coco::projective_interval< I > Class Template Reference
#include <prointerval.h>
Detailed Description
template<class I>
class coco::projective_interval< I >
Definition at line 124 of file prointerval.h.
Constructor & Destructor Documentation
| coco::projective_interval< I >::projective_interval | ( | ) | [inline] |
empty unusable projective interval
Definition at line 143 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const proj_interval & | _p | ) | [inline] |
standard copy constructor
Definition at line 145 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _t | ) | [inline] |
constructors for the first projective interval
Definition at line 148 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _i, | |
| const interval & | _t | |||
| ) | [inline] |
Definition at line 150 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _i, | |
| int | _m, | |||
| const interval & | _t | |||
| ) | [inline] |
Definition at line 152 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _i, | |
| proj_rational | _r, | |||
| const interval & | _t | |||
| ) | [inline] |
Definition at line 154 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _i, | |
| int | _m, | |||
| const proj_interval & | _p | |||
| ) | [inline] |
constructors for dependant projective intervals
Definition at line 158 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | _i, | |
| proj_rational | _r, | |||
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 160 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | double | lo, | |
| double | up, | |||
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 162 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | double | d, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 164 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | int | d, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 166 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | unsigned | d, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 168 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | long | d, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 170 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | unsigned long | d, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 172 of file prointerval.h.
| coco::projective_interval< I >::projective_interval | ( | const interval & | x, | |
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 174 of file prointerval.h.
| virtual coco::projective_interval< I >::~projective_interval | ( | ) | [inline, virtual] |
standard destructor
Definition at line 178 of file prointerval.h.
Member Function Documentation
| bool coco::projective_interval< I >::certain_proper_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 314 of file prointerval.hpp.
| bool coco::projective_interval< I >::certain_proper_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 238 of file prointerval.h.
| bool coco::projective_interval< I >::certain_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 296 of file prointerval.hpp.
| bool coco::projective_interval< I >::certain_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 224 of file prointerval.h.
| bool coco::projective_interval< I >::certainly_contains | ( | const interval & | x | ) | const [inline] |
Definition at line 254 of file prointerval.h.
| double coco::projective_interval< I >::diam | ( | ) | const [inline] |
Definition at line 652 of file prointerval.hpp.
| bool coco::projective_interval< I >::disjoint | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 332 of file prointerval.hpp.
| double coco::projective_interval< I >::dist | ( | const proj_interval & | x | ) | const [inline] |
Returns an upper bound for the Hausdorff distance of this proj_interval and the proj_interval x, i.e.
x.dist(y) == max{ abs(x.inf()-y.inf()), abs(x.sup() - y.sup()) }
Special cases in the extended system:
- x.dist(y) == NaN for x == [ EMPTY ] or y == [ EMPTY ]
Definition at line 689 of file prointerval.hpp.
| bool coco::projective_interval< I >::empty | ( | ) | const [inline] |
Definition at line 205 of file prointerval.h.
| static proj_interval coco::projective_interval< I >::EMPTY | ( | const proj_interval & | p | ) | [inline, static] |
Definition at line 202 of file prointerval.h.
| projective_interval< I > & coco::projective_interval< I >::hull | ( | const proj_interval & | x | ) | [inline] |
Definition at line 373 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::hulldiff | ( | const proj_interval & | x | ) | [inline] |
Definition at line 391 of file prointerval.hpp.
| double coco::projective_interval< I >::i_inf | ( | ) | const [inline] |
Definition at line 194 of file prointerval.h.
| bool coco::projective_interval< I >::i_proper_subset | ( | const interval & | x | ) | const [inline] |
Definition at line 228 of file prointerval.h.
| bool coco::projective_interval< I >::i_proper_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 234 of file prointerval.h.
| bool coco::projective_interval< I >::i_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 216 of file prointerval.h.
| double coco::projective_interval< I >::i_sup | ( | ) | const [inline] |
Definition at line 195 of file prointerval.h.
| bool coco::projective_interval< I >::i_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 220 of file prointerval.h.
| projective_interval< I > & coco::projective_interval< I >::imax | ( | const proj_interval & | x | ) | [inline] |
The method changes this proj_interval to the maximum of itself and x.
Definition at line 432 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::imin | ( | const proj_interval & | x | ) | [inline] |
The method changes this proj_interval to the minimum of itself and x.
Definition at line 413 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_div | ( | const proj_interval & | __i, | |
| const proj_interval & | __j | |||
| ) | [inline] |
Definition at line 460 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_invcos_wc | ( | const proj_interval & | __i, | |
| double | __l, | |||
| double | __d | |||
| ) | [inline] |
Definition at line 517 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_invgauss_wc | ( | const proj_interval & | __i, | |
| double | __l, | |||
| double | __m, | |||
| double | __s | |||
| ) | [inline] |
Definition at line 531 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_invpower_wc | ( | const proj_interval & | __i, | |
| double | __l, | |||
| int | __n | |||
| ) | [inline] |
Definition at line 492 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_invsin_wc | ( | const proj_interval & | __i, | |
| double | __l, | |||
| double | __d | |||
| ) | [inline] |
Definition at line 501 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_invsqr_wc | ( | const proj_interval & | __i, | |
| double | __l, | |||
| double | __d | |||
| ) | [inline] |
Definition at line 483 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersect_power | ( | const proj_interval & | __i, | |
| int | __n | |||
| ) | [inline] |
Definition at line 470 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::intersectwith | ( | const proj_interval & | x | ) | [inline] |
Definition at line 354 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::ipow | ( | int | n | ) | [inline] |
The method changes this interval to the n-th power.
Definition at line 405 of file prointerval.hpp.
| bool coco::projective_interval< I >::is_bounded | ( | ) | const [inline] |
Definition at line 214 of file prointerval.h.
| bool coco::projective_interval< I >::is_empty | ( | ) | const [inline] |
Definition at line 206 of file prointerval.h.
| bool coco::projective_interval< I >::is_entire | ( | ) | const [inline] |
Definition at line 213 of file prointerval.h.
| bool coco::projective_interval< I >::is_i_thin | ( | ) | const [inline] |
Definition at line 207 of file prointerval.h.
| bool coco::projective_interval< I >::is_t_thin | ( | ) | const [inline] |
Definition at line 208 of file prointerval.h.
| bool coco::projective_interval< I >::is_unbounded_above | ( | ) | const [inline] |
Definition at line 211 of file prointerval.h.
| bool coco::projective_interval< I >::is_unbounded_below | ( | ) | const [inline] |
Definition at line 209 of file prointerval.h.
| double coco::projective_interval< I >::mag | ( | ) | const [inline] |
Returns the magnitude of this proj_interval, i.e.
a.mag() == max{abs(y) : y in a.i }
Special cases in the extended system:
Definition at line 683 of file prointerval.hpp.
| double coco::projective_interval< I >::mid | ( | ) | const [inline] |
Returns the midpoint of the interval part of this proj_interval, i.e.
a.mid() == (a.i.inf()+a.i.sup())/2
The following special cases are distinguished:
- a.mid() == NaN for a == [ EMPTY ]
- a.mid() == 0 for a == [ ENTIRE ]
- a.mid() == +INF for a == [ a, INFTY ]
- a.mid() == -INF for a == [ -INFTY, a ]
Definition at line 646 of file prointerval.hpp.
| double coco::projective_interval< I >::mig | ( | ) | const [inline] |
Returns the mignitude of this proj_interval, i.e.
a.mig() == min{abs(y) : y in a.i }
Special cases in the extended system:
- a.mig() == NaN for a == [ EMPTY ]
Definition at line 677 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::operator*= | ( | double | a | ) | [inline] |
Definition at line 639 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::operator*= | ( | const proj_interval & | a | ) | [inline] |
Definition at line 631 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::operator+= | ( | double | a | ) | [inline] |
Definition at line 577 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::operator+= | ( | const proj_interval & | a | ) | [inline] |
Definition at line 559 of file prointerval.hpp.
| proj_interval coco::projective_interval< I >::operator- | ( | ) | const [inline] |
Definition at line 277 of file prointerval.h.
| projective_interval< I > & coco::projective_interval< I >::operator-= | ( | double | a | ) | [inline] |
Definition at line 613 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::operator-= | ( | const proj_interval & | a | ) | [inline] |
Definition at line 595 of file prointerval.hpp.
| proj_interval& coco::projective_interval< I >::operator= | ( | unsigned long | d | ) | [inline] |
Definition at line 273 of file prointerval.h.
| proj_interval& coco::projective_interval< I >::operator= | ( | long | d | ) | [inline] |
Definition at line 272 of file prointerval.h.
| proj_interval& coco::projective_interval< I >::operator= | ( | unsigned | d | ) | [inline] |
Definition at line 271 of file prointerval.h.
| proj_interval& coco::projective_interval< I >::operator= | ( | int | d | ) | [inline] |
Definition at line 270 of file prointerval.h.
| proj_interval& coco::projective_interval< I >::operator= | ( | double | d | ) | [inline] |
Definition at line 269 of file prointerval.h.
| proj_interval& coco::projective_interval< I >::operator= | ( | const proj_interval & | x | ) | [inline] |
Definition at line 268 of file prointerval.h.
| const interval& coco::projective_interval< I >::pi | ( | ) | const [inline] |
Definition at line 190 of file prointerval.h.
| bool coco::projective_interval< I >::possible_proper_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 323 of file prointerval.hpp.
| bool coco::projective_interval< I >::possible_proper_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 240 of file prointerval.h.
| bool coco::projective_interval< I >::possible_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 305 of file prointerval.hpp.
| bool coco::projective_interval< I >::possible_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 226 of file prointerval.h.
| const proj_rational& coco::projective_interval< I >::pr | ( | ) | const [inline] |
Definition at line 192 of file prointerval.h.
| bool coco::projective_interval< I >::probably_contains | ( | const interval & | x | ) | const [inline] |
Definition at line 259 of file prointerval.h.
| double coco::projective_interval< I >::project | ( | double | __d | ) | const [inline] |
Definition at line 545 of file prointerval.hpp.
| const interval& coco::projective_interval< I >::pt | ( | ) | const [inline] |
Definition at line 191 of file prointerval.h.
| double coco::projective_interval< I >::rad | ( | ) | const [inline] |
Returns an upper bound for the radius of this proj_interval, i.e.
a.rad() = (a.i.sup() - a.i.inf()) / 2
Special cases in the extended system:
Definition at line 671 of file prointerval.hpp.
| double coco::projective_interval< I >::rel_width | ( | ) | const [inline] |
Definition at line 244 of file prointerval.h.
| double coco::projective_interval< I >::relDiam | ( | ) | const [inline] |
Returns an upper bound for the relative diameter (width) of this proj_interval, i.e.
a.relDiam == a.diam() if a.i.mig() is less than the smallest normalized number
a.relDiam == a.diam() / a.i.mig() else
Special cases in the extended system:
- a.relDiam() == NaN for a == [ EMPTY ]
- a.relDiam() == +INF for any infinite proj_interval
Definition at line 665 of file prointerval.hpp.
| projective_interval< I > & coco::projective_interval< I >::round_to_integer | ( | ) | [inline] |
This method rounds the proj_interval inward to integer borders.
Definition at line 451 of file prointerval.hpp.
| double coco::projective_interval< I >::safeguarded_mid | ( | ) | const [inline] |
Returns the safeguarded mid of this proj_interval, i.e.
Definition at line 697 of file prointerval.hpp.
| void coco::projective_interval< I >::set | ( | double | lo, | |
| double | up, | |||
| const proj_interval & | _p | |||
| ) | [inline] |
Definition at line 246 of file prointerval.hpp.
| void coco::projective_interval< I >::set_bounds | ( | double | a, | |
| double | b | |||
| ) | [inline] |
Definition at line 264 of file prointerval.h.
| void coco::projective_interval< I >::set_i | ( | const interval & | j | ) | [inline] |
Definition at line 262 of file prointerval.hpp.
| void coco::projective_interval< I >::set_i | ( | double | lo, | |
| double | up | |||
| ) | [inline] |
Definition at line 255 of file prointerval.hpp.
| void coco::projective_interval< I >::set_lb | ( | double | d | ) | [inline] |
Definition at line 265 of file prointerval.h.
| void coco::projective_interval< I >::set_r | ( | const proj_rational & | s | ) | [inline] |
Definition at line 290 of file prointerval.hpp.
| void coco::projective_interval< I >::set_r | ( | int | n, | |
| unsigned int | d | |||
| ) | [inline] |
Definition at line 283 of file prointerval.hpp.
| void coco::projective_interval< I >::set_t | ( | const interval & | u | ) | [inline] |
Definition at line 276 of file prointerval.hpp.
| void coco::projective_interval< I >::set_t | ( | double | lo, | |
| double | up | |||
| ) | [inline] |
Definition at line 269 of file prointerval.hpp.
| void coco::projective_interval< I >::set_ub | ( | double | d | ) | [inline] |
Definition at line 266 of file prointerval.h.
| double coco::projective_interval< I >::t_exp | ( | ) | const [inline] |
Definition at line 198 of file prointerval.h.
| double coco::projective_interval< I >::t_exp_d | ( | ) | const [inline] |
Definition at line 200 of file prointerval.h.
| double coco::projective_interval< I >::t_exp_n | ( | ) | const [inline] |
Definition at line 199 of file prointerval.h.
| double coco::projective_interval< I >::t_inf | ( | ) | const [inline] |
Definition at line 196 of file prointerval.h.
| bool coco::projective_interval< I >::t_proper_subset | ( | const interval & | x | ) | const [inline] |
Definition at line 230 of file prointerval.h.
| bool coco::projective_interval< I >::t_proper_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 236 of file prointerval.h.
| bool coco::projective_interval< I >::t_subset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 217 of file prointerval.h.
| double coco::projective_interval< I >::t_sup | ( | ) | const [inline] |
Definition at line 197 of file prointerval.h.
| bool coco::projective_interval< I >::t_superset | ( | const proj_interval & | x | ) | const [inline] |
Definition at line 222 of file prointerval.h.
| double coco::projective_interval< I >::width | ( | ) | const [inline] |
Definition at line 659 of file prointerval.hpp.
Friends And Related Function Documentation
| projective_interval<J> abs | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> acos | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> acosh | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> acot | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> acoth | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> asin | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> asinh | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> atan | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> atanh | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> cancel | ( | const projective_interval< J > & | a, | |
| const projective_interval< J > & | b | |||
| ) | [friend] |
| projective_interval<J> cos | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> cosh | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> cot | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> coth | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> division_part1 | ( | const projective_interval< J > & | x, | |
| const projective_interval< J > & | y, | |||
| bool & | b | |||
| ) | [friend] |
| projective_interval<J> division_part2 | ( | const projective_interval< J > & | x, | |
| const projective_interval< J > & | y, | |||
| bool | b | |||
| ) | [friend] |
| projective_interval<J> exp | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> exp10 | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> exp2 | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> expm1 | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> imax | ( | const projective_interval< J > & | x, | |
| const projective_interval< J > & | y | |||
| ) | [friend] |
| projective_interval<J> imin | ( | const projective_interval< J > & | x, | |
| const projective_interval< J > & | y | |||
| ) | [friend] |
| projective_interval<J> log | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> log10 | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> log1p | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> log2 | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> operator* | ( | double | b, | |
| const projective_interval< J > & | a | |||
| ) | [friend] |
| projective_interval<J> operator* | ( | const projective_interval< J > & | a, | |
| double | b | |||
| ) | [friend] |
| projective_interval<J> operator* | ( | const projective_interval< J > & | a, | |
| const projective_interval< J > & | b | |||
| ) | [friend] |
| projective_interval<J> operator+ | ( | double | b, | |
| const projective_interval< J > & | a | |||
| ) | [friend] |
| projective_interval<J> operator+ | ( | const projective_interval< J > & | a, | |
| double | b | |||
| ) | [friend] |
| projective_interval<J> operator+ | ( | const projective_interval< J > & | a, | |
| const projective_interval< J > & | b | |||
| ) | [friend] |
| projective_interval<J> operator- | ( | double | b, | |
| const projective_interval< J > & | a | |||
| ) | [friend] |
| projective_interval<J> operator- | ( | const projective_interval< J > & | a, | |
| double | b | |||
| ) | [friend] |
| projective_interval<J> operator- | ( | const projective_interval< J > & | a, | |
| const projective_interval< J > & | b | |||
| ) | [friend] |
| projective_interval<J> operator/ | ( | double | b, | |
| const projective_interval< J > & | a | |||
| ) | [friend] |
| projective_interval<J> operator/ | ( | const projective_interval< J > & | a, | |
| double | b | |||
| ) | [friend] |
| projective_interval<J> operator/ | ( | const projective_interval< J > & | a, | |
| const projective_interval< J > & | b | |||
| ) | [friend] |
| projective_interval<J> pow | ( | const projective_interval< J > & | x, | |
| const projective_interval< J > & | y | |||
| ) | [friend] |
| projective_interval<J> power | ( | const projective_interval< J > & | x, | |
| int | n | |||
| ) | [friend] |
| projective_interval<J> sin | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> sinh | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> sqr | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> sqrt | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> tan | ( | const projective_interval< J > & | x | ) | [friend] |
| projective_interval<J> tanh | ( | const projective_interval< J > & | x | ) | [friend] |
The documentation for this class was generated from the following files:
