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/**************************************************************************
* *
* Regina  A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 19992016, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 021101301, USA. *
* *
**************************************************************************/
/*! \file enumerate/hilbertprimal.h
* \brief Provides a modified primal algorithm for Hilbert basis enumeration.
*/
#ifndef __HILBERTPRIMAL_H
#ifndef __DOXYGEN
#define __HILBERTPRIMAL_H
#endif
#include "reginacore.h"
#include "maths/matrix.h"
#include <iterator>
#include <vector>
namespace regina {
class EnumConstraints;
class ProgressTracker;
class Ray;
/**
* \weakgroup enumerate
* @{
*/
/**
* Implements a modified primal algorithm for enumerating Hilbert bases.
* This incorporates the primal algorithm described in
* "Normaliz: Algorithms for affine monoids and rational cones",
* Winfried Bruns and Bogdan Ichim, J. Algebra 324 (2010), 10981113,
* and has been modified to allow for additional constraints (such as
* the quadrilateral constraints from normal surface theory).
*
* To summarise: the algorithm first enumerates extremal rays of the rational
* cone, and then decomposes the admissible region of the cone (where the
* extra constraints are satisfied) into maximal admissible faces.
* It calls Normaliz directly to enumerate the Hilbert basis for
* each maximal admissible faces, and finally combines these into a basis
* for the entire space.
*
* All routines of interest within this class are static; no object of
* this class should ever be created.
*
* \ifacespython Not present.
*/
class HilbertPrimal {
public:
/**
* Determines the Hilbert basis that generates all integer
* points in the intersection of the <i>n</i>dimensional
* nonnegative orthant with some linear subspace.
* The resulting basis elements will be of the class \a RayClass,
* will be newly allocated, and will be written to the given output
* iterator. Their deallocation is the responsibility of whoever
* called this routine.
*
* The intersection of the nonnegative orthant with this linear
* subspace is a pointed polyhedral cone with apex at the origin,
* and this routine requires the extremal rays of this cone to
* be provided as input. The extremal rays can be computed
* using DoubleDescription::enumerate() in general cases,
* though sometimes (such as with normal surface theory) more
* efficient methods are available.
*
* This routine computes the Hilbert basis of all integer points in
* this cone. The resulting list of basis vectors will contain
* no duplicates or redundancies.
*
* The parameter \a constraints may contain a set of validity
* constraints, in which case this routine will only return \e valid
* basis elements. Each validity constraint is of the form "at
* most one of these coordinates may be nonzero"; see the
* EnumConstraints class for details. These contraints have the
* important property that, although validity is not preserved under
* addition, \e invalidity is.
*
* An optional progress tracker may be passed. If so, this routine
* will update the percentage progress and poll for cancellation
* requests. It will be assumed that an appropriate stage has already
* been declared via ProgressTracker::newStage() before this routine
* is called, and that ProgressTracker::setFinished() will be
* called after this routine returns.
*
* \pre If \a constraints is passed, then the given list of
* extremal rays contains \e only those extremal rays that satisfy
* all of the given constraints.
* \pre The template argument RayClass is derived from Ray (or
* may possibly be Ray itself).
* \pre The template argument RayIterator is a forward iterator type,
* and when dereferenced can be cast to (const Ray&).
*
* \warning If a progress tracker is passed, be aware that the
* present implementation updates percentage progress very infrequently,
* and may take a very long time to honour cancellation requests.
*
* @param results the output iterator to which the resulting basis
* elements will be written; this must accept objects of type
* <tt>RayClass*</tt>.
* @param raysBegin an iterator pointing to the beginning of the
* list of extremal rays.
* @param raysEnd an iterator pointing past the end of the
* list of extremal rays.
* @param constraints a set of validity constraints as described
* above, or 0 if no additional constraints should be imposed.
* @param tracker a progress tracker through which progress
* will be reported, or 0 if no progress reporting is required.
*/
template <class RayClass, class RayIterator, class OutputIterator>
static void enumerateHilbertBasis(OutputIterator results,
const RayIterator& raysBegin, const RayIterator& raysEnd,
const EnumConstraints* constraints,
ProgressTracker* tracker = 0);
private:
/**
* Identical to the public routine enumerateHilbertBasis(),
* except that there is an extra template parameter \a BitmaskType.
* This describes what type should be used for bitmasks that
* represent maximal admissible faces.
*
* All arguments to this function are identical to those for the
* public routine enumerateHilbertBasis().
*
* \pre The bitmask type is one of Regina's bitmask types, such
* as Bitmask, Bitmask1 or Bitmask2.
* \pre The type \a BitmaskType can handle at least \a n bits,
* where \a n is the dimension of the Euclidean space (i.e., the
* number of columns in \a subspace).
*/
template <class RayClass, class BitmaskType,
class RayIterator, class OutputIterator>
static void enumerateUsingBitmask(OutputIterator results,
const RayIterator& raysBegin, const RayIterator& raysEnd,
const EnumConstraints* constraints, ProgressTracker* tracker);
/**
* Determines whether the given ray lies in the face specified
* by the given bitmask.
*
* Faces are described using bitmasks in the same manner as described
* by MaxAdmissible::enumerate(), where \c true represents a
* coordinate that is nonzero in the relative interior of the
* face, and \c false represents a coordinate that is always
* zero throughout the face.
*
* @param ray the ray to test, given as a vector of integers.
* @param face the face to test, given as a bitmask.
* @return \c true if the given ray lies within the given face,
* or \c false otherwise.
*/
template <class BitmaskType>
static bool inFace(const Ray& ray, const BitmaskType& face);
/**
* Private constructor to ensure that objects of this class are
* never created.
*/
HilbertPrimal();
};
/**
* Deprecated typedef for backward compatibility. This typedef will
* be removed in a future release of Regina.
*
* \deprecated The class NHilbertPrimal has now been renamed to HilbertPrimal.
*/
REGINA_DEPRECATED typedef HilbertPrimal NHilbertPrimal;
/*@}*/
// Inline functions for HilbertPrimal
inline HilbertPrimal::HilbertPrimal() {
}
} // namespace regina
// Template definitions
#include "enumerate/hilbertprimalimpl.h"
#endif
