Numerical integrator for $W(x) = e^{-x^{2}}$ . More...

#include <JQuadrature.hh>

Inheritance diagram for JTOOLS::JGaussHermite:

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
	JGaussHermite (const int n, const double eps=1.0e-12)
	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

Numerical integrator for $W(x) = e^{-x^{2}}$ .

Gauss-Hermite integration code is taken from reference: Numerical Recipes in C++, W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press.

Definition at line 249 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

◆ JGaussHermite()

JTOOLS::JGaussHermite::JGaussHermite	(	const int	n,
		const double	eps = 1.0e-12 )

inline

Constructor.

Parameters

n	number of points
eps	precision

Definition at line 259 of file JQuadrature.hh.

                                              :
      JQuadrature()
    {
      resize(n);
 
      const double pii = 1.0 / pow(PI,0.25);
 
      const int number_of_iterations = 100;
 
      const int M = (n + 1) / 2;
      
      double p0, p1, p2, pp;
      double z = 0.0;
      double z1;
      
      for (int i = 0; i < M; ++i) {
 
        switch (i) {
 
        case 0:
          z  = sqrt((double) (2*n+1))  -  1.85575 * pow((double) (2*n+1),-0.16667);
          break;
 
        case 1:
          z -= 1.14 * pow((double) n,0.426) / z;
          break;
 
        case 2:
          z  = 1.86*z + 0.86*at( 0 ).getX();
          break;
 
        case 3:
          z  = 1.91*z + 0.91*at( 1 ).getX();
          break;
 
        default:
          z  = 2.00*z + 1.00*at(i-2).getX();
          break;
        }
 
        for (int k = 0; k != number_of_iterations; ++k) {
          
          p1 = 0.0;
          p2 = pii;
          
          // recurrence relation
          
          for (int j = 0; j < n; ++j) {
            p0 = p1;
            p1 = p2;
            p2 = z * sqrt(2.0/(double) (j+1)) * p1  -  sqrt((double) j / (double) (j+1)) * p0;
          }
          
          pp = sqrt((double) (2*n)) * p1;
          
          z1 = z;
          z  = z1 - p2/pp;
 
          if (fabs(z-z1) < eps)
            break;
        } 
 
        const double y = 2.0 / (pp*pp);
 
        at(  i  ) = JElement2D_t(-z,y);
        at(n-i-1) = JElement2D_t(+z,y);
      }
    }

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

◆ JGaussHermite()

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