Implements an FPRAS for approximating the volume of a set of high-dimensional objects. More...
#include <shark/Algorithms/DirectSearch/HypervolumeApproximator.h>
Public Member Functions | |
template<typename Iterator , typename Extractor , typename VectorType > | |
double | operator() (Iterator begin, Iterator end, Extractor e, const VectorType &referencePoint, double eps=HypervolumeApproximator::DEFAULT_EPSILON, double delta=HypervolumeApproximator::DEFAULT_DELTA) const |
Approximates the volume of the union of high-dimensional axis-parallel boxes. More... | |
Static Public Attributes | |
static double | DEFAULT_EPSILON = 1E-2 |
Default error bound. More... | |
static double | DEFAULT_DELTA = 0.1 |
Default error probability. More... | |
Implements an FPRAS for approximating the volume of a set of high-dimensional objects.
See Bringmann, Friedrich: Approximating the volume of unions and intersections of high-dimensional geometric objects, Computational Geometry, Volume 43, 2010, 601-610. and refer to the unit tests for examples:
Rng | The type of the random number generator. Please note that the performance of the algorithm is determined by the speed of the RNG. |
Definition at line 51 of file HypervolumeApproximator.h.
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Approximates the volume of the union of high-dimensional axis-parallel boxes.
Iterator | Type of the iterator over the range of axis-parallel boxes. |
Extractor | Extractor type for extracting point information from objects. |
[in] | begin | Iterator to the beginning of the range of boxes. |
[in] | end | Iterator pointer after the last valid box. |
[in] | e | Extractor instance |
[in] | referencePoint | Minimization is considered and the reference point usually is chosen as the Nadir-point. |
[in] | eps | Error bound, default value: \(10^{-2}\). |
[in] | delta | Error probability, default value: \(10^{-2}\). |
Definition at line 80 of file HypervolumeApproximator.h.
References shark::blas::distance(), and shark::uni().
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Default error probability.
Definition at line 61 of file HypervolumeApproximator.h.
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Default error bound.
Definition at line 56 of file HypervolumeApproximator.h.