Template base class for spline interpolations. More...

#include <JSpline.hh>

Inheritance diagram for JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >:

Public Types
typedef JCollection_t< JElement_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::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 JArgument_t	argument_type

typedef JResult_t	result_type

typedef JFunctional< argument_type, result_type >	functional_type

Public Member Functions
void	compile (const JSplineBounds< ordinate_type > &bounds)
	Determination of second derivatives with specified bounds.

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

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.

Protected Member Functions
	JSplineCollection ()
	Default constructor.

virtual void	do_compile () override
	Determination of second derivatives with no bounds.

Detailed Description

template<class JElement_t, template< class, class > class JCollection_t, class JDistance_t>
class JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >

Template base class for spline interpolations.

This class partially implements the JFunctional interface.

Note that the data structure of the elements in the collection should have the additional methods:

    ordinate_type getU() const;
    void setU(ordinate_type u);

to get and set the second derivatives, respectively.

Spline interpolation 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 177 of file JSpline.hh.

Member Typedef Documentation

◆ collection_type

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

JCollection_t<JElement_t, JDistance_t> JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::collection_type

Definition at line 183 of file JSpline.hh.

◆ abscissa_type

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

collection_type::abscissa_type JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::abscissa_type

Definition at line 185 of file JSpline.hh.

◆ ordinate_type

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

collection_type::ordinate_type JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::ordinate_type

Definition at line 186 of file JSpline.hh.

◆ value_type

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

collection_type::value_type JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::value_type

Definition at line 187 of file JSpline.hh.

◆ const_iterator

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

collection_type::const_iterator JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::const_iterator

Definition at line 189 of file JSpline.hh.

◆ const_reverse_iterator

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

collection_type::const_reverse_iterator JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::const_reverse_iterator

Definition at line 190 of file JSpline.hh.

◆ iterator

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

collection_type::iterator JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::iterator

Definition at line 191 of file JSpline.hh.

◆ reverse_iterator

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

collection_type::reverse_iterator JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::reverse_iterator

Definition at line 192 of file JSpline.hh.

◆ argument_type

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

inherited

Definition at line 83 of file JFunctional.hh.

◆ result_type

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

inherited

Definition at line 84 of file JFunctional.hh.

◆ functional_type

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

◆ JSplineCollection()

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

JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::JSplineCollection ( )

inlineprotected

Default constructor.

Definition at line 297 of file JSpline.hh.

298 {}

Member Function Documentation

◆ compile()

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

void JTOOLS::JSplineCollection< JElement_t, JCollection_t, JDistance_t >::compile ( const JSplineBounds< ordinate_type > & bounds )

inline

Determination of second derivatives with specified bounds.

Parameters

bounds 1st derivatives at two extrema.

Definition at line 202 of file JSpline.hh.

    {
      const int numberOfElements = this->size();
 
      using namespace std;
 
      if (numberOfElements > 2) {
        
        std::vector<double> buffer(numberOfElements);
 
        if (bounds.hasFirstDerivativeAtXmin()) {
          
          iterator j = this->begin();
          iterator i = j++;
           
          const double        dx = this->getDistance(i->getX(),  j->getX());
          const ordinate_type dy =                  (j->getY() - i->getY());
           
          buffer[0] = -0.5;
 
          i->setU((3.0/dx) * (dy/dx - bounds.getFirstDerivativeAtXmin()));
 
        } else {
 
          buffer[0] = 0.0;
 
          this->begin()->setU(JMATH::zero);
        }
 
        int index = 1;
       
        for (iterator k = this->begin(), i = k++, j = k++; k != this->end(); ++i, ++j, ++k, ++index) {
 
          const abscissa_type  x1 = i->getX();
          const abscissa_type  x2 = j->getX();
          const abscissa_type  x3 = k->getX();
 
          const ordinate_type& y1 = i->getY();
          const ordinate_type& y2 = j->getY();
          const ordinate_type& y3 = k->getY();
 
          const double sig = this->getDistance(x1, x2) / this->getDistance(x1, x3);
          const double h   = sig * buffer[index-1] + 2.0;
         
          buffer[index]    = (sig - 1.0) / h;
         
          j->setU((y3 - y2) / this->getDistance(x2, x3)  -  
                  (y2 - y1) / this->getDistance(x1, x2));
 
          j->setU((6.0 * j->getU() / this->getDistance(x1, x3)  -  sig * i->getU()) / h);
        }
       
 
        if (bounds.hasFirstDerivativeAtXmax()) {
 
          reverse_iterator j = this->rbegin();
          reverse_iterator i = j++;
 
          index = numberOfElements - 2;
          
          const double        dx = this->getDistance(i->getX(),  j->getX());
          const ordinate_type dy =                  (j->getY() - i->getY());
           
          i->setU((3.0/dx) * (bounds.getFirstDerivativeAtXmax() - dy/dx));
 
          i->setU((i->getU() - 0.5*j->getU()) / (0.5*buffer[index] + 1.0));
 
        } else {
 
          this->rbegin()->setU(JMATH::zero);
        }
 
 
        reverse_iterator j = this->rbegin();
        reverse_iterator i = j++;
        
        index = numberOfElements - 2;
        
        for ( ; j != this->rend(); ++i, ++j, --index) {
          j->setU(j->getU() + i->getU() * buffer[index]);
        }
 
      } else {
 
        for (iterator i = this->begin(); i != this->end(); ++i) {
          i->setU(JMATH::zero);
        }
      }
    }

◆ do_compile()

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

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

inlineoverrideprotectedvirtual

Determination of second derivatives with no bounds.

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

Definition at line 304 of file JSpline.hh.

    {
      compile(JSplineBounds<ordinate_type>());
    }

◆ evaluate()

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

pure virtualinherited

Recursive function value evaluation.

Parameters

pX	pointer to abscissa values

Returns: function value

Implemented in JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >, JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >, JTOOLS::JHermiteSplineFunction< JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >, JTOOLS::JSplineFunction< JElement_t, JCollection_t, JResultDerivative< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >, JTOOLS::JSplineFunction< JElement_t, JCollection_t, JResultPDF< typename JResultType< typename JElement_t::ordinate_type >::result_type >, JDistance_t >, and JTOOLS::JSplineFunction< JElement_t, JCollection_t, typename JResultType< typename JElement_t::ordinate_type >::result_type, JDistance_t >.

◆ getValue() [1/2]

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() [2/2]

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()

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:

JSpline.hh

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

◆ collection_type

◆ abscissa_type

◆ ordinate_type

◆ value_type

◆ const_iterator

◆ const_reverse_iterator

◆ iterator

◆ reverse_iterator

◆ argument_type

◆ result_type

◆ functional_type

Constructor & Destructor Documentation

◆ JSplineCollection()

Member Function Documentation

◆ compile()

◆ do_compile()

◆ evaluate()

◆ getValue() [1/2]

◆ getValue() [2/2]

◆ getExceptionHandler()