Template specialisation for spline interpolation method with returning JResultDerivative data structure. More...

#include <JHermiteSpline.hh>

Inheritance diagram for JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >:

Public Types
typedef JHermiteSplineCollection < JElement_t, JCollection_t, JDistance_t >	collection_type

typedef collection_type::abscissa_type	abscissa_type

typedef collection_type::ordinate_type	ordinate_type

typedef collection_type::value_type	value_type

typedef collection_type::distance_type	distance_type

typedef collection_type::const_iterator	const_iterator

typedef collection_type::const_reverse_iterator	const_reverse_iterator

typedef collection_type::iterator	iterator

typedef collection_type::reverse_iterator	reverse_iterator

typedef JResultType < ordinate_type >::result_type	data_type

typedef JFunction < abscissa_type, JResultDerivative< data_type > >	function_type

typedef function_type::argument_type	argument_type

typedef function_type::result_type	result_type

typedef function_type::JExceptionHandler	exceptionhandler_type

typedef JFunctional < argument_type, result_type >	functional_type

typedef JSupervisor	supervisor_type

typedef JFunctional < JElement_t::abscissa_type, JResultDerivative< JResultType < JElement_t::ordinate_type > ::result_type > >	functional_type

typedef JSupervisor	supervisor_type

Public Member Functions
	JHermiteSplineFunction ()
	Default constructor. More...

virtual result_type	evaluate (const argument_type *pX) const override
	Recursive interpolation method implementation. More...

void	compile (const bool monotone)
	Determination of derivatives. More...

virtual result_type	evaluate (const argument_type *pX) const =0
	Recursive function value evaluation. More...

JSupervisor	getSupervisor () const
	Get supervisor. More...

const JExceptionHandler &	getExceptionHandler () const
	Get exception handler. More...

void	setExceptionHandler (const JSupervisor &supervisor)
	Set the supervisor for handling of exceptions. More...

virtual result_type	evaluate (const argument_type *pX) const =0
	Recursive function value evaluation. More...

JSupervisor	getSupervisor () const
	Get supervisor. More...

const JExceptionHandler &	getExceptionHandler () const
	Get exception handler. More...

void	setExceptionHandler (const JSupervisor &supervisor)
	Set the supervisor for handling of exceptions. More...

Static Public Member Functions
static result_type	getValue (const JFunctional &function, const argument_type *pX)
	Recursive function value evaluation. More...

static JClass< result_type > ::argument_type	getValue (typename JClass< result_type >::argument_type value, const argument_type *pX)
	Termination of recursive function value evaluation. More...

static result_type	getValue (const JFunctional &function, const argument_type *pX)
	Recursive function value evaluation. More...

static JClass< result_type > ::argument_type	getValue (typename JClass< result_type >::argument_type value, const argument_type *pX)
	Termination of recursive function value evaluation. More...

Protected Member Functions
virtual void	do_compile () override
	Determination of derivatives. More...

Static Protected Member Functions
static abscissa_type	h00 (abscissa_type t)

static abscissa_type	h10 (abscissa_type t)

static abscissa_type	h01 (abscissa_type t)

static abscissa_type	h11 (abscissa_type t)

static abscissa_type	h00p (abscissa_type t)

static abscissa_type	h10p (abscissa_type t)

static abscissa_type	h01p (abscissa_type t)

static abscissa_type	h11p (abscissa_type t)

static abscissa_type	H00 (abscissa_type t)

static abscissa_type	H10 (abscissa_type t)

static abscissa_type	H01 (abscissa_type t)

static abscissa_type	H11 (abscissa_type t)

Protected Attributes
JSupervisor	supervisor

JSupervisor	supervisor

Private Attributes
result_type	result

Detailed Description

template<class JElement_t, template< class, class > class JCollection_t, class JDistance_t>
class JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >

Template specialisation for spline interpolation method with returning JResultDerivative data structure.

Definition at line 250 of file JHermiteSpline.hh.

Member Typedef Documentation

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef JHermiteSplineCollection<JElement_t, JCollection_t, JDistance_t> JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::collection_type

Definition at line 260 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::abscissa_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::abscissa_type

Definition at line 262 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::ordinate_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::ordinate_type

Definition at line 263 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::value_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::value_type

Definition at line 264 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::distance_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::distance_type

Definition at line 265 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::const_iterator JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::const_iterator

Definition at line 267 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::const_reverse_iterator JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::const_reverse_iterator

Definition at line 268 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::iterator JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::iterator

Definition at line 269 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef collection_type::reverse_iterator JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::reverse_iterator

Definition at line 270 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef JResultType<ordinate_type>::result_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::data_type

Definition at line 272 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef JFunction<abscissa_type, JResultDerivative<data_type> > JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::function_type

Definition at line 273 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef function_type::argument_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::argument_type

Definition at line 275 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef function_type::result_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::result_type

Definition at line 276 of file JHermiteSpline.hh.

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

typedef function_type::JExceptionHandler JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::exceptionhandler_type

Definition at line 277 of file JHermiteSpline.hh.

typedef JFunctional<argument_type, result_type> JTOOLS::JFunctional< JNullType , JNullType >::functional_type

inherited

Definition at line 88 of file JFunctional.hh.

typedef JSupervisor JTOOLS::JFunctional< JNullType , JNullType >::supervisor_type

inherited

Definition at line 89 of file JFunctional.hh.

typedef JFunctional<JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > > JTOOLS::JFunction< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::functional_type

inherited

Definition at line 306 of file JFunctional.hh.

typedef JSupervisor JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::supervisor_type

inherited

Definition at line 89 of file JFunctional.hh.

Constructor & Destructor Documentation

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::JHermiteSplineFunction ( )

inline

Default constructor.

Definition at line 283 of file JHermiteSpline.hh.

284 {}

Member Function Documentation

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

virtual result_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::evaluate ( const argument_type * pX ) const

inlineoverridevirtual

Recursive interpolation method implementation.

Parameters

pX	pointer to abscissa values

Returns: function value

Definition at line 293 of file JHermiteSpline.hh.

     {
       if (this->size() <= 1u) {
         return this->getExceptionHandler().action(JFunctionalException("JHermiteSplineFunction<>::evaluate() not enough data."));
       }
 
       const argument_type x = *pX;
 
       const_iterator p = this->lower_bound(x);
 
 
       if ((p == this->begin() && this->getDistance(x, (p++)->getX()) > distance_type::precision) ||
           (p == this->end()   && this->getDistance((--p)->getX(), x) > distance_type::precision)) {
 
         return this->getExceptionHandler().action(JValueOutOfRange("JHermiteSplineFunction::evaluate() x out of range."));
       }
 
       const_iterator q = p--;
 
       const double dx = this->getDistance(p->getX(), q->getX());
       const double t  = this->getDistance(p->getX(), x) / dx;
 
       result.f  = h00 (t)*p->getY()    + h10 (t)*p->getU()*dx + h01 (t)*q->getY()    + h11 (t)*q->getU()*dx;
       result.fp = h00p(t)*p->getY()/dx + h10p(t)*p->getU()    + h01p(t)*q->getY()/dx + h11p(t)*q->getU();
 
       return result;
     }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

void JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::compile ( const bool monotone )

inlineinherited

Determination of derivatives.

Parameters

monotone monotone

Definition at line 72 of file JHermiteSpline.hh.

     {
       using namespace std;
       
       if (this->size() >= 2u) {
 
         {
           iterator         j = this->begin(), i = j++;
 
           i->setU((j->getY() - i->getY()) / this->getDistance(i->getX(), j->getX()));
         }               
 
         {
           reverse_iterator j = this->rbegin(), i = j++;
 
           i->setU((j->getY() - i->getY()) / this->getDistance(i->getX(), j->getX()));
         }       
         
         for (iterator k = this->begin(), i = k++, j = k++; k != this->end(); ++i, ++j, ++k) {
           j->setU(0.5 * ((j->getY() - i->getY()) / this->getDistance(i->getX(), j->getX()) +
                          (k->getY() - j->getY()) / this->getDistance(j->getX(), k->getX())));
         }
 
         if (monotone) {
           
           for (iterator j = this->begin(), i = j++; j != this->end(); ++i, ++j) {
             if (i->getY() == j->getY()) {
               j->setU(JMATH::zero);
             }
           }
 
           for (iterator j = this->begin(), i = j++; j != this->end(); ++i, ++j) {
 
             const ordinate_type u = (j->getY() - i->getY()) / this->getDistance(i->getX(), j->getX());
             const ordinate_type w = (i->getU()*i->getU() + j->getU()*j->getU());
             
             if (w > 9.0*u*u) {
 
               const ordinate_type v = 3.0*u/sqrt(w);
 
               i->setU(v*i->getU());
               j->setU(v*j->getU());
             }
           }
         }
       }
     }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h00 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 123 of file JHermiteSpline.hh.

123 { return (1.0 + 2*t) * (1.0 - t) * (1.0 - t); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h10 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 124 of file JHermiteSpline.hh.

124 { return t * (1.0 - t) * (1.0 - t); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h01 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 125 of file JHermiteSpline.hh.

125 { return t * t * (3.0 - 2*t); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h11 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 126 of file JHermiteSpline.hh.

126 { return t * t * (t - 1.0); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h00p ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 128 of file JHermiteSpline.hh.

128 { return 6 * t * (t - 1.0); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h10p ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 129 of file JHermiteSpline.hh.

129 { return t * (3*t - 4.0) + 1.0; }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h01p ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 130 of file JHermiteSpline.hh.

130 { return 6 * t * (1.0 -t); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::h11p ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 131 of file JHermiteSpline.hh.

131 { return t * (3*t - 2.0); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::H00 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 133 of file JHermiteSpline.hh.

133 { return t * (t * t * (0.5*t - 1.0) + 1.0); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::H10 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 134 of file JHermiteSpline.hh.

134 { return t * t * (t * (0.25*t - 2.0/3.0) + 0.5); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::H01 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 135 of file JHermiteSpline.hh.

135 { return t * t * t * (1.0 - 0.5*t); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

static abscissa_type JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::H11 ( abscissa_type t )

inlinestaticprotectedinherited

Definition at line 136 of file JHermiteSpline.hh.

136 { return t * t * t * (0.25*t - 1.0/3.0); }

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

virtual void JTOOLS::JHermiteSplineCollection< JElement_t, JCollection_t, JDistance_t >::do_compile ( )

inlineoverrideprotectedvirtualinherited

Determination of derivatives.

Reimplemented in JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >.

Definition at line 149 of file JHermiteSpline.hh.

     {
       compile(true);
     }

virtual result_type JTOOLS::JFunctional< JNullType , JNullType >::evaluate ( const argument_type * pX ) const

pure virtualinherited

Recursive function value evaluation.

Parameters

pX	pointer to abscissa values

Returns: function value

static result_type JTOOLS::JFunctional< JNullType , JNullType >::getValue	(	const JFunctional<> &	function,
		const argument_type *	pX
	)

inlinestaticinherited

Recursive function value evaluation.

Parameters

function	function
pX	pointer to abscissa values

Definition at line 107 of file JFunctional.hh.

     {
       return function.evaluate(pX);
     }

static JClass<result_type>::argument_type JTOOLS::JFunctional< JNullType , JNullType >::getValue	(	typename JClass< result_type >::argument_type	value,
		const argument_type *	pX
	)

inlinestaticinherited

Termination of recursive function value evaluation.

Parameters

value	result
pX	pointer to abscissa values

Definition at line 121 of file JFunctional.hh.

     {
       return value;
     }

JSupervisor JTOOLS::JFunctional< JNullType , JNullType >::getSupervisor ( ) const

inlineinherited

Get supervisor.

Returns: supervisor

Definition at line 266 of file JFunctional.hh.

     {
       return supervisor;
     }

const JExceptionHandler& JTOOLS::JFunctional< JNullType , JNullType >::getExceptionHandler ( ) const

inlineinherited

Get exception handler.

Returns: exception handler

Definition at line 277 of file JFunctional.hh.

     {
       return *supervisor;
     }

void JTOOLS::JFunctional< JNullType , JNullType >::setExceptionHandler ( const JSupervisor & supervisor )

inlineinherited

Set the supervisor for handling of exceptions.

Parameters

supervisor supervisor

Definition at line 288 of file JFunctional.hh.

     {
       this->supervisor = supervisor;
     }

virtual result_type JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::evaluate ( const argument_type * pX ) const

pure virtualinherited

Recursive function value evaluation.

Parameters

pX	pointer to abscissa values

Returns: function value

static result_type JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::getValue	(	const JFunctional< JElement_t::abscissa_type, JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > > &	function,
		const argument_type *	pX
	)

inlinestaticinherited

Recursive function value evaluation.

Parameters

function	function
pX	pointer to abscissa values

Definition at line 107 of file JFunctional.hh.

     {
       return function.evaluate(pX);
     }

static JClass<result_type>::argument_type JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::getValue	(	typename JClass< result_type >::argument_type	value,
		const argument_type *	pX
	)

inlinestaticinherited

Termination of recursive function value evaluation.

Parameters

value	result
pX	pointer to abscissa values

Definition at line 121 of file JFunctional.hh.

     {
       return value;
     }

JSupervisor JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::getSupervisor ( ) const

inlineinherited

Get supervisor.

Returns: supervisor

Definition at line 266 of file JFunctional.hh.

     {
       return supervisor;
     }

const JExceptionHandler& JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::getExceptionHandler ( ) const

inlineinherited

Get exception handler.

Returns: exception handler

Definition at line 277 of file JFunctional.hh.

     {
       return *supervisor;
     }

void JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::setExceptionHandler ( const JSupervisor & supervisor )

inlineinherited

Set the supervisor for handling of exceptions.

Parameters

supervisor supervisor

Definition at line 288 of file JFunctional.hh.

     {
       this->supervisor = supervisor;
     }

Member Data Documentation

template<class JElement_t , template< class, class > class JCollection_t, class JDistance_t >

result_type JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >::result

mutableprivate

Definition at line 335 of file JHermiteSpline.hh.

JSupervisor JTOOLS::JFunctional< JNullType , JNullType >::supervisor

protectedinherited

Definition at line 295 of file JFunctional.hh.

JSupervisor JTOOLS::JFunctional< JElement_t::abscissa_type , JResultDerivative< JResultType< JElement_t::ordinate_type >::result_type > >::supervisor

protectedinherited

Definition at line 295 of file JFunctional.hh.

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

JHermiteSpline.hh

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

template<class JElement_t, template< class, class > class JCollection_t, class JDistance_t> class JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class JElement_t, template< class, class > class JCollection_t, class JDistance_t>
class JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >