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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/hilbertcd.h
* \brief Provides a modified ContejeanDevie algorithm for Hilbert basis
* enumeration.
*/
#ifndef __HILBERTCD_H
#ifndef __DOXYGEN
#define __HILBERTCD_H
#endif
#include "reginacore.h"
#include "maths/ray.h"
#include <iterator>
#include <list>
#include <vector>
namespace regina {
class EnumConstraints;
class Ray;
/**
* \weakgroup enumerate
* @{
*/
/**
* Implements a modified ContejeanDevie algorithm for enumerating Hilbert
* bases. This is based on the stackbased algorithm described in
* "An efficient incremental algorithm for solving systems of linear
* Diophantine equations", Inform. and Comput. 113 (1994), 143172,
* and has been modified to allow for additional constraints (such as
* the quadrilateral constraints from normal surface theory).
*
* All routines of interest within this class are static; no object of
* this class should ever be created.
*
* \warning For normal surface theory, the ContejeanDevie algorithm is
* extremely slow, even when modified to incorporate admissibility
* constraints. Consider using the much faster HilbertPrimal or
* HilbertDual instead.
*
* \ifacespython Not present.
*/
class HilbertCD {
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 nonnegative orthant is an <i>n</i>dimensional cone with
* its vertex at the origin. The extremal rays of this cone are
* the \a n nonnegative coordinate axes. This cone also has \a n
* facets, where the <i>i</i>th facet is the nonnegative
* orthant of the plane perpendicular to the <i>i</i>th coordinate
* axis.
*
* This routine takes a linear subspace, defined by the
* intersection of a set of hyperplanes through the origin (this
* subspace is described as a matrix, with each row giving the
* equation for one hyperplane).
*
* The purpose of this routine is to compute the Hilbert basis of
* the set of all integer points in the intersection of the
* original cone with this linear subspace. 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.
*
* \pre The template argument RayClass is derived from Ray (or
* may possibly be Ray itself).
*
* \warning For normal surface theory, the ContejeanDevie algorithm is
* extremely slow, even when modified to incorporate admissibility
* constraints. Consider using the much faster HilbertPrimal or
* HilbertDual instead.
*
* @param results the output iterator to which the resulting basis
* elements will be written; this must accept objects of type
* <tt>RayClass*</tt>.
* @param subspace a matrix defining the linear subspace to intersect
* with the given cone. Each row of this matrix is the equation
* for one of the hyperplanes whose intersection forms this linear
* subspace. The number of columns in this matrix must be the
* dimension of the overall space in which we are working.
* @param constraints a set of validity constraints as described
* above, or 0 if no additional constraints should be imposed.
*/
template <class RayClass, class OutputIterator>
static void enumerateHilbertBasis(OutputIterator results,
const MatrixInt& subspace, const EnumConstraints* constraints);
private:
/**
* A helper class for Hilbert basis enumeration, describing a
* single candidate basis vector.
*
* The coordinates of the vector are inherited through the
* superclass Ray.
*
* The \a BitmaskType template argument is used to store one bit
* per coordinate, which is \c false if the coordinate is zero
* or \c true if the coordinate is nonzero.
*
* \pre The template argument \a BitmaskType is one of Regina's
* bitmask types, such as Bitmask, Bitmask1 or Bitmask2.
*/
template <class BitmaskType>
struct VecSpec : public Ray {
BitmaskType mask_;
/**< A bitmask indicating which coordinates are zero
(\c false) and which are nonzero (\c true). */
/**
* Creates the zero vector.
*
* @param dim the total dimension of the space (and
* therefore the toatl length of this vector).
*/
inline VecSpec(size_t dim);
};
/**
* 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
* assign flags to individual coordinate positions.
*
* 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 OutputIterator>
static void enumerateUsingBitmask(OutputIterator results,
const MatrixInt& subspace, const EnumConstraints* constraints);
/**
* Private constructor to ensure that objects of this class are
* never created.
*/
HilbertCD();
};
/**
* Deprecated typedef for backward compatibility. This typedef will
* be removed in a future release of Regina.
*
* \deprecated The class NHilbertCD has now been renamed to HilbertCD.
*/
REGINA_DEPRECATED typedef HilbertCD NHilbertCD;
/*@}*/
// Inline functions for HilbertCD
inline HilbertCD::HilbertCD() {
}
// Inline functions for HilbertCD::VecSpec
template <class BitmaskType>
inline HilbertCD::VecSpec<BitmaskType>::VecSpec(size_t dim) :
Ray(dim), mask_(dim) {
// All vector elements are initialised to zero thanks to the
// LargeInteger default constructor.
}
} // namespace regina
// Template definitions
#include "enumerate/hilbertcdimpl.h"
#endif
