This class defines the unimodal map "2 |x|^gamma - a" on [-1,1] without using interval arithmetic. More...
#include </cur/unifexp/mapunim.h>
Public Member Functions | |
| mapUnimodal (const numType &_gamma) | |
| 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]. | |
Private Member Functions | |
| numType | gammaPower (numType x) const |
| An auxiliary function for the computation of the absolute value of a number raised to the power gamma. | |
| numType | gammaPower1 (numType x) const |
| An auxiliary function for the computation of the absolute value of a number raised to the power gamma - 1. | |
| numType | gammaRoot (numType x) const |
| An auxiliary function for the computation of the root of degree gamma of the absolute value of a number. | |
Private Attributes | |
| numType | gamma |
| The exponent of the map. | |
Detailed Description
template<class numType>
class unifexp::mapUnimodal< numType >
This class defines the unimodal map "2 |x|^gamma - a" on [-1,1] without using interval arithmetic.
It is suitable for non-rigorous computations. See the class "mapUnimodalIntv" for a rigorous version which does use interval arithmetic. Recommended values of gamma are between 1 and 3. Valid values of the parameter are between 0.5+ and 1 (optimal value: 1).
Definition at line 58 of file mapunim.h.
Constructor & Destructor Documentation
| unifexp::mapUnimodal< numType >::mapUnimodal | ( | const numType & | _gamma ) | [inline] |
Member Function Documentation
| int unifexp::mapUnimodal< numType >::countCritical | ( | ) | const [inline, virtual] |
Returns the number of critical points.
Implements unifexp::mapType< numType >.
| numType unifexp::mapUnimodal< numType >::criticalPoint | ( | int | n ) | const [inline, virtual] |
Returns the subsequent critical points.
Implements unifexp::mapType< numType >.
| numType unifexp::mapUnimodal< numType >::gammaPower | ( | numType | x ) | const [inline, private] |
| numType unifexp::mapUnimodal< numType >::gammaPower1 | ( | numType | x ) | const [inline, private] |
| numType unifexp::mapUnimodal< numType >::gammaRoot | ( | numType | x ) | const [inline, private] |
| void unifexp::mapUnimodal< 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::mapUnimodal< numType >::leftBound | ( | ) | const [inline, virtual] |
Returns the left bound of the domain of the map.
Implements unifexp::mapType< numType >.
| numType unifexp::mapUnimodal< 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::mapUnimodal< numType >::name | ( | ) | const [inline, virtual] |
Returns the name of the object.
Implements unifexp::mapType< numType >.
| numType unifexp::mapUnimodal< numType >::rightBound | ( | ) | const [inline, virtual] |
Returns the right bound of the domain of the map.
Implements unifexp::mapType< numType >.
Member Data Documentation
numType unifexp::mapUnimodal< numType >::gamma [private] |
The documentation for this class was generated from the following file:
