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 JFunctional< 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 JFunctional< argument_type, result_type >	functional_type

Public Member Functions
	JHermiteSplineFunction ()
	Default constructor.

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

void	compile (const bool monotone)
	Determination of derivatives.

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

virtual const JExceptionHandler &	getExceptionHandler () const=0
	Get exception handler.

virtual const JExceptionHandler &	getExceptionHandler () const=0
	Get exception handler.

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

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

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

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

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

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)

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 278 of file JHermiteSpline.hh.

Member Typedef Documentation

◆ collection_type

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

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 288 of file JHermiteSpline.hh.

◆ abscissa_type

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

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 290 of file JHermiteSpline.hh.

◆ ordinate_type

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

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 291 of file JHermiteSpline.hh.

◆ value_type

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

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 292 of file JHermiteSpline.hh.

◆ distance_type

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

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 293 of file JHermiteSpline.hh.

◆ const_iterator

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

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 295 of file JHermiteSpline.hh.

◆ const_reverse_iterator

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

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 296 of file JHermiteSpline.hh.

◆ iterator

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

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 297 of file JHermiteSpline.hh.

◆ reverse_iterator

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

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 298 of file JHermiteSpline.hh.

◆ data_type

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

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 300 of file JHermiteSpline.hh.

◆ function_type

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

JFunctional<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 301 of file JHermiteSpline.hh.

◆ argument_type

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

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 303 of file JHermiteSpline.hh.

◆ result_type

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

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 304 of file JHermiteSpline.hh.

◆ exceptionhandler_type

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

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 305 of file JHermiteSpline.hh.

◆ functional_type [1/2]

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

inherited

Definition at line 85 of file JFunctional.hh.

◆ functional_type [2/2]

JFunctional<argument_type, result_type> JTOOLS::JFunctional< JArgument_t, JResult_t >::functional_type

inherited

Definition at line 85 of file JFunctional.hh.

Constructor & Destructor Documentation

◆ JHermiteSplineFunction()

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 311 of file JHermiteSpline.hh.

312 {}

Member Function Documentation

◆ evaluate() [1/2]

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

Implements JTOOLS::JFunctional<>.

Definition at line 321 of file JHermiteSpline.hh.

    {
      result_type result;
 
      const argument_type x = *pX;
 
      if (this->size() <= 1u) {
 
        try {
          return this->getExceptionHandler().action();
        }
        catch (const JException& error) {
 
          std::ostringstream os;
 
          os << __FILE__ << ':' << __LINE__ << " not enough data " << STREAM("?") << x;
        
          throw JFunctionalException(os.str());
        }
      }
 
      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)) {
 
        try {
          return this->getExceptionHandler().action();
        }
        catch (const JException& error) {
 
          std::ostringstream os;
 
          os << __FILE__ << ':' << __LINE__ << " abscissa out of range " 
             << STREAM("?") << x                      << " <> " 
             << STREAM("?") << this->begin() ->getX() << ' '
             << STREAM("?") << this->rbegin()->getX();
          
          throw JValueOutOfRange(os.str());
        }
      }
 
      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;
    }

◆ h00()

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 )

inlinestaticprotected

Definition at line 127 of file JHermiteSpline.hh.

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

◆ h10()

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 )

inlinestaticprotected

Definition at line 128 of file JHermiteSpline.hh.

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

◆ h01()

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 )

inlinestaticprotected

Definition at line 129 of file JHermiteSpline.hh.

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

◆ h11()

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 )

inlinestaticprotected

Definition at line 130 of file JHermiteSpline.hh.

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

◆ h00p()

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 )

inlinestaticprotected

Definition at line 132 of file JHermiteSpline.hh.

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

◆ h10p()

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 )

inlinestaticprotected

Definition at line 133 of file JHermiteSpline.hh.

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

◆ h01p()

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 )

inlinestaticprotected

Definition at line 134 of file JHermiteSpline.hh.

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

◆ h11p()

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 )

inlinestaticprotected

Definition at line 135 of file JHermiteSpline.hh.

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

◆ compile()

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 76 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());
            }
          }
        }
      }
    }

◆ H00()

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 137 of file JHermiteSpline.hh.

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

◆ H10()

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 138 of file JHermiteSpline.hh.

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

◆ H01()

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 139 of file JHermiteSpline.hh.

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

◆ H11()

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 140 of file JHermiteSpline.hh.

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

◆ do_compile()

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 153 of file JHermiteSpline.hh.

    {
      compile(true);
    }

◆ evaluate() [2/2]

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

◆ getValue() [1/4]

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 103 of file JFunctional.hh.

    {
      return function.evaluate(pX);
    }

◆ getValue() [2/4]

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 117 of file JFunctional.hh.

    {
      return value;
    }

◆ getExceptionHandler() [1/2]

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

pure virtualinherited

Get exception handler.

Returns: exception handler

◆ getValue() [3/4]

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

inlinestaticinherited

Recursive function value evaluation.

Parameters

function	function
pX	pointer to abscissa values

Definition at line 103 of file JFunctional.hh.

    {
      return function.evaluate(pX);
    }

◆ getValue() [4/4]

static JClass< result_type >::argument_type JTOOLS::JFunctional< JArgument_t, JResult_t >::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 117 of file JFunctional.hh.

    {
      return value;
    }

◆ getExceptionHandler() [2/2]

virtual const JExceptionHandler & JTOOLS::JFunctional< JArgument_t, JResult_t >::getExceptionHandler ( ) const

pure virtualinherited

Get exception handler.

Returns: exception handler

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

Detailed Description

Member Typedef Documentation

◆ collection_type

◆ abscissa_type

◆ ordinate_type

◆ value_type

◆ distance_type

◆ const_iterator

◆ const_reverse_iterator

◆ iterator

◆ reverse_iterator

◆ data_type

◆ function_type

◆ argument_type

◆ result_type

◆ exceptionhandler_type

◆ functional_type [1/2]

◆ functional_type [2/2]

Constructor & Destructor Documentation

◆ JHermiteSplineFunction()

Member Function Documentation

◆ evaluate() [1/2]

◆ h00()

◆ h10()

◆ h01()

◆ h11()

◆ h00p()

◆ h10p()

◆ h01p()

◆ h11p()

◆ compile()

◆ H00()

◆ H10()

◆ H01()

◆ H11()

◆ do_compile()

◆ evaluate() [2/2]

◆ getValue() [1/4]

◆ getValue() [2/4]

◆ getExceptionHandler() [1/2]

◆ getValue() [3/4]

◆ getValue() [4/4]

◆ getExceptionHandler() [2/2]