unifexp::mapCubicIntv< numType > Class Template Reference

This class defines the cubic map -x^3 + 3x - a on [-4,4] with the usage of interval arithmetic. More...

#include </cur/unifexp/mapcubi.h>

Inheritance diagram for unifexp::mapCubicIntv< numType >:

unifexp::mapType< numType >

List of all members.

Public Member Functions

 mapCubicIntv ()
 The constructor.
std::string name () const
 Returns the name of the object.
int countCritical () const
 Returns the number of critical points.
numType criticalPoint (int n) const
 Returns the subsequent critical points.
numType leftBound () const
 Returns the left bound of the domain of the map.
numType rightBound () const
 Returns the right bound of the domain of the map.
void image (const numType &x1, const numType &x2, numType &y1, numType &y2) const
 Computes an enclosure of the image of the given interval.
numType minLogDerivative (const numType &x1, const numType &x2, const numType &y1, const numType &y2) const
 Computes the minimal log of the derivative over those points in the interval [x1,x2] whose images may fall into [y1,y2].


Detailed Description

template<class numType>
class unifexp::mapCubicIntv< numType >

This class defines the cubic map -x^3 + 3x - a on [-4,4] with the usage of interval arithmetic.

It is suitable for rigorous computations. Good values of the parameter are between 0 and 2, more or less (the optimal value is 2, I think).

Definition at line 58 of file mapcubi.h.


Constructor & Destructor Documentation

template<class numType>
unifexp::mapCubicIntv< numType >::mapCubicIntv (  )  [inline]

The constructor.

Definition at line 93 of file mapcubi.h.


Member Function Documentation

template<class numType>
std::string unifexp::mapCubicIntv< numType >::name (  )  const [inline, virtual]

Returns the name of the object.

Implements unifexp::mapType< numType >.

Definition at line 99 of file mapcubi.h.

template<class numType>
int unifexp::mapCubicIntv< numType >::countCritical (  )  const [inline, virtual]

Returns the number of critical points.

Implements unifexp::mapType< numType >.

Definition at line 105 of file mapcubi.h.

template<class numType>
numType unifexp::mapCubicIntv< numType >::criticalPoint ( int  n  )  const [inline, virtual]

Returns the subsequent critical points.

Implements unifexp::mapType< numType >.

Definition at line 111 of file mapcubi.h.

template<class numType>
numType unifexp::mapCubicIntv< numType >::leftBound (  )  const [inline, virtual]

Returns the left bound of the domain of the map.

Implements unifexp::mapType< numType >.

Definition at line 117 of file mapcubi.h.

Referenced by unifexp::mapCubicIntv< numType >::image(), and unifexp::mapCubicIntv< numType >::minLogDerivative().

template<class numType>
numType unifexp::mapCubicIntv< numType >::rightBound (  )  const [inline, virtual]

Returns the right bound of the domain of the map.

Implements unifexp::mapType< numType >.

Definition at line 123 of file mapcubi.h.

Referenced by unifexp::mapCubicIntv< numType >::image().

template<class numType>
void unifexp::mapCubicIntv< numType >::image ( const numType &  x1,
const numType &  x2,
numType &  y1,
numType &  y2 
) const [inline, virtual]

Computes an enclosure of the image of the given interval.

Implements unifexp::mapType< numType >.

Definition at line 129 of file mapcubi.h.

References unifexp::mapCubicIntv< numType >::leftBound(), unifexp::mapType< numType >::paramMax, unifexp::mapType< numType >::paramMin, and unifexp::mapCubicIntv< numType >::rightBound().

template<class numType>
numType unifexp::mapCubicIntv< numType >::minLogDerivative ( const numType &  x1,
const numType &  x2,
const numType &  y1,
const numType &  y2 
) const [inline, virtual]

Computes the minimal log of the derivative over those points in the interval [x1,x2] whose images may fall into [y1,y2].

Implements unifexp::mapType< numType >.

Definition at line 174 of file mapcubi.h.

References unifexp::mapCubicIntv< numType >::leftBound().


The documentation for this class was generated from the following file:
Generated on Wed Nov 21 11:08:42 2007 for The Uniform Expansion Software by  doxygen 1.5.3