| # Gaudi Framework, version v21r11 |

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# Genfun::GaudiMathImplementation::NumericalDefiniteIntegral Class Reference

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

`#include <NumericalDefiniteIntegral.h>`

Collaboration diagram for Genfun::GaudiMathImplementation::NumericalDefiniteIntegral:
[legend]

List of all members.

## Public Types
typedef std::vector< double > | Points
| typedef for vector of singular points
## 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.
| 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:.
| 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:.
| 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:.
| 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:.
| NumericalDefiniteIntegral (const NumericalDefiniteIntegral &)
| copy constructor
virtual | ~NumericalDefiniteIntegral ()
| destructor
virtual unsigned int | dimensionality () const
| dimensionality of the problem
virtual double | operator() (double argument) const
| Function value.
virtual double | operator() (const Argument &argument) const
| Function value.
virtual bool | hasAnalyticDerivative () const
| Does this function have an analytic derivative?
virtual Genfun::Derivative | partial (unsigned int index) const
| Derivatives.
const AbsFunction & | function () const
| accessor to the function itself
double | a () const
| integration limit
double | b () const
const Points & | points () const
| known singularities
double | epsabs () const
| absolute precision
double | epsrel () const
| relatiove precision
double | result () const
| previous result
double | error () const
| evaluate of previous error
size_t | size () const
GaudiMath::Integration::Type | type () const
| integration type
GaudiMath::Integration::Category | category () const
| integration category
GaudiMath::Integration::KronrodRule | rule () const
| integration rule
## 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
_Workspace * | ws () const
StatusCode | Exception (const std::string &message, const StatusCode &sc=StatusCode::FAILURE) const
## Private Member Functions
| NumericalDefiniteIntegral ()
NumericalDefiniteIntegral & | operator= (const NumericalDefiniteIntegral &)
## Private Attributes
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
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
Argument | m_argF
## Classes
struct | _Function
struct | _Workspace

## Detailed Description

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

Author:
  Vanya BELYAEV Ivan.Belyaev@itep.ru

Date:
  2003-08-31

Definition at line 72 of file NumericalDefiniteIntegral.h.

## Member Typedef Documentation

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

typedef for vector of singular points

Definition at line 76 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:

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

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

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 104 of file NumericalDefiniteIntegral.cpp.

    00113       : AbsFunction ()
    00114       , m_function  ( function.clone          ()    )
    00115       , m_DIM       ( 0                             )
    00116       , m_index     ( index                         )
    00117       , m_a         ( a      )
    00118       , m_b         ( b      )
    00119       , m_ia        ( false  )
    00120       , m_ib        ( false  )
    00121       , m_type      ( type   )
    00122       , m_category  ( GaudiMath::Integration::Finite )
    00123       , m_rule      ( rule       )
    00124       , m_points    (            )
    00125       , m_pdata     ( 0          )
    00126       , m_epsabs    ( epsabs     )
    00127       , m_epsrel    ( epsrel     )
    00128       , m_result    ( GSL_NEGINF )
    00129       , m_error     ( GSL_POSINF )
    00130       , m_size      ( size       )
    00131       , m_ws        ()
    00132       , m_argument  ()
    00133       , m_argF      ()
    00134     {
    00135       if ( GaudiMath::Integration::Fixed == m_rule )
    00136         { m_rule = GaudiMath::Integration::Default ; }
    00137       if ( function.dimensionality() < 2          )
    00138         { Exception("::constructor: invalid dimensionality ") ; }
    00139       if ( m_index >= function.dimensionality()   )
    00140         { Exception("::constructor: invalid variable index") ; }
    00141
    00142       m_DIM = function.dimensionality() - 1 ;
    00143       m_argument = Argument( m_DIM      ) ;
    00144       m_argF     = Argument( m_DIM + 1  ) ;
    00145
    00146     }

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

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 159 of file NumericalDefiniteIntegral.cpp.

    00167       : AbsFunction ()
    00168       , m_function  ( function.clone()             )
    00169       , m_DIM       ( 0                            )
    00170       , m_index     ( index                        )
    00171       , m_a         ( a                            )
    00172       , m_b         ( b                            )
    00173       , m_ia        ( false  )
    00174       , m_ib        ( false  )
    00175       , m_type      ( GaudiMath::Integration::    Other )
    00176       , m_category  ( GaudiMath::Integration:: Singular )
    00177       , m_rule      ( GaudiMath::Integration::    Fixed )
    00178       , m_points    ( points  )
    00179       , m_pdata     ( 0       )
    00180       , m_epsabs    ( epsabs  )
    00181       , m_epsrel    ( epsrel  )
    00182       //
    00183       , m_result    ( GSL_NEGINF                          )
    00184       , m_error     ( GSL_POSINF                          )
    00185       //
    00186       , m_size      ( size                                )
    00187       , m_ws        ( 0                                   )
    00188       , m_argument  ()
    00189       , m_argF      ()
    00190     {
    00191       if ( function.dimensionality() < 2          )
    00192         { Exception("::constructor: invalid dimensionality ") ; }
    00193       if ( m_index >= function.dimensionality()   )
    00194         { Exception("::constructor: invalid variable index") ; }
    00195
    00196       m_DIM = function.dimensionality() - 1 ;
    00197       m_argument = Argument( m_DIM      ) ;
    00198       m_argF     = Argument( m_DIM + 1  ) ;
    00199
    00200       const double l1 = std::min ( a , b ) ;
    00201       const double l2 = std::max ( a , b ) ;
    00202       m_points.push_back ( l1 ) ;
    00203       m_points.push_back ( l2 ) ;
    00204       std::sort ( m_points.begin() , m_points.end() ) ;
    00205       m_points.erase( std::unique( m_points.begin () ,
    00206                                    m_points.end   () ) ,
    00207                       m_points.end() );
    00208
    00209       Points::iterator lower =
    00210         std::lower_bound ( m_points.begin () , m_points.end () , l1 ) ;
    00211       m_points.erase     ( m_points.begin () , lower                ) ;
    00212       Points::iterator upper =
    00213         std::upper_bound ( m_points.begin () , m_points.end () , l2 ) ;
    00214       m_points.erase     ( upper             , m_points.end ()      ) ;
    00215
    00216       m_pdata = new double[ m_points.size() ] ;
    00217       std::copy( m_points.begin() , m_points.end() , m_pdata );
    00218     }

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:.

- 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

- 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 246 of file NumericalDefiniteIntegral.cpp.

    00253       : AbsFunction()
    00254       , m_function  ( function.clone()             )
    00255       , m_DIM       ( 0                            )
    00256       , m_index     ( index                        )
    00257       , m_a         ( a                            )
    00258       , m_b         ( GSL_POSINF                   )
    00259       , m_ia        ( false  )
    00260       , m_ib        ( true   )
    00261       , m_type      ( GaudiMath::Integration::    Other )
    00262       , m_category  ( GaudiMath::Integration:: Infinite )
    00263       , m_rule      ( GaudiMath::Integration::    Fixed )
    00264       , m_points    (         )
    00265       , m_pdata     ( 0       )
    00266       , m_epsabs    ( epsabs  )
    00267       , m_epsrel    ( epsrel  )
    00268       //
    00269       , m_result    ( GSL_NEGINF                          )
    00270       , m_error     ( GSL_POSINF                          )
    00271       //
    00272       , m_size      ( size                                )
    00273       , m_ws        ( 0                                   )
    00274       , m_argument  ()
    00275       , m_argF      ()
    00276     {
    00277       if ( function.dimensionality() < 2          )
    00278         { Exception("::constructor: invalid dimensionality ") ; }
    00279       if ( m_index >= function.dimensionality()   )
    00280         { Exception("::constructor: invalid variable index") ; }
    00281
    00282       m_DIM = function.dimensionality() - 1 ;
    00283       m_argument = Argument( m_DIM      ) ;
    00284       m_argF     = Argument( m_DIM + 1  ) ;
    00285
    00286     }

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:.

- 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

- 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 315 of file NumericalDefiniteIntegral.cpp.

    00322       : AbsFunction()
    00323       , m_function  ( function.clone()             )
    00324       , m_DIM       ( 0                            )
    00325       , m_index     ( index                        )
    00326       , m_a         ( GSL_NEGINF                   )
    00327       , m_b         ( b                            )
    00328       , m_ia        ( true   )
    00329       , m_ib        ( false  )
    00330       , m_type      ( GaudiMath::Integration::    Other )
    00331       , m_category  ( GaudiMath::Integration:: Infinite )
    00332       , m_rule      ( GaudiMath::Integration::    Fixed )
    00333       , m_points    (         )
    00334       , m_pdata     ( 0       )
    00335       , m_epsabs    ( epsabs  )
    00336       , m_epsrel    ( epsrel  )
    00337       //
    00338       , m_result    ( GSL_NEGINF                          )
    00339       , m_error     ( GSL_POSINF                          )
    00340       //
    00341       , m_size      ( size                                )
    00342       , m_ws        ( 0                                   )
    00343       , m_argument  ()
    00344       , m_argF      ()
    00345     {
    00346       if ( function.dimensionality() < 2          )
    00347         { Exception("::constructor: invalid dimensionality ") ; }
    00348       if ( m_index >= function.dimensionality()   )
    00349         { Exception("::constructor: invalid variable index") ; }
    00350
    00351       m_DIM = function.dimensionality() - 1 ;
    00352       m_argument = Argument( m_DIM      ) ;
    00353       m_argF     = Argument( m_DIM + 1  ) ;
    00354     }

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:.

- 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

- 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 380 of file NumericalDefiniteIntegral.cpp.

    00385       : AbsFunction()
    00386       , m_function  ( function.clone()             )
    00387       , m_DIM       ( 0      )
    00388       , m_index     ( index                        )
    00389       , m_a         ( GSL_NEGINF                   )
    00390       , m_b         ( GSL_POSINF                   )
    00391       , m_ia        ( true   )
    00392       , m_ib        ( true   )
    00393       , m_type      ( GaudiMath::Integration::    Other )
    00394       , m_category  ( GaudiMath::Integration:: Infinite )
    00395       , m_rule      ( GaudiMath::Integration::    Fixed )
    00396       , m_points    (         )
    00397       , m_pdata     ( 0       )
    00398       , m_epsabs    ( epsabs  )
    00399       , m_epsrel    ( epsrel  )
    00400       //
    00401       , m_result    ( GSL_NEGINF                          )
    00402       , m_error     ( GSL_POSINF                          )
    00403       //
    00404       , m_size      ( size                                )
    00405       , m_ws        ( 0                                   )
    00406       , m_argument  ()
    00407       , m_argF      ()
    00408     {
    00409       if ( function.dimensionality() < 2          )
    00410         { Exception("::constructor: invalid dimensionality ") ; }
    00411       if ( m_index >= function.dimensionality()   )
    00412         { Exception("::constructor: invalid variable index") ; }
    00413
    00414       m_DIM = function.dimensionality() - 1 ;
    00415       m_argument = Argument( m_DIM      ) ;
    00416       m_argF     = Argument( m_DIM + 1  ) ;
    00417
    00418     }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral | ( | const NumericalDefiniteIntegral & | right | ) |

copy constructor

Definition at line 422 of file NumericalDefiniteIntegral.cpp.

    00423       : AbsFunction ()
    00424       , m_function  ( right.m_function->clone() )
    00425       , m_DIM       ( right.m_DIM      )
    00426       , m_index     ( right.m_index    )
    00427       , m_a         ( right.m_a        )
    00428       , m_b         ( right.m_b        )
    00429       , m_ia        ( right.m_ia       )
    00430       , m_ib        ( right.m_ib       )
    00431       , m_type      ( right.m_type     )
    00432       , m_category  ( right.m_category )
    00433       , m_rule      ( right.m_rule     )
    00434       , m_points    ( right.m_points   )
    00435       , m_pdata     ( 0                )
    00436       , m_epsabs    ( right.m_epsabs   )
    00437       , m_epsrel    ( right.m_epsrel   )
    00438       , m_result    ( GSL_NEGINF       )
    00439       , m_error     ( GSL_POSINF       )
    00440       , m_size      ( right.m_size     )
    00441       , m_ws        ( 0                )
    00442       , m_argument  ( right.m_argument )
    00443       , m_argF      ( right.m_argF     )
    00444     {
    00445       if( 0 != right.m_pdata )
    00446         {
    00447           m_pdata = new double[m_points.size()] ;
    00448           std::copy( m_points.begin() , m_points.end() , m_pdata );
    00449         }
    00450     }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::~NumericalDefiniteIntegral | ( |  | ) | `[virtual]`

destructor

Definition at line 452 of file NumericalDefiniteIntegral.cpp.

    00453     {
    00454       if( 0 != m_function ) { delete m_function ; m_function = 0 ; }
    00455       if( 0 != m_pdata    ) { delete m_pdata    ; m_pdata    = 0 ; }
    00456     }

Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::NumericalDefiniteIntegral | ( |  | ) | `[private]`

## Member Function Documentation

virtual unsigned int Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::dimensionality | ( |  | ) | const`[inline, virtual]`

dimensionality of the problem

Definition at line 304 of file NumericalDefiniteIntegral.h.

    00304 { return m_DIM ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::operator() | ( | double | argument | ) | const`[virtual]`

Function value.

evaluate the function

Definition at line 475 of file NumericalDefiniteIntegral.cpp.

    00476     {
    00477       // reset the result and the error
    00478       m_result = GSL_NEGINF ;
    00479       m_error  = GSL_POSINF ;
    00480
    00481       // check the argument
    00482       if( 1 != m_DIM ) { Exception ( "operator(): invalid argument size " ) ; };
    00483
    00484       m_argument[0] = argument ;
    00485       return (*this) ( m_argument );
    00486     }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::operator() | ( | const Argument & | argument | ) | const`[virtual]`

Function value.

evaluate the function

Definition at line 508 of file NumericalDefiniteIntegral.cpp.

    00509     {
    00510       // reset the result and the error
    00511       m_result = GSL_NEGINF ;
    00512       m_error  = GSL_POSINF ;
    00513
    00514       // check the argument
    00515       if( argument.dimension() != m_DIM )
    00516         { Exception ( "operator(): invalid argument size " ) ; };
    00517
    00518       // copy the argument
    00519
    00520       for( size_t i  = 0 ; i < m_DIM ; ++i )
    00521         {
    00522           m_argument [i] = argument [i] ;
    00523           const size_t j =  i < m_index ? i : i + 1 ;
    00524           m_argF     [j] = argument [i] ;
    00525         };
    00526
    00527       // create the helper object
    00528       GSL_Helper helper( *m_function , m_argF , m_index );
    00529
    00530       // use GSL to evaluate the numerical derivative
    00531       gsl_function F ;
    00532       F.function = &GSL_Adaptor ;
    00533       F.params   = &helper                 ;
    00534       _Function F1    ;
    00535       F1.fn      = &F ;
    00536
    00537       if        (  GaudiMath::Integration::Infinite         == category () )
    00538         { return   QAGI ( &F1 ) ; }                                // RETURN
    00539
    00540       if ( m_a == m_b )
    00541         {
    00542           m_result = 0    ; m_error  = 0    ;                      // EXACT
    00543           return m_result ;                                       // RETURN
    00544         }
    00545
    00546       if        (  GaudiMath::Integration::Singular         == category () )
    00547          { return   QAGP ( &F1 ) ; }                                // RETURN
    00548       else if   (  GaudiMath::Integration::Finite           == category () )
    00549         if      (  GaudiMath::Integration::NonAdaptive      == type     () )
    00550           { return QNG  ( &F1 ) ; }                                // RETURN
    00551         else if (  GaudiMath::Integration::Adaptive         == type     () )
    00552           { return QAG  ( &F1 ) ; }                                // RETURN
    00553         else if (  GaudiMath::Integration::AdaptiveSingular == type     () )
    00554           { return QAGS ( &F1 ) ; }                                // RETURN
    00555         else
    00556           { Exception ( "::operator(): invalid type "  ); }
    00557       else
    00558         { Exception ( "::operator(): invalid category "  ); }
    00559
    00560       return 0 ;
    00561     }

virtual bool Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::hasAnalyticDerivative | ( |  | ) | const`[inline, virtual]`

Does this function have an analytic derivative?

Definition at line 312 of file NumericalDefiniteIntegral.h.

    00312 { return true ;}

Genfun::Derivative Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::partial | ( | unsigned int | index | ) | const`[virtual]`

Derivatives.

Definition at line 493 of file NumericalDefiniteIntegral.cpp.

    00494     {
    00495       if      ( idx >= m_DIM   )
    00496         { Exception ( "::partial(i): invalid variable index " ) ; };
    00497       //
    00498       const AbsFunction& aux = NumericalDerivative( *this , idx ) ;
    00499       return Genfun::FunctionNoop( &aux ) ;
    00500     }

const AbsFunction& Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::function | ( |  | ) | const`[inline]`

accessor to the function itself

Definition at line 320 of file NumericalDefiniteIntegral.h.

    00320 { return *m_function ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::a | ( |  | ) | const`[inline]`

integration limit

Definition at line 322 of file NumericalDefiniteIntegral.h.

    00322 { return         m_a ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::b | ( |  | ) | const`[inline]`

Definition at line 323 of file NumericalDefiniteIntegral.h.

    00323 { return         m_b ; }

const Points& Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::points | ( |  | ) | const`[inline]`

known singularities

Definition at line 325 of file NumericalDefiniteIntegral.h.

    00325 { return    m_points ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsabs | ( |  | ) | const`[inline]`

absolute precision

Definition at line 327 of file NumericalDefiniteIntegral.h.

    00327 { return    m_epsabs ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::epsrel | ( |  | ) | const`[inline]`

relatiove precision

Definition at line 329 of file NumericalDefiniteIntegral.h.

    00329 { return    m_epsrel ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::result | ( |  | ) | const`[inline]`

previous result

Definition at line 332 of file NumericalDefiniteIntegral.h.

    00332 { return    m_result ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::error | ( |  | ) | const`[inline]`

evaluate of previous error

Definition at line 334 of file NumericalDefiniteIntegral.h.

    00334 { return     m_error ; }

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::size | ( |  | ) | const`[inline]`

Definition at line 337 of file NumericalDefiniteIntegral.h.

    00337 { return      m_size ; }

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::type | ( |  | ) | const`[inline]`

integration type

Definition at line 341 of file NumericalDefiniteIntegral.h.

    00341 { return      m_type ; }

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::category | ( |  | ) | const`[inline]`

integration category

Definition at line 344 of file NumericalDefiniteIntegral.h.

    00344 { return  m_category ; }

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::rule | ( |  | ) | const`[inline]`

integration rule

Definition at line 347 of file NumericalDefiniteIntegral.h.

    00347 { return      m_rule ; }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGI | ( | _Function * | fun | ) | const`[protected]`

Definition at line 583 of file NumericalDefiniteIntegral.cpp.

    00584     {
    00585       // check the argument
    00586       if ( 0 == F    ) { Exception("::QAGI: invalid function"); }
    00587
    00588       // allocate workspace
    00589       if ( 0 == ws() ) { allocate() ; }
    00590
    00591       int ierror = 0 ;
    00592
    00593       if ( m_ia && m_ib )
    00594         {
    00595           ierror = gsl_integration_qagi  ( F->fn                ,
    00596                                            m_epsabs  , m_epsrel ,
    00597                                            size ()   , ws()->ws ,
    00598                                            &m_result , &m_error ) ;
    00599         }
    00600       else if ( m_ia )
    00601         {
    00602           ierror = gsl_integration_qagil ( F->fn     , m_b      ,
    00603                                            m_epsabs  , m_epsrel ,
    00604                                            size ()   , ws()->ws ,
    00605                                            &m_result , &m_error ) ;
    00606         }
    00607       else if ( m_ib )
    00608         {
    00609           ierror = gsl_integration_qagiu ( F->fn     , m_a      ,
    00610                                            m_epsabs  , m_epsrel ,
    00611                                            size ()   , ws()->ws ,
    00612                                            &m_result , &m_error ) ;
    00613         }
    00614       else
    00615         { Exception ( "::QAGI: invalid mode" ) ; };
    00616
    00617       if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGI" ,
    00618                                 __FILE__ , __LINE__ , ierror ) ;}
    00619
    00620       return m_result ;
    00621     }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGP | ( | _Function * | fun | ) | const`[protected]`

Definition at line 627 of file NumericalDefiniteIntegral.cpp.

    00628     {
    00629       if( 0 == F ) { Exception("QAGP::invalid function") ; }
    00630
    00631       // no known singular points ?
    00632       if( points().empty() || 0 == m_pdata ) { return QAGS( F ) ; }
    00633
    00634       const size_t npts = points().size();
    00635
    00636       // use GSL
    00637       int ierror =
    00638         gsl_integration_qagp ( F->fn                ,
    00639                                m_pdata   , npts     ,
    00640                                m_epsabs  , m_epsrel ,
    00641                                size ()   , ws()->ws ,
    00642                                &m_result , &m_error ) ;
    00643
    00644       if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGI " ,
    00645                                 __FILE__ , __LINE__ , ierror ) ; }
    00646
    00647       // the sign
    00648       if ( m_a > m_b ) { m_result *= -1 ; }
    00649
    00650       return m_result ;
    00651     }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QNG | ( | _Function * | fun | ) | const`[protected]`

Definition at line 657 of file NumericalDefiniteIntegral.cpp.

    00658     {
    00659       if( 0 == F ) { Exception("QNG::invalid function") ; }
    00660
    00661       // integration limits
    00662       const double low  = std::min ( m_a , m_b ) ;
    00663       const double high = std::max ( m_a , m_b ) ;
    00664
    00665       size_t neval = 0 ;
    00666       int ierror =
    00667         gsl_integration_qng ( F->fn                 ,
    00668                               low       ,      high ,
    00669                               m_epsabs  ,  m_epsrel ,
    00670                               &m_result , &m_error  , &neval  ) ;
    00671
    00672       if( ierror ) { gsl_error( "NumericalIndefiniteIntegral::QNG " ,
    00673                                 __FILE__ , __LINE__ , ierror ) ; }
    00674
    00675       // sign
    00676       if ( m_a > m_b ) { m_result *= -1 ; }
    00677
    00678       return m_result ;
    00679     }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAG | ( | _Function * | fun | ) | const`[protected]`

Definition at line 686 of file NumericalDefiniteIntegral.cpp.

    00687     {
    00688       if( 0 == F ) { Exception("QAG::invalid function") ; }
    00689
    00690       // allocate workspace
    00691       if( 0 == ws () ) { allocate () ; }
    00692
    00693       // integration limits
    00694       const double low  = std::min ( m_a , m_b ) ;
    00695       const double high = std::max ( m_a , m_b ) ;
    00696
    00697       int ierror =
    00698         gsl_integration_qag ( F->fn                    ,
    00699                               low       ,         high ,
    00700                               m_epsabs  ,     m_epsrel ,
    00701                               size   () , (int) rule() , ws ()->ws ,
    00702                               &m_result ,     &m_error             );
    00703
    00704       if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAG " ,
    00705                                 __FILE__ , __LINE__ , ierror ) ; }
    00706
    00707       // sign
    00708       if ( m_a > m_b ) { m_result *= -1 ; }
    00709
    00710       return m_result ;
    00711     }

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::QAGS | ( | _Function * | fun | ) | const`[protected]`

Definition at line 717 of file NumericalDefiniteIntegral.cpp.

    00718     {
    00719       if( 0 == F ) { Exception("QAG::invalid function") ; }
    00720
    00721       if ( m_a == m_b )
    00722         {
    00723           m_result = 0    ;
    00724           m_error  = 0    ;   // EXACT !
    00725           return m_result ;
    00726         }
    00727
    00728       // allocate workspace
    00729       if( 0 == ws () ) { allocate () ; }
    00730
    00731       // integration limits
    00732       const double low  = std::min ( m_a , m_b ) ;
    00733       const double high = std::max ( m_a , m_b ) ;
    00734
    00735       int ierror =
    00736         gsl_integration_qags ( F->fn                ,
    00737                                low       , high     ,
    00738                                m_epsabs  , m_epsrel ,
    00739                                size   () , ws()->ws ,
    00740                                &m_result , &m_error );
    00741
    00742       if( ierror ) { gsl_error( "NumericalDefiniteIntegral::QAGS " ,
    00743                                 __FILE__ , __LINE__ , ierror ) ; }
    00744
    00745       // sign
    00746       if ( m_a > m_b ) { m_result *= -1 ; }
    00747
    00748       return m_result ;
    00749     }

NumericalDefiniteIntegral::_Workspace * Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::allocate | ( |  | ) | const`[protected]`

allocate the integration workspace

Definition at line 568 of file NumericalDefiniteIntegral.cpp.

    00569     {
    00570       if ( 0 != m_ws ) { return m_ws; }
    00571       gsl_integration_workspace* aux =
    00572         gsl_integration_workspace_alloc( size () );
    00573       if ( 0 == aux ) { Exception ( "allocate()::invalid workspace" ) ; };
    00574       m_ws = new _Workspace() ;
    00575       m_ws->ws = aux ;
    00576       return m_ws ;
    00577     }

_Workspace* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::ws | ( |  | ) | const`[inline, protected]`

Definition at line 365 of file NumericalDefiniteIntegral.h.

    00366       { return m_ws ; };

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

Definition at line 462 of file NumericalDefiniteIntegral.cpp.

    00464     {
    00465       throw GaudiException( "NumericalDefiniteIntegral::" + message ,
    00466                             "*GaudiMath*" , sc ) ;
    00467       return sc ;
    00468     }

NumericalDefiniteIntegral& Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::operator= | ( | const NumericalDefiniteIntegral & |  | ) | `[private]`

## Member Data Documentation

const AbsFunction* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_function`[private]`

Definition at line 382 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_DIM`[private]`

Definition at line 383 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_index`[private]`

Definition at line 384 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_a`[private]`

Definition at line 386 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_b`[private]`

Definition at line 387 of file NumericalDefiniteIntegral.h.

bool Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ia`[private]`

Definition at line 388 of file NumericalDefiniteIntegral.h.

bool Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ib`[private]`

Definition at line 389 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::Type Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_type`[private]`

Definition at line 391 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::Category Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_category`[private]`

Definition at line 392 of file NumericalDefiniteIntegral.h.

GaudiMath::Integration::KronrodRule Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_rule`[private]`

Definition at line 393 of file NumericalDefiniteIntegral.h.

Points Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_points`[private]`

Definition at line 395 of file NumericalDefiniteIntegral.h.

double* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_pdata`[private]`

Definition at line 396 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_epsabs`[private]`

Definition at line 398 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_epsrel`[private]`

Definition at line 399 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_result`[mutable, private]`

Definition at line 401 of file NumericalDefiniteIntegral.h.

double Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_error`[mutable, private]`

Definition at line 402 of file NumericalDefiniteIntegral.h.

size_t Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_size`[private]`

Definition at line 404 of file NumericalDefiniteIntegral.h.

_Workspace* Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_ws`[mutable, private]`

Definition at line 405 of file NumericalDefiniteIntegral.h.

Argument Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_argument`[mutable, private]`

Definition at line 407 of file NumericalDefiniteIntegral.h.

Argument Genfun::GaudiMathImplementation::NumericalDefiniteIntegral::m_argF`[mutable, private]`

Definition at line 408 of file NumericalDefiniteIntegral.h.

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

- /afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v21r11/GaudiGSL/GaudiMath/NumericalDefiniteIntegral.h
- /afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v21r11/GaudiGSL/src/Lib/NumericalDefiniteIntegral.cpp