Type definition for numerical integration. More...

#include <JQuadrature.hh>

Inheritance diagram for JTOOLS::JQuadrature:

Public Types
typedef JElement_t::abscissa_type	abscissa_type

typedef JElement_t::ordinate_type	ordinate_type

typedef JElement2D_t	value_type

typedef JDistance< typename JElement_t::abscissa_type >	distance_type

typedef JCollection< JElement2D_t, JDistance< typename JElement_t::abscissa_type > >	collection_type

typedef std::vector< value_type >	container_type

typedef container_type::const_iterator	const_iterator

typedef container_type::const_reverse_iterator	const_reverse_iterator

typedef container_type::iterator	iterator

typedef container_type::reverse_iterator	reverse_iterator

typedef JCollectionElementTransformer< value_type >	transformer_type

typedef std::pair< const_iterator, bool >	pair_type

typedef JElement_t::abscissa_type	key_type

typedef JElement_t::ordinate_type	mapped_type

Public Member Functions
	JQuadrature ()
	Default constructor.

template<class JFunction_t >
	JQuadrature (const double xmin, const double xmax, const int nx, JFunction_t integral, const double eps=1.0e-4)
	General purpose constructor.

virtual void	clear () override
	Clear.

virtual const ordinate_type &	get (typename JClass< abscissa_type >::argument_type x) const override
	Get ordinate value.

virtual ordinate_type &	get (typename JClass< abscissa_type >::argument_type x) override
	Get ordinate value.

virtual int	getSize () const override
	Get number of elements.

virtual abscissa_type	getX (int index) const override
	Get abscissa value.

virtual abscissa_type	getXmin () const override
	Get minimal abscissa value.

virtual abscissa_type	getXmax () const override
	Get maximal abscissa value.

const ordinate_type &	getY (int index) const
	Get ordinate value.

ordinate_type &	getY (int index)
	Get ordinate value.

void	transform (const transformer_type &transformer)
	Transform collection.

void	sort ()
	Sort elements.

const_iterator	lower_bound (typename JClass< abscissa_type >::argument_type x) const
	Get first position of element `i`, where `x >= i->getX()`.

iterator	lower_bound (typename JClass< abscissa_type >::argument_type x)
	Get first position of element `i`, where `x >= i->getX()`.

pair_type	insert (const value_type &element)
	Insert element.

void	configure (const JAbstractCollection< abscissa_type > &bounds)
	Configure collection.

void	configure (const JAbstractCollection< abscissa_type > &bounds, typename JClass< ordinate_type >::argument_type value)
	Configure collection.

void	configure (const JAbstractCollection< abscissa_type > &bounds, const JFunction1D_t &function)
	Configure collection.

bool	is_compatible (const JCollection &collection) const
	Test whether collections are compatible.

bool	in_range (typename JClass< abscissa_type >::argument_type x) const
	Check if given abscissa is in range of this collection.

JCollection &	negate ()
	Negate collection.

JCollection &	add (const JCollection &collection)
	Add collection.

JCollection &	add (typename JClass< ordinate_type >::argument_type value)
	Add offset.

JCollection &	add (const JFunction1D_t &function)
	Add function.

JCollection &	sub (const JCollection &collection)
	Subtract collection.

JCollection &	sub (typename JClass< ordinate_type >::argument_type value)
	Subtract offset.

JCollection &	sub (const JFunction1D_t &function)
	Subtract function.

JCollection &	mul (const double value)
	Scale contents.

JFirst_t &	mul (const JSecond_t &object)
	Multiply with object.

JCollection &	div (const double value)
	Scale contents.

const JComparator &	getComparator () const
	Get comparator.

const mapped_type &	operator[] (typename JClass< key_type >::argument_type key) const
	Get mapped value.

mapped_type &	operator[] (typename JClass< key_type >::argument_type key)
	Get mapped value.

void	put (typename JClass< key_type > ::argument_type key, typename JClass< mapped_type >::argument_type value)
	Put pair-wise element (key,value) into collection.

bool	is_equal (const JAbstractCollection &collection) const
	Test whether abstract collections are equal.

Public Attributes
JDistance< typename JElement_t::abscissa_type >	getDistance
	Function object for distance evaluation.

Protected Member Functions
void	resize (typename container_type::size_type size)
	Resize collection.

Protected Attributes
JComparator	compare
	Function object for comparison.

Private Member Functions
void	erase ()

void	push_back ()

void	pop_back ()

Detailed Description

Type definition for numerical integration.

     \f[\displaystyle \int_{x_1}^{x_2} f(x) dx = \sum_{i=1}^{N} w_i f(x_i) \f]

The abscissa and ordinate values of the collection can be used as abscissa and weight values of the summation to approximately determine the integral of the function.

Definition at line 37 of file JQuadrature.hh.

Member Typedef Documentation

◆ abscissa_type

typedef JElement_t::abscissa_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::abscissa_type

inherited

Definition at line 82 of file JCollection.hh.

◆ ordinate_type

typedef JElement_t::ordinate_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::ordinate_type

inherited

Definition at line 83 of file JCollection.hh.

◆ value_type

typedef JElement2D_t JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::value_type

inherited

Definition at line 84 of file JCollection.hh.

◆ distance_type

typedef JDistance<typename JElement_t::abscissa_type> JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::distance_type

inherited

Definition at line 85 of file JCollection.hh.

◆ collection_type

typedef JCollection<JElement2D_t , JDistance<typename JElement_t::abscissa_type> > JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::collection_type

inherited

Definition at line 87 of file JCollection.hh.

◆ container_type

typedef std::vector<value_type> JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::container_type

inherited

Definition at line 89 of file JCollection.hh.

◆ const_iterator

typedef container_type::const_iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::const_iterator

inherited

Definition at line 91 of file JCollection.hh.

◆ const_reverse_iterator

typedef container_type::const_reverse_iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::const_reverse_iterator

inherited

Definition at line 92 of file JCollection.hh.

◆ iterator

typedef container_type::iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::iterator

inherited

Definition at line 93 of file JCollection.hh.

◆ reverse_iterator

typedef container_type::reverse_iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::reverse_iterator

inherited

Definition at line 94 of file JCollection.hh.

◆ transformer_type

typedef JCollectionElementTransformer<value_type> JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::transformer_type

inherited

Definition at line 96 of file JCollection.hh.

◆ pair_type

typedef std::pair<const_iterator, bool> JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::pair_type

inherited

Definition at line 97 of file JCollection.hh.

◆ key_type

typedef JElement_t::abscissa_type JTOOLS::JMappableCollection< JElement_t::abscissa_type , JElement_t::ordinate_type >::key_type

inherited

Definition at line 33 of file JMappableCollection.hh.

◆ mapped_type

typedef JElement_t::ordinate_type JTOOLS::JMappableCollection< JElement_t::abscissa_type , JElement_t::ordinate_type >::mapped_type

inherited

Definition at line 34 of file JMappableCollection.hh.

Constructor & Destructor Documentation

◆ JQuadrature() [1/2]

JTOOLS::JQuadrature::JQuadrature ( )

inline

Default constructor.

Definition at line 44 of file JQuadrature.hh.

45 {}

◆ JQuadrature() [2/2]

template<class JFunction_t >

JTOOLS::JQuadrature::JQuadrature	(	const double	xmin,
		const double	xmax,
		const int	nx,
		JFunction_t	integral,
		const double	eps = 1.0e-4 )

inline

General purpose constructor.

The template argument should correspond to a function requiring two arguments.
These two arguments should correspond to the lower and upper integration limit, respectively.
The given function should return the value of the integral between the two integration limits.

Parameters

xmin	minimal x
xmax	maximal x
nx	number of points
integral	integral
eps	precision

Definition at line 62 of file JQuadrature.hh.

    {
      double Xmin = xmin;
      double Xmax = xmax;
 
      const double Vmin = integral(Xmin, Xmax) / (double) nx;
    
      for (int i = 0; i != nx; ++i) {
      
        for (double xmin = Xmin, xmax = Xmax; ; ) {
          
          const double x = 0.5 * (xmin + xmax);
          const double v = integral(Xmin, x);
        
          if (fabs(Vmin - v)    < eps *  Vmin ||
              fabs(xmax - xmin) < eps * (Xmax - Xmin)) {
            
            const double __x = 0.5 * (Xmin + x);
            const double __y = Vmin / integral(__x);
          
            insert(JElement2D_t(__x,__y));
          
            Xmin = x;
            xmax = Xmax;
            
            break;
          }
          
          if (v < Vmin)
            xmin = x;
          else
            xmax = x;
        }
      }
    }

Member Function Documentation

◆ clear()

virtual void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::clear ( )

inlineoverridevirtualinherited

Clear.

Implements JTOOLS::JMappableCollection< JElement_t::abscissa_type, JElement_t::ordinate_type >.

Definition at line 150 of file JCollection.hh.

◆ get() [1/2]

virtual const ordinate_type & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::get ( typename JClass< abscissa_type >::argument_type x ) const

inlineoverridevirtualinherited

Get ordinate value.

Parameters

x	abscissa value

Returns: ordinate value

Implements JTOOLS::JMappableCollection< JElement_t::abscissa_type, JElement_t::ordinate_type >.

Definition at line 162 of file JCollection.hh.

◆ get() [2/2]

virtual ordinate_type & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::get ( typename JClass< abscissa_type >::argument_type x )

inlineoverridevirtualinherited

Get ordinate value.

Parameters

x	abscissa value

Returns: ordinate value

Implements JTOOLS::JMappableCollection< JElement_t::abscissa_type, JElement_t::ordinate_type >.

Definition at line 180 of file JCollection.hh.

◆ getSize()

virtual int JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getSize ( ) const

inlineoverridevirtualinherited

Get number of elements.

Returns: number of elements

Implements JTOOLS::JAbstractCollection< JElement_t::abscissa_type >.

Definition at line 197 of file JCollection.hh.

◆ getX()

virtual abscissa_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getX ( int index ) const

inlineoverridevirtualinherited

Get abscissa value.

Parameters

index index

Returns: abscissa value

Implements JTOOLS::JAbstractCollection< JElement_t::abscissa_type >.

Definition at line 209 of file JCollection.hh.

◆ getXmin()

virtual abscissa_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getXmin ( ) const

inlineoverridevirtualinherited

Get minimal abscissa value.

Returns: abscissa value

Implements JTOOLS::JAbstractCollection< JElement_t::abscissa_type >.

Definition at line 220 of file JCollection.hh.

◆ getXmax()

virtual abscissa_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getXmax ( ) const

inlineoverridevirtualinherited

Get maximal abscissa value.

Returns: abscissa value

Implements JTOOLS::JAbstractCollection< JElement_t::abscissa_type >.

Definition at line 231 of file JCollection.hh.

◆ getY() [1/2]

const ordinate_type & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getY ( int index ) const

inlineinherited

Get ordinate value.

Parameters

index index

Returns: ordinate value

Definition at line 244 of file JCollection.hh.

◆ getY() [2/2]

ordinate_type & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getY ( int index )

inlineinherited

Get ordinate value.

Parameters

index index

Returns: ordinate value

Definition at line 256 of file JCollection.hh.

◆ transform()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::transform ( const transformer_type & transformer )

inlineinherited

Transform collection.

Parameters

transformer element transformer

Definition at line 267 of file JCollection.hh.

◆ sort()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::sort ( )

inlineinherited

Sort elements.

Definition at line 280 of file JCollection.hh.

◆ lower_bound() [1/2]

const_iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::lower_bound ( typename JClass< abscissa_type >::argument_type x ) const

inlineinherited

Get first position of element i, where x >= i->getX().

Parameters

x	abscissa value

Returns: position of corresponding element

Definition at line 292 of file JCollection.hh.

◆ lower_bound() [2/2]

iterator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::lower_bound ( typename JClass< abscissa_type >::argument_type x )

inlineinherited

Get first position of element i, where x >= i->getX().

Parameters

x	abscissa value

Returns: position of corresponding element

Definition at line 304 of file JCollection.hh.

◆ insert()

pair_type JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::insert ( const value_type & element )

inlineinherited

Insert element.

Parameters

element element

Returns: (iterator, status), where status is true if inserted; else false

Definition at line 316 of file JCollection.hh.

◆ configure() [1/3]

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::configure ( const JAbstractCollection< abscissa_type > & bounds )

inlineinherited

Configure collection.

Parameters

bounds abscissa values

Definition at line 332 of file JCollection.hh.

◆ configure() [2/3]

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::configure	(	const JAbstractCollection< abscissa_type > &	bounds,
		typename JClass< ordinate_type >::argument_type	value )

inlineinherited

Configure collection.

Parameters

bounds	abscissa values
value	ordinate value

Definition at line 344 of file JCollection.hh.

◆ configure() [3/3]

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::configure	(	const JAbstractCollection< abscissa_type > &	bounds,
		const JFunction1D_t &	function )

inlineinherited

Configure collection.

Parameters

bounds	abscissa values
function	function

Definition at line 365 of file JCollection.hh.

◆ is_compatible()

bool JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::is_compatible ( const JCollection< JElement2D_t > & collection ) const

inlineinherited

Test whether collections are compatible.

Parameters

collection collection

Returns: true if collections are compatible; else false

Definition at line 394 of file JCollection.hh.

◆ in_range()

bool JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::in_range ( typename JClass< abscissa_type >::argument_type x ) const

inlineinherited

Check if given abscissa is in range of this collection.

Parameters

x	abscissa value

Returns: true if in tange: else false

Definition at line 437 of file JCollection.hh.

◆ negate()

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::negate ( )

inlineinherited

Negate collection.

Returns: this collection

Definition at line 452 of file JCollection.hh.

◆ add() [1/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::add ( const JCollection< JElement2D_t > & collection )

inlineinherited

Add collection.

Parameters

collection collection

Returns: this collection

Definition at line 468 of file JCollection.hh.

◆ add() [2/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::add ( typename JClass< ordinate_type >::argument_type value )

inlineinherited

Add offset.

Parameters

value offset

Returns: this collection

Definition at line 620 of file JCollection.hh.

◆ add() [3/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::add ( const JFunction1D_t & function )

inlineinherited

Add function.

Parameters

function function

Returns: this collection

Definition at line 653 of file JCollection.hh.

◆ sub() [1/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::sub ( const JCollection< JElement2D_t > & collection )

inlineinherited

Subtract collection.

Parameters

collection collection

Returns: this collection

Definition at line 528 of file JCollection.hh.

◆ sub() [2/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::sub ( typename JClass< ordinate_type >::argument_type value )

inlineinherited

Subtract offset.

Parameters

value offset

Returns: this collection

Definition at line 636 of file JCollection.hh.

◆ sub() [3/3]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::sub ( const JFunction1D_t & function )

inlineinherited

Subtract function.

Parameters

function function

Returns: this collection

Definition at line 670 of file JCollection.hh.

◆ mul() [1/2]

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::mul ( const double value )

inlineinherited

Scale contents.

Parameters

value multiplication factor

Returns: this collection

Definition at line 588 of file JCollection.hh.

◆ mul() [2/2]

template<class JFirst_t , class JSecond_t >

JFirst_t & JMATH::JMath< JFirst_t, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 354 of file JMath.hh.

    {
      return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
    }

◆ div()

JCollection & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::div ( const double value )

inlineinherited

Scale contents.

Parameters

value division factor

Returns: this collection

Definition at line 604 of file JCollection.hh.

◆ getComparator()

const JComparator & JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getComparator ( ) const

inlineinherited

Get comparator.

Returns: comparator

Definition at line 784 of file JCollection.hh.

◆ resize()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::resize ( typename container_type::size_type size )

inlineprotectedinherited

Resize collection.

Parameters

size size

Definition at line 808 of file JCollection.hh.

◆ erase()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::erase ( )

privateinherited

◆ push_back()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::push_back ( )

privateinherited

◆ pop_back()

void JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::pop_back ( )

privateinherited

◆ operator[]() [1/2]

const mapped_type & JTOOLS::JMappableCollection< JElement_t::abscissa_type , JElement_t::ordinate_type >::operator[] ( typename JClass< key_type >::argument_type key ) const

inlineinherited

Get mapped value.

Parameters

key key

Returns: value

Definition at line 73 of file JMappableCollection.hh.

◆ operator[]() [2/2]

mapped_type & JTOOLS::JMappableCollection< JElement_t::abscissa_type , JElement_t::ordinate_type >::operator[] ( typename JClass< key_type >::argument_type key )

inlineinherited

Get mapped value.

Parameters

key key

Returns: value

Definition at line 85 of file JMappableCollection.hh.

◆ put()

void JTOOLS::JMappableCollection< JElement_t::abscissa_type , JElement_t::ordinate_type >::put	(	typename JClass< key_type > ::argument_type	key,
		typename JClass< mapped_type >::argument_type	value )

inlineinherited

Put pair-wise element (key,value) into collection.

Parameters

key	key
value	value

Definition at line 97 of file JMappableCollection.hh.

◆ is_equal()

bool JTOOLS::JAbstractCollection< JElement_t::abscissa_type >::is_equal ( const JAbstractCollection< JElement_t::abscissa_type > & collection ) const

inlineinherited

Test whether abstract collections are equal.

Parameters

collection abstract collection

Returns: true if collections are equals; else false

Definition at line 72 of file JAbstractCollection.hh.

Member Data Documentation

◆ getDistance

JDistance<typename JElement_t::abscissa_type> JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::getDistance

inherited

Function object for distance evaluation.

Definition at line 793 of file JCollection.hh.

◆ compare

JComparator JTOOLS::JCollection< JElement2D_t , JDistance<typename JElement_t::abscissa_type> >::compare

protectedinherited

Function object for comparison.

Definition at line 800 of file JCollection.hh.

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

JQuadrature.hh

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ abscissa_type

◆ ordinate_type

◆ value_type

◆ distance_type

◆ collection_type

◆ container_type

◆ const_iterator

◆ const_reverse_iterator

◆ iterator

◆ reverse_iterator

◆ transformer_type

◆ pair_type

◆ key_type

◆ mapped_type

Constructor & Destructor Documentation

◆ JQuadrature() [1/2]

◆ JQuadrature() [2/2]

Member Function Documentation

◆ clear()

◆ get() [1/2]

◆ get() [2/2]

◆ getSize()

◆ getX()

◆ getXmin()

◆ getXmax()

◆ getY() [1/2]

◆ getY() [2/2]

◆ transform()

◆ sort()

◆ lower_bound() [1/2]

◆ lower_bound() [2/2]

◆ insert()

◆ configure() [1/3]

◆ configure() [2/3]

◆ configure() [3/3]

◆ is_compatible()

◆ in_range()

◆ negate()

◆ add() [1/3]

◆ add() [2/3]

◆ add() [3/3]

◆ sub() [1/3]

◆ sub() [2/3]

◆ sub() [3/3]

◆ mul() [1/2]

◆ mul() [2/2]

◆ div()

◆ getComparator()

◆ resize()

◆ erase()

◆ push_back()

◆ pop_back()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ put()

◆ is_equal()

Member Data Documentation

◆ getDistance

◆ compare