Interval_Fun.hpp File Reference
Interval Arithmetics - elementary functions such as: sin, cos, tan, exp, log, power,... More...
#include <iostream>#include <cmath>#include <limits>Namespaces | |
| capd | |
| capd::intervals | |
| Interval arithmetics. | |
Functions | |
| template<typename T_Bound > | |
| T_Bound | capd::intervals::positivePower (T_Bound value, unsigned exponent) |
| a computation of value^{exponent} with current rounding settings (exponent has to be positive) More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::diam (const Interval< T_Bound, T_Rnd > &A_iVal) |
| upper bound for a diameter of an interval More... | |
| template<typename T_Bound , typename T_Rnd > | |
| T_Bound | capd::intervals::width (const Interval< T_Bound, T_Rnd > &A_iVal) |
| non-rigorous diameter of an interval More... | |
| template<typename T_Bound , typename T_Rnd > | |
| bool | capd::intervals::intersection (Interval< T_Bound, T_Rnd > A_iv1, Interval< T_Bound, T_Rnd > A_iv2, Interval< T_Bound, T_Rnd > &A_rInter) |
| Intersection of two intervals. More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::intervalHull (const Interval< T_Bound, T_Rnd > &A_iv1, const Interval< T_Bound, T_Rnd > &A_iv2) |
| returns an interval containing A_iv1 and A_iv2 More... | |
| template<typename T_Bound , typename T_Rnd > | |
| void | capd::intervals::split (Interval< T_Bound, T_Rnd > &A_iv, Interval< T_Bound, T_Rnd > &A_rMid, T_Bound &A_diam) |
On output: ![$ iv \subset Mid + [-diam , diam] $](form_0.png) . More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::power (const Interval< T_Bound, T_Rnd > &base, int exponent) |
| a computation of base^{exponent} More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::power (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &b) |
| a computation of a^b More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::sqrt (const Interval< T_Bound, T_Rnd > &x) |
| square root of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledSin2 (const Interval< T_Bound, T_Rnd > &x) |
| a rigorous computation of sin(x) for 0 <= x <= pi More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledSin1 (const Interval< T_Bound, T_Rnd > &x) |
the function computes sin(x) for ![$ x \subset [0,\infty] $](form_1.png) More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::sin (const Interval< T_Bound, T_Rnd > &x) |
| sinus of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::cos (const Interval< T_Bound, T_Rnd > &x) |
| cosinus of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::tan (const Interval< T_Bound, T_Rnd > &x) |
| tangens of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::cot (const Interval< T_Bound, T_Rnd > &x) |
| cotangens of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledAtan2 (const Interval< T_Bound, T_Rnd > &x) |
| a rigorous computation of atan(x) for 0 <= x <= sqrt(2)-1 More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledAtan1 (const Interval< T_Bound, T_Rnd > &x) |
| a rigorous computation of atan(x) for 0 <= x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::atan (const Interval< T_Bound, T_Rnd > &x) |
| arctangens of x More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledAsin1 (const Interval< T_Bound, T_Rnd > &x) |
| A rigorous computation of asin(x) far from -1 and 1 i.e. for -0.7 <= x <= 0.7. More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledAsin2 (const Interval< T_Bound, T_Rnd > &x) |
| A rigorous computation of asin(x) for 0.7 < x <=1. More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::pointAsin (const Interval< T_Bound, T_Rnd > &x) |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::asin (const Interval< T_Bound, T_Rnd > &x) |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::scaledAcos (const Interval< T_Bound, T_Rnd > &x) |
| A rigorous computation of acos(x) for point intervals. More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::acos (const Interval< T_Bound, T_Rnd > &x) |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::sinh (const Interval< T_Bound, T_Rnd > &x) |
| sinh More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::cosh (const Interval< T_Bound, T_Rnd > &x) |
| cosh More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::tanh (const Interval< T_Bound, T_Rnd > &x) |
| tanh More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::coth (const Interval< T_Bound, T_Rnd > &x) |
| coth More... | |
| template<typename T_Bound > | |
| T_Bound | capd::intervals::scaledExp (T_Bound x, int expTaylorOrder) |
| returns exp(x) for x in [0,1] with actual rounding More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::exp (const Interval< T_Bound, T_Rnd > &x) |
| returns exp(x) More... | |
| template<typename T_Bound > | |
| T_Bound | capd::intervals::scaledLogUp (const T_Bound &x, int logTaylorOrder) |
computes upper bound for log(1+x) for ![$ x \in [0,1/2] $](form_2.png) More... | |
| template<typename T_Bound > | |
| T_Bound | capd::intervals::scaledLogDown (const T_Bound &x, int logTaylorOrder) |
| computes lower bound for log(1+x) for More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::log (const Interval< T_Bound, T_Rnd > &x) |
| computes natural logarithm of x, x>0 More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::solveAffineInclusion (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &p, const Interval< T_Bound, T_Rnd > &c) |
solves inclusion ![$ a+[0,t]*p\subset c for t $](form_3.png) More... | |
| template<typename T_Bound , typename T_Rnd > | |
| Interval< T_Bound, T_Rnd > | capd::intervals::solveAffineInclusion (const Interval< T_Bound, T_Rnd > &a, const Interval< T_Bound, T_Rnd > &p, const Interval< T_Bound, T_Rnd > &c, int &dir) |
Detailed Description
Interval Arithmetics - elementary functions such as: sin, cos, tan, exp, log, power,...
- Date
- 11-01-2006
