILE__ , __LINE__ , ierror ) ; }
 
       // sign
       if      ( GaudiMath::Integration::VariableHighLimit == limit()
                 &&  x < m_a  ) { m_result *= -1 ; }
       else if ( GaudiMath::Integration::VariableLowLimit  == limit()
                 &&  x > m_a  ) { m_result *= -1 ; }
 
       return m_result ;
     }

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

protected

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

protected

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

protected

Definition at line 469 of file NumericalIndefiniteIntegral.cpp.

     {
       if( 0 == F ) { Exception("QNG::invalid function") ; }
 
       const double x = m_argument[m_index] ;
       if ( m_a == x  )
         {
           m_result = 0    ;
           m_error  = 0    ;   // EXACT !
           return m_result ;
         }
 
       // integration limits
       const double a = std::min ( m_a , x ) ;
       const double b = std::max ( m_a , x ) ;
 
       size_t neval = 0 ;
       int ierror =
         gsl_integration_qng ( F->fn                 ,
                               a         ,         b ,
                               m_epsabs  ,  m_epsrel ,
                               &m_result , &m_error  , &neval  ) ;
 
       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QNG " ,
                                 __FILE__ , __LINE__ , ierror ) ; }
 
       // sign
       if      ( GaudiMath::Integration::VariableHighLimit == limit()
                 &&  x < m_a  ) { m_result *= -1 ; }
       else if ( GaudiMath::Integration::VariableLowLimit  == limit()
                 &&  x > m_a  ) { m_result *= -1 ; }
 
       return m_result ;
     }

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

inline

previous result

Definition at line 305 of file NumericalIndefiniteIntegral.h.

305 { return m_result ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_result

double m_result

Definition: NumericalIndefiniteIntegral.h:376

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

inline

previous result

Definition at line 305 of file NumericalIndefiniteIntegral.h.

305 { return m_result ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_result

double m_result

Definition: NumericalIndefiniteIntegral.h:376

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

inline

integration rule

Definition at line 323 of file NumericalIndefiniteIntegral.h.

323 { return m_rule ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_rule

GaudiMath::Integration::KronrodRule m_rule

Definition: NumericalIndefiniteIntegral.h:368

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

inline

integration rule

Definition at line 323 of file NumericalIndefiniteIntegral.h.

323 { return m_rule ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_rule

GaudiMath::Integration::KronrodRule m_rule

Definition: NumericalIndefiniteIntegral.h:368

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

inline

Definition at line 310 of file NumericalIndefiniteIntegral.h.

310 { return m_size ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_size

size_t m_size

Definition: NumericalIndefiniteIntegral.h:379

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

inline

Definition at line 310 of file NumericalIndefiniteIntegral.h.

310 { return m_size ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_size

size_t m_size

Definition: NumericalIndefiniteIntegral.h:379

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

inline

integration type

Definition at line 317 of file NumericalIndefiniteIntegral.h.

317 { return m_type ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_type

GaudiMath::Integration::Type m_type

Definition: NumericalIndefiniteIntegral.h:366

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

inline

integration type

Definition at line 317 of file NumericalIndefiniteIntegral.h.

317 { return m_type ; }

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_type

GaudiMath::Integration::Type m_type

Definition: NumericalIndefiniteIntegral.h:366

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

inlineprotected

Definition at line 341 of file NumericalIndefiniteIntegral.h.

342 { return m_ws ; };

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_ws

_Workspace * m_ws

Definition: NumericalIndefiniteIntegral.h:380

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

inlineprotected

Definition at line 341 of file NumericalIndefiniteIntegral.h.

342 { return m_ws ; };

Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_ws

_Workspace * m_ws

Definition: NumericalIndefiniteIntegral.h:380

Member Data Documentation

double Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_a

private

Definition at line 363 of file NumericalIndefiniteIntegral.h.

Argument Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_argument

mutableprivate

Definition at line 382 of file NumericalIndefiniteIntegral.h.

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_category

private

Definition at line 367 of file NumericalIndefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_DIM

private

Definition at line 360 of file NumericalIndefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsabs

private

Definition at line 373 of file NumericalIndefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_epsrel

private

Definition at line 374 of file NumericalIndefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_error

mutableprivate

Definition at line 377 of file NumericalIndefiniteIntegral.h.

const AbsFunction * Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_function

private

Definition at line 359 of file NumericalIndefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_index

private

Definition at line 361 of file NumericalIndefiniteIntegral.h.

GaudiMath::Integration::Limit Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_limit

private

Definition at line 365 of file NumericalIndefiniteIntegral.h.

double * Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_pdata

private

Definition at line 371 of file NumericalIndefiniteIntegral.h.

Points Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_points

private

Definition at line 370 of file NumericalIndefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_result

mutableprivate

Definition at line 376 of file NumericalIndefiniteIntegral.h.

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_rule

private

Definition at line 368 of file NumericalIndefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_size

private

Definition at line 379 of file NumericalIndefiniteIntegral.h.

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_type

private

Definition at line 366 of file NumericalIndefiniteIntegral.h.

_Workspace * Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::m_ws

mutableprivate

Definition at line 380 of file NumericalIndefiniteIntegral.h.

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

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

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