This class defines the cubic map -x^3 + 3x - a on [-4,4] without using interval arithmetic. More...
#include </cur/unifexp/mapcub.h>
Public Member Functions | |
| mapCubic () | |
| 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::mapCubic< numType >
This class defines the cubic map -x^3 + 3x - a on [-4,4] without using interval arithmetic.
It is suitable for non-rigorous computations. See the class "mapCubicIntv" for a rigorous version which does use interval arithmetic. Good values of the parameter are between 0 and 2, more or less (the optimal value is 2, I think).
Definition at line 57 of file mapcub.h.
Constructor & Destructor Documentation
| unifexp::mapCubic< numType >::mapCubic | ( | ) | [inline] |
Member Function Documentation
| int unifexp::mapCubic< numType >::countCritical | ( | ) | const [inline, virtual] |
Returns the number of critical points.
Implements unifexp::mapType< numType >.
| numType unifexp::mapCubic< numType >::criticalPoint | ( | int | n ) | const [inline, virtual] |
Returns the subsequent critical points.
Implements unifexp::mapType< numType >.
| void unifexp::mapCubic< 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 >.
| numType unifexp::mapCubic< numType >::leftBound | ( | ) | const [inline, virtual] |
Returns the left bound of the domain of the map.
Implements unifexp::mapType< numType >.
| numType unifexp::mapCubic< 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 >.
| std::string unifexp::mapCubic< numType >::name | ( | ) | const [inline, virtual] |
Returns the name of the object.
Implements unifexp::mapType< numType >.
| numType unifexp::mapCubic< numType >::rightBound | ( | ) | const [inline, virtual] |
Returns the right bound of the domain of the map.
Implements unifexp::mapType< numType >.
The documentation for this class was generated from the following file:
