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# Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral Class Reference

The simple class for numerical integrations. More...

`#include <NumericalIndefiniteIntegral.h>`

Collaboration diagram for Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral:
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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
| 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.
| 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
| 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:
| NumericalIndefiniteIntegral (const NumericalIndefiniteIntegral &)
| copy constructor
virtual | ~NumericalIndefiniteIntegral ()
| 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
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::Limit | limit () const
| integration limit
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
| 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:

Author:
  Vanya BELYAEV Ivan.Belyaev@itep.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.

## 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:

for value of `limit` = `VariableHighLimit` and the integral

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:

for value of `limit` = `VariableHighLimit` and the integral

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

for value of `limit` = `VariableHighLimit` and the integral

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]`

## Member Function Documentation

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

integration limit

Definition at line 296 of file NumericalIndefiniteIntegral.h.

    { return         m_a ; }

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 ;
        }

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

integration category

Definition at line 320 of file NumericalIndefiniteIntegral.h.

    { return  m_category ; }

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

dimensionality of the problem

Definition at line 278 of file NumericalIndefiniteIntegral.h.

    { return m_DIM ; }

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

absolute precision

Definition at line 300 of file NumericalIndefiniteIntegral.h.

    { return    m_epsabs ; }

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

relatiove precision

Definition at line 302 of file NumericalIndefiniteIntegral.h.

    { return    m_epsrel ; }

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

evaluate of previous error

Definition at line 307 of file NumericalIndefiniteIntegral.h.

    { return     m_error ; }

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 ;
        }

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

accessor to the function itself

Definition at line 294 of file NumericalIndefiniteIntegral.h.

    { return *m_function ; }

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

Does this function have an analytic derivative?

Definition at line 286 of file NumericalIndefiniteIntegral.h.

    { return true ;}

GaudiMath::Integration::Limit Genfun::GaudiMathImplementation::NumericalIndefiniteIntegral::limit | ( | ) | const`[inline]`

integration limit

Definition at line 314 of file NumericalIndefiniteIntegral.h.

    { return     m_limit ; }

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 ;
        }

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 );
        }

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 ) ;
        }

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

known singularities

Definition at line 298 of file NumericalIndefiniteIntegral.h.

    { return    m_points ; }

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::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::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::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.

    { return    m_result ; }

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

integration rule

Definition at line 323 of file NumericalIndefiniteIntegral.h.

    { return      m_rule ; }

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

Definition at line 310 of file NumericalIndefiniteIntegral.h.

    { return      m_size ; }

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

integration type

Definition at line 317 of file NumericalIndefiniteIntegral.h.

    { return      m_type ; }

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

Definition at line 341 of file NumericalIndefiniteIntegral.h.

          { return m_ws ; };

## Member Data Documentation

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

Definition at line 363 of file NumericalIndefiniteIntegral.h.

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

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`[mutable, private]`

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`[mutable, private]`

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`[mutable, private]`

Definition at line 380 of file NumericalIndefiniteIntegral.h.

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

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

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