Template specialisation for function evaluation of Legendre polynome of quaternions for defined number of degrees. More...

#include <JEigen3D.hh>

Inheritance diagram for JMATH::JLegendre< JQuaternion3D, N >:

Public Types
typedef std::vector< JQuaternion3D >::const_iterator	const_iterator

typedef std::vector< JQuaternion3D >::iterator	iterator

typedef std::vector< JQuaternion3D >::const_reverse_iterator	const_reverse_iterator

typedef std::vector< JQuaternion3D >::reverse_iterator	reverse_iterator

Public Member Functions
	JLegendre ()
	Default constructor.

	JLegendre (const double xmin, const double xmax)
	Constructor.

template<class T >
	JLegendre (T __begin, T __end)
	Constructor.

template<class T >
void	set (T __begin, T __end)
	Set Legendre polynome of quaternions.

template<class T >
void	set (T __begin, T __not, T __end)
	Set Legendre polynome of quaternions.

virtual JQuaternion3D	getValue (const double x) const override
	Function value.

JQuaternion3D	operator() (const double x) const
	Function value.

double	getXmin () const
	Get minimal abscissa value.

double	getXmax () const
	Get maximal abscissa value.

double	getX (const double x) const
	Get normalised abscissa value.

void	reset ()
	Reset.

void	set (const double xmin, const double xmax)
	Set abscissa values.

Protected Attributes
double	xmin
	minimal abscissa

double	xmax
	maximal abscissa

Private Member Functions
void	clear ()

void	resize ()

void	erase ()

void	push_back ()

void	pop_back ()

Friends
std::istream &	operator>> (std::istream &in, JLegendre &object)
	Read Legendre polynome from input.

Detailed Description

template<size_t N>
struct JMATH::JLegendre< JQuaternion3D, N >

Template specialisation for function evaluation of Legendre polynome of quaternions for defined number of degrees.

Definition at line 257 of file JEigen3D.hh.

Member Typedef Documentation

◆ const_iterator

std::vector<JQuaternion3D>::const_iterator JMATH::JLegendre_t< JQuaternion3D >::const_iterator

inherited

Definition at line 29 of file JLegendre.hh.

◆ iterator

std::vector<JQuaternion3D>::iterator JMATH::JLegendre_t< JQuaternion3D >::iterator

inherited

Definition at line 30 of file JLegendre.hh.

◆ const_reverse_iterator

std::vector<JQuaternion3D>::const_reverse_iterator JMATH::JLegendre_t< JQuaternion3D >::const_reverse_iterator

inherited

Definition at line 31 of file JLegendre.hh.

◆ reverse_iterator

std::vector<JQuaternion3D>::reverse_iterator JMATH::JLegendre_t< JQuaternion3D >::reverse_iterator

inherited

Definition at line 32 of file JLegendre.hh.

Constructor & Destructor Documentation

◆ JLegendre() [1/3]

template<size_t N>

JMATH::JLegendre< JQuaternion3D, N >::JLegendre ( )

inline

Default constructor.

Definition at line 266 of file JEigen3D.hh.

    {
      this->JLegendre<JQuaternion3D>::resize(N+1);
    }

◆ JLegendre() [2/3]

template<size_t N>

JMATH::JLegendre< JQuaternion3D, N >::JLegendre	(	const double	xmin,
		const double	xmax )

inline

Constructor.

Parameters

xmin	minimal abscissa value
xmax	maximal abscissa value

Definition at line 278 of file JEigen3D.hh.

    {
      this->JLegendre<JQuaternion3D>::resize(N+1);
      this->set(xmin, xmax);
    }

◆ JLegendre() [3/3]

template<size_t N>

template<class T >

JMATH::JLegendre< JQuaternion3D, N >::JLegendre	(	T	__begin,
		T	__end )

inline

Constructor.

The template argument T refers to an iterator of a data structure which should have the following data members:

double first; // abscissa
JQuaternion3D second; // ordinate

which conforms with std::pair.

Parameters

__begin	begin of data
__end	end of data

Definition at line 299 of file JEigen3D.hh.

    {
      this->JLegendre<JQuaternion3D>::resize(N+1);
      this->set(__begin, __end);
    }

Member Function Documentation

◆ set() [1/3]

template<size_t N>

template<class T >

void JMATH::JLegendre< JQuaternion3D, N >::set	(	T	__begin,
		T	__end )

inline

Set Legendre polynome of quaternions.

The template argument T refers to an iterator of a data structure which should have the following data members:

double first; // abscissa
JQuaternion3D second; // ordinate

which conforms with std::pair.

Parameters

__begin	begin of data
__end	end of data

Definition at line 319 of file JEigen3D.hh.

    {
      this->set(__begin, __end, __end);
    }

◆ set() [2/3]

template<size_t N>

template<class T >

void JMATH::JLegendre< JQuaternion3D, N >::set	(	T	__begin,
		T	__not,
		T	__end )

inline

Set Legendre polynome of quaternions.

The template argument T refers to an iterator of a data structure which should have the following data members:

double first; // abscissa
JQuaternion3D second; // ordinate

which conforms with std::pair.

Parameters

__begin	begin of data
__not	not in data
__end	end of data

Definition at line 339 of file JEigen3D.hh.

    {
      // factor to be applied as power to eigen value obtained with JAverage when degree larger than zero.
 
      static const double factor = 1.0 / (PI * 45.0 / 180.0);
 
      for (size_t n = 0; n != N + 1; ++n) {
        (*this)[n] = JQuaternion3D();
      }
 
      this->xmin = std::numeric_limits<double>::max();
      this->xmax = std::numeric_limits<double>::lowest();
 
      for (T i = __begin; i != __end; ++i) {
        if (i != __not) {
          if (i->first < this->xmin) { this->xmin = i->first; }
          if (i->first > this->xmax) { this->xmax = i->first; }
        }
      }
 
      for (size_t n = 0; n != N + 1; ++n) {
 
        JAverage<JQuaternion3D> Q;
 
        for (T i = __begin; i != __end; ++i) {
 
          if (i != __not) {
            const double         x = i->first;
            const JQuaternion3D& y = i->second;
            const double         z = this->getX(x);
            const double         w = legendre(n, z);
            const JQuaternion3D  q = this->getValue(x).getConjugate() * y;
 
            Q.put(q, w);
          }
        }
 
        (*this)[n] = Q;
 
        if (n != 0) {
          (*this)[n].pow(factor);
        }
      }
    }

◆ clear()

template<size_t N>

void JMATH::JLegendre< JQuaternion3D, N >::clear ( )

private

◆ resize()

template<size_t N>

void JMATH::JLegendre< JQuaternion3D, N >::resize ( )

private

◆ erase()

template<size_t N>

void JMATH::JLegendre< JQuaternion3D, N >::erase ( )

private

◆ push_back()

template<size_t N>

void JMATH::JLegendre< JQuaternion3D, N >::push_back ( )

private

◆ pop_back()

template<size_t N>

void JMATH::JLegendre< JQuaternion3D, N >::pop_back ( )

private

◆ getValue()

virtual JQuaternion3D JMATH::JLegendre< JQuaternion3D,(size_t) -1 >::getValue ( const double x ) const

inlineoverridevirtualinherited

Function value.

Parameters

x	abscissa value

Returns: function value

Implements JMATH::JLegendre_t< JQuaternion3D >.

Definition at line 239 of file JEigen3D.hh.

    {
      const double  z = this->getX(x);
      JQuaternion3D y = zero;
 
      for (size_t n = 0; n != this->size(); ++n) {
        y *= pow((*this)[n], legendre(n,z));
      }
 
      return y.normalise();
    }

◆ operator()()

JQuaternion3D JMATH::JLegendre_t< JQuaternion3D >::operator() ( const double x ) const

inlineinherited

Function value.

Parameters

x	abscissa value

Returns: function value

Definition at line 79 of file JLegendre.hh.

    {
      return this->getValue(x);
    }

◆ getXmin()

double JMATH::JLegendre_t< JQuaternion3D >::getXmin ( ) const

inlineinherited

Get minimal abscissa value.

Returns: minimal abscissa value

Definition at line 90 of file JLegendre.hh.

    {
      return xmin;
    }

◆ getXmax()

double JMATH::JLegendre_t< JQuaternion3D >::getXmax ( ) const

inlineinherited

Get maximal abscissa value.

Returns: maximal abscissa value

Definition at line 101 of file JLegendre.hh.

    {
      return xmax;
    }

◆ getX()

double JMATH::JLegendre_t< JQuaternion3D >::getX ( const double x ) const

inlineinherited

Get normalised abscissa value.

Parameters

x	abscissa value

Returns: normalised abscissa value

Definition at line 113 of file JLegendre.hh.

    {
      return 2.0 * (x - xmin) / (xmax - xmin)  -  1.0;
    }

◆ reset()

void JMATH::JLegendre_t< JQuaternion3D >::reset ( )

inlineinherited

Reset.

Definition at line 122 of file JLegendre.hh.

    {
      for (iterator i = this->begin(); i != this->end(); ++i) {
        *i = zero;
      }
    }

◆ set() [3/3]

void JMATH::JLegendre_t< JQuaternion3D >::set	(	const double	xmin,
		const double	xmax )

inlineinherited

Set abscissa values.

Parameters

xmin	minimal abscissa value
xmax	maximal abscissa value

Definition at line 136 of file JLegendre.hh.

    {
      this->xmin = xmin;
      this->xmax = xmax;
    }

Friends And Related Symbol Documentation

◆ operator>>

template<size_t N>

std::istream & operator>>	(	std::istream &	in,
		JLegendre< JQuaternion3D, N > &	object )

friend

Read Legendre polynome from input.

Parameters

in	input stream
object	Legendre polynome

Returns: input stream

Definition at line 392 of file JEigen3D.hh.

    {
      for (typename JLegendre::iterator i = object.begin(); i != object.end(); ++i) {
        in >> *i;
      }
 
      return in;
    }

Member Data Documentation

◆ xmin

double JMATH::JLegendre_t< JQuaternion3D >::xmin

protectedinherited

minimal abscissa

Definition at line 204 of file JLegendre.hh.

◆ xmax

double JMATH::JLegendre_t< JQuaternion3D >::xmax

protectedinherited

maximal abscissa

Definition at line 205 of file JLegendre.hh.

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

JEigen3D.hh

Public Types

Public Member Functions

Protected Attributes

Private Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ const_iterator

◆ iterator

◆ const_reverse_iterator

◆ reverse_iterator

Constructor & Destructor Documentation

◆ JLegendre() [1/3]

◆ JLegendre() [2/3]

◆ JLegendre() [3/3]

Member Function Documentation

◆ set() [1/3]

◆ set() [2/3]

◆ clear()

◆ resize()

◆ erase()

◆ push_back()

◆ pop_back()

◆ getValue()

◆ operator()()

◆ getXmin()

◆ getXmax()

◆ getX()

◆ reset()

◆ set() [3/3]

Friends And Related Symbol Documentation

◆ operator>>

Member Data Documentation

◆ xmin

◆ xmax