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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.

## Classes
struct | _Function
struct | _Workspace
## 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

## 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

Definition at line 110 of file NumericalDefiniteIntegral.cpp.

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

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

        }

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

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

standard constructor

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 165 of file NumericalDefiniteIntegral.cpp.

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

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

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

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

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

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

Definition at line 252 of file NumericalDefiniteIntegral.cpp.

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

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

        }

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

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

- 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 321 of file NumericalDefiniteIntegral.cpp.

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

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

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

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

- 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 386 of file NumericalDefiniteIntegral.cpp.

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

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

        }

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

copy constructor

Definition at line 428 of file NumericalDefiniteIntegral.cpp.

          : AbsFunction ()
          , m_function  ( right.m_function->clone() )
          , m_DIM       ( right.m_DIM      )
          , m_index     ( right.m_index    )
          , m_a         ( right.m_a        )
          , m_b         ( right.m_b        )
          , m_ia        ( right.m_ia       )
          , m_ib        ( right.m_ib       )
          , m_type      ( right.m_type     )
          , m_category  ( right.m_category )
          , m_rule      ( right.m_rule     )
          , m_points    ( right.m_points   )
          , m_pdata     ( 0                )
          , 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_argF      ( right.m_argF     )
        {
          if( 0 != right.m_pdata )
            {
              m_pdata = new double[m_points.size()] ;
              std::copy( m_points.begin() , m_points.end() , m_pdata );
            }
        }

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

destructor

Definition at line 458 of file NumericalDefiniteIntegral.cpp.

        {
          if( 0 != m_function ) { delete   m_function ; m_function = 0 ; }
          if( 0 != m_pdata    ) { delete[] m_pdata    ; m_pdata    = 0 ; }
        }

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

## Member Function Documentation

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

integration limit

Definition at line 322 of file NumericalDefiniteIntegral.h.

    { return         m_a ; }

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

allocate the integration workspace

Definition at line 574 of file NumericalDefiniteIntegral.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 ;
        }

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

Definition at line 323 of file NumericalDefiniteIntegral.h.

    { return         m_b ; }

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

integration category

Definition at line 344 of file NumericalDefiniteIntegral.h.

    { return  m_category ; }

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

dimensionality of the problem

Definition at line 304 of file NumericalDefiniteIntegral.h.

    { return m_DIM ; }

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

absolute precision

Definition at line 327 of file NumericalDefiniteIntegral.h.

    { return    m_epsabs ; }

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

relatiove precision

Definition at line 329 of file NumericalDefiniteIntegral.h.

    { return    m_epsrel ; }

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

evaluate of previous error

Definition at line 334 of file NumericalDefiniteIntegral.h.

    { return     m_error ; }

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

Definition at line 468 of file NumericalDefiniteIntegral.cpp.

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

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

accessor to the function itself

Definition at line 320 of file NumericalDefiniteIntegral.h.

    { return *m_function ; }

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

Does this function have an analytic derivative?

Definition at line 312 of file NumericalDefiniteIntegral.h.

    { return true ;}

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

Function value.

evaluate the function

Definition at line 481 of file NumericalDefiniteIntegral.cpp.

        {
          // reset the result and the error
          m_result = GSL_NEGINF ;
          m_error  = GSL_POSINF ;

          // check the argument
          if( 1 != m_DIM ) { Exception ( "operator(): invalid argument size " ) ; };

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

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

Function value.

evaluate the function

Definition at line 514 of file NumericalDefiniteIntegral.cpp.

        {
          // reset the result and the error
          m_result = GSL_NEGINF ;
          m_error  = GSL_POSINF ;

          // check the argument
          if( argument.dimension() != m_DIM )
            { Exception ( "operator(): invalid argument size " ) ; };

          // copy the argument

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

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

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

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

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

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

          return 0 ;
        }

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

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

Derivatives.

Definition at line 499 of file NumericalDefiniteIntegral.cpp.

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

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

known singularities

Definition at line 325 of file NumericalDefiniteIntegral.h.

    { return    m_points ; }

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

Definition at line 692 of file NumericalDefiniteIntegral.cpp.

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

          // allocate workspace
          if( 0 == ws () ) { allocate () ; }

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

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

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

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

          return m_result ;
        }

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

Definition at line 589 of file NumericalDefiniteIntegral.cpp.

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

          // allocate workspace
          if ( 0 == ws() ) { allocate() ; }

          int ierror = 0 ;

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

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

          return m_result ;
        }

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

Definition at line 633 of file NumericalDefiniteIntegral.cpp.

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

          // no known singular points ?
          if( points().empty() || 0 == m_pdata ) { return QAGS( F ) ; }

          const size_t npts = points().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( "NumericalDefiniteIntegral::QAGI " ,
                                    __FILE__ , __LINE__ , ierror ) ; }

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

          return m_result ;
        }

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

Definition at line 723 of file NumericalDefiniteIntegral.cpp.

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

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

          // allocate workspace
          if( 0 == ws () ) { allocate () ; }

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

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

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

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

          return m_result ;
        }

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

Definition at line 663 of file NumericalDefiniteIntegral.cpp.

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

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

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

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

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

          return m_result ;
        }

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

previous result

Definition at line 332 of file NumericalDefiniteIntegral.h.

    { return    m_result ; }

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

integration rule

Definition at line 347 of file NumericalDefiniteIntegral.h.

    { return      m_rule ; }

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

Definition at line 337 of file NumericalDefiniteIntegral.h.

    { return      m_size ; }

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

integration type

Definition at line 341 of file NumericalDefiniteIntegral.h.

    { return      m_type ; }

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

Definition at line 365 of file NumericalDefiniteIntegral.h.

          { return m_ws ; };

## Member Data Documentation

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

Definition at line 386 of file NumericalDefiniteIntegral.h.

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

Definition at line 408 of file NumericalDefiniteIntegral.h.

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

Definition at line 407 of file NumericalDefiniteIntegral.h.

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

Definition at line 387 of file NumericalDefiniteIntegral.h.

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

Definition at line 392 of file NumericalDefiniteIntegral.h.

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

Definition at line 383 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_error`[mutable, private]`

Definition at line 402 of file NumericalDefiniteIntegral.h.

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

Definition at line 382 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.

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

Definition at line 384 of file NumericalDefiniteIntegral.h.

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

Definition at line 396 of file NumericalDefiniteIntegral.h.

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

Definition at line 395 of file NumericalDefiniteIntegral.h.

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

Definition at line 401 of file NumericalDefiniteIntegral.h.

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

Definition at line 393 of file NumericalDefiniteIntegral.h.

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

Definition at line 404 of file NumericalDefiniteIntegral.h.

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

Definition at line 391 of file NumericalDefiniteIntegral.h.

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

Definition at line 405 of file NumericalDefiniteIntegral.h.

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

- /afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v22r4/GaudiGSL/GaudiMath/NumericalDefiniteIntegral.h
- /afs/cern.ch/sw/Gaudi/releases/GAUDI/GAUDI_v22r4/GaudiGSL/src/Lib/NumericalDefiniteIntegral.cpp

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